CN105458372B - A kind of side milling error tool path scheduling method based on non-extended straight-line surface - Google Patents

Abstract

The invention relates to the field of mechanical processing, in particular to a side milling error compensation device based on a non-developable ruled surface and a tool position planning method thereof, including a chucking plate, a workpiece, and a milling cutter arranged above the workpiece for side milling , the workpiece is arranged on the clamping disc, and it is characterized in that: it also includes a three-dimensional scanner, a microcomputer, a column and a tool position compensation mechanism, and the tool position compensation mechanism is arranged below the clamping disc, and the present invention adopts four-point offset Plan the five-axis side milling tool path for the non-developable ruled surface in a new way, and judge whether there is interference in real time online, and adjust online according to the judgment result, which reduces the processing error and avoids the collision, to achieve the purpose of fast and efficient processing; the invention further optimizes the generated tool position, and is completed by the cooperation of the error compensation device, which further reduces the error.

Description

A Tool Position Planning Method for Side Milling Errors Based on Non-Developable Ruled Surfaces

technical field

The invention relates to the field of mechanical processing, in particular to a method for planning a side milling error tool position based on a non-developable ruled surface.

Background technique

A non-developable ruled surface is formed by sweeping a straight generatrix along a wire, and is non-developable. Discrete the surface can obtain multiple straight lines with different directions on the surface. Due to the different directions of the normal vectors of the points on the straight generatrix, as long as a tool with a non-zero radius is used for side milling, overcut and undercut errors will inevitably occur, and during the machining process, due to the vibration, vibration, and There is a gap in the drive chain and the wear of the actuator will cause the tool movement to deviate from the ideal trajectory, resulting in machining errors. For non-developable ruled surfaces, these errors are fatal. Part scrapped.

Contents of the invention

The technical problem to be solved by the present invention is to provide a side milling error tool position planning method based on non-developable ruled surface, which can monitor online, adjust in real time, reduce errors, improve processing efficiency and effectively improve processing quality.

In order to solve the above technical problems, the present invention adopts the following technical solutions:

Technical solution one:

A side milling error compensation device based on a non-developable ruled surface, comprising a chuck, a workpiece, and a milling cutter arranged above the workpiece for side milling, the workpiece is arranged on the chuck, and a three-dimensional scanning Instrument, microcomputer, column and tool position compensation mechanism, the tool position compensation mechanism is arranged under the chucking plate; the tool position compensation mechanism includes: the first translation stage, the second translation stage, the first nut pair, the first wire rod, the second nut pair, the second lead screw, the first servo motor and the second servo motor; Cooperate, the first lead screw is connected with the output end of the first servo motor, the second nut pair is arranged under the second translation platform, the second lead screw cooperates with the second nut pair through balls, the first The second lead screw is connected to the output end of the second servo motor; the three-dimensional scanner is arranged on the column, the column is arranged on the first translation platform, the three-dimensional scanner is connected to the microcomputer, and the first servo motor is connected to the second servo motor. The second servo motor is connected with the microcomputer through the logic control board, and the microcomputer is connected with the main shaft of the milling cutter through the servo driver. The number of the first lead screw and the first nut pair is 2, and they are arranged in parallel under the first translation table; the number of the second lead screw and the second nut pair is 2, and they are arranged in parallel on the Below the second translation stage. The axes of the first lead screw and the second lead screw are perpendicular to each other.

Technical solution two:

The steps of the tool position planning method of the present invention are as follows (using the side milling error compensation device based on non-developable ruled surface):

① Measure the data of the real-time 3D model diagram of the processed part through the 3D scanner;

②Compare the measured model data with the design surface, and use the four-point offset method to generate the initial tool position:

201 defines the design surface and equidistant surface, the design surface equation is S(u,v)=(1-v)B ₀ (u)+vB ₁ (u), u,v∈[0,1], where u, v are the curve coordinates of the surface, and its equidistant surface is defined as Sˊ(u,v)=S(u,v)+R n(u,v), where R is the radius of the column cutter, B ₀ (u ) and B ₁ (u) are the vector diameters of the two curves, n(u, v) is the unit normal vector of the surface, and the machining error of the surface is represented by the extreme difference between the equidistant surface and the tool axis trajectory surface;

202 Select the two ends of the busbar on the design surface, extract the corresponding points P ₀ and P ₃ on the equidistant surface, and the offset distance is the tool radius; The positions of points P ₁ and P ₂ , where v∈[0,1], its value indicates the position of the point on the tool axis, and E ₁ and E ₂ represent the extreme difference between the two points and the equidistant surface of the design surface;

