GB2584524A

GB2584524A - Method of toolpath generation for a spin forming process

Info

Publication number: GB2584524A
Application number: GB2002649.8A
Authority: GB
Inventors: G Loukaides Evripides; Maria Russo Iacopo
Original assignee: Renault SAS; Nissan Motor Manufacturing UK Ltd
Current assignee: Renault SAS; Nissan Motor Manufacturing UK Ltd
Priority date: 2019-06-03
Filing date: 2020-02-25
Publication date: 2020-12-09
Anticipated expiration: 2040-02-25
Also published as: GB2584524B; GB2584525B; GB2584523B; GB202002651D0; GB2584526A; GB202002661D0; GB2584523A; GB2584525A; GB202002648D0; GB201907825D0; GB2584526B; GB202002649D0

Abstract

A method of controlling a mandrel-free spinning apparatus 20. The workpiece 2 is deformed towards a target shape. The method includes: receiving a CAD model of the target shape; determining toolpaths for the tools, wherein the toolpath of the second tool 22 is complementary to the toolpath of the first tool 6 so that the tools engage opposing surfaces of the workpiece to deform the workpiece towards the target shape. Preferably the first tool is a forming tool and the second tool is a support tool and they move synchronously, at the same rate and in phase. The CAD model may comprise target shape points on a co-ordinate system and the route of the tools may comprise control positions, offset from the target points, and the tools may be moved between successive control positions. Preferably the control positions of the second tool are based on and offset from the control positions of the first tool. Preferably the target shape is non-axisymmetric and the CAD model includes and 3D model of the target shape. Two workpieces may be mounted together.

Description

METHOD OF TOOLPATH GENERATION FOR A SPIN FORMING PROCESS

TECHNICAL FIELD

The present disclosure relates to a method of controlling a spin forming machine.

BACKGROUND

Metal spinning is a metal forming process that has traditionally been used to produce hollow, axially symmetric (axisymmetric) items or articles from a metal blank. Figure 1 illustrates a traditional spin forming apparatus 1 used for such purposes. As shown, a workpiece 2, typically in the form of a metal blank, is secured to a mandrel 3 on a lathe 4. The workpiece 2 is then gradually deformed into a desired shape by moving a forming tool 6 so as to apply pressure to an outer surface 8 of the rotating workpiece 2 and trace the surfaces of the rotating mandrel 3. This process may, for example, be used to produce any of the axisymmetric articles shown in Figure 2 and may be completed in a single pass of the forming tool 6 over the workpiece 2 (e.g. in shear spinning) or by multiple passes over the workpiece 2 (conventional spinning).

Metal spinning is advantageous in that there is minimal springback of the finished article and the initial tooling costs are relatively low. However, conventional spinning methods face challenges when producing re-entrant shapes, due to the need to remove the finished article from the underlying mandrel 3. As a result, the finished articles are generally axisymmetric with little complexity. Furthermore, a new mandrel 3 is also required whenever the shape of the desired article changes. Accordingly, the costs associated with design variations are high and controlling the forming tool 6 requires technical expertise in order to avoid damaging the workpiece 2 or the machinery.

The forming tool 6 may be controlled by manual inputs from an operator or by computer numeric control (CNC). When using CNC, the operator determines a suitable route (toolpath) for the forming tool 6 to follow in order to deform the workpiece 2 into the desired shape. However, a skilled operator is required to make changes to the toolpath, which can be expensive and time consuming.

More recently, metal spinning machines have been developed that are mandrel-free. WO 2012/042221 Al describes a mandrel-free spinning apparatus 20 for spin forming both axisymmetric and non-axisymmetric articles. The mandrel-free spinning apparatus 20, illustrated in Figures 3 to 5, includes mobile support tools that support key areas of the workpiece 2 as the workpiece 2 rotates, replacing the functionality of the fully formed mandrel 3.

Figure 3 illustrates the principle features of a mandrel-free spinning apparatus 20. As shown, the mandrel-free spinning apparatus 20 includes: a rotatable mounting point, such as a lathe 4, to which the workpiece 2 is secured; a forming tool 6; and a first support tool 22. The forming tool 6 is arranged to act on an outer surface 8 of the rotating workpiece 2. The first support tool 22, shown proximal to the lathe 4, is arranged to act on an opposing inner surface 10 of the rotating workpiece 2.

The mandrel-free spinning apparatus 20 may, for example, further include one or more further forming tools, such as the second and third support tools 24, 26, shown in Figure 3. The second and third support tools 24, 26 may be arranged to act on the inner or outer surfaces 28, 8 of the workpiece 2, for example acting on areas of the workpiece 2 that are distal from the lathe 4.

Figure 4 illustrates an end view of the mandrel-free spinning apparatus 20 shown in Figure 3. In this example, the forming tool 6 and the first support tool 22 of the mandrel-free spinning apparatus 20, are arranged to move within a horizontal plane 28 aligned with both a longitudinal axis 30 of the lathe 4 and a perpendicular radial axis 32. The second and third support tools 24, 26 are arranged to move within and outside of the plane 28 and may, for example, move symmetrically to one another about the horizontal plane 28.

Figure 5 shows a practical embodiment of the mandrel-free spinning apparatus 20, as depicted in WO 2012/042221 Al and as illustrated conceptually in Figures 3 and 4. The positions of the forming tool 6 and of the first, second and third support tools 22, 24, 26 are adjustable relative to the workpiece 2 by a respective set of actuators 34 controlled by CNC, for example. The set of actuators 34 may include a respective servomotor, e.g. with a ball-screw, for the purpose of moving each of the forming tool 6, the lathe 4 and the first, second and third support tools 22, 24, 26.

Figure 6 shows a plan view of the mandrel-free spinning apparatus 20 shown in Figure 5.

As illustrated, the set of actuators 34 are able to adjust the positions of the forming tool 6 and the first support tool 22 relative to the lathe 4, and hence the workpiece 2, along the longitudinal axis 30 and the radial axis 32. In this manner, the longitudinal axis 30 acts as a first axis of movement and the radial axis 32 acts as a second axis of movement for each of the forming tool 6 and the first support tool 22.

The forming tool 6, which may take the form of a so-called working roller, is shown supported at one end of a first arm member 36 and the first support tool 22, which may take the form of a so-called blending roller, is shown attached to one end of a second arm member 38.

Each of the working and blending rollers may be metallic and may feature a ceramic coating that provides enhanced durability and/or minimises friction. Such rollers are known in the art and may have a general disc-like shape with a rounded, often semicircular, nose profile that extends around the circumference of the roller.

In use, the forming tool 6 and the first support tool 22 can be moved along the radial and longitudinal axes 32, 30 to engage the inner and outer surfaces 28, 8 of the workpiece 2 and deform the rotating workpiece 2 into the shape of the desired article. For this purpose, the second arm member 38 may be shaped to allow insertion/removal of the first support tool 22 into/from an interior volume of the article as the workpiece 2 is deformed into a concave or tubular shape.

As illustrated in Figure 6, the orientation 8, or angle of inclination, of the working roller and the first arm member 36 may also be adjustable in the plane 28 of the longitudinal and radial axes 30, 32 to vary the angle of engagement of the forming tool 6 with the workpiece 2. Hence, during the spin forming process, the orientation 0 may generally remain constant or the orientation 0 may be variable, for example being adjusted between successive passes along the workpiece 2.

In this manner, the mandrel-free spinning apparatus 20 possesses sufficient mobility to deform a metal workpiece 2 into a variety of both axisymmetric and non-axisymmetric shapes, such as those shown in Figure 7. The absence of a fully formed mandrel also enables the production of re-entrant shapes, as illustrated by the profile in Figure 7(a). In addition, the spinning process can be completed in a single pass of the forming tool 6 over the workpiece 2 (shear spinning) or in multiple passes over the workpiece 2 (conventional spinning) as practised on traditional spin forming machines.

Despite its potential advantages, the mandrel-free spinning technology is immature and the apparatus has not been used to produce non-axisymmetric articles. Further, the existing methods of controlling the mandrel-free spinning apparatus 20 have relied on CNC toolpaths defined by manual inputs corresponding to specific article shapes. As a result, the metal forming process is currently inefficient, expensive and unsuitable for commercial exploitation.

The present invention has been developed to attend to at least some of the above-mentioned problems.

SUMMARY OF THE INVENTION

According to an aspect of the present invention there is provided a method of controlling a spin forming machine. The spin forming machine comprising a rotatable mounting point for a workpiece and a forming tool controllable to deform the workpiece as the workpiece rotates. The method being arranged to produce an article, having an article shape, from the workpiece in one or more passes. The method including: receiving a computerised representation of the article shape; optionally receiving a number of passes for producing the article shape; determining a computerised representation of a target shape for each, or at least one or more, passes based on the computerised representation of the article shape; determining a toolpath for the forming tool, wherein determining the toolpath for the forming tool comprises: determining a route of the forming tool between a start point and an end point for each pass based on the respective target shape; and controlling the forming tool according to the toolpath, whilst rotating the workpiece with respect to the forming tool, to deform the workpiece towards a second shape that substantially matches the article shape.

By 'second shape', it is intended to mean the product of the workpiece's deformation into a shape that substantially reproduces the three dimensional shape of the desired article, allowing for manufacturing tolerances. In this manner, the dimensions, curvatures and volumes of the second shape should match the dimensions, curvatures and volumes of the article shape, within allowable tolerances.

According to another aspect of the present invention there is provided a method of controlling a spin forming machine, comprising a rotatable mounting point for a workpiece and a forming tool controllable to deform the workpiece as the workpiece rotates, to produce an article having an article shape from the workpiece, the method including: receiving a CAD model of the article shape; determining a series of three dimensional target shapes based on the CAD model of the article shape, wherein successive target shapes in the series of target shapes represent successive states of the workpiece between an initial shape and the article shape; generating a first toolpath for the forming tool comprising a plurality of passes, at least one pass of the plurality of passes corresponding to each target shape and being based on that target shape so that said at least one pass is configured to deform the workpiece towards that target shape; and controlling the forming tool according to the generated first toolpath, whilst rotating the workpiece on the rotatable mounting point, to deform the workpiece towards the article shape.

The CAD model of the article shape may include a three-dimensional model of the article shape, for example, which represents the article in three-dimensional space.

Advantageously, determining a toolpath for the forming tool in dependence on the CAD model of the article shape allows the toolpath to be reconfigurable as the article shape changes. Consequently, the toolpath can be efficiently redesigned to accommodate changes to the design of the article by updating the CAD model. The method also facilitates operation of the spin forming machine by a relatively unskilled operator since the toolpaths are generated based on the CAD model.

Reference to the term 'article shape' is intended to mean the three dimensional shape of a desired article or target part, which comprises all of the article's visible surfaces.

The number of passes received for producing the article shape may, for example, only relate to a number of passes for producing the article shape according to the method and the production of the article may, in fact, include one or more additional passes.

Optionally, the CAD model of the article shape comprises a plurality of article shape points on a co-ordinate system. Determining each target shape, in the series of target shapes, may comprise determining a plurality of target points, each target point of said target shape relating to a respective article shape point, for example. The article shape may comprise enough article shape points o produce an adequate representation of the shape of the article.

