Dressing method of minor axis point of drum worm grinding wheel

Abstract

The present invention discloses a method for dressing a drum worm grinding wheel with a few axis points. The method improves the dressing accuracy of the face gear worm grinding wheel by avoiding the need for the grinding wheel to tilt the machine tool axis. By introducing a nominal gear shaping cutter that is perpendicular to the grinding wheel axis and whose end face profile is consistent with the cross-sectional profile of the grinding wheel axis, the method avoids the need for the dressing wheel to tilt the machine tool axis, thereby reducing the number of machine tool motion axes involved in the linkage during the grinding wheel dressing process and further improving the grinding wheel dressing accuracy. The method of the present invention uses only three machine tool axes to link the face gear worm grinding wheel, including the grinding wheel rotation axis, radial movement axis, and axial movement axis, and proposes a method for uniformizing the dressing path to ensure precise and efficient dressing of the worm grinding wheel profile. The method of the present invention can avoid the shortcomings of the formed dressing wheel, such as high cost, poor flexibility, and principle error, and lays a theoretical foundation for realizing the face gear grinding error reversal or the complex modified face gear tooth surface development grinding.

Description

Technical Field

[0001] The invention belongs to the technical field of gear processing, and specifically relates to a method for dressing the minor axis point of a drum-shaped worm grinding wheel. Background Art

[0002] Face gear pairs have great application potential in high-end equipment with intersecting and staggered axis transmission systems due to their large transmission ratio, smooth transmission, and ease of flow distribution. The worm grinding wheel continuously indexes when grinding face gears, resulting in high grinding efficiency and high gear pitch accuracy. The accuracy of the grinding wheel profile directly affects the grinding accuracy of the gear, and the grinding wheel will wear during the grinding process, requiring regular precision dressing. However, since the outer circle of the face gear worm grinding wheel is drum-shaped, the tooth profile extends along the spiral line distributed on the outer circle of the drum. When dressing the drum-shaped worm grinding wheel, multiple motion axes of the machine tool need to be involved in the linkage, making the precision dressing of the face gear worm grinding wheel very difficult.

[0003] The profile of the forming dressing wheel is consistent with that of the virtual gear shaping cutter, and it can cut the tooth surfaces on both sides of the grinding wheel at the same time. It has high dressing efficiency and has been widely used in the dressing process of face gear worm grinding wheels. However, the complex profile of the forming dressing wheel leads to high production costs and difficulty in ensuring the profile accuracy. It is only used for the dressing process of face gear worm grinding wheels with a fixed profile. In addition, the standard double-cone dressing wheel is also being explored for the dressing of face gear worm grinding wheels, but the number of machine tool motion axes involved in the linkage is the same as that of the forming dressing. The existing dressing wheels and their dressing methods have the following problems when processing face gear worm grinding wheels:

[0004] (1) Principle error. According to the research of Litvin et al., the worm grinding wheel should tilt around the axis of the gear shaping cutter based on the deflection of its lead angle, and rotate around its own axis at the same time. As a result, the rotation axis of the grinding wheel and the tilting axis are not orthogonal, and the correct profile cannot be machined on the machine tool. In actual processing, the dressing wheel deflects the grinding wheel lead angle instead of the grinding wheel to ensure that the rotation axis of the grinding wheel is orthogonal to the tilting axis. This method will produce principle error.

[0005] (2) It is difficult to improve the accuracy of the machine tool's tilt axis. The tilt axis is the active axis in the machine tool's linkage axis during worm wheel dressing processing. Its positioning error will significantly affect the tooth surface accuracy of the worm wheel. Since the structure of the machine tool limits the travel range of the tilt axis, and the weight of the tool holder suspended on the tilt axis is large and unevenly distributed, the positioning error of the tilt axis is difficult to identify and compensate, resulting in a large error in the axis and difficulty in improving its tilt accuracy. In addition, the dressing wheel needs to be deflected to a lead angle related to the grinding wheel diameter, but the accuracy of the machine tool axis that drives the dressing wheel deflection is also low.

[0006] (3) The dressing motion involves multiple machine tool axes, and accuracy is difficult to guarantee. During the dressing process of the face gear worm grinding wheel, four machine tool motion axes are required to participate in the linkage (including the tilt axis), and the dressing wheel requires an additional deflection axis. The grinding wheel dressing process involves two machine tool axes with lower precision (the tilt axis and the deflection axis), and the multi-axis linkage makes the machine tool motion relationship very complex. The motion error of the coupled machine tool axes is difficult to identify and compensate, and it is very difficult to accurately dress the worm grinding wheel tooth surface.

[0007] (4) It is difficult to dress non-involute worm grinding wheels. If the worm grinding wheel profile is non-involute, it will be very difficult to correctly dress the grinding wheel tooth profile. The cost of forming dressing wheels is relatively high and their profile is only applicable to worm grinding wheels with a certain set of fixed parameters; double-cone dressing wheels can be used for worm grinding wheels with involute profiles of multiple sets of parameters, but it is difficult to dress non-involute profiles. When the face gear has a complex modified tooth surface or the tooth surface error needs to be reversed, the worm grinding wheel will have a non-standard curve profile, and the existing dressing wheels and dressing methods will not be able to be used for the precision expansion grinding of such face gears. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a method for dressing the minor axis points of a drum worm grinding wheel, which can avoid the shortcomings of high cost, poor flexibility and principle error of the forming dressing wheel, and lay a theoretical foundation for realizing the gear grinding error reversal or complex modified gear tooth surface generation grinding.