204 Fix point P ₀ , let point P ₃ slide on B ₁ ”(u), and a family of P ₀ P ₃ can be obtained, and the sliding range of point P ₃ in each tool position is set as [u ₀ -0.5h, u ₀ +0.5 h], where u ₀ is the initial coordinate value of u in 201, h is the ratio of the cutting step length to the directrix length, set the standard value ε, and calculate E=E ₁ ² +E ₂ ² in each step respectively, when When E<ε is satisfied, P ₀ P ₃ is determined as the initial tool position;

205 Select two points on a straight generatrix under the design surface and repeat the above steps to calculate all initial tool positions;

③Using the least squares method to generate optimized tool positions:

301 fits the initial tool position into a curved surface, and the initial tool axis trajectory surface is expressed as:

Where v is the direction parameter of the straight generatrix, N _i,k (u) is the B-spline basis function, b _i and d _i are the control vertices of the two directrixes;

302 Take M data points P _s (s=0,1,...,M-1) on the equidistant surface of the design surface, and compare their corresponding points (u _s ,v _s ) on the tool axis trajectory plane , into the expression in step 301,

303 regard b _i and d _i as unknown quantities, and use the least square method to calculate the formula in step 302 to obtain optimized tool location information;

④ Check the generated optimized tool position. If there is interference, calculate the deflection angle θ, and adjust the cutter axis of the milling cutter through the microcomputer control servo driver; if there is no interference, use the optimized tool position for processing.

When adjusting the cutter shaft of the milling cutter in the step ④, the microcomputer controls the first servo motor and the second servo motor to drive the first translation platform and the second translation platform through the logic control board to complete auxiliary positioning.

In the step ④, the maximum tangent point of the tool position is determined by the secondary search method; and then the deflection angle θ is deflected along the normal direction of the maximum tangent point of the tool position.

The maximum deflection angle θ in the normal direction of the tangent point is used and Determine, that is, through the tangent ratio of x, y Determine θ.

The positive effects of the present invention are as follows: the present invention collects the three-dimensional model data of the processed non-extensible ruled surface through a three-dimensional scanner, which ensures online real-time monitoring in the process and greatly reduces processing errors; the present invention adopts The four-point offset method plans the five-axis side milling tool path for non-extensible ruled surfaces, and judges whether there is interference in real time online, and adjusts online according to the judgment results to reduce machining errors while avoiding The collision in the processing process is eliminated, and the purpose of fast and efficient processing is realized; the present invention further optimizes the generated tool position, and the error compensation device cooperates to further reduce the error; the present invention controls the cutter shaft and the first translation stage through a microcomputer Cooperating with the second translation stage to complete tool position generation and tool axis adjustment, it is closer to the surface contour of the non-developable ruled surface, making the machining process more stable and effectively ensuring the machining accuracy.

Description of drawings

Fig. 1 is a structural representation of the present invention;

Fig. 2 is a schematic diagram of the relationship between curved surfaces of the present invention;

Fig. 3 is the flowchart of the inventive method;

Fig. 4 is a schematic diagram of a four-point offset method model of the present invention;

Fig. 5 is a schematic diagram of the tool axis vector deflection model of the present invention;

Fig. 6 is a schematic diagram of the deflection angle of the cutter shaft of the present invention;

Fig. 7 is a schematic diagram of the tool overcut error of the present invention;

Fig. 8 is a flow chart of the non-developable ruled surface five-axis side milling method of the present invention;

Fig. 9 is a schematic diagram of generating an isometric surface from a designed curved surface in the present invention;

Fig. 10 is a schematic diagram of the distribution of initial tool position machining errors in the present invention;

Fig. 11 is a schematic diagram of the distribution of tool position machining errors after optimization in the present invention.

In the figure: 1 workpiece, 2 milling cutter, 3 three-dimensional scanner, 4 chucking plate, 5 first translation stage, 6 second translation stage, 7 nut pair, 8 lead screw, 9 second servo motor, 10 first Servo motor, 11 microcomputer, S1 is the design surface, S2 is the tool envelope surface, S3 is the equidistant surface of the design surface, S4 is the tool axis track surface, R is the tool radius, O is the tool center point, O' is the rotation The heart of the knife.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific examples.