The plurality of target points may relate to positions on the co-ordinate system. The plurality of target points may, for example, include a first set of target points and a second set of target points. Each target point in the first set may relate to a respective article shape point, and each target point in the second set may be determined by interpolating between target points in the first set. Interpolating between the target points in the first set may provide additional target points to produce a more accurate representation of the target shape.

Interpolating between two or more target points in the first set may, for example, include determining, or receiving, a gradient function defining the gradient of the target shape between the two or more target points. Each target point in the second set may, for example, be associated with an interval of rotation of the workpiece and have a distance along the longitudinal axis corresponding to the respective command position for said interval of rotation.

For each pass, the target shape represents a desired shape of the workpiece upon completion of the pass. Accordingly, the series of target shapes may include a final target shape, corresponding to the article shape, and successive intermediate target shapes, corresponding to intermediate states of the workpiece. Optionally, for each intermediate target shape, determining each target point of said intermediate target shape comprises: applying a transformation function to the related article shape point. In this manner, the intermediate target shapes relate to so-called intermediate mandrel surfaces, defining an iteration of the deformation of the workpiece between the initial shape of the workpiece, or blank, and the final shape of the article. Advantageously, this allows for gradual deformation of the workpiece that reduces spin forming effects such as cracking and wrinkling. For example, the target points of the final target shape may correspond to the article shape points.

In an example, the transformation function is a function of the distance of the article shape point along the longitudinal axis. Optionally, the CAD model of the article shape includes a base portion at a first end of the article shape and the transformation function is a function of the distance of the article shape point along the longitudinal axis (from the first end). In this manner, the target points related to article shape points further from the first end may be offset to a greater extent from said article shape points than those target points relating to article shape points that are closer to the first end. This has the effect of minimising the deformation at the outer edges of the workpiece, which reduces susceptibility to wrinkling.

Optionally, the method comprises determining the transformation function for each target point based on: a unit normal vector to the CAD model of the article shape at the related article shape point; and a scaling coefficient for the unit normal vector, wherein the scaling coefficient is determined based on the distance of the article shape point along a longitudinal axis of the CAD model of the article shape.

In an example, the article shape points may be defined by an m x 3 coordinate matrix, B: B = [x; y; z] where m is the number of article shape points and x; y; z are m-tuples representing components of standard Cartesian coordinates. For each target shape, i, the target shape points may be defined by an m x 3 coordinate matrix, C: Ci = [x, i; i; where xi; z are m-tuples for target shape, i, representing components of standard Cartesian coordinates. The unit normal vectors to the article shape points may be defined by an m x 3 matrix, N: N = [n.,; ny,nd where rt.i; ny;71, are m-tuples representing components of standard Cartesian coordinates. Optionally, for each target shape, i: ix, i; = [x; y] + f(z). [nx; ny] where f(z) is the transformation function, the transformation function being a function of the distance (z) of each article shape point along the longitudinal axis. Advantageously, parametric equations can be used in the transformation function to adjust the target shapes and plot the trajectory of the forming tool in a convenient manner.

In an example, f(z) = (atznf + to); where a and n are parameters defined for target shape, i; and to is a thickness of the article shape.

0, z < Lpi In an example, f(z) = f (aizni z> L. for each target shape, i; and to is a thickness of the article shape.

Optionally, the method further comprises receiving a user input that defines at least one of the parameters a, n and/or LIJ of said transformation function. The user input allows reconfiguration of the toolpath.

In an example, each pass may relate to a route of the forming tool between a respective start point and a respective end point. For each pass, determining the route of the forming tool may comprise determining a plurality of command positions for the forming tool, each command position being based on a respective target point of the corresponding target shape, such that moving the forming tool between the plurality of command positions of said pass, deforms the workpiece towards the corresponding target shape as the workpiece rotates.

The plurality of command positions for the forming tool relate to positions of the forming tool during the pass. Each command position may, for example, also be defined on a coordinate system.

Optionally, for each pass, each command position may be associated with an angle of rotation or orientation of the workpiece and each command position may be defined by a first distance along the axis of rotation of the rotatable mounting point, and a second distance along a second axis perpendicular to the axis of rotation of the rotatable mounting point.

where, Lp, a and n are parameters defined In this manner, the rotation of the workpiece can be discretized into intervals of rotation and each toolpath can be defined by positions of, for example, radial and longitudinal distance for each interval of rotation. These positions may, for example, correspond to sequential points on the surfaces of the respective target shape. Thus, the forming tool can be moved dynamically, as the workpiece rotates, to deform the workpiece towards the target shape. The method may further comprise conversion from one co-ordinate system to another co-ordinate system, for example converting between Cartesian and polar co-ordinate systems.

Optionally, the plurality of passes are sequential, and the toolpath may include moving the forming tool from the end point of a first pass to the start point of a second pass.

In an example, the forming tool does not contact the workpiece during the motion towards the start point. In an example, the forming tool may follow an arced motion between passes. For example, an arced motion between the end point of one pass and the start point of the subsequent pass.

Each command position may be offset from the respective target point to account for the shape of the forming tool, i.e. to position the forming tool suitably to engage and deform the workpiece into the target shape. For each pass, the command positions may, for example, be joined into a continuous path, for example using a spline fitting function.

Optionally, the method comprises receiving information indicative of the shape of the forming tool, wherein each command position is determined based on the respective target point and the information indicative of the shape of the forming tool. Each command position may then be offset from the respective target point so as to engage the forming tool with the workpiece at a position corresponding to the respective target point.

Advantageously, the method effectively uses the information relating to the shape of the forming tool, the CAD model of the article shape and one or more target shapes to determine the relative positions of the forming tool and the workpiece in 3D space as the workpiece is deformed towards the article shape.

Optionally, the forming tool is a forming roller and the information indicative of the shape of the forming tool comprises a radius of the forming roller, a nose radius of the forming roller and an orientation of the forming roller. The forming roller may be a so-called working roller.

Determining each command position may, for example, comprise: determining the coordinates of the centre of a sphere, having a radius equal to the radius of the forming roller minus the nose radius of the forming roller, at which a point on the sphere intersects both: a plane inclined by the orientation of the forming roller; and a point translated from the respective target point, by a distance equal to the nose radius of the forming roller, along a unit normal vector of the respective target point.

Optionally, the information indicative of the shape of the forming tool comprises the orientation of the roller, the radius of the roller and the roller nose radius. For each pass, determining each command position may, for example, comprise: determining a position of the centre of the roller that causes the computerised representation of the forming tool to intersect the respective target point based on a function that relates the orientation of the roller, the radius of the roller, the roller nose radius and the co-ordinates of the respective target point to the centre of the roller.

Optionally, the co-ordinates of the centre of the sphere, [xo; ye; za], are given by: xo = xe ± (rrol-rn)2-Yc2. 1+(c4,2) zo = + x(x0 -x0); and Yo = 0 where the respective target point has the co-ordinates: [xtp; ytp; ztp]; [2(,; Yc; zj = [xtp; ytp; ztp] + rn[nxtp; nytp; nztpb where: [nxtp; nytp; nztp] is the unit normal vector at the respective target point; [cx; cy; cz] = [sin(0); 0; cos(0)]; B is the orientation of the forming roller; Trot is the radius of the forming roller; and rn is the nose radius of the forming roller.

In an example, for each pass, each command position may be defined by a first distance along the axis of rotation of the rotatable mounting point and a second distance along an axis perpendicular to the axis of rotation of the rotatable mounting point, the first distance increasing between successive command positions. Optionally, for each command position, the method includes determining the respective target point from a set of target points that are arranged in a transverse plane extending through the corresponding target shape at a longitudinal position corresponding to the first distance of the command position along the longitudinal axis, the respective target point being determined from the set of target points on the basis that the sphere is positionable so as to intersect the respective target point without intersecting any of the other target points in the set of target points. In this manner, the method accounts for kinematic constraints on the spin forming machine.

In an example. the respective target point for each command position relates to an associated interval of rotation of the workpiece; the interval of rotation defining a distance along the longitudinal axis of a plane in which the respective target point is positioned; and the respective target point being determined, from a set of target points within the plane, by determining whether the forming tool is positionable so as to intersect said target point without intersecting any of the other target points in the set.

In an example, the article shape may be non-axisymmetric and/or asymmetric.

Controlling the forming tool according to the toolpath enables the production of nonaxisymmetric and/or asymmetric articles. In this manner, the method widens the capabilities of the spin forming process.

In an example, the method further comprises determining the toolpath for the forming tool in dependence on at least one of: a rate of rotation of the workpiece; a number of command positions per revolution; and a feed rate, the feed rate being a rate of relative movement between the forming tool and the workpiece mounting point along the axis of rotation of the rotatable mounting point.

Optionally, the method further comprises receiving a user input and determining at least one of: the number of passes; for each pass, the computerised representation of the target shape; for each pass, the plurality of command positions; the start point of each pass; and/or the end point of each pass; in dependence on the user input.

Advantageously, the user input allows recalibration of the toolpath. This may facilitate iterative improvements of the toolpath and provide the flexibility required to produce more complex target shapes.

In an example, the method may comprise determining the transformation function in dependence on the user input, for example determining one or more of the parameters of the transformation function based on the user input. Optionally, one or more selected from: the rate of rotation of the workpiece; the number of command positions per revolution; and/or the feed rate; are determined in dependence on the user input.

Optionally, the workpiece is metallic.

In an example, the spin forming machine may be a mandrel-free spinning apparatus further including a first support tool controllable to support the workpiece as the forming tool deforms the workpiece towards the article shape. Optionally, the method includes: generating a second toolpath for the first support tool of the spin forming machine comprising a route of the first support tool for each pass, wherein, for each pass, determining said route of the first support tool comprises determining a plurality of support positions for the first support tool, each support position being based on a respective target point of the corresponding target shape; and controlling the first support tool according to the second toolpath, whilst rotating the workpiece and controlling the forming tool according to the first toolpath. Advantageously, the mandrel-free spinning apparatus is configured to produce asymmetric and non-axisymmetric shapes and replaces the need for a physical mandrel.

In an example, the article shape includes a base portion at one end of the article shape, a rounded portion extending from the base portion, and a body portion extending from the rounded portion. The base portion may, for example, be a central flat region used to mount the workpiece to the spin forming machine.

Optionally, for each pass, each of the plurality of support positions are determined based on a respective target point of the corresponding target shape that relates to an article shape point on the base portion of the article shape. Moving the first support tool between the plurality of support positions, as the workpiece rotates, as the workpiece rotates, may define a route of the first support tool corresponding to a base portion of said target shape, for example.

Optionally, the route of the first support tool may be arranged to resist deformation of the workpiece, in use, to form the base portion of the target shape.

Optionally, the second toolpath substantially matches the first toolpath and includes offsets to engage the first support tool and the forming tool with opposing surfaces of the workpiece.

Consequently, the second toolpath can be efficiently redesigned to accommodate changes to the design of the article by updating the computerised representation. The method also facilitates operation of the spin forming machine by a relatively unskilled operator since the second toolpath is generated based on the computerised representation of the article shape.

In an example, the method may comprise mounting a first workpiece to the workpiece mounting point; and mounting a second workpiece to the workpiece mounting point such that relative movement between the first and second workpieces is substantially inhibited at the workpiece mounting point.