[0009] In order to achieve the above object, the present invention provides the following technical solutions:

[0010] A method for dressing the minor axis point of a drum-shaped worm grinding wheel comprises the following steps:

[0011] Step 1: Determine the worm wheel tooth surface based on the nominal gear shaping cutter

[0012] According to the helix angle of the worm grinding wheel, the basic design parameters of the nominal gear shaping cutter consistent with the cross-sectional profile of the worm grinding wheel shaft are derived, and the tooth surface of the worm grinding wheel is obtained from the nominal gear shaping cutter through coordinate transformation.

[0013] Step 2: Profiling the worm grinding wheel tooth profile based on the nominal gear shaping cutter

[0014] The profile equation of a round-end dressing wheel is established, and the tooth profile of the nominal gear shaping cutter is copied using the dressing wheel. The contact point between the dressing wheel and the nominal gear shaping cutter is the dressing point of the worm grinding wheel. Based on the correct contact conditions at the dressing point and the relative position relationship between the dressing wheel and the nominal gear shaping cutter, the theoretical point dressing tooth surface of the drum worm grinding wheel is solved.

[0015] Step 3: Solve the machine tool linkage relationship for worm wheel point dressing

[0016] The contact point between the dressing wheel and the nominal gear shaping cutter is converted to the dressing point on the worm grinding wheel tooth surface, and the homogeneous transformation matrix of the theoretical dressing is equal to the actual dressing matrix considering the machine tool structure. The linkage relationship of the machine tool motion axis in the drum worm grinding wheel point dressing process is obtained.

[0017] Step 4: Evenly adjust the worm grinding wheel point path

[0018] According to the value range of the worm grinding wheel tooth profile, the highest point of the tooth surface is taken as the first dressing point at the initial position of the grinding wheel, and the maximum dressing step length between the dressing paths is calculated to meet the requirements of the residual height. Based on the previous dressing point, the next contact point on the nominal gear shaping cutter profile is solved with the maximum dressing step length as the next dressing point on the grinding wheel until the limit point of the other value range of the grinding wheel tooth profile is reached. All dressing points are transformed through coordinates to obtain a uniform grinding wheel point dressing path with equal step length.

[0019] Furthermore, in the step 1, the tooth profile of the nominal gear shaping cutter is the same as the theoretical gear shaping cutter profile on the grinding wheel axis plane; let the theoretical gear shaping cutter be represented by r s (N s ,m,α0), then the nominal gear shaping cutter r a (N a ,m a ,α a ) are:

[0020]

[0021] Where: N s , m and α0 are the basic design parameters of the theoretical gear shaping cutter, and N s represents the number of teeth; m represents the module; α0 represents the pressure angle; N a , m a and α a is the basic design parameter of the nominal gear shaping cutter, and N a Indicates the number of teeth; m a Represents the modulus; α a represents the pressure angle; λ is the lead angle of the worm grinding wheel;

[0022] The tooth surface of the worm grinding wheel is obtained by coordinate transformation from the nominal gear shaping cutter profile;

[0023]

[0024] in: Indicates the tooth surface of the grinding wheel; is the meshing equation between the worm grinding wheel and the nominal gear shaping cutter tooth surface; is the coordinate transformation matrix from the nominal gear shaping cutter to the worm grinding wheel; r a (u r ,u z) represents the nominal gear shaping cutter profile; u r Indicates the tooth profile variable of the nominal gear shaping cutter; u z represents the tooth direction variable of the nominal gear shaping cutter; Indicates the nominal gear shaping cutter angle.

[0025] Furthermore, in step 2, the theoretical contact point between the dressing wheel and the nominal gear shaping cutter is set to point P0. Then, the correct contact condition between the dressing wheel and the nominal gear shaping cutter at the theoretical dressing point P0 is:

[0026]

[0027] in: and Respectively represent the position vector and normal vector of the nominal gear shaping cutter at the theoretical trimming point P0; and Respectively represent the position vector and normal vector of the dressing wheel at the theoretical dressing point P0;

[0028] Then in the nominal gear shaping cutter coordinate system S a0 In the figure, the position vector and normal vector of the actual contact point P1 between the dressing wheel and the nominal gear shaping cutter are:

[0029]

[0030] in: and In the nominal gear shaping cutter coordinate system S a0 , the position vector and normal vector of the nominal gear shaping cutter at the actual contact point P1; and Respectively represent the position vector and normal vector of the nominal gear shaping cutter at the actual contact point P1; M a0a The coordinate transformation equation representing the nominal gear shaping cutter's dynamic coordinate system to its static coordinate system; Indicates the rotation angle during the coordinate change process, which is an auxiliary angle;

[0031] Then in the nominal gear shaping cutter coordinate system S a0 In the figure, the contact angle of the actual contact point P1 is:

[0032]

[0033] Where: ρ1 is the contact angle of the dressing wheel at the actual contact point P1; is the component of the normal vector of the actual contact point P1 on the nominal gear shaping cutter in the y direction;

[0034] When using the round head dressing wheel to profile the nominal gear shaping cutter tooth profile, the dressing point on the dressing wheel is converted to the nominal gear shaping cutter coordinate system S a0In the figure, the tooth surface of the worm grinding wheel is obtained by using the relative motion relationship between the nominal gear shaping cutter and the worm grinding wheel:

[0035]

[0036] in: Indicates that the dressing wheel is in the coordinate system S a0 The silhouette in Indicates the tooth surface of the worm grinding wheel based on the round head dressing wheel; M ad M represents the transformation matrix from the dressing wheel coordinate system to the nominal gear shaping cutter dynamic coordinate system; ww0 M represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the worm grinding wheel; w0a0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; Indicates trimming of the contour.