Example 1

As shown in Figure 1, a side milling error compensation device based on a non-developable ruled surface includes a clamping plate 4, a workpiece 1 and a milling cutter 2 arranged above the workpiece 1 for side milling, the workpiece 1 It is arranged on the chucking disk 4, and also includes a three-dimensional scanner 3, a microcomputer 11, a column 12 and a tool position compensation mechanism, and the knife position compensation mechanism is arranged under the chucking disk 4;

The tool position compensation mechanism includes: a first translation platform 5, a second translation platform 6, a first nut pair 7-1, a first lead screw 8-1, a second nut pair 7-2, a second lead screw 8- 2. The first servo motor 10 and the second servo motor 9; the first nut pair 7-1 is arranged under the first translation table 5, and the first lead screw 8-1 connects with the first nut pair 7-1 through balls. 1, the first lead screw 8-1 is connected to the output end of the first servo motor 10, the second nut pair 7-2 is arranged under the second translation table 6, and the second lead screw 8-2 The ball is matched with the second nut pair 7-2, and the second lead screw 8-2 is connected to the output end of the second servo motor 9;

The three-dimensional scanner 3 is arranged on the column 12, the column 12 is arranged on the first translation platform 5, the three-dimensional scanner 3 is connected to the microcomputer 11, and the first servo motor 10 and the second servo motor 9 pass through The logic control board is connected with the microcomputer 11, and the microcomputer 11 is connected with the main shaft of the milling cutter 2 through a servo driver.

The number of the first lead screw 8-1 and the first nut pair 7-1 is 2, and they are arranged in parallel under the first translation platform (5); the second lead screw (8-2) and the second The number of the two nut pairs 7-2 is 2, and they are arranged below the second translation platform 6 in parallel. The axes of the first lead screw 8-1 and the second lead screw 8-2 are perpendicular to each other. Microcomputer 11 among the present invention is PC or notebook computer.

Example 2:

Because the non-developable ruled surface is characterized by the different normal vector directions of points on the straight generatrix, any tool with a non-zero radius will have a theoretical error in side milling, and the tool envelope cannot be completely tangent to the design surface. For the side milling of this kind of curved surface, surface approximation is used. As shown in Figure 2, the tool position planning for side milling non-developable ruled surface mainly includes: design surface S1, tool envelope surface S2, and equidistant surface of design surface S3, the tool axis trajectory surface S4, the milling cutter envelope surface and the tool axis trajectory surface are a pair of equidistant surfaces. According to the range invariance under equidistant mapping in differential geometry, the range and The range between the tool axis trajectory surface and the isometric surface of the design surface is equal, so the optimization problem of the tool position can be transformed into how to minimize the error between the tool axis trajectory surface and the isometric surface of the design surface. The tool axis trajectory surface contains all the information of the tool space movement, so the tool position planning is essentially to construct a tool axis trajectory surface, so that the tool envelope surface is as close as possible to the design surface, thereby reducing the machining error. The four-point offset method is based on the two-point offset method to slide the tool axis, and the error between the four points on the tool axis and the equidistant surface of the design surface is used as a limiting condition to determine the tool position. The two ends of the tool axis are directly offset from the normal direction of the points on the design surface, so the machining error is zero, and the positions of the other two points are represented by the introduced λ, and the extreme difference between the two points and the equidistant surface meets the agreement condition, the initial tool position is determined. The essence of the four-point offset method is to find four points on the four curves of the design surface, and let them offset a tool radius R along the normal vector of the surface to obtain the corresponding four points, so that they can accurately approach a straight line. The direction of this straight line is Tool axis direction.

As shown in Figure 3, using the device described in Embodiment 1 to carry out the tool position planning method is characterized in that the steps are as follows:

① Measure the data of the three-dimensional model diagram of the real-time processed part through the three-dimensional scanner 3;

② Compare the measured model data with the design surface, as shown in Figure 4, use the four-point offset method to generate the initial tool position:

201 defines the design surface and equidistant surface, the design surface equation is S(u,v)=(1-v)B ₀ (u)+vB ₁ (u), u,v∈[0,1], where u, v are the curve coordinates of the surface, and its equidistant surface is defined as Sˊ(u,v)=S(u,v)+R n(u,v), where R is the radius of the column cutter, B ₀ (u ) and B ₁ (u) are the vector diameters of the two curves, n(u, v) is the unit normal vector of the surface, and the machining error of the surface is represented by the extreme difference between the equidistant surface and the tool axis trajectory surface;