In an example, the method includes determining a second toolpath for the first support tool of the spin forming machine, wherein said second toolpath is complementary to said first toolpath so as to deform the workpiece between the forming tool and the first support tool as the workpiece rotates; and controlling the first support tool according to the second toolpath, whilst rotating the workpiece with respect to the forming tool and the first support tool, to deform the workpiece into a second shape that substantially matches the article shape.

Optionally, the method further comprises: receiving a computerised representation of the first support tool; wherein, for each pass, determining each support position comprises: determining a position, for example, a co-ordinate position, of a reference point of the computerised representation of the first support tool that causes the computerised representation of the first support tool to intersect the target shape. Optionally, intersecting the target shape at the position, along the longitudinal axis, of the respective target point. Optionally, intersecting the target shape at the respective target point. Advantageously, this allows for accurate reproduction of the inner surfaces of the respective target shape.

In an example, the first support tool comprises a support roller and the computerised representation of the first support tool comprises at least one of the following: an orientation of the support roller, a centre of the support roller; a plurality of dimensions of the support roller, optionally, including a radius of the support roller and a radius of a nose of the support roller; a three-dimensional model of the support roller; and/or an equation defining a surface of the support roller.

Optionally, the computerised representation of the first support tool comprises the orientation of the support roller, the radius of the support roller and the support roller nose radius. For each support position, determining the position of the reference point of the computerised representation of the first support tool that causes the computerised representation of the first support tool to intersect the target shape may, for example, comprise: use of a function that relates the orientation of the support roller, the radius of the support roller, the support roller nose radius and the co-ordinates of the respective target point to the position of the reference point that causes the computerised representation of the first support tool to intersect the target point.

In an example, the function is derivable from the co-ordinate position of the centre of a sphere, having a radius equal to the radius of the support roller minus the support roller nose radius, at which a point on the sphere intersects both: a plane inclined by the orientation of the first support tool; and a point translated from the target point along a unit normal vector of the target point by a distance equal to the support roller nose radius.

In an example. the respective target point for each support position relates to an associated interval of rotation of the workpiece; the interval of rotation defining a distance along the longitudinal axis of a plane in which the respective target point is positioned; and the respective target point being determined, from a set of target points within the plane, by determining whether the computerised representation of the first support tool is positionable so as to intersect said target point without intersecting any of the other target points in the set; optionally, the respective target point is determined using the function that relates the orientation of the support roller, the radius of the support roller, the support roller nose radius and the target point to a position of the reference point on the computerised representation of the first support tool.

In an example, the co-ordinate position of the centre of the sphere, [xos; yos; zos], is given by: (7.57.01-r5732 Ysc 2 xos -XCS ± c 2 1+(c, z2 c zso = zsc +" 727 (xsc -zso); and Yso Where the intersected target point has the co-ordinates: [xstp; ystp; zstp]; [xsc; Ysc; zsc[ = [xstp; Ystp; zstpi rsn[nsxtp; nsytp; nsztp] [nsxtp; lisytp; nsztp] is the normal at the intersected target point; [csx; csy; c."] = [sin(0s); 0; cos(Os)]; Os is the orientation of the support roller; rsrai is the radius of the support roller; and r" is the support roller nose radius.

Optionally, the second toolpath may move the first support tool in planar alignment with the forming tool.

In an example, the method further comprises determining the second toolpath for the first support tool in dependence on at least one of: a rate of rotation of the workpiece; a number of support positions per revolution; and a feed rate, the feed rate being a rate of relative movement between the first support tool and the workpiece mounting point along the axis of rotation of the rotatable mounting point.

Optionally, the method further comprises receiving a user input and determining at least one of the plurality of support positions; the start point of each pass; and/or the end point of each pass; in dependence on the user input.

Advantageously, the user input allows recalibration of the second toolpath. This may facilitate iterative improvements of the second toolpath and provide the flexibility required to produce more complex target shapes.

Optionally, for each pass, each support position may be associated with an angle of rotation of the workpiece and each support position may be defined by a first distance along the axis of rotation of the rotatable mounting point, and a second distance along a second axis perpendicular to the axis of rotation of the rotatable mounting point. In this manner, the rotation of the workpiece can be discretized into intervals of rotation and each toolpath can be defined by positions of, for example, radial and longitudinal distance for each interval of rotation. These positions may, for example, correspond to sequential points on the surfaces of the target shape. Thus, the first support tool can be moved dynamically, as the workpiece rotates. The method may further comprise conversion from one co-ordinate system to another co-ordinate system, for example converting between Cartesian and polar co-ordinate systems.

Optionally, the plurality of passes are sequential, and the second toolpath may include moving the first support tool from the end point of a first pass to the start point of a second pass.

In an example, the first support tool does not contact the workpiece during the motion towards the start point. In an example, the first support tool may follow an arced motion between passes. For example, an arced motion between the end point of the present pass and the start point of the subsequent pass.

In an example, the spin forming machine further includes; a second support tool and a third support tool controllable of support the workpiece as the workpiece is deformed towards the second shape such that the wall portion of the article shape can be formed; wherein, in use, the spin forming machine is configured to rotate the workpiece with respect to the forming tool, the first support tool, the second support tool and the third support tool.

In an example, the method further includes: determining a third toolpath for the second and third support tools of the spin forming machine; wherein determining the third toolpath for the second and third support tools comprises: determining, for each pass, a route of the second and third support tools based on the target shape; and controlling the second and third support tools according to the third toolpath, whilst rotating the workpiece with respect to the forming tool, the first support tool and the second and third support tools, to deform the workpiece into a second shape that substantially matches the article shape.

Advantageously, the workpiece is supported on opposing surfaces during deformation, reducing stress concentrations.

Another aspect of the invention relates to a method of controlling a spin forming machine, comprising a rotatable mounting point for a workpiece and a forming tool in the form of a roller, controllable to deform the workpiece as the workpiece rotates, towards a target shape. The method includes: receiving a CAD model of the target shape comprising a plurality of target points; receiving information indicative of the shape of the forming tool; generating a toolpath for the forming tool comprising a route of the forming tool between a start point and an end point; wherein generating the route of the forming tool comprises determining a plurality of command positions for the forming tool, each command position being based on a respective target point and the information indicative of the shape of the forming tool, and each command position being offset from the respective target point so as to engage the forming tool with the workpiece at a position corresponding to the respective target point; and controlling the forming tool according to the toolpath, whilst rotating the workpiece on the rotatable mounting point, to deform the workpiece towards the target shape.

The target shape may, for example, be a geometric representation of a desired article.

Advantageously, the method is arranged to control the forming tool in dependence on the CAD model of the target shape, the control being updated in response to changes to the CAD model.

Optionally, the forming tool is a forming roller and the information indicative of the shape of the forming tool comprises a radius of the forming roller, a nose radius of the forming roller and an orientation of the forming roller.

In an example, determining each command position may comprise: determining the co-ordinates of the centre of a sphere, having a radius equal to the radius of the forming roller minus the nose radius of the forming roller, at which a point on the sphere intersects both: a plane inclined by the orientation of the forming roller; and a point translated from the respective target point, by a distance equal to the nose radius of the forming roller, along a unit normal vector of the respective target point. Advantageously, this method allows for accurate positioning of the forming tool so as to trace the target shape.

Optionally, the co-ordinates of the centre of the sphere, [xo; yo; zo], are given by: x, = xe + (rroi-rn)2-Ye2.

1+ (Z 2) zo = zo + (x, -x0); and C, Yo = where the respective target point has the co-ordinates: [xto; AD; zip]; [xt; ye; Zc] = [xtp; ytp; zep] + 7;21 Lnxtp; nytp; nztpi; and where: [nxtp; riytp; nztp] is the unit normal vector at the respective target point; [c,; cy; = [sin(0); 0; cos(0)]; 0 is the orientation of the forming roller; rroi is the radius of the forming roller; and rn is the nose radius of the forming roller.

In an example, each command position is defined by a first distance along the axis of rotation of the rotatable mounting point and a second distance along an axis perpendicular to the axis of rotation of the rotatable mounting point, the first distance increasing between successive command positions. For each command position, the method may include determining the respective target point from a set of target points that are arranged in a transverse plane extending through the target shape at a longitudinal position corresponding to the first distance of the command position along the longitudinal axis, the respective target point being determined from the set of target points on the basis that the sphere is positionable so as to intersect the respective target point without intersecting any of the other target points in the set of target points.

A further aspect of the invention relates to a method of controlling a mandrel-free spinning apparatus. The mandrel-free spinning apparatus comprising a rotatable mounting point for a workpiece, a forming tool controllable to deform the workpiece as the workpiece rotates and a first support tool controllable to support the workpiece as the workpiece rotates. The method being arranged to produce an article, having an article shape, from the workpiece in one or more passes. The method including: receiving a computerised representation of the article shape; optionally receiving a number of passes for producing the article shape; determining a computerised representation of a target shape for each, or at least one or more, passes based on the computerised representation of the article shape; determining a first toolpath for one of the forming tool and the first support tool, wherein the first toolpath comprises a route of said tool between a start point and an end point for each pass based on the respective target shape; determining a second toolpath for the other of the forming tool and the first support tool, wherein said second toolpath is complementary to said first toolpath; and controlling the forming tool and the first support tool according to the respective first and second toolpaths, whilst rotating the workpiece with respect to the forming tool and the first support tool, to deform the workpiece between the forming tool and the first support tool towards a second shape that substantially matches the article shape.

According to another aspect of the invention there is provided a method of controlling a mandrel-free spinning apparatus, comprising: a rotatable mounting point for a workpiece; and first and second tools that are movable relative to the workpiece and controllable to deform the workpiece as the workpiece rotates. The method is arranged to deform the workpiece in one or more passes towards a target shape. The method includes: receiving a CAD model of the target shape; determining a first toolpath for the first tool, wherein the first toolpath comprises a route of the first tool between a start point and an end point for each pass based on the CAD model of the target shape; determining a second toolpath for the second tool, wherein the second toolpath is complementary to the first toolpath so that, collectively, the first and second toolpaths move the first and second tools during each pass so as to engage opposing surfaces of the workpiece and deform the workpiece towards the target shape; and controlling the first and second tools according to the respective first and second toolpaths, whilst rotating the workpiece on the rotatable mounting point, to deform the workpiece towards the target shape.

In this manner, the first tool may, for example, be controlled to substantially follow the motion of the forming tool during the spin forming process. The first support tool may support a first surface of the workpiece against deformation and the forming tool may apply a force to an opposing second surface of the workpiece, bending the workpiece about the point supported by the first support tool, for example.

Optionally, the second toolpath may be complementary to the first toolpath so as to move the first and second tools substantially synchronously. For example, so as to deform the workpiece between the forming tool and the first support tool, during each pass towards, towards the respective target shape. For example, moving the first and second tools in phase or substantially in phase.

Optionally, the second toolpath may be complementary to the first toolpath so as to move the first and second tools at substantially the same rate along the axis of rotation of the rotatable mounting point.

Optionally, the second toolpath is based on the first toolpath. Optionally, the second toolpath substantially matches, or corresponds to, the first toolpath and includes offsets from the first toolpath to engage the first and second tools with opposing surfaces of the workpiece.

Optionally, determining the second toolpath comprises determining a route of the second tool between a start point and an end point for each pass based on the CAD model of the target shape.