[0037] Furthermore, in step 3, from the dressing wheel coordinate system S d To the grinding wheel coordinate system S w The theoretical homogeneous transformation matrix is:

[0038]

[0039] in: Indicates the coordinate system S from the dressing wheel d To the grinding wheel coordinate system S w Theoretical homogeneous transformation matrix of; M represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the worm grinding wheel; w0Sa0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; The coordinate transformation equation representing the nominal gear shaping cutter's dynamic coordinate system to its static coordinate system; Represents the transformation matrix from the dressing wheel coordinate system to the nominal gear shaping cutter dynamic coordinate system; is the grinding wheel angle, and:

[0040] Considering the actual structure of the machine tool, the actual coordinate transformation matrix from the dressing wheel to the worm grinding wheel is:

[0041] M BB2 (D B ,D X ,D Y ,D Z )=M BB0 (D B )M B0Y (D Y )M YA M AZ (D Z )M ZX (DX )M Xbase M baseB2

[0042] Where: M BB2 (D B ,D X ,D Y ,D Z ) represents the actual coordinate transformation matrix from the dressing wheel to the worm grinding wheel; M BB0 (D B ) represents the transformation matrix from the B-axis static coordinate system to the dynamic coordinate system; MB 0Y (D Y ) represents the transformation matrix from the Y axis to the B axis static coordinate system; M YA Represents the transformation matrix from A axis to Y axis; M AZ (D Z ) represents the transformation matrix from the Z axis to the A axis; M ZX (D X ) represents the transformation matrix from the X axis to the Z axis; M Xbase Represents the transformation matrix from the bed to the X axis; M baseB2 Represents the transformation matrix from B2 axis to bed; D J (J = X, Y, Z, B) represents the amount of motion along the J axis;

[0043] By making the theoretical homogeneous transformation matrix from the dressing wheel to the worm grinding wheel equal to the actual coordinate transformation matrix, the linkage relationship of the machine tool motion axis in the dressing process is obtained:

[0044]

[0045] in: and Represents the position vector of point P0 on the dressing wheel Components in the x and y directions.

[0046] Furthermore, the tooth surface after point dressing of the worm grinding wheel using the round head dressing wheel and considering the machine tool structure is obtained:

[0047]

[0048] in: Represents the transformation matrix from the machine tool B2 axis to the B axis; r d (ρ(u r )) indicates trimming the contour.

[0049] Furthermore, in step 4, let the dressing point on the grinding wheel dressing path i be LP i , let the trimming point LP i―1 and LP i+1 Relative to the trim point LP i The residual heights are δci―1 and δ ci , the distance between two adjacent trimming points is t pi―1 and t pi , then the nominal gear shaping cutter tooth surface t pi for:

[0050]

[0051] in: and The contact points LP on the nominal gear shaping cutter tooth surface are i The components of the position vector on the x-axis and y-axis; and The contact points LP on the nominal gear shaping cutter tooth surface are i+1 The components of the position vector on the x-axis and y-axis;

[0052] According to the different curvatures in the nominal gear shaping cutter tooth height direction, a series of trimming residual heights are obtained; the maximum value of the trimming residual heights is selected as the final value, and the value is guaranteed to meet the requirements. Then the residual height between any adjacent trimming points satisfies:

[0053] t pi―1 =t pi =t p

[0054] Where: t p is the maximum value of the trimmed residual height;

[0055] Taking the nominal gear shaping cutter tooth top as the first dressing point, the position vectors and normal vectors of all contact points on the nominal gear shaping cutter tooth surface are calculated in sequence; then the uniformized worm grinding wheel tooth profile dressing points and the uniformized worm grinding wheel tooth profile dressing path are obtained.

[0056] The beneficial effects of the present invention are:

[0057] The drum worm grinding wheel minor axis point dressing method of the present invention improves the dressing accuracy of the face gear worm grinding wheel by avoiding the need of the grinding wheel for the machine tool tilting axis; by introducing a nominal gear shaping cutter that is perpendicular to the grinding wheel axis and whose end face profile is consistent with the cross-sectional profile of the grinding wheel axis, the need of the dressing wheel for the machine tool deflection axis is avoided, thereby reducing the number of machine tool motion axes involved in the linkage during the grinding wheel dressing process and further improving the grinding wheel dressing accuracy; the method of the present invention uses only three machine tool axes to link the face gear worm grinding wheel, including the grinding wheel rotation axis, the radial movement axis and the axial movement axis, and proposes a dressing path homogenization method to ensure precise and efficient dressing processing of the worm grinding wheel profile.