202 Select the two ends of the generatrix on the design surface, extract the corresponding points P ₀ and P ₃ on the equidistant surface, and the offset distance is the tool radius;

203 introduces λ, selects the positions of the middle two points P ₁ and P ₂ with v=λ and v=1-λ respectively, where v∈[0,1], its value indicates the position of the point on the tool axis, and respectively uses E ₁ and E ₂ represent the extreme difference between two points and the equidistant surface of the design surface;

204 Fix point P ₀ , let point P ₃ slide on B ₁ ”(u), and a family of P ₀ P ₃ can be obtained, and the sliding range of point P ₃ in each tool position is set as [u ₀ -0.5h, u ₀ +0.5 h], where u ₀ is the initial coordinate value of u in 201, h is the ratio of the cutting step length to the directrix length, set the standard value ε, and calculate E=E ₁ ² +E ₂ ² in each step respectively, when When E<ε is satisfied, P ₀ P ₃ is determined as the initial tool position, and its calculation flow chart is shown in Figure 8;

205 Select two points on a straight generatrix under the design surface and repeat the above steps to calculate all initial tool positions;

③Using the least squares method to generate optimized tool positions:

301 As shown in Figure 9, the initial tool position is fitted into a curved surface, and the initial tool axis trajectory surface is expressed as:

Where v is the direction parameter of the straight generatrix, is the B-spline basis function, and b _i and d _i are the control vertices of the two directrixes;

302 Take M data points P _s (s=0,1,...,M-1) on the equidistant surface of the design surface, and compare their corresponding points (u _s ,v _s ) on the tool axis trajectory plane , into the expression in step 301, 303 regard b _i and d _i as unknown quantities, and use the least square method to calculate the formula in step 302 to obtain optimized tool location information;

④ Check the generated optimized tool positions, as shown in Figures 5, 6, and 7, if there is interference, calculate the deflection angle θ, and adjust the servo driver through the microcomputer 11 to complete the adjustment of the cutter axis of the milling cutter 2; if there is no interference, Machining with optimized tool positions.

When adjusting the cutter shaft of the milling cutter 2 in the step ④, the microcomputer 11 controls the first servo motor 10 and the second servo motor 9 to drive the first translation platform 5 and the second translation platform 6 through the logic control board to complete auxiliary positioning.

In the step ④, the maximum tangent point of the tool position is determined by the secondary search method; and then the deflection angle θ is deflected along the normal direction of the maximum tangent point of the tool position. The maximum deflection angle θ in the normal direction of the tangent point is used and Determine, that is, through the tangent ratio of x, y Determine θ.

As shown in Figures 10 and 11 (the negative value indicates overcutting, and the positive value indicates undercutting), using the above method and error compensation device, the overcutting error value after the tool position optimization is significantly smaller, and the undercutting error can be obtained by The next cutting is reduced, and the machining accuracy is further improved compared with before optimization.

The implementation manners described above are only preferred embodiments of the present invention, rather than an exhaustive list of feasible implementations of the present invention. For those skilled in the art, any obvious changes made without departing from the principle and spirit of the present invention should be considered to be included in the protection scope of the claims of the present invention.

Claims (6)