In an example, the CAD model of the target shape may comprise a plurality of target shape points on a co-ordinate system; and, for each pass of said first toolpath, determining the route of the first tool may comprises determining a first set of control positions for the first tool, wherein each control position is based on a respective target point, such that the first tool is moved between successive ones of the first set of control positions as the workpiece rotates.

Optionally, each control position in the first set of control positions is offset from said respective target point to position the first tool in engagement with the workpiece.

In an example, for each pass of the second toolpath, determining the route of the second tool comprises determining a second set of control positions for the second tool. Consequently, the second tool may be moved between successive ones of the second set of control positions as the workpiece rotates.

Each control position in the second set of control positions may, for example, be based on a respective target point and be offset from said respective target point so as to position the first and second tools in engagement with opposing surfaces of the workpiece.

Optionally, each control position in the second set of control positions is based on a respective control position in the first set of control positions and is offset from said respective control position in the first set of control positions so as to position the first and second tools in engagement with opposing surfaces of the workpiece. This may reduce the computational requirements of the method.

One of the first and second tools may be a forming tool that is controllable to deform the workpiece as the workpiece rotates and the other of the first and second tools may be a support tool controllable to support the workpiece as the workpiece rotates.

Optionally, the target shape is non-axisymmetric.

The CAD model of the target shape may, for example, includes a three-dimensional model of the target shape.

Another aspect of the invention relates to a method of controlling a spin forming machine to produce an article, having an article shape; the spin forming machine comprising a rotatable workpiece mounting point and a forming tool that is moveable, in use, to deform a rotating workpiece; the method comprising: mounting a first workpiece to the workpiece mounting point; mounting a second workpiece to the workpiece mounting point such that relative movement between the first and second workpieces is substantially inhibited at the workpiece mounting point; rotating the first and second workpieces on the workpiece mounting point; and moving the forming tool according to a first toolpath based on the article shape, so as to deform the rotating first and second workpieces towards the article shape.

Advantageously, the method can reduce the local stresses on the second workpiece leading to a reduction in thinning and mitigating failure of the second workpiece. Effectively, the first workpiece may act to spread the forming tool loads over a large area of the second workpiece.

Optionally, moving the forming tool according to the toolpath comprises deforming the second workpiece into a second shape that substantially matches the article shape. Advantageously, the method is arranged to provide improved surface finish on the second workpiece, at least relative to conventional methods where a single workpiece is spun during the spin forming process. Furthermore, by spin forming the first and second workpieces simultaneously, the forming time per article can be significantly reduced compared to the conventional methods. Optionally, a shape of the first workpiece substantially matches a shape of the second workpiece.

The first workpiece may, for example, comprise first and second opposing surfaces. The first toolpath may be arranged to engage the forming tool with the first surface of the first workpiece and the second workpiece may abut against the second surface of the first workpiece, for example. In this manner, the forming tool may exert force on the first workpiece and deform the first and, optionally, second workpieces.

The first workpiece may, for example, be a protective layer that reduces the pressure from the forming tool acting on the second workpiece. Optionally, the first workpiece is made from a flexible material. This may reduce the forming tool forces during the spin forming process. The first workpiece may be elastic or have some resiliency to springback to another shape for use in a further spin forming process, for example.

Optionally, the thickness of the first workpiece substantially matches the thickness of the second workpiece.

In an example, the thickness of the first workpiece may be less than the thickness of the second workpiece. In this manner, the thinner first workpiece, which may be disposed after the spin forming process, may waste less material whilst reducing the stresses on the second workpiece.

In an example, the thickness of the first workpiece may be greater than the thickness of the second workpiece. The first workpiece is subjected to greater local stresses and the increased thickness mitigates the possibility of the first workpiece failing.

Optionally, the stiffness of the first workpiece is less than the stiffness of the second workpiece. This reduces the forming tool forces during the spin forming process.

Optionally, the first and second workpieces may be substantially the same shape. This may minimise any differences between the first and second workpieces during deformation.

The first and second workpieces may, for example, be made from the same material.

Optionally, the spin forming machine is a mandrel-free spinning apparatus further including: a first support tool controllable to support the second workpiece as the forming tool engages the first workpiece. In use, the spin forming machine may be configured to rotate the first and second workpieces with respect to the forming tool and the first support tool.

In an example, the method further includes: determining a second toolpath for the first support tool of the spin forming machine, wherein said second toolpath is complementary to said first toolpath to deform the first and second workpieces; and controlling the first support tool according to the second toolpath, whilst rotating the first and second workpieces on the workpiece mounting point and controlling the forming tool according to the first toolpath to deform the first and second workpieces between the forming tool and the first support tool towards the article shape.

Optionally, the method further comprises receiving a computerised representation, or CAD model, of the article shape and determining the first toolpath for the forming tool based on the computerised representation of the article shape.

The second toolpath may, for example, be based on the computerised representation of the article shape.

Optionally, the computerised representation of the article shape comprises an enlarged wall thickness relative to a wall thickness of the article shape. This thickness may account for the additional thickness of the first workpiece.

The enlarged wall thickness may be less than or equal to the total thickness of the first and second workpieces, for example.

Optionally, the method further comprises receiving a user input and determining the first toolpath for the forming tool based on the user input.

Optionally, the method further comprises receiving a user input and the toolpath for the forming tool may be determined based on the user input, for example.

Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, in the claims and/or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and/or features of any embodiment can be combined in any way and/or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and/or incorporate any feature of any other claim although not originally claimed in that manner.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which: Figures 1 illustrates the operation of a traditional spin forming apparatus to form an article; Figures 2 illustrates a range of articles, shown form a side view, that may be formed by the traditional spin forming apparatus, shown in Figure 1; Figure 3 illustrates the operation of a mandrel-free spinning apparatus to form an article; Figure 4 illustrates an end view of the mandrel free spinning apparatus, shown in Figure 3; Figure 5 illustrates a practical arrangement of the mandrel free spinning apparatus, shown in Figure 3; Figure 6 shows a plan view of the mandrel-free spinning apparatus, shown in Figure 5; Figures 7(a) to 7(c) illustrate a range of non-axisymmetric articles that may be formed by the mandrel free spinning apparatus, shown in Figure 5; Figures 8(a) and 8(b) illustrate an example of an article which may be formed in accordance with the method of the invention, the article taking the form of a square cup; Figure 9 illustrates a system of devices that may be used to operate a spin forming machine in accordance with the methods of the invention; Figure 10 illustrates a method, in accordance with an embodiment of the invention, of controlling a spin forming machine to produce an article; Figure 11 illustrates a CAD model of the square cup-shaped article, shown in Figure 8; Figure 12 illustrates the CAD model of Figure 8, discretized into a plurality of article shape points; Figure 13 illustrates a series of target shapes determined based on the CAD model shown in Figures 11 and 12; Figure 14 illustrates the CAD model of Figure 8 and a target shape of the series of target shapes shown in Figure 13; Figure 15 illustrates the interaction between a forming tool of the mandrel free spinning apparatus, shown in Figure 5, and the target shape of Figure 14; Figure 16 shows a sequence of command positions arranged in a helical pass around one of the target shapes shown in Figure 13; Figure 17 shows a toolpath for the forming tool produced in accordance with the method of Figure 10; Figure 18 shows a two-dimensional plot of an example series of passes that may be generated in accordance with the method shown in Figure 10; Figure 19 shows two-dimensional plots of example toolpaths that may be generated in accordance with the method shown in Figure 10; Figure 20 illustrates a further method, in accordance with an embodiment of the invention, of controlling a spin forming machine to produce an article; Figure 21 illustrates another method, in accordance with an embodiment of the invention, of controlling a spin forming machine in dependence on a CAD model of a target shape; Figure 22 illustrates another method, in accordance with an embodiment of the invention, of controlling a spin forming machine to produce multiple articles simultaneously; Figure 23 shows a plot of the axial force on the forming tool for each pass of an example toolpath used to form a discoidal article from a 1mm workpiece, a 2mm workpiece and two 1mm workpieces spun at the same time respectively; Figure 24 shows an example pair of articles formed in accordance with the method shown in Figure 22.

DETAILED DESCRIPTION

Embodiments of the present invention relate to a method of controlling a spin forming machine to produce an article from a workpiece based on a CAD model that represents the shape (or geometry) of a desired article, i.e. the 'article shape'.

As shall become clear in the following description, the method is configured to form the desired article in an incremental manner using the following steps.

Firstly, using the CAD model of the article shape to determine a series of three dimensional target shapes that correspond to successive states of the workpiece between an initial shape of the workpiece and the desired article shape.

Secondly, generating a first toolpath that moves the forming tool so as to deform the workpiece into the article shape. This includes determining a plurality of passes or routes along which the forming tool is moved with respect to the workpiece. Each pass is determined based on a respective target shape and each pass is arranged to move the forming tool so as to effectively trace that target shape as the workpiece rotates.

Thirdly, controlling the forming tool according to the generated first toolpath, whilst rotating the workpiece on the rotatable mounting point, to incrementally deform the workpiece through the successive states and towards the article shape.

By virtue of this approach, the method provides enhanced control over the forming tool, improving the accuracy of the formed article. Furthermore, generating the toolpath based on the CAD model of the article shape is advantageous in that the toolpath can be efficiently redesigned by updating the CAD model, for example to accommodate changes to the article design.

The workpiece may, for example, initially take the form of a blank sheet of ductile metal, such as aluminium, stainless steel or alloys thereof. Alternatively, the workpiece may comprise any other similarly ductile material that is suitable for use in a spin forming process.

The spin forming machine may take the form of a traditional spin forming apparatus 1 with a mandrel 3, as shown in Figure 1, or the spin forming machine may take the form of a mandrel-free spinning apparatus 20, such as the example illustrated in Figures 5 and 6.

In the following description of the invention, the spin forming machine takes the form of a mandrel-free spinning apparatus 20 substantially as described previously with reference to Figures 3 to 6. However, it shall be appreciated that this is not intended to be limiting on the method of the invention.

Embodiments of the invention are suitable for producing articles that have a variety of shapes, including axisymmetric, non-axisymmetric and even asymmetric shapes.

By way of example, Figures 8(a) and 8(b) show a square cup-shaped article 50 that may be formed in accordance with the invention. The article 50 consists of a single workpiece 2 that has been deformed into a hollow shape, featuring three regions that are common to spin formed articles.

Firstly, the article 50 includes a substantially planar central region that forms a base portion 52 at a first end 54 of the article 50, where the workpiece 2 is secured to the lathe 4.

Secondly, the article 50 includes a rounded portion 56 that borders the base portion 52 and curves along a longitudinal axis 57 of the article 50 away from the base portion 52, where the workpiece 2 is bent away from the lathe 4.

Thirdly, the article 50 includes a body portion 58 that extends from the rounded portion 56 to a second end 60 of the article 50 where the workpiece 2 terminates in a rim 62.

At the second end 60, the article 50 features an opening 61 which provides access to an interior volume of the article 50. The rim 62 effectively separates interior surfaces 64 of the article 50 from exterior surfaces 66 of the article 50.

The square cup shown in Figure 8(a) and 8(b) is one such example of an article 50 that may be formed by the method of this invention and is not intended to be limiting.

Figure 9 schematically illustrates a system of devices 70 that may be used to form an article, such as the square cup-shaped article 50, in accordance with methods of the invention.

