CN111203594A - Method for grinding conical-surface gear by using disc-shaped grinding wheel - Google Patents
Method for grinding conical-surface gear by using disc-shaped grinding wheel Download PDFInfo
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- CN111203594A CN111203594A CN202010038557.XA CN202010038557A CN111203594A CN 111203594 A CN111203594 A CN 111203594A CN 202010038557 A CN202010038557 A CN 202010038557A CN 111203594 A CN111203594 A CN 111203594A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/02—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by grinding
- B23F5/08—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by grinding the tool being a grinding disc having the same profile as the tooth or teeth of a rack
Abstract
The invention relates to a method for grinding a conical surface gear by using a disc grinding wheel, and provides a method for processing the conical surface gear, which realizes the precise processing of the conical surface gear, enables a coaxial torque splitting configuration to better play a role, solves the problem that the tooth side clearance of each branch surface gear pair cannot be ensured to be equal in the torque splitting configuration of a helicopter transmission system in advance, and has very important significance for the practical application of novel conical surface gear pair transmission.
Description
Technical Field
The invention belongs to the field of face gear processing methods, and particularly relates to a method for grinding a conical face gear by using a disc grinding wheel.
Background
In a new generation of helicopter transmission system adopting face gears, the configuration adopts a coaxial face gear torque-dividing design, five pinions are arranged between an upper face gear and a lower face gear, two of the pinions are input, and three idlers are arranged. Because the cylindrical gear confluence stage is omitted, the power-weight ratio is further improved by 40%, and the noise is reduced by more than 15 dB. This configuration places greater demands on the face gear pair, and in order to ensure the effectiveness of the face gear coaxial split configuration, the loads transferred between the two input pinion branches and between the three idler branches should be approximately equal. It has been shown that the loads of the different branches are closely related to the backlash of the face gear pairs of the branches.
However, in the novel helicopter transmission system with coaxial split transmission of the face gear, due to the existence of manufacturing and installation errors, the equal tooth side clearance of each branch face gear pair cannot be guaranteed, so that a novel face gear needs to be researched to solve the problems.
The most critical factor for moving the conical surface gear pair from design analysis to practical application is to improve the tooth surface precision of the gear. Grinding is the most common and effective means of ensuring high tooth surface accuracy. The cutters of the conical involute gear are relatively common, the tooth-direction shape of the tooth surface of the conical surface gear matched with the cutters is complex, and the grinding method is not published in relevant researches until now.
Disclosure of Invention
The technical problem solved by the invention is as follows: the invention provides a point-to-point grinding method for a conical surface gear based on a disc grinding wheel, which can determine a grinding path of the disc grinding wheel according to the grinding precision requirement, realizes the gear grinding processing of the conical surface gear, and is simultaneously suitable for grinding the tooth surfaces of a conventional surface gear and a modified surface gear.
The technical scheme of the invention is as follows: a method of grinding a conical faced gear with a grinding disc comprising the steps of:
the method comprises the following steps: the method for obtaining the disc grinding wheel cutter before grinding comprises the following sub-steps:
substep 1: the geometric shape of the tool with the tooth surface of the dish-shaped grinding wheel is defined, the tooth profile shape of the dish-shaped grinding wheel is completely consistent with the geometric shape of the virtual cone involute gear tool at the small end, and the top thickness t of the dish-shaped grinding wheelgIs less than or equal to the top thickness t of the big-end tooth profile of the virtual cutterl
Substep 2: the section shape of the disc-shaped grinding wheel cutter is obtained by trimming a diamond roller;
step two: determining a grinding point of the disc grinding wheel before grinding: and defining a part of instantaneous contact line of the conical involute gear cutter and the conical surface gear as a grinding path on the tooth surface of the conical surface gear. The meshing lines (U lines) of the conical involute gear cutter and the conical surface gear form transverse grid lines in the profile direction of the gear of the grid surface; the grid lines in the tooth direction of the conical surface gear are a group of parallel straight lines (V-shaped lines) which are distributed at equal intervals in the tooth direction, and each intersection point formed by the straight lines is used as a grinding target point;
step three: mounting a conical surface gear on a machine tool, mounting a disc-shaped grinding wheel on a main shaft of the machine tool, and moving the disc-shaped grinding wheel to a tool setting position at a tooth groove of the conical surface gear to finish tool setting;
step four: the grinding machining of the conical surface gear comprises the following substeps:
substep 1: establishing a grinding coordinate system, and defining a grinding method: determining the motion relationship between the disc grinding wheel and the face gear at each ground point on the tooth surface of the face gear, and grinding the tooth surface of the face gear from a grinding path closest to the tooth top of the face gear to a grinding path closest to the common tangent line of the tooth surface of the face gear in sequence along the paths one by one, thus finishing the grinding of the single tooth surface of the face gear. After grinding of one tooth surface is completed, the face gear is indexed to the next tooth groove, and grinding of the next tooth surface is performed. The above process is repeated until all the tooth surfaces of the face gear are ground.