1. a side milling error tool position planning method based on non-extensible ruled surface, it is characterized in that the steps are as follows: ① Measure the data of the three-dimensional model diagram of the real-time processed parts; The data of the three-dimensional model map is obtained by means of a compensation device, which includes a chucking disc (4), a workpiece (1) and a milling cutter (2) arranged above the workpiece (1) for side milling, the The workpiece (1) is set on the clamping disc (4); it also includes a three-dimensional scanner (3), a microcomputer (11), a column (12) and a tool position compensation mechanism, and the tool position compensation mechanism is arranged on the clamping disc ( 4) Below; the tool position compensation mechanism includes: the first translation platform (5), the second translation platform (6), the first nut pair (7-1), the first lead screw (8-1), the second A nut pair (7-2), a second lead screw (8-2), a first servo motor (10) and a second servo motor (9); the first nut pair (7-1) is arranged in the first translation Below the platform (5), the first lead screw (8-1) cooperates with the first nut pair (7-1) through balls, and the first lead screw (8-1) is connected with the first servo motor (10 ) output end connection, the second nut pair (7-2) is arranged below the second translation platform (6), and the second lead screw (8-2) is connected to the second nut pair (7-2) through the ball In cooperation, the second lead screw (8-2) is connected to the output end of the second servo motor (9); the three-dimensional scanner (3) is arranged on the column (12), and the column (12) is arranged on On the first translation platform (5), the three-dimensional scanner (3) is connected to the microcomputer (11), and the first servo motor (10) and the second servo motor (9) are connected to the microcomputer (11) through a logic control board. Connect, described microcomputer (11) is connected with the main shaft of milling cutter (2) by servo driver; Measure the data of real-time processing part three-dimensional model figure by three-dimensional scanner (3); ②Compare the measured model data with the design surface, and use the four-point offset method to generate the initial tool position: 201 defines the design surface and equidistant surface, the design surface equation is S(u,v)=(1-v)B ₀ (u)+vB ₁ (u), u,v∈[0,1], where u, v are the curve coordinates of the surface, and its equidistant surface is defined as Sˊ(u,v)=S(u,v)+R n(u,v), where R is the radius of the column cutter, B ₀ (u ) and B ₁ (u) are the vector diameters of the two curves, n(u, v) is the unit normal vector of the surface, and the machining error of the surface is represented by the extreme difference between the equidistant surface and the tool axis trajectory surface; 202 Select the two ends of the busbar on the design surface, extract the corresponding points P ₀ and P ₃ on the equidistant surface, and the offset distance is the tool radius; The positions of points P ₁ and P ₂ , where v∈[0,1], its value indicates the position of the point on the tool axis, and E ₁ and E ₂ represent the extreme difference between the two points and the equidistant surface of the design surface; 204 Fix point P ₀ , let point P ₃ slide on B ₁ ”(u), and a family of P ₀ P ₃ can be obtained, and the sliding range of point P ₃ in each tool position is set as [u ₀ -0.5h, u ₀ +0.5 h], where u ₀ is the initial coordinate value of u in 201, h is the ratio of the cutting step length to the directrix length, set the standard value ε, and calculate E=E ₁ ² +E ₂ ² in each step respectively, when When E<ε is satisfied, P ₀ P ₃ is determined as the initial tool position; 205 Select two points on a straight generatrix under the design surface and repeat the above steps to calculate all initial tool positions; ③Using the least squares method to generate optimized tool positions: 301 fits the initial tool position into a curved surface, and the initial tool axis trajectory surface is expressed as: u∈[0,1],v∈[0,1], where v is the direction parameter of the straight generatrix, N _i,k (u) is the B-spline basis function, b _i and d _i are the two directrix control vertices; 302 Take M data points P _s (s=0,1,...,M-1) on the equidistant surface of the design surface, and compare their corresponding points (u _s ,v _s ) on the tool axis trajectory plane , into the expression in step 301, s=0,1,...,M-1; 303 regard b _i and d _i as unknown quantities, and use the least square method to calculate the formula in step 302 to obtain optimized tool location information; ④ Check the generated optimized tool position, if there is interference, calculate the deflection angle θ, and adjust the cutter axis of the milling cutter (2) through the microcomputer (11) to control the servo drive; if there is no interference, use the optimized tool position for processing . 2. A method for planning a side milling error tool position based on a non-developable ruled surface according to claim 1, characterized in that: the first lead screw (8-1) and the first nut pair (7- 1) The number is 2, and it is arranged in parallel under the first translation platform (5); the number of the second lead screw (8-2) and the second nut pair (7-2) is 2, And it is arranged below the second translation stage (6) in parallel. 3. A method for planning a side milling error tool position based on a non-developable ruled surface according to claim 2, characterized in that: the first lead screw (8-1) and the second lead screw (8-1) 2) The axes are perpendicular to each other. 4. A kind of side milling error tool location planning method based on non-developable ruled surface according to claim 1, characterized in that: when the cutter axis of the milling cutter (2) is adjusted in the step ④, the microcomputer (11) Control the first servo motor (10) and the second servo motor (9) through the logic control board to drive the first translation platform (5) and the second translation platform (6) to complete auxiliary positioning. 5. A kind of side milling error tool position planning method based on non-developable ruled surface according to claim 1, characterized in that: said step ④ determines the maximum overcut point of the tool position by the secondary search method; and then The deflection angle θ along the normal direction of the maximum tangent point of the tool position. 6. A side milling error tool position planning method based on non-developable ruled surface according to claim 5, characterized in that: the maximum deflection angle θ of the normal direction of the tangential point is used and Determine, that is, through the tangent ratio of x, y Determine θ.