The system of devices 70 includes a spin forming machine, which takes the form of the mandrel free-spinning apparatus 20 in this example, a control system 71 and a sensor system.

The control system 71 comprises a controller 74 for operating the spin forming machine and one or more computing or processing devices 76. The computing device(s) 76 are configured to determine a set of computer readable instructions that the controller 74 can use to generate control signals for operating the mandrel free-spinning apparatus 20 in accordance with the invention.

For example, the mandrel-free spinning apparatus 20 is configured to receive control signals from the controller 74 and to: i) rotate the workpiece 2 on the lathe 4, e.g. at a particular rate (degrees/second); and ii) move the forming tool 6 and/or the support tools 22, 24, 26 in accordance with respective toolpaths; in dependence on the control signals.

The computer readable instructions may, for example, take the form of computer generated code that the controller 74 processes to determine the corresponding control signals.

In some embodiments, the one or more computing devices 76 are configured to receive inputs from one or more other systems or devices (not shown), such as a memory storage device and/or from a user, for example through a human-machine interface device. The control system 71 or computing device 76 may be configured to use such inputs to determine suitable instructions for operating the mandrel-free spinning apparatus 20 in accordance with the methods of the present invention.

Such inputs are discussed in more detail in the description of the method of operation but may, for example, include the CAD model 80 of the article shape and/or inputs that define one or more toolpath parameters, as shall be discussed in more detail in other parts of the description.

The sensor system 72 comprises one or more sensors (not shown) configured to monitor the operation of the spin forming machine and may include one or more: accelerometers; actuation sensors; and/or force sensors. The sensor system 72 may, for example, be configured to determine the loading on the forming tool 6 and/or one or more of the first, second and third support tools 22, 24, 26 and to relay such measurements back to the control system 71.

The control system 71 may adapt the operation of the mandrel-free spinning apparatus 20 based on feedback from the sensor system 72. For example, if the loading on one of the tools 6, 22, 24, 26 exceeds a predetermined threshold, the control system 71 may stop the movement of said tool 6, 22, 24, 26 and return said tool 6, 22, 24, 26 to a default position until instructed to proceed.

Figure 10 illustrates a method 100, in accordance with an embodiment of the invention, of controlling a spin forming machine to produce the example square cup-shaped article 50 shown in Figure 8.

In step 102, the method 100 includes receiving a CAD model 80 of the desired shape of the article 50. As shown in Figure 11, the CAD model 80 provides a three-dimensional representation of the article 50 and may have been designed using suitable CAD software, for example. The CAD model 80 may be received from any suitable means, including: the memory storage device; the human-machine interface device; a CAD system; a connected three-dimensional scanning device; and/or a connected cloud storage system.

In step 104, the method 100 includes discretizing the CAD model 80 of the article shape such that the CAD model 80 includes a plurality of article shape points 82, or nodes, on a co-ordinate system. For example, a triangulated, or rectangular, mesh can be applied to, or featured on, the CAD model 80 to discretize the CAD model 80 into a plurality of article shape points 82, as shown in Figure 12.

It shall be appreciated that, in Figure 12, some, but not all of, the article shape points 82 are shown for the sake of visual clarity. In particular, article shape points 82 are only shown on certain portions of the CAD model 80, but it shall be appreciated that such article shape points 82 may be featured throughout the CAD model 80.

The article shape points 82 provide a coordinate based representation of the article 50 for use in determining the first toolpath for the forming tool 6. Accordingly, the size of the mesh and/or the density of the article shape points 82 may be adjusted as necessary to provide enough article shape points 82 to form an adequate representation of the article 50.

The coordinate system may, for example, take the form of a Cartesian coordinate system, as shown in Figure 12, with each article shape points 82 being defined by a longitudinal position, 'z', a position on a first transverse axis, 'x', and a position on a perpendicular second transverse axis, 'y'.

Accordingly, in general, the article shape may include m article shape points 82, or nodes of a mesh, which may form a connectivity matrix and an m x 3 coordinate matrix, B: B = [x; y; z] where m is the number of article shape points 82, or nodes, and x; y; z are m-tuples representing components of standard Cartesian coordinates.

In steps 106 and 108, the method 100 is configured to determine a series of three dimensional target shapes 84(h-k) that represent successive states of the workpiece 2 during the forming process, as shown in Figure 13.

In particular, the method 100 includes receiving, or otherwise determining, one or more toolpath parameters, in step 106, and then using the toolpath parameters and the CAD model 80 of the article shape to determine the series of target shapes 84(h-k), in step 108.

The toolpath parameters are inputs that are used to control the operation of the mandrel-free spinning apparatus 20 and/or to vary the geometry of each of the target shapes 84(h-k) relative to the article shape. These toolpath parameters may, for example, be received at the computing device 76 from one or more user inputs at the human-machine interface device.

Such toolpath parameters may, for example, include: a feed rate or ratio, F; a number of passes, k; a start point for each pass; an end point for each pass; a length of each pass; a transformation function used to determine the target shape associated with each pass, and/or one or more parameters defining the transformation function for each pass; and/or the parameter, P, defining a number of command positions per revolution of the workpiece.

In this manner, the toolpath parameters allow investigation of common parameters that cause forming errors and/or workpiece 2 failure. For example, the feed ratio, F (mm/rev), defines the movement of the forming tool 6 along the longitudinal axis 30 of the mandrel-free spinning apparatus 20 per revolution of the workpiece 2 and the parameter, P, defines the number of command positions to which the forming tool 6 is moved during each revolution of the workpiece.

It follows that, during each pass, the forming tool 6 is made to move through P command positions per revolution and successive command positions are separated by F/P mm intervals along the longitudinal axis 30. The parameter, P, therefore relates to the resolution that the hardware can provide for the motion of the servomotors. P may also define the number of target shape points per revolution. Accordingly, the parameters F and P may be adjusted to balance limitations of the hardware with the requirements of the shape. It shall be appreciated that more command positions may need to be defined per revolution as the complexity of the article shapes increases.

Furthermore, a common cause of workpiece 2 failure is that the forming forces are too large. In relation to this, the toolpath parameter, k, defines the number of passes (or times that the forming tool 6 is moved across the workpiece) and, for each pass, the transformation function, or parameters thereof, control the respective target shape that the workpiece 2 is urged towards.

Hence, the number of passes, k, and the transformation function for each pass may be varied to mould the workpiece 2 into the article shape more gradually, with lower forming forces, or more aggressively, with larger forces.

This affords the user a wide range of control over the forming process whilst keeping the number of relevant parameters to a minimum.

Now considering step 108 in more detail, the method 100 includes determining a series of three dimensional target shapes 84(h-k) based on the CAD model 80 of the article shape and the toolpath parameters.

In general, one or more of the target shapes 84(h-k) may diverge away from the article shape along its length (representing the gradual inward deformation of the workpiece), but successive target shapes 84(h-k) in the series of target shapes 84(h-k) converge on the article shape.

As shall become clear in the following description, each target shape 84 comprises a plurality of target points 86 that collectively represent the respective target shape on a co-ordinate system, as shown in Figure 14. The co-ordinate system may be a Cartesian co-ordinate system, for example.

Each of the target points 86 corresponds to a respective article shape point 82 and, for each pass, the plurality of target points 86 may be determined as a function of the respective article shape points 82. The function used to determine the plurality of target points 86 is referred to as the 'transformation function' in the following description.

The transformation function is configured to offset each target point 86 from the respective article shape points 82 in dependence on: i) the toolpath parameters defined for the respective pass; and ii) the distance of the respective article shape points 82 along the article shape.

Accordingly, for each target point 86, the transformation function includes: a unit normal vector to the CAD model 80 of the article shape at the respective article shape point 82; and a scaling coefficient for the unit normal vector. It shall be appreciated that the scaling coefficient may be a function of one or more toolpath parameters and the distance of the respective article shape points 82 along a longitudinal axis of the article shape, i.e. the distance from one end of the article shape.

Hence, in step 108, the method 100 determines the series of target shapes 84(h-k) as follows.

First, the Cartesian components of the unit normal vectors to the surface of the CAD model 80 of the article shape are determined at each article shape point 82, represented here by the m x 3 matrix, N: N = [mx; ny;nz] where nx; n y; it, are m-tuples representing components of standard Cartesian coordinates of the unit normal vectors to the article shape points 82.

For each pass, i = 1, . . . , k, the target points 86 can then be defined by an m x 3 coordinate matrix, C: Ci = [xe t;Yci;ZJ where x,; y,; z are m-tuples for each pass, i, representing components of standard Cartesian coordinates. Notably, the longitudinal position, z, of each target point 86 remains the same as the article shape point 82.

For each pass, i, the respective target shape 84(h-k), or matrix of target points 86, C, can therefore be determined using the transformation function: [xci; yci] = [x; y] + f(z). [nx; ny] Where x and y are components of the article shape co-ordinate matrix B and f(z) is the scaling coefficient part of the transformation function.

In this example, f(z) is a function of the position (z) of each article shape points 82 along the longitudinal axis of the article shape. For each pass, the scaling coefficient part of the transformation function, f(z), may, for example, take the form: 0, z < Lp f(z) = i (stizn, + t0), Z > L. where, Lp, a and n are toolpath parameters defined for each pass, /; and to is a constant offset for the pass that may correspond to the thickness of the article and/or workpiece,

for example.

In this example, the parameters a and n are toolpath parameters that are defined for each pass to alter the geometry (slope and concavity) of the respective target shape 84(h-k). Parameters a and n are used to define an offset with respect to the axial location (z) of each article shape points 82 on the article shape.

The toolpath parameter, Lp, may be defined so that the target shapes 84(h-k) relating to one or more passes are only offset from the article shape beyond a certain length, Lp, from one end of the article shape.

For example, Lp can define the distance along the article shape's meridian where the offset should start. This may refer to the length of the section of the workpiece 2 that has already been formed into the article shape and does not need to be deformed in subsequent passes of the forming tool 6, as shown in Figure 14.

The parametric equation (aizn0 is used in this example because it only requires two toolpath parameters (which a user may provide for each pass), whilst offering a diversity of resulting shapes. In other examples, the scaling coefficient part of the transformation equation can be replaced by any other expression that achieves a desired series of target shapes 84(h-k).

At the end of step 108, a matrix, C, of target points 86 is determined for each pass. Each matrix, C, of target points 86 represents a respective target shape 84(h-k) in the series of target shapes 84(h-k), which includes a final target shape 84(k), corresponding to the article shape, and k-1 successive intermediate target shapes 84(h-j), relating to so-called intermediate mandrel surfaces, as shown in Figure 13.

Each of the intermediate target shapes 84(h-j) corresponds to an intermediate state of the workpiece, between the initial shape of the workpiece 2 and the final shape of the article. Accordingly, the series of target shapes 84(h-k) iteratively converge on the article shape, as shown in Figure 13.

It shall be appreciated that the scaling coefficient part of the transformation function f (z) may be effectively zero, or equal to the thickness of the workpiece, in the final pass, i=k, so that the target points 86 in the final target shape 84(k) correspond to the article shape points 82.

Once the series of target shapes 84(h-k) have been obtained, the method 100 can proceed to generate a first toolpath for the forming tool 6, in steps 110 to 114.

As mentioned previously, the first toolpath for the forming tool 6 comprises k passes and each pass is determined based on the toolpath parameters and a respective target shape 84(h-k) associated with that pass.