Substep 2: calculation of grinding residual
To obtain the value of the envelope residual λ, the coordinates of the T point in the face gear coordinate system are first calculated. In-plane gear coordinate system S2The T point coordinates can be expressed as:
in the formula:
r2 (g1)-grinding by means of a grinding disc M1At point time, its curved surface equation is in coordinate system S2The following representation;
r2 (g2)-grinding by means of a grinding disc M2At point time, its curved surface equation is in coordinate system S2The following representation;
x2 (g1),y2 (g1)-position vector r2 (g1)X, y components of (a).
Grinding residual calculation formula:
in the formula: r isTFor an in-plane gear coordinate system S2A position vector of a lower T point;
r2and coordinates of projection points of the T point on the tooth surface of the face gear.
Substep 3: determining a grinding path based on the grinding residual calculation and the given tooth surface machining precision
Lambda for maximum envelope residual allowed for face gear tooth surfacekThis value is expressed as being determined by a predetermined face gear tooth face machining accuracy. For a full face gear tooth surface, the maximum envelope residual between any two adjacent grinding paths should be less than or equal to lambdakTo meet the predetermined face gear tooth face precision requirement. This condition is expressed mathematically as:
in the formula:
λ(i-1～i,j)-envelope residual error of a series of points between the i-1 th grinding wheel diameter and the i-th grinding path.
When defining the first grinding path closest to the tooth top on the tooth surface of the face gear, the corresponding virtual gear cutter is extended to form a rotation angle
Greater than psis *The minimum value of (1) to (3). Spreading noodlesAngle psi of virtual gear cutter required for full tooth surface of gears *The range may be determined by the TCA algorithm. Each virtual gear cutter corner
Corresponds to a grinding path on the tooth surface of one face gear.
Substep 4: the above steps complete the determination of the one-side tooth surface, and therefore the above steps are repeated to complete the grinding of the other-side tooth surface.
The further technical scheme of the invention is as follows: origin O of the coordinate systemfIs a fixed point in space. dx,dyAnd dzShowing the linear displacement of the various moving parts of the machine along the x, y and z axes. Coordinate system SmAnd S2Rigidly connected to face gear, wherein SmRigidly fixed to the face gear, translating only with the face gear, S2Translates and rotates with the face gear. The rotation of the grinding disc passes through two auxiliary coordinate systems ScAnd SqAnd (5) realizing. Coordinate system SgIs rigidly connected with the disc-shaped grinding wheel.
Effects of the invention
The invention has the technical effects that: the method for machining the conical surface gear is provided, the conical surface gear is precisely machined, the coaxial torque splitting structure can better play a role, the problem that the tooth side clearance of each branch surface gear pair cannot be equal in the torque splitting structure of the advanced helicopter transmission system is solved, and the method has very important significance for the transmission application of a novel conical surface gear pair in practice.
Drawings
FIG. 1 shows a simulation platform based on a numerical control machine tool
FIG. 2 is a sectional coordinate system for obtaining the tooth profile of the grinding disc
FIG. 3. coordinate system of grinding disc
FIG. 4. dressing coordinate system of grinding disc
FIG. 5 radial rotation projection of conical surface gear tooth surface grinding discrete grid point
FIG. 6. disc grinding wheel grinding conical surface gear coordinate system
FIG. 7. NC program segment of the conical surface gear grinding part
FIG. 8 is a taper face gear tooth surface grinding envelope residual error
FIG. 9 grinding route determining process
FIG. 10. grinding path for grinding simulation
Detailed Description
Referring to fig. 1 to 10, the technical scheme of the invention is as follows:
the method comprises the following steps: obtaining disc-shaped grinding wheel tools before grinding
Substep 1: geometry of tool with grinding disk tooth surface
The section shape of the tooth profile of the dish grinding wheel is completely matched with the small-end tooth profile of the virtual cutter gear. The tooth profile shape of the grinding disc is completely consistent with the geometric shape of the virtual cone involute gear cutter at the small end, but the top thickness t of the grinding disc is tgIs less than or equal to the top thickness t of the big-end tooth profile of the virtual cutterl(see fig. 2). Otherwise, over-cutting is likely to occur at the large end roots of the face gear being ground because the face gear root width is progressively reduced from the small end to the large end.
