Drum-shaped worm grinding wheel few-axis-point dressing method

Abstract

The invention discloses a few-axis-point dressing method for a drum-shaped worm grinding wheel. The dressing precision of a face gear worm grinding wheel is improved by avoiding the requirement of the grinding wheel for a tilting axis of a machine tool. The nominal slotting cutter is perpendicular to the axis of the grinding wheel, and the end face profile of the nominal slotting cutter is consistent with the section profile of a grinding wheel shaft, so that the requirement of a dressing wheel on a machine tool deflection shaft is avoided, the number of machine tool movement shafts participating in linkage in the grinding wheel dressing process is reduced, and the grinding wheel dressing precision is further improved; according to the method, only three machine tool shafts are used for finishing the worm grinding wheel of the opposite gear in a linkage mode, a grinding wheel rotating shaft, a radial moving shaft and an axial moving shaft are included, and a finishing path uniformizing method is provided so that precise and efficient finishing machining of the worm grinding wheel profile can be guaranteed. According to the method, the defects of high cost, poor flexibility and existence of principle errors of the formed dressing wheel can be avoided, and a theoretical foundation is laid for reverse adjustment of the tooth grinding error of the face gear or generating grinding of the tooth surface of the complex modified face gear.

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 easy flow distribution. The worm grinding wheel is continuously indexed when grinding face gears, with high grinding efficiency and high gear pitch accuracy. The accuracy of the grinding profile directly affects the grinding accuracy of the gear, and the grinding wheel will wear during the grinding process, so it must be precisely dressed regularly. 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, which makes the precision dressing of the face gear worm grinding wheel very difficult.

[0003] The profile of the forming dressing wheel is consistent with the virtual gear 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 of face gear worm grinding wheels. However, the complex profile of the forming dressing wheel leads to high production costs and difficult to ensure profile accuracy, and it is only used for the dressing 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 cutter on the basis of deflecting its lead angle, and rotate around its own axis at the same time, resulting in the rotation axis of the grinding wheel being not orthogonal to the tilting axis, 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 errors.

[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 the worm wheel dressing process. 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 tool holder suspended on the tilt axis is heavy 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 the accuracy is difficult to guarantee. During the dressing process of the face gear worm 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 complicated. The motion error of the coupled machine tool axis is difficult to identify and compensate, and it is very difficult to accurately dress the tooth surface of the worm wheel.

[0007] (4) It is difficult to dress non-involute worm grinding wheels. If the worm grinding wheel profile is not involute, it will be very difficult to correctly dress the grinding wheel tooth profile. The cost of the formed dressing wheel is relatively high and its profile is only applicable to a certain set of fixed parameters of the worm grinding wheel; the double-cone dressing wheel can be used for worm grinding wheels with multiple sets of parameters and involute profiles, 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 wheel and its dressing method will not be able to be used for the precision development 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 the generation grinding of the complex modified gear tooth surface.

[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 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 of the worm wheel tooth profile based on the nominal gear shaping cutter

[0014] The profile equation of the round-head dressing wheel is established, and the dressing wheel is used to profile the nominal gear shaping cutter tooth profile. 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 conditions at the dressing point, based on the relative position relationship between the dressing wheel and the nominal gear shaping cutter, the theoretical point dressing tooth surface of the drum-shaped worm grinding wheel is solved.

[0015] Step 3: Solving 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 tooth surface of the worm grinding wheel, and the homogeneous transformation matrix of the theoretical dressing is equal to the actual dressing matrix considering the machine tool structure, and the linkage relationship of the machine tool motion axis in the process of the drum worm grinding wheel point dressing is obtained;

[0017] Step 4: Evenly distribute the worm wheel points

[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 that can meet the requirements of the residual height 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 another value range of the grinding wheel tooth profile; all the dressing points are transformed through coordinates to obtain a grinding wheel point dressing path with equal step length.