As shall become clear in the following description, each pass is defined by a plurality of command positions through which the forming tool 6 is moved to effectively trace the respective target shape 84(h-k) as the workpiece 2 rotates on the lathe 4. Each command position is a position, having co-ordinates, through which a reference point of the working roller, such as the centre of the working roller, is moved.

For each pass, the toolpath parameters define a start point and an end point, as well as a distance, L, that the forming tool 6 is moved between the start and end points (along the longitudinal axis 30 of the mandrel-free spinning apparatus 20).

The toolpath parameters also define the distance, F mm, that the forming tool 6 moves along the longitudinal axis 30 per revolution of the workpiece 2 and the number of command positions, P, that the forming tool 6 is moved to per revolution of the workpiece. Hence, the workpiece 2 completes L/F revolutions during each pass and each pass includes command positions through which the forming tool 6 is moved.

Accordingly, for each pass: i) a sequence ofLF command positions are determined that move the forming tool 6, in synchronisation with the rotation of the workpiece, so as to effectively trace the respective target shape 84(h-k) in a helical manner; ii) successive command positions in the sequence increase in F/P mm increments along the longitudinal axis 30 of the mandrel-free spinning apparatus 20, whilst the workpiece 2 rotates through 360°/P degree increments; and iii) each command position corresponds to a particular time stamp and/or orientation of the workpiece 2 relative to an initial reference orientation.

Accordingly, to trace the respective target shape 84(h-k) in a helical manner the command positions may be determined on the basis of desired contact points on the respective target shape 84(h-k) that: i) increase in F/P mm increments along the longitudinal axis of the respective target shape 84(h-k); and ii) are arranged in consecutive angular planes through the respective target shape 84(h-k) that increase in 360°/P degree increments, having corresponding x and y co-ordinates.

These command positions may be offset from the desired contact points so as to account for the shape of the forming too. Also, while it is often assumed that the contact between the workpiece 2 and the forming tool 6 occurs in the plane of motion 28 of the forming tool 6 in axisymmetric spinning, in asymmetric spinning this is no longer the case.

Accordingly, the method 100 includes receiving information relating to the shape of the forming tool 6, in step 110, determining command positions for each pass using the information relating to the shape of the forming tool 6, in step 112, and merging the command positions into a toolpath, in step 114.

The information relating to the shape of the forming tool 6, received in step 110, is used to mathematically represent the shape of the forming tool 6 in 3D space and may be received from one or more user inputs, for example. With this approach the method 100 effectively simulates engagement between the forming tool 6 and each target shape 84(h-k) to determine where to position the forming tool 6 so as to effectively trace the sequence of desired contact points on the target shape 84(h-k).

Accordingly, in step 110, the information received may, for example, include: a radius of the working roller, a nose radius of the working roller and an orientation of the working roller. The nose radius of the working roller is the radius of the rounded nose profile at the edge of the working roller. The radius of the working roller is the total radius of the working roller to the extremity at the nose profile. The orientation of the working roller is the angle of inclination of a mid-plane through the working roller to the radial axis of the mandrel-free spinning apparatus 20 and, in this example, the orientation is equivalent to the orientation 0 of the first arm member 36.

Next, in step 112, the command positions are determined for each pass using the respective target shape 84(h-k) and the information relating to the shape of the forming tool 6.

This process is demonstrated in the following description by way of determining an example command position, in the sequence of command positions, based on a corresponding desired contact point on the target shape 84(h-k). However, it shall be appreciated that the process may be repeated substantially as described below to determine each command position of each pass.

Since the feed rate, F, is chosen by the user, the longitudinal position of the desired contact point can be calculated simply by considering the time step or orientation of the workpiece 2 in the pass. Hence, the desired contact point is positioned: i) at a longitudinal position on the target shape 84(h-k) corresponding to the orientation of the workpiece 2 (or time step in the spin forming process); and ii) in an angular plane through the target shape 84(h-k) corresponding to the orientation of the workpiece; having corresponding x, y and z co-ordinates. For the sake of simplicity, in this example, the desired contact point is one of the target points 86.

Figure 15 illustrates how the shape of the forming tool 6 and, in particular the roller nose radius and the working roller radius, are used to determine where to position the forming tool 6 so as to trace the desired contact point on the respective target shape 84(h-k).

Figure 15 shows a circle, representing a mid-plane through the working roller, which has a radius equal to the working roller radius, rroi, minus the roller nose radius, rp. Since the roller nose radius, ru, is known, the minimum distance that the edge of the circle can have from the surface of the target shape 84(h-k) (at the desired contact point) can also be determined from a normal vector at the desired contact point having a length equal to the roller nose radius.

Hence, in step 112, a unit normal vector [nnp; nytp; %go] at each target point 86 (or just at the desired contact point) on the respective target shape 84(h-k) may be calculated.

The unit normal vector may then be extended by a distance equal to the roller nose radius, rn, and translated from the desired contact point (or target point 86 in this example) accordingly. This defines the distance of the edge of the circle from the desired contact point and provides the point, [xc; yc; zj, given by: [xc; Yc; zc] = [xtp; Ytp; ztp] + rn[nxtp; nytp; nztp]; where: [xfp; yip; zrp] are the target point 86 co-ordinates; [nxtp; nytp; nztp] is the unit normal vector at the respective target point 86; and rn is the nose radius of the working roller.

The command position for the forming tool 6 can subsequently be determined by finding the intersection between: i) a sphere centred at (xo; yo; zo) having a radius equal to the working roller radius, Trot, minus the roller nose radius, rn; ii) the mid-plane of the working roller; and iii) the translated contact point [xc; yc; zc].

The mid-plane of the working roller is found by a plane inclined by the orientation of the working roller, 8, with respect to the x-axis, which passes through the centre of the sphere (where yo= 0).

The roller centre location, zo, is not the same as the longitudinal position of the desired contact point. Hence, the co-ordinates of the centre of the working roller at the command position [xo; yo; zo] are determined according to the equation: xo = xe + (rrol-rn)2-Ye 2 t2 1+ (2) zo = z, + cc(x, -x0); and Yo = 0 Where [cx; cy; cz] = [sin(0); 0; cos(0)]; 0 is the orientation of the working roller; Trot is the radius of the working roller; and rn is the nose radius of the working roller.

Solving this equation gives the co-ordinates of the command position, or at least the centre of the forming tool 6, which causes the forming tool 6 to trace the desired contact point.

In some cases, the kinematic constraints on the machine and the target shape geometry are such that, if the desired contact point was fixed as an input, e.g. at the target point 86 in the example above, there is no guarantee that the machine would be capable of moving the forming tool 6 into contact with the target shape 84(h-k) at that point. Instead, in this case, the machine may only be able to move the forming tool 6 into contact with the target shape 84(h-k) around that point, in the same axial plane.

For completeness, the following description also demonstrates how step 114 is adapted where the kinematic constraints on the machine and the target shape 84(h-k) geometry are such that they do not allow the forming tool 6 to make contact with the workpiece 2 at a particular target point 86. In which case, each command position may be determined in accordance with the following method instead.

Instead of assuming contact with the desired contact point, the method determines where, based on the information relating to the shape of the forming tool 6, the forming tool 6 is positionable so as to intersect the target shape 84(h-k) around the desired contact point.

For this purpose, a number of target points 86 on the surface of the target shape 84(h-k) are selected near and around the desired contact point, for example, in a transverse plane arranged at the longitudinal position of the desired contact point.

The selected target points 86 on the surface of the target shape 84(h-k) are used to define an interpolant, which is used to produce an array of points on the surface of the target shape 84(h-k) (in the transverse plane).

These points form a set of candidate contact points that includes the desired contact point and one or more points determined by interpolating between adjacent target points 86 in the same transverse plane of the target shape 84(h-k).

For each candidate contact point, a unit normal vector is found as described previously. For example, a unit normal vector may be found for each candidate contact point by interpolating between the normals of the three closest target points 86 on the target shape 84(h-k).

Once the normal vectors are obtained, they are extended by a distance equal to the roller nose radius r,, as in the previous example, to give a set of translated candidate contacts points, each having co-ordinates ['Ca; yc2; zcd given by: [xat; ycc; zee] = [xcp; ycy; zcp] + 7-,[nny; nycy; nzcp]; where: [xap; yap; zap] are the co-ordinates of a particular candidate contact point in this example; [71np; nycp; nny] is the unit normal vector at that candidate contact point; and 7-2, is the nose radius of the working roller.

This allows calculation of the centre of the roller, in a similar manner to the previous example, given the correct contact point. However, there is still a need to find the correct contact point among the set of candidate contact points.

It can be assumed that the y-location of the forming tool 6 is fixed (y0=0) because the forming tool 6 does not move outside of the plane 28 and so the centre of the working roller lies on the xz-plane 28. Therefore, the method needs to establish xo and zo. This is done numerically in this example using the set of translated candidate contacts points to find the point closest to the requirements, i.e. the candidate contact point that allows contact between the target shape 84(h-k) and the forming tool 6, without any intersection with the target shape 84(h-k) at other locations.

This problem may be solved by trial and error, in step 112, for example using the function, described above, to relate the co-ordinates of the centre of the working roller to each candidate contact point.

In which case, the corresponding co-ordinates of the centre of the working roller [xo; yo; zo] for each candidate contact point are determined according to the equation: xo = xcc o1-rrt)2; Ycc2; 7-7(cx,) c, zo = zcc + (x, -x0); and c, Yu = 0 Where [cx; cy; cz] = [sin(0); 0; cos(0)]; 0 is the orientation of the working roller; rrol is the radius of the working roller; and rh is the nose radius of the working roller.

Once the co-ordinates of the centre of the working roller have been found for each candidate contact point, the correct contact point is found by the candidate contact point with the maximum distance to the position of the centre of the sphere. This ensures that the forming tool 6 will only contact the respective candidate contact point and no other points on the target shape 84(h-k).

It follows that the command position is provided by the co-ordinates of the centre of the working roller corresponding to that contact point.

Once the command positions for each pass have been determined, in step 112, the method includes connecting the command positions into a toolpath, in step 114.

The process described above finds one command position for the forming tool 6, but 20 further command positions may be found for each of the PF cL command positions through which the forming tool 6 is moved during each pass. All those command positions may then be placed in a table to instruct the machine.

The command positions for each pass may be joined into a continuous pass between the respective start and end points (i.e. until the prescribed pass length L is reached), which roughly corresponds to a helical shape. For example, the command positions may be joined using a spline fitting function to create a helical pass 88 on the target shape 84(h-k), as illustrated in Figure 16. A Catmull-Rom spline may be selected for the trajectory generation because, as opposed to a Cubic B Spline, it ensures that the trajectory passes through all points commanded.

The helical pass 88 in (x; y z) coordinates may then be converted to cylindrical coordinates having a radial position, r, on the radial axis of the mandrel-free spinning apparatus 20; a longitudinal position, 'z', on the longitudinal axis 30 of the mandrel-free spinning apparatus 20; and an angular coordinate, 13', related to the orientation of the workpiece 2 during the spin forming process; such that each command position, T, is represented by the co-ordinates 'fry, , with a corresponding orientation of the Successive passes may then be joined together, for example by a circular arc, to merge a whole toolpath together. An example toolpath 90 having seventeen passes 91(a-q) shown in Figure 17. Each pass 91(a-q) is oscillatory along the radial axis in order to define the non-axisymmetric shape of the square-cup shaped article 50 but, to avoid obscuring other details, such radial oscillations are not illustrated in Figure 17.