Substep 2: dressing of disc grinding wheels
The section shape of the disc grinding wheel cutter is obtained by trimming a diamond roller. The disc grinding wheel is arranged on a machine tool, and the diamond roller dresser finishes dressing of the disc grinding wheel. And meanwhile, determining the motion relation between the disc-shaped grinding wheel and the diamond roller, writing a grinding wheel dressing NC program in Matlab according to the motion relation, and realizing grinding wheel dressing on a machine tool.
Step two: determination of the point to be ground before grinding of the grinding disk
The invention takes a part of instantaneous contact line of a conical involute gear cutter and a conical surface gear as a grinding path on the tooth surface of the conical surface gear. FIG. 6 shows a rotational projection of a face of a bevel gear tooth ground at discrete grid points. The meshing lines (U lines) of the conical involute gear cutter and the conical surface gear form transverse grid lines in the outline direction of the grid surface gear; the grid lines in the tooth direction of the conical surface gear are a group of parallel straight lines (V lines in total) which are distributed at equal intervals along the tooth direction. Each intersection they form will be referred to as a grinding target point.
Step three: installing a conical surface gear on a machine tool and finishing cutter tool setting
The conical surface gear is arranged on a machine tool workpiece shaft, the disc grinding wheel is arranged on a machine tool main shaft, and the disc grinding wheel is moved to a tool setting position at the tooth groove of the conical surface gear to complete tool setting.
Step four: grinding machining of conical surface gear
Substep 1: grinding method and grinding coordinate system establishment
In the processing process, the conical surface gear rotates along with the workpiece shaft, and the disc-shaped grinding wheel swings along a certain grinding path. In the process of feeding the conical surface gear in the tooth direction, a coordinate system consisting of 5 coordinate systems is established, and the origin OfIs a fixed point in space. dx,dyAnd dzShowing the linear displacement of the various moving parts of the machine along the x, y and z axes. Coordinate system SmAnd S2Rigidly connected to face-bevel gear, wherein SmRigidly fixed to the conical-faced gear and only translating with the conical-faced gear, S2Translates and rotates with the bevel gear. The rotation of the grinding disc passes through two auxiliary coordinate systems ScAnd SqAnd (5) realizing. Coordinate system SgIs rigidly connected with the disc-shaped grinding wheel. To express the process of the grinding face gear of the disc grinding wheel. The relative motion of the grinding wheel and the conical surface gear is controlled, so that the tooth surface of the dish-shaped grinding wheel is always in point contact with the tooth surface of the conical surface gear, and each tooth direction feed is along a theoretical contact line of the conical surface gear and the cutter gear. During grinding, the grinding path from one grinding path closest to the tooth top of the conical surface gear to the grinding path closest to the common tangent of the tooth surface of the conical surface gear is ground in sequence along the path one by one, and then the grinding of the single tooth surface of the conical surface gear can be completed. After grinding of one tooth surface is completed, the conical surface gear is indexed to the next tooth groove, and grinding of the next tooth surface is performed. Repeating the above process until all the tooth surfaces of the conical surface gear are ground.
Substep 2: calculation of grinding residual
When the method is used for grinding, because the grinding paths on the tooth surface of the conical surface gear are distributed at intervals, a residual narrow belt is formed between two adjacent grinding paths. The deviation of a point on this narrow band from the ideal tooth surface is defined as the envelope residual. The conical surface gear tooth surface envelope residual error must be strictly controlled, because the conical surface gear tooth surface envelope residual error is an important index for determining the surface smoothness of the tooth surface, and the conical surface gear tooth surface envelope residual error based on grinding of the disc grinding wheel is calculated by the method.