[0019] Further, in the step 1, the tooth profile of the nominal gear shaping cutter is the same as the profile of the theoretical gear shaping cutter 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 wheel;

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

[0023]

[0024] in: Indicates the grinding wheel tooth surface; 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 assumed to be point P0, and 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 They represent the position vector and normal vector of the nominal gear shaping cutter at the theoretical trimming point P0 respectively; 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 They are respectively 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 dynamic coordinate system to its static coordinate system; Indicates the rotation angle during the coordinate change process, which is the 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 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 S a0In the figure, the tooth surface of the worm grinding wheel obtained by using the relative motion relationship between the nominal gear shaping cutter and the worm grinding wheel is:

[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 wheel; w0a0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; Indicates trimming contour shape.

[0037] Further, 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 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 dynamic coordinate system to its static coordinate system; The transformation matrix representing 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 static coordinate system to the dynamic coordinate system of the B axis; 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] Let the theoretical homogeneous transformation matrix from the dressing wheel to the worm wheel be equal to the actual coordinate transformation matrix, and obtain the linkage relationship of the machine tool motion axis during the dressing process:

[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 shape.

[0049] Further, 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] The nominal gear shaping cutter tooth top is taken as the first dressing point, and 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 are obtained, and the uniformized worm grinding wheel tooth profile dressing path is 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 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, so as to reduce the number of machine tool motion axes involved in the linkage during the grinding wheel dressing process and further improve the grinding wheel dressing accuracy; the method of the present invention only uses 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 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 error reversal of face gear grinding or the generation grinding of complex modified face gear tooth surface. The method of the present invention can be applied to all precision dressing technologies of non-standard profile worm grinding wheels due to tooth surface error reversal or complex tooth surface modification, and can be used for precision grinding of face gears, complex modified external / internal cylindrical gears, etc., and has the characteristics of low cost, good flexibility and simple adjustment. The method of the present invention can be realized by a five-axis, four-axis or three-axis linkage CNC machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, 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 It is the profile diagram of the tooth surface of the nominal gear shaping cutter 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 round head dressing wheel to the worm grinding wheel;

[0065] Figure 6 This is a 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 tooth surface of the worm grinding wheel. DETAILED DESCRIPTION

[0067] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but 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 which is 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 cutter end plane is as follows: Figure 2 The existence of the worm 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 profile on the gear shaping cutter end plane not coinciding.

[0072] In order to avoid the difficulties caused by the angle λ during the dressing process of the worm wheel, a nominal gear shaping cutter (auxiliary component) is provided, and 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 angle between the worm wheel axis section Γ and the gear cutter end plane is λ, and the two have the same profile on the 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 S is the worm wheel coordinate system w The static coordinate system, S a0 Is the nominal gear cutter S a The static coordinate system. and are the rotation angles of the worm wheel and the nominal gear 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 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 of the worm wheel tooth profile based on the nominal gear shaping cutter

[0080] The profile equation of the round-head dressing wheel is established, and the dressing wheel is used to profile the nominal gear shaping cutter tooth profile. 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 conditions 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 solved.

[0081] When a round-end dressing wheel is used to dress a worm wheel, the contact area between the worm wheel tooth surface and the dressing wheel tooth surface is a point on the grinding wheel axis plane Γ, which is called the dressing point. The presence of the nominal gear shaping cutter avoids the need for the grinding wheel or the dressing wheel to be tilted at an angle λ. All dressing points in the entire dressing process are located on plane Γ because the centers of the dressing wheel, nominal gear shaping cutter and worm wheel are located on the same plane.

[0082] The worm wheel dressing process is equivalent to the process of dressing the grinding wheel tooth profile on plane Γ with a dressing wheel. Since the profile of the worm 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 for profile fitting with the dressing wheel and then converted to the worm wheel tooth surface.

[0083] When the worm wheel stays in 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 They represent the position vector and normal vector of the nominal gear shaping cutter at the theoretical trimming point P0 respectively; and They respectively represent the position vector and normal vector of the dressing wheel at the theoretical dressing point P0.

[0087] Theoretical point dressing process 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 Respectively represent the initial and actual positions of the dressing wheel, 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 rotation angle of the nominal gear shaping cutter 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 cutter in the x and y directions are L x1 and L y1 .