Since a mandrel-free spinning apparatus 20 is used in this example, the method 100 may control the first support tool 22 so as to support the inner surface 10 of the workpiece 2, during the spin forming process, and define the base portion 52 of the article 50.

Hence, if the article 50 is axisymmetric the first support tool 22 may be moved to and held at a static support position during the spin forming process. However, if the article 50 is non-axisymmetric, the method 100 includes determining a second toolpath that moves the first support tool 22 around the base portion 52 of the article 50, in step 116.

The determination of the first support tool 22 toolpath is not described in detail to avoid obscuring the invention, but it shall be appreciated that the first support tool 22 toolpath may be determined in substantially the same manner as the forming tool 6 toolpath, as described in steps 110 to 114, mutatis mutandis as necessary for suitability to the use of the first support tool 22.

In which case, it shall be appreciated that determining the second toolpath, in step 116, includes several obvious modifications to the method of determining the first toolpath in steps 110 to 114.

For example, as the first support tool 22 is held at a fixed position along the longitudinal axis 30 of the mandrel-free spinning apparatus 20, i.e. F = 0 mm/rev and L = 0mm, the first support tool 22 may be moved to P different command positions per revolution of the workpiece 2, each position having the same axial location, zo.

This axial location, zo, may be defined so as to engage the first support tool 22 with the inner surface 10 of the workpiece 2, such that the first support tool 22 is moved around the base portion 52 of the article 50 whilst the workpiece 2 rotates in the spin forming process.

Advantageously, the same method can be repeated for a variety of article shapes without necessarily making any changes to the user inputs because the first and second toolpaths are based on the article shape. Instead, the control system 71 or computing device 76 will determine new toolpaths based on the updates to the article shape.

In step 118, the method includes converting the first and second toolpaths into a form that the controller 74 can understand, for example, as computer readable code. The code may be suitable for a CNC controller and the control system 71 may output the code to the controller 74.

The mandrel-free spinning apparatus 20 may, for example, be controlled using a

RTM

National Instruments CompactRIO-based real-time system. Furthermore, motion applications may, for example, be programmed using LabVIEV1714nd the SoftMotion module.

Synchronisation of all the machine axes may be achieved by organising them in coordinates and using a contour move type. In this manner, the SoftMotion trajectory generation engine can ensure that all axes reach the commanded position at the same time, thus guaranteeing synchronisation.

The workpiece 2 is then mounted on the lathe 4 of the mandrel-free spinning apparatus 20, in step 120. The workpiece 2 may have been designed based on the shape of the desired article 50 and may have an approximately square initial shape.

The initial shape of the workpiece 2 may be designed by modelling a forming process using Finite element analysis and iteratively refining the initial shape or by using an analytical design method.

If the article and/or workpiece 2 is non-axisymmetric, then the workpiece 2 may be mounted on the lathe 4 such that the orientation of the workpiece 2 corresponds to a particular orientation of the CAD model 80 of the article shape and/or the target shapes 84(h-k).

In step 122, the method 100 initiates the spin forming process and the controller 74 uses the computer readable code to determine corresponding control signals and operate the mandrel-free spinning apparatus 20. The control signals dictate the rotation of the workpiece 2 on the lathe 4 and control the movement of the forming tool 6 and the first support tools 32 according to the respective toolpaths.

In step 124, the first support tool 22 moves according to the second toolpath and the forming tool 6 moves according to the first toolpath. The motion of the first support tool 22 resists deformation of the workpiece 2 at the inner surface 10 of the workpiece 2 to form the base portion 52 of the article shape whilst the forming tool 6 completes each pass of the first toolpath. Each pass of the forming tool 6 deforms the workpiece 2 into the respective target shapes 84(h-k) and, upon completion of the final pass, the workpiece 2 is moulded into a shape that substantially matches the article shape.

The article 50 can then be removed from the mandrel-free spinning apparatus 20.

If the results are unsatisfactory, the operator may choose to repeat the process and apply different user inputs or toolpath parameters to refine the toolpath. For example, a first toolpath that features additional passes and/or different target shape transformation functions may be less prone to wrinkling or thinning of the workpiece 2 during the spin forming operation.

It is noted that the steps of method 100 are merely provided as an example of the invention and the steps are not intended to limit the method of controlling the spin forming machine. Accordingly, it is understood that steps may be altered, reordered, added and removed as will be appreciated by the person skilled in the art.

Figure 18 illustrates a 2D profile of an example of the first toolpath generated in step 114, showing 5 passes in rotational sequence, followed by (k -5) passes advancing 5 mm on the mandrel each in a translational sequence.

The design of the toolpath was developed by trial and error after a few exploratory trials on different article designs. It is optimised for the article wall profile used in this example, but is easily adapted to other wall profile geometries (vertical, conical and hemispherical walls). F= 1 mm/rev in the direction of roller motion.

All passes have concave or nearly linear geometry and only forward passes are used. A rotational toolpath sequence is selected for the first 5 passes, until the workpiece 2 flange forms an angle of 45° with the r-axis. Then, the sequence is translational in the following passes: Lo is increased by 5 mm in each pass, and the workpiece 2 flange is kept at the same angle of 35-40° with the r-axis (depending on the length of the pass). The length L of the first pass is set equal to Lo; each subsequent pass increases in length by 1-5 mm to account for thinning in the workpiece 2 and consequent lengthening of the flange.

The following toolpath parameters were used in this example.

For the full toolpath: k 15 or more P 36 for asymmetric shapes; 1 for the axisymmetric shape F 1 mm/rev For each toolpass: Pass number, i 1 2 3 4 5 6 7 8 9 10 onward s n 1.8 1.8 1.6 1.5 1.3 1.7 1.7 1.7 1.7 1.8 m 1.1 0.27 0.24 0.21 0.32 0.075 0.071 0.067 0.064 0.043 Lp (mm) 7 8.6 10.1 11.8 13.5 18.5 23.5 28.5 33.5 Lp(i-1) +5 Figure 19 illustrates the complete toolpaths output by the toolpath generation algorithm for a circular cup-shaped article (Cr), an elliptical cup-shaped article (El) and a square cup-shaped article (Sq) repectively.

The profile of the toolpath (shown in Figure 19) is the same for all three articles. The flexibility of the toolpath generation algorithm is demonstrated by Figure 19. The user only needs to specify the toolpath parameters and the target component geometry; the toolpath generation algorithm will output the correct trajectory for the forming tool 6 to follow. This will account for roller-workpiece 2 contact occurring outside of the plane 28 of the rollers, and will work for axisymmetric and asymmetric shapes alike.

Embodiments of the invention also relate to a method of controlling a mandrel-free spinning apparatus 20 to deform a rotating workpiece 2 towards a target shape 84(h-k) by determining toolpaths for the forming tool 6 and the first support tool 22 that are complementary to one another.

In particular, the respective toolpaths are complementary to one another such that they engage the forming tool 6 and the first support tool 22 with opposing surfaces of the workpiece 2 in order to deform the workpiece 2 towards the target shape 84(h-k) as the workpiece 2 rotates. Advantageously, this method reduces springback during the spin forming process and upon formation of the article.

Figure 20 illustrates a method 200 in accordance with an embodiment of the invention of forming an article, such as the square cup-shaped article 50 shown in Figure 8, in a spin forming process.

As shown, the method 200 may proceed through steps 102 to 114, substantially as described above in relation to method 100.

However, once the first toolpath for the forming tool 6 has been determined, in step 114, the method 200 is configured to determine a second toolpath for the first support tool 22 that is complementary to the first toolpath of the forming tool 6, in step 216.

In other words, in step 216, the method 200 is configured to determine a second toolpath that moves the first support tool 22 so as to engage the inner surface 10 of the workpiece 2 and effectively follow the forming tool 6 as the workpiece 2 rotates, thereby bending the workpiece 2 between the forming tool 6 and the first support tool 22 into the article shape. This is in contrast to the method 100, in which the first support tool 22 is positioned near the mounting point 4 of the workpiece 2 and only moved radially, as described in step 116.

In an example of step 216, the method 200 is configured to determine the second toolpath for the first support tool 22 based on the first toolpath.

In which case, the second toolpath may substantially match the first toolpath and include a corresponding command position, to which the first support tool 22 is moved, for each command position of the first toolpath.

Hence, in step 216, the method 200 may determine the second toolpath by adding an offset to each command position of the first toolpath. The offset may, for example, have an axial component and a radial component to ensure that the first support tool 22 engages the inner surface 10 of the workpiece 2 and follows the forming tool 6. Accordingly, the size of the offset may relate to the thickness of the workpiece 2 and may account for the relative sizes of the first support tool 22 and the forming tool 6.

In this manner, for each pass, moving the first support tool 22 through the command positions of the second toolpath may effectively trace the inner surface of the respective target shape 84(h-k) and the first support tool 22 may support an inner or more central portion of the workpiece 2 as the forming tool 6 deforms an outer portion of the workpiece 2 into the target shape 84(h-k).

The command positions for each pass of the second toolpath may then be joined into a continuous helical pass using a spline function, as in step 114, and successive passes may be joined together, for example by a circular arc, to merge the whole toolpath together.

In another example of step 216, the method 200 is configured to determine the second toolpath based on the series of target shapes 84(h-k) determined in step 108.

This may be achieved using substantially the same methodology and calculations described above for the forming tool 6 toolpath, with the equations modified to refer to the first support tool 22 as opposed to the forming tool 6.

In which case, the second toolpath includes a plurality of command positions that are each determined based on a desired point of contact between the first support tool 22 and the respective target shape 84(h-k).

Hence, determining the second toolpath in step 216 may include repeating steps 110 to 114, mutatis mutandis as necessary for application to the first support tool 22 instead of the forming tool 6.

In particular, in step 216, information relating to the shape of the first support tool 22 is received, instead of the information relating to the shape of the forming tool 6. Said information includes a radius of the blending roller, a nose radius of the blending roller and an orientation of the blending roller.

Furthermore, for each command position of the second toolpath, a point, [xe2; V 7 Z 1 c2, -c2,7 translated from the desired point of contact on the respective target shape 84(h-k) may be determined in the same manner as described in step 114 of method 100, but according to the equation: [xe2; yc2; Zci = [Xtp2; ytp2; Ztp2i -7121rixtp2; rlytp2; Tiztp2i; where: the desired point of contact has the co-ordinates: [xtp2; ytp2; ztp2]; [nxtp2; nytp2; nztp2] is the unit normal vector at the desired point of contact and rn2 is the nose radius of the blending roller.

Notably, in this example, the normal vector is subtracted from the co-ordinates of the desired point of contact so as to position the first support tool 22 in engagement with the inner surface of the respective target shape 84(h-k).

The co-ordinates of the centre of the blending roller at the command position [x02; Y02; z02] may then be determined according to the equation: X02 = xa (r,iz -rn2)2-ycz 2.

ZO2 = Zc2 CX2 t.XC2 x02); and C72 Yoz = 0 Where [Q2; cy2; Q2] = [sin 02; 0; cos 02]; 02 is the orientation of the blending roller; r rol2 is the radius of the blending roller; andrn2 is the nose radius of the working roller.