Substep 3: determining the grinding residual for the grinding path based on the grinding residual calculation and the given tooth surface machining precisionkIt is shown that the magnitude of this value is determined by the predetermined accuracy of the tooth surface machining of the bevel gear. The maximum envelope residual between any two adjacent grinding paths should be less than or equal to λ for the entire conical-faced gear tooth surfacekTo meet the predetermined face gear tooth face precision requirement. Each virtual gear cutter corner
Corresponds to a grinding path on the tooth surface of one of the conical-faced gears. And (5) finishing solving when the finally solved grinding path covers the full tooth surface of the conical surface gear. And the relative positional relationship of the grinding wheel and the bevel gear required for grinding each ground point on the tooth surface when determining the grinding path has also been determined. And (4) according to the solving result, writing a corresponding gear grinding NC program, and finishing the grinding of the tooth surface of the conical surface gear on an actual numerical control machine tool.
Substep 4: since the calculation is performed only on one side of the tooth surface, indexing is required, and the above-mentioned repeated steps are performed to finish grinding of the other side of the tooth surface, which is embodied in the grinding NC program written in Matlab.
Each step is described in detail below with reference to the accompanying drawings:
the method comprises the following steps: obtaining disc-shaped grinding wheel tools before grinding
Substep 1: geometry of tool with grinding disk tooth surface
An important component in the grinding process of the conical surface gear is a cutterThe section shape of the tooth profile of the disc grinding wheel used in the gear grinding is obtained by the virtual installation position relation between the disc grinding wheel and the virtual cone involute gear cutter. Fig. 2 shows a virtual mounting relationship between the grinding disc and the cone involute gear cutter. With OtCoordinate system S as origintBuilt on the central axis of the grinding disc, xtIn the radial direction of the grinding wheel, ztIn the axial direction of the grinding wheel, ytAnd xt、ztPerpendicular, and the relationship satisfies the right hand rule. In the invention, all the rectangular coordinate systems are established for the convenience of coordinate conversion, and the establishment of the coordinate systems conforms to the right-hand rule.
Cutting the small end of the conical involute gear cutter from a coordinate system Ss(wherein: O)sIs the gear center, xsIn the radial direction of the gear, zsIn the axial direction of the gear, ysIs equal to xs、zsAll in a vertical direction. ) Conversion to coordinate system StThe tooth profile of the grinding disc can be obtained by (taking into account the variation in the top thickness of the grinding wheel):
wherein:
in the formula:
Mtsfrom the virtual gear tool coordinate system SsTo a coordinate system StThe coordinate transformation matrix of (2);
rs(us,ls) -an equation of the tooth flanks of the conical involute gear tool taking into account the meshing equation;
ts-the thickness of the tooth tip of the virtual gear cutter tip;
Egs-axis z of the grinding disctAnd virtual gear tool axis zsThe spatial distance therebetween;
bacoordinate system S of the virtual gear cuttersOrigin OsDistance to the small end section of the gear;
in formula (2)
Respectively corresponding to the left and right tooth profiles of the virtual rack cutter. Vector [ (t)s-tl)/2,0,0,1]TThe top thickness of the disc grinding wheel is consistent with that of the large end of the virtual gear cutter.
To obtain a complete grinding wheel flank, a new coordinate system S is established in FIG. 3gIs fixedly connected to a disc-shaped grinding wheel cutter to establish a coordinate system SgThe purpose of this is to form a complete grinding wheel tooth flank. Its origin OgAnd a coordinate system StOrigin O oftAnd (4) overlapping. x is the number ofgIs the radial direction of the grinding wheel, ygIs equal to xgThe vertical direction. RhogRepresenting the radius of the grinding disc, the value of which is predetermined Egs(disc wheel axis z in FIG. 2tAnd virtual gear tool axis zsThe spatial distance between the two) and the radius of the virtual gear cutter small end section. Coordinate system StSection of the tooth profile of the grinding disc in ZtRotate by any angle theta for axisgSo as to obtain the complete tooth surface sigma of the disc grinding wheelg。
Coordinate system StSection of the tooth profile of the grinding disc in ZtRotate by any angle theta for axisgThe tooth surface sigma of the disc grinding wheel can be obtainedgThe complete expression:
wherein:
in the formula:
Mgt(θg) From the coordinate system StTo the coordinate system S of the grinding discgThe coordinate transformation matrix of (2);
θg-the surface equation corner parameters of the dish grinding wheel;
so far, the complete tooth surface equation of the grinding disc can be obtained by simultaneously considering the formula (1) and the formula (3).