[0058] The method of the present invention avoids the high cost, poor flexibility, and principle errors inherent in conventional shaping dressing wheels, laying a theoretical foundation for achieving error reversal in face gear grinding or generation grinding of complex modified face gear tooth surfaces. The method of the present invention is applicable to all precision dressing technologies for non-standard profile worm grinding wheels due to tooth surface error reversal or complex tooth surface modification. It is suitable for precision grinding of face gears and complex modified external / internal cylindrical gears, featuring low cost, excellent flexibility, and simple adjustment. The method of the present invention can be implemented on five-axis, four-axis, or three-axis CNC machine tools. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0060] Figure 1 It is a flow chart of an embodiment of a method for dressing the minor axis point of a drum-shaped worm grinding wheel according to the present invention;

[0061] Figure 2 This is the relationship diagram between the worm wheel axis plane and the gear shaping cutter end plane;

[0062] Figure 3 This is the profile of the nominal gear shaping cutter tooth surface based on the round head dressing wheel;

[0063] Figure 4 This is a profile diagram of the tooth surface of the worm grinding wheel based on the round head dressing wheel;

[0064] Figure 5 The coordinate change diagram from the ball-end dressing wheel to the worm grinding wheel;

[0065] Figure 6 Schematic diagram of the uniformity of the dressing points on the tooth surface of the worm grinding wheel;

[0066] Figure 7 This is a simulation diagram of the minor axis point dressing on the worm grinding wheel tooth surface. DETAILED DESCRIPTION

[0067] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0068] like Figure 1 As shown, the method for dressing the minor axis point of the drum worm grinding wheel in this embodiment includes the following steps.

[0069] Step 1: Determine the worm wheel tooth surface based on the nominal gear shaping cutter

[0070] According to the helix angle of the worm grinding wheel, the basic design parameters of the nominal gear shaping cutter consistent with the cross-sectional profile of the worm grinding wheel shaft are derived, and the tooth surface of the worm grinding wheel is obtained from the nominal gear shaping cutter through coordinate transformation.

[0071] The relationship between the worm wheel axis plane and the gear shaping cutter end plane is as follows: Figure 2 The existence of the worm grinding wheel lead angle λ makes the grinding wheel axis and the gear shaping cutter axis non-orthogonal, resulting in the gear shaping cutter profile on the grinding wheel axis plane and the gear shaping cutter end plane not coinciding.

[0072] In order to avoid the difficulty caused by the angle λ during the dressing process of the worm grinding wheel, a nominal gear shaping cutter (auxiliary component) is provided. The tooth profile of the nominal gear shaping cutter is the same as the theoretical gear shaping cutter profile on the grinding wheel axis plane. Let the theoretical gear shaping cutter be represented by r s (N s ,m,α0), then the nominal gear shaping cutter r a (N a ,m a ,α a ) are:

[0073]

[0074] Where: N s , m and α0 are the basic design parameters of the theoretical gear shaping cutter, and N s represents the number of teeth; m represents the module; α0 represents the pressure angle; N a , m a and α a is the basic design parameter of the nominal gear shaping cutter, and N a Indicates the number of teeth; m a Represents the modulus; α a represents the pressure angle; λ is the lead angle of the worm grinding wheel.

[0075] The included angle between the worm wheel axis section Γ and the gear shaping cutter end plane is λ, and the two have the same profile on the grinding wheel axis plane. w and nominal gear shaping cutter S a They are respectively fixed on the worm grinding wheel and the nominal gear shaping cutter, and S w0 is the worm grinding wheel coordinate system S w The static coordinate system, S a0 Is the nominal gear shaping cutter S a The static coordinate system. and They are the rotation angles of the worm grinding wheel and the nominal gear shaping cutter respectively. If the number of grinding wheel heads is 1, then the rotation angles of the two satisfy

[0076] The tooth surface of the worm grinding wheel is obtained by coordinate transformation from the nominal gear shaping cutter;

[0077]

[0078] in: Indicates the tooth surface of the grinding wheel; is the meshing equation between the worm grinding wheel and the nominal gear shaping cutter tooth surface; is the coordinate transformation matrix from the nominal gear shaping cutter to the worm grinding wheel; r a (u r ,u z ) represents the nominal gear shaping cutter profile; u r Indicates the tooth profile variable of the nominal gear shaping cutter; u z represents the tooth direction variable of the nominal gear shaping cutter; Indicates the nominal gear shaping cutter angle.

[0079] Step 2: Profiling the worm grinding wheel tooth profile based on the nominal gear shaping cutter

[0080] The profile equation of the round-end dressing wheel is established, and the dressing wheel is used to imitate the tooth profile of the nominal gear shaping cutter. The contact point between the dressing wheel and the nominal gear shaping cutter is the dressing point of the worm grinding wheel. Through the correct contact condition at the dressing point and based on the relative position relationship between the dressing wheel and the nominal gear shaping cutter, the tooth surface of the worm grinding wheel is obtained.

[0081] When using a round-end dressing wheel to dress a worm grinding wheel, the contact area between the worm and dressing wheel teeth is a point on the grinding wheel axis plane Γ, known as the dressing point. The nominal gear shaping cutter eliminates the need to tilt the grinding wheel or dressing wheel at an angle λ. All dressing points during the entire dressing process lie on plane Γ because the centers of the dressing wheel, nominal gear shaping cutter, and worm are coplanar.

