A form grinding method for simultaneously grinding multiple tooth grooves of internal gears

Abstract

The present invention belongs to the field of involute gear processing, and specifically relates to a forming gear grinding method for simultaneously grinding multiple tooth grooves of an internal gear. The grinding wheel for grinding the internal gear is a combined grinding wheel including a fine grinding wheel and a rough grinding wheel. The internal gear forming grinding wheel gear grinding machine includes five numerical control axes, namely, machine tool linear axes X, Y, and Z, a grinding wheel swing axis B, and a workpiece rotation axis C. When the grinding wheel is used on the internal gear forming grinding wheel gear grinding machine to form-grind the tooth surface of the internal gear, the grinding wheel simultaneously performs rough grinding and fine grinding of different tooth grooves. The present invention respectively adopts different rough grinding allowances and fine grinding allowances to calculate the contour shape of the corresponding grinding wheel, and then uses a grinding wheel dressing tool on the internal gear forming grinding wheel gear grinding machine to simultaneously dress the tooth profiles of the rough grinding wheel teeth and the fine grinding wheel teeth, and then grinds the tooth surface of the internal gear, thereby achieving the purpose of simultaneously performing the rough grinding and fine grinding processes of the internal gear forming grinding, and improving the grinding efficiency and grinding accuracy of the internal gear.

Description

Technical Field

[0001] The invention belongs to the technical field of involute gear processing, and in particular relates to a profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear. Background Art

[0002] Form grinding of internal gears is a precision gear machining method widely used in mechanical manufacturing, particularly for high-precision grinding of hardened internal gears. The process of form grinding of internal gears typically involves coarse grinding of the tooth grooves using a form grinding wheel. After all tooth grooves are rough-ground, the form grinding wheel is dressed with a grinding wheel dressing tool. Finally, the internal gear is fine-ground, tooth by tooth groove, to achieve the final geometric accuracy and surface quality. Depending on the grinding process, the grinding wheel materials and grit sizes used for coarse and fine grinding should be different. Using the same grinding wheel for coarse grinding, followed by dressing and fine grinding, results in a poor tooth surface finish and difficulty controlling tooth surface waviness. Using different form grinding wheels for coarse and fine grinding can lead to errors caused by wheel replacement, reducing internal gear grinding efficiency and accuracy. Therefore, a form grinding method is needed that allows for continuous coarse and fine grinding of internal gear tooth grooves. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a form grinding method for simultaneously grinding multiple tooth grooves of an internal gear, aiming to solve the problems of low grinding efficiency, low grinding accuracy and low tooth surface quality caused by separate steps of rough grinding and fine grinding of tooth grooves during form grinding of internal gears.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear, wherein the grinding wheel for grinding the internal gear is a combined grinding wheel including a fine grinding wheel and a rough grinding wheel; the internal gear profile grinding wheel grinding machine includes five numerically controlled axes, namely, machine tool linear axes X, Y, and Z, a grinding wheel swing axis B, and a workpiece rotation axis C; when the combined grinding wheel is used on the internal gear profile grinding machine to perform profile grinding on the tooth surface of the internal gear, the combined grinding wheel simultaneously performs rough grinding and fine grinding of different tooth grooves, comprising the following steps:

[0006] Step 1: Establish the tooth surface equation and three-dimensional model of the first tooth groove of the internal gear;

[0007] According to the rotation direction of the internal gear during the grinding process, the installation position of the fine grinding wheel and the rough grinding wheel is determined; according to the geometric parameters of the internal gear and the outer diameter of the grinding wheel, the internal gear coordinate system is established. S 0( O 0: x 0, y 0, z 0) Grinding wheel coordinate system S1 ( O 1: x 1, y 1, z 1) and the rough grinding wheel coordinate system S 2 ( O 2: x 2, y 2, z 2); x 0. x 1. x The 2 coordinate axes have the same direction, x 0. x 1. The axis direction of the coordinate axis points to the first tooth groove of the internal gear, which is the tooth depth feed direction during grinding; y 1 and y 2 coordinate axes have the same direction; the z0 coordinate axis is y 1 axis and y The angle between the two coordinate axes is the internal gear helix angle; the internal gear coordinate system S Origin 0 O 0 is at the center of the inner gear and the coordinate system of the grinding wheel S 1's coordinate origin O 1 is the center distance a ; In the internal gear coordinate system S 1, establish the final tooth surface equation of the first tooth groove of the internal gear R 1 and tooth surface 3D model D 1; the tooth groove adjacent to the first tooth groove of the internal gear is the second tooth groove;