Substep 2: dressing of disc grinding wheels
In the actual grinding process, the disc wheel cutter is dressed by a diamond roller to obtain its sectional shape. For a five-axis numerical control machine tool, the dresser and the workpiece shaft are positioned on the same platform and are positioned on the rear side of the dresser. The dressing coordinate system of the disc wheel is shown in fig. 4, and the diamond roller dresser is cylindrical. During dressing, the machine tool y-axis (i.e. the linear displacement of the machine tool on which the grinding wheel is mounted) is first moved so that the central section x of the grinding dish isc-zcCross section x of diamond rollerf-zfCoplanar; and secondly, moving the linear axes x and z of the machine tool and the main shaft rotating shaft in a combined manner to enable a point B to be trimmed on the disc grinding wheel to be in contact with a trimming point A on the diamond roller. Wherein, the points B to be modified of the disc grinding wheel are evenly distributed with a plurality of points from the tooth top to the tooth root of the tooth profile, and the points B are sequentially modified. During the dressing process, the diamond roller and the disc grinding wheel rotate at high speed along respective axes. The positional relationship between the grinding disc and the diamond roller at dressing is shown in fig. 4. Therefore, the shape of the disc grinding wheel can be finished by the diamond roller to finish the precise grinding of the conical surface gear. According to the position relation between the diamond roller and the disc-shaped grinding wheel calculated by the algorithm, an NC program for trimming the disc-shaped grinding wheel based on a Siemens 840D system is written in Matlab.
During dressing, the diamond roller and the disc grinding wheel are in contact with each other, and the following conditions are met:
wherein:
in the formula:
rq (B)-the position vector of the point B to be modified on the grinding disc in the coordinate system SqThe following representation;
nq (B)-the unit normal vector of the point B to be modified on the grinding disc is in the coordinate system SqThe following representation;
rf (A)-the position vector of the dressing point A on the diamond roller is in the coordinate system SfThe following representation;
nf (A)-the unit normal vector of the finishing point A on the diamond roller is in the coordinate system SfThe following representation;
Mfc-coordinate system ScTo SfThe coordinate transformation matrix of (2);
Mcq-coordinate system SqTo ScThe coordinate transformation matrix of (2);
Lfc-coordinate system ScTo SfConverting the coordinates of the matrix submatrix by taking MfcThe first three rows and three columns;
Lcq-coordinate system SqTo ScConverting the coordinates of the matrix submatrix by taking McqThe first three rows and three columns.
The trimming point A on the diamond roller is usually the most marginal point (the marginal point is slightly inside) on the cylindrical end surface, once the parameters of the diamond roller are determined, the position vector of the point and the unit normal vector are in the coordinate system S in the formula (5)fIs readily shown.
Step two: determination of the point to be ground before grinding of the grinding disk
The invention takes a part of instantaneous contact line of a conical involute gear cutter and a conical surface gear as a grinding path on the tooth surface of the conical surface gear. FIG. 5 shows a rotated projection of a face of a bevel gear tooth ground at discrete grid points. The meshing lines (U lines) of the conical involute gear cutter and the conical surface gear form transverse grid lines in the tooth profile direction of the grid conical surface gear; the grid lines in the tooth direction of the conical surface gear are a group of parallel straight lines (V lines in total) which are distributed at equal intervals along the tooth direction. Each intersection they form will be referred to as a grinding target point.
Step three: installing a conical surface gear on a machine tool and finishing cutter tool setting
The conical surface gear is arranged on a machine tool workpiece shaft, the disc grinding wheel is arranged on a machine tool main shaft, and the disc grinding wheel is moved to a tool setting position at the tooth groove of the conical surface gear to complete tool setting. Fig. 1 shows a simulation platform based on a numerical control machine tool. The conical face gear and the grinding disc are mounted as shown in figure 1. And (3) the conical surface gear is arranged on a workpiece shaft of the numerical control machine tool and can be translated and rotated, the disc grinding wheel obtained in the step one is arranged on a main shaft of the numerical control machine tool, and the swinging and rotating movement of the disc grinding wheel is completed in the grinding process.
Step four: grinding machining of conical surface gear
Substep 1: grinding method and grinding coordinate system establishment
In order to clearly express the tooth grinding process, as shown in fig. 6, a coordinate system consisting of 5 coordinate systems is established, including: 1. coordinate system Sm: rigidly connected to a bevel gear, wherein SmRigidly fixed to the face gear, translating only with the face gear, OmIs the center of a circle at the bottom of the conical surface gear, xmIn the radial direction of the bevel gear, from the small end to the large end, zmIn the axial direction of the bevel gear, ymIs equal to xm、zmAre all vertical and meet the right hand rule.