[0082] The worm grinding wheel dressing process is equivalent to the process of dressing the grinding wheel tooth profile on plane Γ using a dressing wheel. Since the profile of the worm grinding wheel tooth surface is the same as the profile of the nominal gear shaping cutter on plane Γ, the tooth surface of the nominal gear shaping cutter is used to fit the profile with the dressing wheel and then converted into the worm grinding wheel tooth surface.

[0083] When the worm grinding wheel stays at the initial position, its tooth surface fits the profile of the round head dressing wheel as shown in the figure. Figure 3 Coordinate system S d0 and S a0 They are fixed on the dressing wheel and the nominal gear shaping cutter respectively. Let the theoretical contact point between the dressing wheel and the nominal gear shaping cutter be point P0 on plane Γ, which is also the dressing point P0. The parameter ρ0 represents the contact angle of the dressing wheel at point P0.

[0084] It should be noted that the left (right) profile of the dressing wheel should contact the right tooth profile (left tooth profile) of the nominal gear shaping cutter. The correct contact condition between the dressing wheel and the nominal gear shaping cutter at the theoretical dressing point P0 is:

[0085]

[0086] in: and Respectively represent the position vector and normal vector of the nominal gear shaping cutter at the theoretical trimming point P0; and They represent the position vector and normal vector of the dressing wheel at the theoretical dressing point P0 respectively.

[0087] Theoretical point dressing processing of worm grinding wheel based on round head dressing wheel Figure 4 As shown. Figure 4 As shown, the coordinate system S d0 and S d Represent the initial and actual positions of the dressing wheel, respectively, and the coordinate system S a Fixed on the nominal gear shaping cutter, coordinate system S a0 is its static coordinate system. P0 and P1 are the theoretical and actual contact positions of the dressing wheel, respectively. The angle between the two contact points is ∠P0O a0 P1 is equal to the nominal gear shaping cutter rotation angle Correspondingly, ρ0 and ρ1 are the contact angles of the dressing wheel at the two contact points, n P0 and n P1 are the corresponding normal vectors. For the contact point P1, the distances from the center of the dressing wheel to the nominal gear shaping cutter in the x and y directions are L x1 and L y1 .

[0088] The relative motion relationship between the dressing wheel, nominal gear shaping cutter and worm grinding wheel is as follows: Figure 4 As shown in the right figure. Coordinate system S w Fixed on the worm grinding wheel, S w0 is its static coordinate system. The actual tooth surface of the nominal gear shaping cutter should be transformed into the coordinate system S a0 In the nominal gear shaping cutter coordinate system S a0 In the figure, the position vector and normal vector of the actual contact point P1 between the dressing wheel and the nominal gear shaping cutter are:

[0089]

[0090] in: and In the nominal gear shaping cutter coordinate system S a0 , the position vector and normal vector of the nominal gear shaping cutter at the actual contact point P1; and Respectively represent the position vector and normal vector of the nominal gear shaping cutter at the actual contact point P1; M a0a The coordinate transformation equation representing the nominal gear shaping cutter's dynamic coordinate system to its static coordinate system; Indicates the rotation angle during the coordinate change process, which is an auxiliary angle.

[0091] Then in the nominal gear shaping cutter coordinate system S a0 In the figure, the contact angle of the actual contact point P1 is:

[0092]

[0093] Where: ρ1 is the contact angle of the dressing wheel at the actual contact point P1; It is the component of the normal vector of the actual contact point P1 on the nominal gear shaping cutter in the y direction.

[0094] When using the round head dressing wheel to profile the nominal gear shaping cutter tooth profile, the dressing point on the dressing wheel is converted to the nominal gear shaping cutter coordinate system S a0 In the Figure 4 In the figure, the tooth surface of the worm grinding wheel is obtained by using the relative motion relationship between the nominal gear shaping cutter and the worm grinding wheel:

[0095]

[0096] in: Indicates that the dressing wheel is in the coordinate system S a0 The silhouette in Indicates the tooth surface of the worm grinding wheel based on the round head dressing wheel; M ad M represents the transformation matrix from the dressing wheel coordinate system to the nominal gear shaping cutter dynamic coordinate system; ww0 M represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the worm grinding wheel; w0a0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; Indicates trimming of the contour.

[0097] The worm grinding wheel only rotates around its own axis y w Rotate without tilting Therefore, the tooth surface of the worm grinding wheel based on the round head dressing wheel can be expressed as

[0098] Step 3: Solve the machine tool linkage relationship for worm wheel point dressing

[0099] The contact point between the dressing wheel and the nominal gear shaping cutter is converted to the dressing point on the tooth surface of the worm grinding wheel. The homogeneous transformation matrix of the theoretical dressing is equal to the actual dressing matrix considering the machine tool structure. The linkage relationship of the machine tool motion axis in the drum worm grinding wheel point dressing process is obtained.

[0100] In the actual machining of worm wheel tooth flanks, the machine tool structure must be considered to determine the linkage relationship between the machine tool's motion axes during the grinding wheel dressing process. Combining the theoretical and practical transformation matrices between the worm wheel and the ball-end dressing wheel, the linkage relationship between the motion axes can be derived. The application of an auxiliary nominal gear shaping cutter eliminates the influence of the worm wheel lead angle λ in the transformation matrix, thereby reducing the number of machine tool motion axes involved in the linkage.