[0008] Step 2: The first tooth groove is ground by the fine grinding wheel, and the second tooth groove is ground by the rough grinding wheel as the starting state of grinding; according to the total grinding amount of the internal gear, the grinding amount of the tooth surface fine grinding is determined. d 1 and coarse grinding amount d 2;

[0009] Step 3: Fine grinding the tooth surface d 1 and the final 3D model of the internal gear tooth surface D 1. Superimpose and establish the tooth surface equation of the second tooth groove of the internal gear corresponding to the rough grinding wheel R 2 and the corresponding three-dimensional model of the tooth surface D 2;

[0010] Step 4: According to the tooth surface equation R 1. R 2 and the installation position of the corresponding fine grinding wheel and rough grinding wheel, respectively solve the contact line between the tooth surface at the first tooth groove and the tooth surface at the second tooth groove and the combined grinding wheel L 1 and L 2 coordinate point;

[0011] Step 5: Use coordinate transformation to transform the contact line L 1 and L 2 coordinate points are converted to the grinding wheel coordinate system S 1 and rough grinding wheel coordinate system S In step 2, the axial cross-sectional profiles of the rough grinding wheel and the fine grinding wheel are obtained, and the profiles of the rough grinding wheel and the fine grinding wheel are smoothly connected to form a complete combined grinding profile;

[0012] Step 6: According to the axial cross-section profile coordinates of the rough grinding wheel and the fine grinding wheel, calculate the motion trajectory of the dressing roller, and simultaneously dress the profiles of the rough grinding wheel and the fine grinding wheel on the internal gear forming grinding wheel grinding machine. Then, use the dressed combined grinding wheel to grind the tooth surface of the internal gear; first adjust the relative position of the fine grinding wheel and the first tooth groove of the internal gear, starting from the initial contact position of the fine grinding wheel and the rough grinding wheel with the tooth surface of the internal gear, according to the total grinding allowance, along the internal gear x 0 In the direction of the coordinate axis, feed multiple times and gradually feed to the final grinding position of the internal gear. Then keep the feed position of the combined grinding wheel unchanged and grind the tooth surfaces corresponding to the remaining tooth grooves of the internal gear according to the motion relationship of the formed grinding until the grinding of all the tooth surfaces of the internal gear is completed.

[0013] Furthermore, in step 1, the fine grinding wheel and the rough grinding wheel are coaxially installed along the grinding wheel axis direction, and the internal gear coordinate system S 0 coordinate origin O 0 and the grinding wheel coordinate system S 1 origin O 1 Center distance in the direction of the internal gear axis x0 a for r 0- r 1, r 0 is the pitch radius of the internal gear, r 1 is the pitch radius of the fine grinding wheel;

[0014] The rotation direction of the internal gear is viewed from the positive direction of the z0 axis of the internal gear to the negative direction. When the internal gear rotates clockwise, the rough grinding wheel is installed along the negative direction of the z1 axis. If the internal gear rotates counterclockwise, the rough grinding wheel is installed along the positive direction of the z1 axis.

[0015] Furthermore, in step 2, the installation distance between the fine grinding wheel and the rough grinding wheel on the central axis is determined according to the relative position of the first tooth groove and the second tooth groove and the rotation direction of the internal gear during the grinding process. d；

[0016] (1);

[0017] In formula (1),β is the helix angle of the internal gear, r 0 is the pitch radius of the internal gear, z is the number of teeth on the internal gear.