[0088] The relative motion relationship between the dressing wheel, nominal gear cutter and worm grinding wheel is as follows: Figure 4 The coordinate system S w Fixed on the worm wheel, S w0 is its static coordinate system. The actual tooth surface of the nominal gear shaping cutter should be transformed to 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 They are respectively 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 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 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 S a0 In the Figure 4 In the figure, the tooth surface of the worm grinding wheel obtained by using the relative motion relationship between the nominal gear shaping cutter and the worm grinding wheel is:

[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 wheel; w0a0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; Indicates trimming contour shape.

[0097] The worm 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: Solving 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, and the homogeneous transformation matrix of the theoretical dressing is equal to the actual dressing considering the machine tool structure, and the linkage relationship of the machine tool motion axis in the drum worm grinding wheel point dressing process is obtained.

[0100] In the actual processing of the worm wheel tooth surface, it is necessary to consider the machine tool structure to determine the machine tool motion axis linkage relationship in the grinding wheel dressing process. Combining the theoretical and actual transformation matrix between the worm wheel and the round head dressing wheel, the motion axis linkage relationship can be obtained. The application of the auxiliary nominal gear shaping cutter avoids 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] Because there is no need to tilt the dressing wheel or tilt the worm grinding wheel, the grinding wheel can be dressed on the left side or below the dressing wheel according to the machine tool structure. In the present embodiment, the worm grinding wheel is located on the left side of the dressing wheel, making the processing safer and more flexible.

[0102] The force coordinate changes from the round head 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 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 dynamic coordinate system to its static coordinate system; ad The transformation matrix representing 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 the worm wheel on the machine tool, the machine tool motion chain is B2-axis (dressing wheel)-bed-X-axis-Z-axis-A-axis-Y-axis-B-axis (worm wheel). In the traditional worm wheel dressing method, due to the limitation of the machine tool tool holder, the grinding wheel must be located directly below the dressing wheel. Due to the introduction of the nominal gear shaping cutter, during the grinding wheel dressing process, the machine tool motion axis does not need to tilt the lead angle λ of the grinding wheel.

[0106] Therefore, according to the difference of machine tool structure, the grinding wheel can be dressed on the left side or below 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 dressed at any required height.

[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 wheel tooth profile, the theoretical homogeneous transformation matrix from the dressing wheel to the worm wheel is made equal to the actual coordinate transformation matrix, that is, The linkage relationship of the machine tool motion axis during the finishing process is obtained:

[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 the worm grinding wheel point dressing 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 shape.

[0116] Step 4: Evenly distribute the worm wheel points

[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 satisfies 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 another value range of the grinding wheel tooth surface; all dressing points are transformed through coordinates to obtain a 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 the adjacent contact points on the dressing wheel and the nominal gear cutter tooth surface is variable, and the distribution of the contact points from the nominal gear cutter tooth top to the tooth root is very sparse to very dense. At the same time, the extremely uneven distribution of the contact points on the nominal gear cutter will lead to an uneven distribution of the dressing points of the dressing wheel on the worm grinding profile, resulting in an extremely uneven distribution of the actual dressing path of the grinding wheel, affecting the dressing accuracy of the grinding profile. Since residues will appear between two adjacent dressing paths when the round head dressing wheel is used to dress the grinding wheel tooth surface, it is very necessary to even out the dressing points on the worm grinding wheel tooth surface.

[0119] like Figure 6 As shown in Figure 1, there is a residue between 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 cross section of the grinding wheel is a constant.

[0120] In the worm wheel axis section Γ, the worm wheel has the same profile as the nominal gear shaping cutter, and the worm wheel tooth profile dressing point homogenization process can be equivalent to the homogenization of the nominal gear shaping cutter tooth profile and the contact point of the dressing wheel. 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 is variable, the residual heights between trimming paths are not equal. 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 height 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:

[0124] t pi―1 =t pi =t p

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

[0126] The nominal gear shaping cutter tooth top is taken as the first dressing point, and 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 are obtained, and the uniformized worm grinding wheel tooth profile dressing path is 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 combines the uniform dressing path with the linkage relationship of the machine tool motion axis to obtain the worm grinding wheel tooth surface point dressing cutting simulation result as shown in the figure. Figure 7As shown. The cross section of the working part of the dressing wheel is circular, which corresponds to the cutter marks on the tooth surface after the worm grinding wheel dressing simulation. The cutter marks are evenly distributed on the tooth surface of the worm grinding wheel, which is consistent with the pre-designed equidistant distribution method. From the simulation results, it can be seen that the worm grinding wheel minor axis point dressing method and the dressing path homogenization method proposed in this embodiment are correct.