[0101] Owing to need not tilting dressing wheel or tilting worm grinding wheel, grinding wheel can be carried out dressing processing on the dressing wheel left side or below according to machine tool structure.In the present embodiment, worm grinding wheel is positioned at dressing wheel left side, makes processing safer and more flexible.

[0102] The force coordinate changes from the ball-end dressing wheel to the worm grinding wheel are as follows: Figure 5 As shown. Is the grinding wheel angle The associated auxiliary angle, therefore from the dressing wheel coordinate system S d To the grinding wheel coordinate system S w The theoretical homogeneous transformation matrix is:

[0103]

[0104] in: Indicates the coordinate system S from the dressing wheel d To the grinding wheel coordinate system S w Theoretical homogeneous transformation matrix; N ww0 M represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the worm grinding wheel; w0a0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; M represents the coordinate transformation equation from the nominal gear shaping cutter's dynamic coordinate system to its static coordinate system; ad Represents the transformation matrix from the dressing wheel coordinate system to the nominal gear shaping cutter dynamic coordinate system; is the grinding wheel angle, and: N a ;

[0105] During the dressing process of a worm grinding wheel on a machine tool, the machine kinematic chain is: B2-axis (dressing wheel) - bed - X-axis - Z-axis - A-axis - Y-axis - B-axis (worm grinding wheel). In traditional worm grinding wheel dressing methods, the grinding wheel must be positioned directly below the dressing wheel due to limitations in the machine tool's toolholder. With the introduction of a nominal gear shaping cutter, the machine's kinematic axes no longer need to tilt the grinding wheel's lead angle λ during the dressing process.

[0106] Therefore, according to the difference of machine tool structure, the grinding wheel can be carried out dressing process on the left side or below of the dressing wheel. In the present embodiment, the worm grinding wheel is installed on the left side of the dressing wheel, which makes processing safer and can be carried out dressing process at any height required.

[0107] S base It is fixed to the machine tool bed and is a static coordinate system. K (K=X,Y,Z,A,B,B2) is fixed to the K axis. J(J = X, Y, Z, B) represents the motion of the J axis. Considering the actual structure of the machine tool, the actual coordinate transformation matrix from the dressing wheel to the worm grinding wheel is:

[0108] M BB2 (D B ,D X ,D Y ,D Z )=M BB0 (D B )M B0Y (D Y )M YA N AZ (D Z )M ZX (D X )M Xbase M base2

[0109] Where: M BB2 (D B ,D X ,D Y ,D Z ) represents the actual coordinate transformation matrix from the dressing wheel to the worm grinding wheel; M BB0 (D B ) represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the B axis; M B0Y (D Y ) represents the transformation matrix from the Y axis to the B axis static coordinate system; M YA Represents the transformation matrix from A axis to Y axis; M AZ (D Z ) represents the transformation matrix from the Z axis to the A axis; M ZX (D X ) represents the transformation matrix from the X axis to the Z axis; M Xbase Represents the transformation matrix from the bed to the X axis; M baseB2 Represents the transformation matrix from B2 axis to bed; D J (J=X, Y, Z, B) represents the amount of movement along the J axis.

[0110] In order to dress the correct worm grinding wheel tooth profile, the theoretical homogeneous transformation matrix from the dressing wheel to the worm grinding wheel is made equal to the actual coordinate transformation matrix, that is, Get the linkage relationship of the machine tool motion axis during the finishing process:

[0111]

[0112] in: and Represents the position vector of point P0 on the dressing wheel Components in the x and y directions.

[0113] Accordingly, the linkage relationship of the machine tool motion axis is substituted into the actual coordinate transformation matrix M from the dressing wheel to the worm grinding wheel. BB2 (D D ,D X ,D Y ,D Z ), the tooth surface after point dressing of the worm grinding wheel using the round head dressing wheel and considering the machine tool structure can be obtained:

[0114]

[0115] in: Represents the transformation matrix from the machine tool B2 axis to the B axis; r d (ρ(u r )) indicates trimming the contour.

[0116] Step 4: Evenly adjust the worm grinding wheel point path

[0117] According to the value range of the dressing wheel tooth profile, the highest point of the tooth surface is taken as the first dressing point at the initial position of the grinding wheel, and the maximum dressing step length that meets the dressing residual height requirement is calculated; based on the previous dressing point, the next contact point on the nominal gear shaping cutter profile is solved with the maximum dressing step length as the next dressing point on the grinding wheel, until the limit point of the other value range of the grinding wheel tooth surface is obtained; all dressing points are transformed through coordinates to obtain a uniform grinding wheel point dressing path with equal step length.

[0118] Specifically, when the nominal gear shaping cutter tooth surface variable u r When the increment is fixed, the distance between adjacent contact points on the dressing wheel and the nominal gear shaping cutter tooth surface varies, and the distribution of contact points from the nominal gear shaping cutter tooth top to the tooth root changes from very sparse to very dense. Furthermore, the extremely uneven distribution of contact points on the nominal gear shaping cutter will lead to an uneven distribution of dressing points on the worm grinding profile by the dressing wheel, resulting in an extremely uneven distribution of the actual dressing paths of the grinding wheel, affecting the dressing accuracy of the grinding profile. Because residual material will remain between adjacent dressing paths when dressing the grinding wheel tooth surface with a rounded dressing wheel, it is very necessary to equalize the dressing points on the worm grinding wheel tooth surface.