2. Coordinate system S2: rigidly connected to face bevel gear, S2Translates and rotates with the face gear. O is2And OmAnd (4) overlapping. x is the number of2In the radial direction of the bevel gear, from the small end to the large end, z2In the axial direction of the bevel gear, y2Is equal to x2、z2Are all verticalAnd the right-hand rule is satisfied.
3. Coordinate system Sc: auxiliary coordinate system, performing the swinging motion of the grinding disc, OcIs a reaction with OgA distance of s0And is at OgJust above. x is the number ofcIn the radial direction of the grinding disc, zcIn the axial direction of the grinding disc, ycIs equal to xc、zcAre all vertical and meet the right hand rule.
4. Coordinate system Sq: auxiliary coordinate system, performing the swinging motion of the grinding disc, OqAnd OcAnd (4) overlapping. x is the number ofqIn the radial direction of the disc-shaped grinding wheel, from the small end to the large end, zqIn the axial direction of the grinding disc, yqIs equal to xq、zqAre all vertical and meet the right hand rule.
5. Coordinate system Sg: its origin OgAnd a coordinate system StOrigin O oftAnd (4) overlapping. x is the number ofgIs the radial direction of the grinding wheel, ygIs equal to xgThe vertical direction.
The process of grinding a conical-faced gear by a grinding disc is expressed by the above 5 coordinate systems. The coordinate system is constructed based on a five-axis numerical control machine tool (shown in figure 1). Origin OfIs a fixed point in space. dx,dyAnd dzShowing the linear displacement of the various moving parts of the machine along the x, y and z axes. Coordinate system SmAnd S2Rigidly connected to face-bevel gear, wherein SmRigidly fixed to the conical-faced gear and only translating with the conical-faced gear, S2Translates and rotates with the bevel gear. The rotation of the grinding disc passes through two auxiliary coordinate systems ScAnd SqAnd (5) realizing. Coordinate system SgIs rigidly and fixedly connected with the disc-shaped grinding wheel. As shown in fig. 5, each tooth feed of the grinding wheel for grinding the conical gear tooth surface follows a theoretical contact line between the conical gear and the cutter gear. The grinding sequence is from top to bottom, from the tooth crest of the conical surface gear to the common tangent on the tooth surface of the conical surface gear. Assuming that N points on the profile of the grinding wheel cutter will be used to grind the corresponding points on the conical-faced gear tooth flankAnd (4) point. The active grinding point N on the grinding disc and the corresponding point on the grinded tooth surface are always kept in contact with each other. The condition shows that the position vectors and normal vectors of the N points on the disc grinding wheel and the corresponding points on the tooth surface of the conical surface gear always keep equal in the same coordinate system at any grinding time, and the motion relation of the five-axis grinding point of the machine tool is determined according to the contact relation in the grinding process.
The theoretical instantaneous contact line between the conical surface gear and the virtual involute gear cutter is selected as the grinding path of the disc grinding wheel, the grinding process is carried out along the theoretical contact line, and the conical surface gear and the conical involute gear cutter are in line contact relation at different moments. Given a gear cutter rotation angle psis *And then the contact line on the tooth surface of the conical surface gear and the tooth surface of the gear cutter corresponding to the rotation angle can be obtained. In order to generate the full tooth surface of the conical surface gear, a virtual conical involute gear cutter needs to wind around the ZaThe axis rotates a certain angle. Within the range of the rotation angle, a series of contact lines on the tooth surface of the conical face gear can be obtained, and the contact line covering the whole tooth surface of the face gear can be obtained, namely the tooth surface of the face gear can be ground along the contact line. According to the position relation between the disc grinding wheel and the conical surface gear calculated by the algorithm, an NC program for grinding the surface gear based on a Siemens 840D system is written in Matlab. As can be seen from fig. 7, when the grinding disc advances along a grinding path on the face gear tooth surface, only the y-axis of the machine tool is fed in the face gear tooth width direction, and all other axes remain stationary. In the feeding process of the machine tool, the space shape formed by the section of the disc grinding wheel is superposed with a virtual gear cutter for generating the conical surface gear.