Other modifications, such as this, will be apparent to the skilled person and are not described in more detail to avoid obscuring the invention.

As in the previous example, the command positions for each pass of the second toolpath may then be joined into a continuous helical pass using a spline function in the same manner as described in step 114. Successive passes may also be joined together, for example by a circular arc, to merge the whole toolpath together.

Thereafter, the method 200 may proceed through steps 118 to 124, substantially as described above in relation to method 100.

It shall be appreciated that, as a consequence of step 216, the first support tool 22 moves so as to effectively follow the forming tool 6 in step 124 of method 200, as opposed to moving around the base portion 52. For example, the second toolpath may move the forming tool 6 and the first support tool 22 substantially synchronously and in phase with one another, with the first support tool 22 being offset from the first support tool 22 so as to engage opposing surfaces of the workpiece.

Embodiments of the invention also relate to a method of controlling a spin forming machine to deform a workpiece 2 into a target shape using: i) a CAD model 80 of the target shape; and ii) information relating to the shape of the forming tool 6; to determine a toolpath that moves the forming tool 6 so as to effectively trace the target shape and urge the workpiece 2 towards that target shape, as the workpiece 2 rotates.

The method may be used to generate a toolpath corresponding to a given target shape, solely for the purposes of forming that target shape. Alternatively, the method may be incorporated into the method 100, described above, in which the workpiece 2 is formed into the shape of a desired article through a series of passes, each pass deforming the workpiece 2 into a respective target shape 84(h-k).

Conventional methods of controlling a spin forming machine do not make use of CAD models, in part, because it was not known how to control the motion of the forming tool 6 based on a three-dimensional CAD model of a target shape.

Figure 21 illustrates such a method 300, in accordance with an embodiment of the invention, of controlling a spin forming machine to deform a workpiece 2 into a target shape based on a CAD model of the target shape.

In step 302, the method 300 includes receiving a CAD model of the target shape. The CAD model provides a three-dimensional representation of the target shape and may, for example, be designed using a suitable CAD software. The CAD model may be received from any suitable means, including: the memory storage device; the human-machine interface device; a CAD system; a connected three-dimensional scanning device; and/or a connected cloud storage system.

Alternatively, in step 302, the CAD model of the target shape may be determined, as described in step 108 of method 100, based on a CAD model of an article shape and one or more toolpath parameters.

In step 304, the method 300 includes generating a toolpath for the forming tool 6. The toolpath includes a single pass comprising a plurality of command positions through which a reference point of the forming tool 6, such as a centre of the working roller, is moved to effectively trace the target shape. Accordingly, the toolpath for the forming tool 6 may be determined substantially as described for each target shape in steps 110 to 114 of method 100 described above.

Since a mandrel-free spinning apparatus 20 may be used in this example, the method 300 may control the first support tool 22 so as to support the inner surface of the workpiece, during the spin forming process, and define the base portion 52 of the article or follow the forming tool 6.

Accordingly, in step 306, the method 300 includes generating a second toolpath for the first support tool 22.

The second toolpath may be determined as described in step 116 of method 100, such that the first support tool 22 is only moved radially during the forming process so as to support the central region of the target shape where the workpiece 2 is secured to the lathe 4.

Alternatively, the second toolpath may be determined as described in step 216 of method 200, such that the first support tool 22 effectively follows the forming tool 6 during the spin forming process.

Thereafter, the method 300 may proceed through steps 118 to 124, substantially as described previously in relation to method 100.

Embodiments of the invention also relate to a method of controlling a spin forming machine to simultaneously deform multiple workpieces towards a desired shape of an article.

Figure 22 illustrates a method 400 in accordance with an embodiment of the invention of forming multiples articles, such as the square cup-shaped article 50 shown in Figure 8, in a spin forming process.

In step 402, the method 400 includes determining toolpaths for the forming tool 6 and, optionally, the first support tool 22 corresponding to the desired shape of the article.

For example, the toolpaths for the forming tool 6 and the first support tool 22 may be determined substantially as described in step 102 to 118 of method 100, which are arranged to generate toolpaths for the forming tool 6 and the first support tool 22 based on a CAD model 80 of the desired shape of the article.

The skilled person shall appreciate that minor modifications to the steps 102 to 116, described previously, would be required to account for the thickness of multiple workpieces.

For example, the target shape for each pass of the forming tool 6 may be determined substantially as described previously, in step 108, in which the target shape points are defined by the m x 3 coordinate matrix, C: Ci = [xc 1; Yci;zj where xi; y; z are m-tuples for each pass, i, representing components of standard Cartesian coordinates. Furthermore, for each moulding pass, i, the target shape may be determined according to the equation: i; Yci] = [x; y] + f(z). [nx; ny] where f (z) is the transformation function: 0, z < L Pi f (z) = f(aieL + to), z Lp However, in this example, to, may relate to a total thickness of the first and second workpieces, instead of the thickness of the article shape, as described in the previous 30 example.

In step 404, the method includes mounting a first workpiece to the workpiece mounting point 4. The first workpiece may be substantially as described in the previous embodiments and the first workpiece may be mounted mandrel-free spinning apparatus 20 substantially as described in step 120.

In step 406, the method includes mounting a second workpiece to the workpiece mounting point 4 such that relative movement between the first and second workpieces is substantially inhibited at the workpiece mounting point 4. The second workpiece may, for example, be mounted on the lathe 4 coaxially with the first workpiece and the skilled person will appreciate that there are various method by which the second workpiece may be mounted such that relative movement between the first and second workpieces is substantially inhibited. For example, the second workpiece may be positioned in abutment with the first workpiece and the first and second workpieces may be secured to the lathe 4, for example by bolts that substantially inhibit relative rotation and/or axial movement of the second workpiece relative to the first workpiece.

Thereafter, the method 400 may proceed through steps 122 to 124, substantially as described above in relation to method 100, such that the first and second workpieces are rotated on the workpiece mounting point 4 as the first support tool 22 and the forming tool 6 are moved according to the respective toolpaths.

It shall be appreciated that, in this example, the first support tool 22 will move according to the respective second toolpath and engage the second workpiece to resist deformation. Meanwhile, the forming tool 6 will simultaneously move according to the first toolpath to bear against the first workpiece and bend the first and second workpieces about the point of support.

In this manner, the method is arranged to deform both the first and second workpieces towards the target shape as the workpieces rotate.

In some examples, the increased forces need to bend the pair of workpieces causes the first workpiece to fail in the manner described above. Accordingly, in some examples, the first workpiece is used as a sacrificial layer to improve the finish quality of the second workpiece and the first workpiece may, for example, be made from cheaper, less robust materials, such as a lower grade alloy than the second workpiece or a softer material than the second workpiece. For example, if the second workpiece is steel, the first workpiece may be Aluminium.

Figure 23 shows plots of the axial force on the forming tool 6 for each pass of an example toolpath used to form a discoidal article from a 1mm workpiece, a 2mm workpiece and two 1 mm workpieces spun at the same time, respectively. This was done using a known toolpath that was successful for an equivalent 2mm blank in AA1050. As illustrated, the forces on the workpiece increase substantially when comparing the trial with the 1mm workpiece to the two 1mm workpieces, which results in increased thinning and eventually cracking of one of the workpieces.

The articles resulting from the two 1mm workpieces being spun together are shown in Figure 24. The second (outer) article is shown on the left and the first (inner) article is shown on the right.

Many modifications may be made to the above examples without departing from the scope of the present invention as defined in the accompanying claims.

Claims

Claims 1. A method (200) of controlling a mandrel-free spinning apparatus (20), comprising: a rotatable mounting point (4) for a workpiece (2); and first and second tools (6, 22) that are movable relative to the workpiece (2) and controllable to deform the workpiece (2) as the workpiece (2) rotates; the method (200) being arranged to deform the workpiece (2) in one or more passes towards a target shape (84(h-k)); the method (200) including: receiving a CAD model of the target shape (84(h-k)); determining a first toolpath for the first tool (6), wherein the first toolpath comprises a route of the first tool (6) between a start point and an end point for each pass based on the CAD model of the target shape (84(h-k)); determining a second toolpath for the second tool (22), wherein the second toolpath is complementary to the first toolpath so that, collectively, the first and second toolpaths move the first and second tools (6, 22) during each pass so as to engage opposing surfaces of the workpiece (2) and deform the workpiece (2) towards the target shape (84(h-k)); and controlling the first and second tools (6, 22) according to the respective first and second toolpaths, whilst rotating the workpiece (2) on the rotatable mounting point (4), to deform the workpiece (2) towards the target shape (84(h-k)).
2. A method (200) according to claim 1, wherein the second toolpath is complementary to the first toolpath so as to move the first and second tools (6, 22) substantially synchronously and in phase with one another.
3. A method (200) according to claim 1 or claim 2, wherein the second toolpath corresponds to the first toolpath with positional offsets from the first toolpath to engage the first and second tools (6, 22) with opposing surfaces of the workpiece (2).
4. A method (200) according to any preceding claim, wherein determining the second toolpath comprises determining a route of the second tool (22) between a start point and an end point for each pass based on the CAD model of the target shape (84(h-k)).
5. A method (200) according to any preceding claim, wherein the second toolpath is complementary to the first toolpath so as to move the first and second tools (6, 22) at substantially the same rate along the axis of rotation (30) of the rotatable mounting point (4).
6. A method (200) according to any preceding claim, wherein the CAD model of the target shape (84(h-k)) comprises a plurality of target shape points (86) on a co-ordinate system; and wherein, for each pass of said first toolpath, determining the route of the first tool (6) comprises determining a first set of control positions for the first tool (6), wherein each control position is based on a respective target point (86), such that the first tool (6) is moved between successive ones of the first set of control positions as the workpiece (2) rotates.
7. A method (200) according to claim 6, wherein each control position in the first set of control positions is offset from said respective target point (86) to position the first tool (6) in engagement with the workpiece (2).
8. A method (200) according to claim 6 or claim 7, when dependent on claim 4, wherein, for each pass of the second toolpath, determining the route of the second tool (22) comprises determining a second set of control positions for the second tool (22), such that the second tool (22) is moved between successive ones of the second set of control positions as the workpiece (2) rotates.
9. A method (200) according to claim 8, wherein each control position in the second set of control positions is based on a respective target point (86) and is offset from said respective target point (86) so as to position the first and second tools (6, 22) in engagement with opposing surfaces of the workpiece (2).
10. A method (200) according to claim 8, wherein each control position in the second set of control positions is based on a respective control position in the first set of control positions and is offset from said respective control position in the first set of control positions so as to position the first and second tools (6, 22) in engagement with opposing surfaces of the workpiece (2).
11. A method (200) according to any preceding claim, wherein one of the first and second tools (6, 22) is a forming tool (6) that is controllable to deform the workpiece (2) as the workpiece (2) rotates and the other of the first and second tools (6, 22) is a support tool (22) controllable to support the workpiece (2) as the workpiece (2) rotates.
12. A method (200) according to any preceding claim, wherein the target shape (84(h-k)) is non-axisymmetric.
13. A method (200) according to any preceding claim, wherein the CAD model of the target shape (84(h-k)) includes a three-dimensional model of the target shape (84(h-k)).