[0119] like Figure 6 As shown in the figure, there is a residue between the two adjacent dressing paths of the round head dressing wheel on the tooth surface of the worm grinding wheel. In the worm grinding wheel axis section Γ, the dressing points on the grinding wheel dressing path i and path i+1 are LP i and LP i+1 Parameter t pi It represents the distance between two dressing points. The distance between the dressing points corresponding to the dressing paths i and i+1 on each section of the grinding wheel is a constant.

[0120] In the worm grinding wheel axis section Γ, the worm grinding wheel has the same profile as the nominal gear shaping cutter. The worm grinding wheel tooth profile dressing point homogenization process can be equivalent to the homogenization of the nominal gear shaping cutter tooth profile and the dressing wheel contact point. Let the dressing point on the grinding wheel dressing path i be LP i , let the trimming point LP i―1 and LP i+1 Relative to the trim point LP i The residual heights are δ ci―1 and δ ci , the distance between two adjacent trimming points is t pi―1 and t pi , then the nominal gear shaping cutter tooth surface t pi for:

[0121]

[0122] in: and The contact points LP on the nominal gear shaping cutter tooth surface are i The components of the position vector on the x-axis and y-axis; and The contact points LP on the nominal gear shaping cutter tooth surface are i+1 The components of the position vector on the x-axis and y-axis;

[0123] The maximum trimming residual height is determined by the accuracy grade of the tooth surface. Since the curvature of the nominal gear shaping cutter tooth surface varies, the residual heights between trimming paths are not equal. Based on the different curvatures in the nominal gear shaping cutter tooth height direction, a series of trimming residual heights are obtained; the maximum of these trimming residual heights is selected as the final value, and this value is guaranteed to meet the requirements. Then the residual heights between any adjacent trimming points meet the following requirements:

[0124] t pi―1 =t pi =t p

[0125] Where: t p The maximum value of the trimmed stub height.

[0126] Taking the nominal gear shaping cutter tooth top as the first dressing point, the position vectors and normal vectors of all contact points on the nominal gear shaping cutter tooth surface are calculated in sequence; then the uniformized worm grinding wheel tooth profile dressing points and the uniformized worm grinding wheel tooth profile dressing path are obtained.

[0127] According to the actual structure of the machine tool, a cutting simulation model is established. pi The calculation formula determines the uniform dressing point, and the uniform dressing path and the linkage relationship of the machine tool motion axis are combined to obtain the worm grinding wheel tooth surface point dressing cutting simulation results as shown below: Figure 7As shown in the figure, the cross-section of the working portion of the dressing wheel is circular, corresponding to the cutter marks on the tooth surface after the worm grinding wheel dressing simulation. The cutter marks are evenly distributed on the worm grinding wheel tooth surface, consistent with the pre-designed equidistant distribution method. The simulation results demonstrate the correctness of the worm grinding wheel minor axis point dressing method and the dressing path homogenization method proposed in this embodiment.

[0128] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A method for dressing the minor axis point of a drum worm grinding wheel, characterized in that: The steps include: Step 1: Determine the worm wheel tooth surface based on the nominal gear shaping cutter According to the helix angle of the worm grinding wheel, the basic design parameters of the nominal gear shaping cutter consistent with the cross-sectional profile of the worm grinding wheel shaft are derived, and the tooth surface of the worm grinding wheel is obtained from the nominal gear shaping cutter through coordinate transformation. Step 2: Profiling the worm grinding wheel tooth profile based on the nominal gear shaping cutter The profile equation of a round-end dressing wheel is established, and the tooth profile of the nominal gear shaping cutter is copied using the dressing wheel. The contact point between the dressing wheel and the nominal gear shaping cutter is the dressing point of the worm grinding wheel. Based on the correct contact conditions at the dressing point and the relative position relationship between the dressing wheel and the nominal gear shaping cutter, the theoretical point dressing tooth surface of the drum worm grinding wheel is solved. Step 3: Solve the machine tool linkage relationship for worm wheel point dressing The contact point between the dressing wheel and the nominal gear shaping cutter is converted to the dressing point on the worm grinding wheel tooth surface, and the homogeneous transformation matrix of the theoretical dressing is equal to the actual dressing matrix considering the machine tool structure. The linkage relationship of the machine tool motion axis in the drum worm grinding wheel point dressing process is obtained. Step 4: Evenly adjust the worm grinding wheel point path Based on the range of tooth profile values ​​of the worm grinding wheel, the highest point on the tooth surface is used as the first dressing point at the initial position of the grinding wheel. The maximum dressing step length between dressing paths that satisfies the residual height requirement is calculated. Based on the previous dressing point, the next contact point on the nominal gear shaping cutter profile is solved with the maximum dressing step length as the next dressing point on the grinding wheel, until the next limit point of the grinding wheel tooth profile is reached. All dressing points are transformed through coordinates to obtain a uniform grinding wheel point dressing path with equal step length. In step 1, let the theoretical gear shaping cutter be expressed as , then the nominal gear shaping cutter The basic design parameters are: in: , and are the basic design parameters of the theoretical gear shaping cutter, and Indicates the number of teeth; Represents the modulus; represents the pressure angle; , and are the basic design parameters of the nominal gear shaping cutter, and Indicates the number of teeth; Represents the modulus; represents the pressure angle; is the lead angle of the worm grinding wheel; The tooth surface of the worm grinding wheel is obtained by coordinate transformation from the nominal gear shaping cutter profile; in: Indicates the tooth surface of the grinding wheel; is the meshing equation between the worm grinding wheel and the nominal gear shaping cutter tooth surface; is the coordinate transformation matrix from the nominal gear shaping cutter to the worm grinding wheel; Indicates the nominal gear shaping cutter profile; represents the tooth profile variable of the nominal gear shaping cutter; represents the tooth direction variable of the nominal gear shaping cutter; Indicates the nominal gear shaping cutter angle.

2. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, wherein: In the step 2, the theoretical contact point between the dressing wheel and the nominal gear shaping cutter is set as point , then the dressing wheel and the nominal gear shaping cutter are at the theoretical dressing point The correct contact conditions at are: in: and Respectively represent the nominal gear shaping cutter at the theoretical trimming point The position vector and normal vector at ; and Respectively represent the dressing wheel at the theoretical dressing point The position vector and normal vector at ; In the nominal gear shaping cutter coordinate system The actual contact point between the dressing wheel and the nominal gear shaping cutter The position vector and normal vector are: in: and In the nominal gear shaping cutter coordinate system In the figure, the nominal gear shaping cutter is at the actual contact point The position vector and normal vector of and Represents the nominal gear shaping cutter at the actual contact point The position vector and normal vector at ; The coordinate transformation equation representing the nominal gear shaping cutter's dynamic coordinate system to its static coordinate system; Indicates the rotation angle during the coordinate change process, which is an auxiliary angle; In the nominal gear shaping cutter coordinate system Actual contact points The contact angle is: in: The actual contact point of the dressing wheel The contact angle at The actual contact point The normal vector on the nominal gear shaping cutter is y Directional component; When using a round head dressing wheel to profile the nominal gear shaping cutter tooth profile, the dressing point on the dressing wheel is converted to the nominal gear shaping cutter coordinate system. In the figure, the tooth surface of the worm grinding wheel is obtained by using the relative motion relationship between the nominal gear shaping cutter and the worm grinding wheel: in: Indicates the dressing wheel in the coordinate system The silhouette in Indicates the tooth surface of the worm grinding wheel based on the round head dressing wheel; Represents the transformation matrix from the dressing wheel coordinate system to the nominal gear shaping cutter dynamic coordinate system; Represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the worm grinding wheel; Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; Indicates trimming of the contour.

3. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, wherein: In the step 3, from the dressing wheel coordinate system To the grinding wheel coordinate system The theoretical homogeneous transformation matrix is: in: Indicates the coordinate system from the dressing wheel To the grinding wheel coordinate system Theoretical homogeneous transformation matrix of; Represents the transformation matrix from the static coordinate system to the dynamic coordinate system of the worm grinding wheel; Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; The coordinate transformation equation representing the nominal gear shaping cutter's dynamic coordinate system to its static coordinate system; Represents the transformation matrix from the dressing wheel coordinate system to the nominal gear shaping cutter dynamic coordinate system; is the grinding wheel angle, and: ; Considering the actual structure of the machine tool, the actual coordinate transformation matrix from the dressing wheel to the worm grinding wheel is: in: Represents the actual coordinate transformation matrix from the dressing wheel to the worm grinding wheel; express B Transformation matrix from the axis static coordinate system to the moving coordinate system; express Y Axis to B Transformation matrix of the axis-static coordinate system; express A Axis to Y The transformation matrix of the axis; express Z Axis to A The transformation matrix of the axis; express X Axis to Z The transformation matrix of the axis; express Bed arrive X The transformation matrix of the axis; express B 2-axis to bed transformation matrix; express The amount of movement of the axis; By making the theoretical homogeneous transformation matrix from the dressing wheel to the worm grinding wheel equal to the actual coordinate transformation matrix, the linkage relationship of the machine tool motion axis in the dressing process is obtained: in: and Indicates the top point of the dressing wheel Position vector exist x and y Directional component.

4. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 3, characterized in that: The tooth surface after worm grinding wheel point dressing using a round head dressing wheel and considering the machine tool structure is obtained: in: Indicates machine tools B 2 axis to B The transformation matrix of the axis; Indicates trimming of the contour.

5. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, wherein: In step 4, the grinding wheel is adjusted to the path The trimming point on , so that the trimming point and Relative to the trim point The residual heights are and , the distances between two adjacent trimming points are and , then the nominal gear shaping cutter tooth surface for: in: and The contact points on the nominal gear shaping cutter tooth surface are The position vector of x -Axis and y - axis components; and The contact points on the nominal gear shaping cutter tooth surface are The position vector of x -Axis and y - axis components; According to the different curvatures in the nominal gear shaping cutter tooth height direction, a series of trimming residual heights are obtained; the maximum value of the trimming residual heights is selected as the final value, and the value is guaranteed to meet the requirements. Then the residual height between any adjacent trimming points satisfies: in: is the maximum value of the trimmed residual height; Taking the nominal gear shaping cutter tooth top as the first dressing point, the position vectors and normal vectors of all contact points on the nominal gear shaping cutter tooth surface are calculated in sequence; then the uniformized worm grinding wheel tooth profile dressing points and the uniformized worm grinding wheel tooth profile dressing path are obtained.

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