Substep 2: calculation of grinding residual
Lambda for maximum envelope residual allowed for face gear tooth surfacekThis value is expressed as being determined by a predetermined face gear tooth face machining accuracy. For a full face gear tooth surface, the maximum envelope residual between any two adjacent grinding paths should be less than or equal to lambdakTo meet the predetermined face gear tooth face precision requirement. This condition is expressed mathematically as:
in the formula:
λ(i-1～i,j)-envelope residual error of a series of points between the i-1 th grinding wheel diameter and the i-th grinding path.
When the conical surface gear is ground by the method, because the grinding paths on the tooth surface of the conical surface gear are distributed at intervals, a residual narrow belt is formed between two adjacent grinding paths. The deviation of a point on this narrow band from the ideal tooth surface is defined as the envelope residual. For the preset grinding precision of the tooth surface of the conical surface gear, a method for determining a grinding path on the tooth surface of the conical surface gear is provided. As shown in FIG. 8, let Γ be1And Γ2Two adjacent grinding paths on the tooth surface of the conical surface gear. When the grinding disc is along gamma1And Γ2When grinding the conical surface gear, a space curved surface sigma is respectively formedg1Sum Σg2。ΓeIs a space curved surface sigmag1Sum Σg2The intersection line of (a). Suppose there are two points M to be ground1And M2Respectively located in the grinding path Γ1And Γ2The above. And the two points are located on the same radial line of the discrete grid being ground (fig. 5). The grinding residual point T is positioned on the space curved surface Sigmag1Sum Σg2Of (a) intersection line gammaeAnd with M1And M2On the same radial line of the discrete grid being ground. Curve M1T and M2The distance from a point on T to the theoretical tooth surface of the bevel face gear is defined as the bevel face gear tooth surface envelope residual. The invention assumes the distance lambda from the T point to the theoretical tooth surface of the face gear as M1And M2The maximum envelope residual between points. In order to obtain the value of envelope residual lambda, first, the T point under the conical surface gear coordinate system is calculatedThe coordinates of (a). Next, as shown in fig. 8, a point W on the tooth surface of the face gear is regarded as a projection of a point T along the normal vector direction of the tooth surface of the conical face gear, and after obtaining the coordinates of the point M, the value of the envelope residual λ can be obtained. Based on intersecting lines ΓeThe coordinate of the upper point T and the coordinate of the projection point W of the point T on the tooth surface of the face gear, and the envelope residual error of the point T can be obtained.
Substep 3: determining a grinding path based on the grinding residual calculation and the given tooth surface machining precision
The maximum envelope residual between any two adjacent grinding paths should be less than or equal to λkTo meet the predetermined conical surface gear tooth surface accuracy requirement. When defining the first grinding path closest to the tooth top on the tooth surface of the conical surface gear, the corresponding virtual gear cutter is expanded to form a rotation angle
Greater than psis *The minimum value of (A) is 0.1 to 0.3 degrees. The rotation angle psi of the virtual gear cutter required for generating the full tooth surface of the conical surface gears *The range may be determined by the TCA algorithm. Each virtual gear cutter corner
Corresponds to a grinding path on the tooth surface of the conical surface gear. To show more clearly
The detailed solving flow is shown in fig. 9.
And (5) finishing solving when the finally solved grinding path covers the full tooth surface of the conical surface gear. And the relative positional relationship of the grinding wheel and the bevel gear required for grinding each ground point on the tooth surface when determining the grinding path has also been determined. And according to the solving result, writing a corresponding gear grinding NC program in Matlab, and finishing the grinding of the tooth surface of the conical surface gear on an actual numerical control machine tool.
In order to realize the full-tooth-surface grinding of the conical surface gear, as shown in fig. 10, 3-5 mm grinding head amount is set outside three boundaries of the tooth crest, the large end and the small end of the conical surface gear. The bevel face gear tooth surface grinding point beyond the boundary is still calculated based on the meshing equation.
Substep 4: since the calculation is performed only for one side tooth surface, indexing is required, and the above-described repeated steps are performed to finish grinding of the other side tooth surface, specifically in the grinding NC program written in Matlab.