[0128] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope 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 of the worm wheel tooth profile based on the nominal gear shaping cutter The profile equation of the round-head dressing wheel is established, and the dressing wheel is used to profile the nominal gear shaping cutter tooth profile. 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 conditions at the dressing point, based on the relative position relationship between the dressing wheel and the nominal gear shaping cutter, the theoretical point dressing tooth surface of the drum-shaped worm grinding wheel is solved. Step 3: Solving 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 tooth surface of the worm grinding wheel, and the homogeneous transformation matrix of the theoretical dressing is equal to the actual dressing matrix considering the machine tool structure, and the linkage relationship of the machine tool motion axis in the process of the drum worm grinding wheel point dressing is obtained; Step 4: Evenly distribute the worm wheel point dressing path 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 that can meet the requirements of the residual height 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 another value range of the grinding wheel tooth profile; all the dressing points are transformed through coordinates to obtain a grinding wheel point dressing path with equal step length.

2. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, characterized in that: 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: 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 wheel; The tooth surface of the worm wheel is obtained by coordinate transformation from the nominal gear shaping cutter profile; in: Indicates the grinding wheel tooth surface; 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.

3. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, characterized in that: In step 2, the theoretical contact point between the dressing wheel and the nominal gear shaping cutter is assumed to be point P0, and the correct contact condition between the dressing wheel and the nominal gear shaping cutter at the theoretical dressing point P0 is: in: and They represent the position vector and normal vector of the nominal gear shaping cutter at the theoretical trimming point P0 respectively; and Respectively represent the position vector and normal vector of the dressing wheel at the theoretical dressing point P0; 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: in: and They are respectively 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 dynamic coordinate system to its static coordinate system; Indicates the rotation angle during the coordinate change process, which is the auxiliary angle; Then in the nominal gear shaping cutter coordinate system S a0 In the figure, the contact angle of the actual contact point P1 is: 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; 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 S a0 In the figure, the tooth surface of the worm grinding wheel obtained by using the relative motion relationship between the nominal gear shaping cutter and the worm grinding wheel is: 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 wheel; w0a0 Represents the transformation matrix between the nominal gear shaping cutter and the static coordinate system of the worm grinding wheel; Indicates trimming contour shape.

4. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, characterized in that: 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: 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 wheel; w0a0 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 dynamic coordinate system to its static coordinate system; The transformation matrix representing 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: M BB2 (D B ,D X ,D Y ,D Z )=M BB0 (D B )M B0Y (D Y )M YA M AZ (D Z )D ZX (D X )M Xbase M baseB2 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 AX (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 Xbase2 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; Let the theoretical homogeneous transformation matrix from the dressing wheel to the worm wheel be equal to the actual coordinate transformation matrix, and obtain the linkage relationship of the machine tool motion axis during the dressing process: in: and Represents the position vector of point P0 on the dressing wheel Components in the x and y directions.

5. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 4, characterized in that: The tooth surface after worm grinding wheel point dressing using round head dressing wheel and considering the machine tool structure is obtained: in: Represents the transformation matrix from the machine tool B2 axis to the B axis; r d (ρ(u r )) indicates trimming the contour shape.

6. The method for dressing the minor axis point of a drum worm grinding wheel according to claim 1, characterized in that: 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 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: 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; 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: t pi―1 =t pi =t p Where: t p is the maximum value of the trimmed residual height; The nominal gear shaping cutter tooth top is taken as the first dressing point, and 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 are obtained, and the uniformized worm grinding wheel tooth profile dressing path is obtained.

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