Claims (2)
1. A method of grinding a conical faced gear with a grinding disc comprising the steps of:
the method comprises the following steps: the method for obtaining the disc grinding wheel cutter before grinding comprises the following sub-steps:
substep 1: the geometric shape of the tool with the tooth surface of the dish-shaped grinding wheel is defined, the tooth profile shape of the dish-shaped grinding wheel is completely consistent with the geometric shape of the virtual cone involute gear tool at the small end, and the top thickness t of the dish-shaped grinding wheelgIs less than or equal to the top thickness t of the big-end tooth profile of the virtual cutterl
Substep 2: the section shape of the disc-shaped grinding wheel cutter is obtained by trimming a diamond roller;
step two: determining a grinding point of the disc grinding wheel before grinding: and defining a part of instantaneous contact line of the conical involute gear cutter and the conical surface gear as a grinding path on the tooth surface of the conical surface gear. The meshing lines (U lines) of the conical involute gear cutter and the conical surface gear form transverse grid lines in the outline direction of the grid surface gear; the grid lines in the tooth direction of the conical surface gear are a group of parallel straight lines (V-shaped lines) which are distributed at equal intervals in the tooth direction, and each intersection point formed by the straight lines is used as a grinding target point;
step three: mounting a conical surface gear on a machine tool, mounting a disc-shaped grinding wheel on a main shaft of the machine tool, and moving the disc-shaped grinding wheel to a tool setting position at a tooth groove of the conical surface gear to finish tool setting;
step four: the grinding machining of the conical surface gear comprises the following substeps:
substep 1: establishing a grinding coordinate system, and defining a grinding method: determining the motion relationship between the disc grinding wheel and the face gear at each ground point on the tooth surface of the face gear, and grinding the tooth surface of the face gear from a grinding path closest to the tooth top of the face gear to a grinding path closest to the common tangent line of the tooth surface of the face gear in sequence along paths one by one to finish the grinding of the single tooth surface of the face gear. After grinding of one tooth surface is completed, the face gear is indexed to the next tooth groove, and grinding of the next tooth surface is performed. The above process is repeated until all the tooth surfaces of the face gear are ground.
Substep 2: calculation of grinding residual
To obtain the value of the envelope residual λ, the coordinates of the T point in the face gear coordinate system are first calculated. In-plane gear coordinate system S2The T point coordinates can be expressed as:
in the formula:
r2 (g1)-grinding by means of a grinding disc M1At point time, its curved surface equation is in coordinate system S2The following representation;
r2 (g2)-grinding by means of a grinding disc M2At point time, its curved surface equation is in coordinate system S2The following representation;
x2 (g1),y2 (g1)-position vector r2 (g1)X, y components of (a).
Grinding residual calculation formula:
in the formula: r isTFor an in-plane gear coordinate system S2A position vector of a lower T point;
r2and coordinates of projection points of the T point on the tooth surface of the face gear.
Substep 3: determining a grinding path based on the grinding residual calculation and the given tooth surface machining precision
Maximum envelope residual allowed for face gear tooth surfaceBy λkThis value is expressed as being determined by a predetermined face gear tooth face machining accuracy. For a full face gear tooth surface, the maximum envelope residual between any two adjacent grinding paths should be less than or equal to lambdakTo meet the predetermined face gear tooth face precision requirement. This condition is expressed by a mathematical expression as:
in the formula:
ψs i*generating a turning angle of the virtual gear cutter corresponding to the ith grinding path on the tooth surface of the face gear;
λ(i-1～i,j)-envelope residual error of a series of points between the i-1 th grinding wheel diameter and the i-th grinding path.
When defining the first grinding path closest to the tooth crest on the tooth surface of the face gear, the corresponding virtual gear cutter is generated to the rotary angle psis 1*Greater than psis *The minimum value of (1) to (3). The angle psi of rotation of the virtual gear cutter required for generating the full tooth flank of the face gears *The range may be determined by the TCA algorithm. Each virtual gear cutter corner psis i*Corresponds to a grinding path on the tooth face of a face gear.
Substep 4: the above steps complete the determination of the one-side tooth surface, and therefore the above steps are repeated to complete the grinding of the other-side tooth surface.
2. The method of grinding a bevel gear with a grinding disc of claim 1 wherein said coordinate system origin OfIs a fixed point in space. dx,dyAnd dzShowing the linear displacement of the various moving parts of the machine along the x, y and z axes. Coordinate system SmAnd S2Rigidly connected to face gear, wherein SmRigidly fixed to the face gear, translating only with the face gear, S2Translates and rotates with the face gear. The rotation of the grinding disc passes through two auxiliary coordinate systems ScAnd SqAnd (5) realizing. Coordinate system SgIs rigidly connected with the disc-shaped grinding wheel.
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