[0018] Furthermore, in step 1, the final tooth surface equation of the first tooth groove is R The expression for 1 is:

[0019] (2);

[0020] In formula (2), the “+” in the “±” sign corresponds to the end face involute of the left tooth surface of the first tooth space, and the “-” in the “±” sign corresponds to the end face involute of the right tooth surface of the first tooth space. r b is the base circle radius of the internal gear; m is the involute angle; s 0 is the tooth half angle; matrix M g Expressed as,

[0021] (3);

[0022] In formula (3), the matrix M g The “+” and “ "-" in the symbol corresponds to the tooth surface of the right-hand internal gear; the matrix M g The “-” in the “±” and the “+” in the “∓” symbol correspond to the tooth surface of the left-handed internal gear; P 1 is the internal gear helical parameter, i is the rotation angle.

[0023] Furthermore, in step 3, the tooth surface equation at the second tooth groove is R The expression for 2 is:

[0024] (4);

[0025] In formula (4), r 0 is the pitch radius of the internal gear, r b is the base circle radius of the internal gear, z is the number of teeth on the internal gear, M g is a matrix M g .

[0026] Furthermore, in step 4, the contact line L 1 and L The calculated distribution of 2 satisfies the tooth surface contact condition:

[0027] (5);

[0028] In formula (5), x, y, z ) is based on the tooth surface equation of the first tooth space of the internal gear R 1 or tooth surface equation at the second tooth groove R 2 The coordinates of the tooth contact point obtained, ( n x ，n y ，n z ) are the three components of the tooth surface normal vector at the contact point of the internal gear tooth surface, P 1 is the internal gear spiral parameter, Σ is the angle between the grinding wheel axis and the internal gear axis, z is the number of teeth on the internal gear; a = r 0- r 1, r 0 is the pitch radius of the internal gear, r 1 is the pitch radius of the fine grinding wheel.

[0029] Furthermore, in step 5, the internal gear coordinate system S 0 To the grinding wheel coordinate system S The transformation matrix of 1 is:

[0030] (6);

[0031] From the internal gear coordinate system S 0 to the coarse grinding wheel coordinate system S The transformation matrix of 2 is:

[0032] (7);

[0033] In the above formula, Σ is the angle between the grinding wheel axis and the internal gear axis, z is the number of teeth on the internal gear, β is the helix angle of the internal gear; a = r 0- r 1, r 0 is the pitch radius of the internal gear, r 1 is the pitch radius of the fine grinding wheel.

[0034] Furthermore, after obtaining the complete combined sand profile in step 5, coordinate transformation is performed, and the tooth surface contact line obtained by step 4 is calculated. L 1 and L 2 coordinates are converted to the grinding wheel coordinate system S1 and rough grinding wheel coordinate system S 2, obtain the coordinates of the axial cross-section profiles of the fine grinding wheel and the rough grinding wheel; L 1 and L 2 Converted to the corresponding coordinate system, the axis section coordinates of the combined grinding wheel are:

[0035] (8);

[0036] In formula (8), ( X j , Y j , Z j ) is the coordinate value of the point on the contact line obtained by solution, R j It is the turning radius formed by the point on the contact line along the axis of the grinding wheel.

[0037] Furthermore, the combined grinding wheel includes one or more rough grinding gears and fine grinding gears; according to processing requirements, the grinding wheel materials of the rough grinding wheel and the fine grinding wheel are the same or different, and the grinding wheel grit sizes of the rough grinding wheel and the fine grinding wheel are different.

[0038] On the basis of the present invention, according to the total grinding amount of the internal gear and the size of the internal gear radius, three or more tooth grooves can also be ground at the same time, and the grinding process can also be divided into different processes such as rough grinding, semi-finishing and fine grinding. For example, the combined grinding wheel includes a first grinding wheel, a second grinding wheel and a third grinding wheel arranged side by side, which are respectively used for rough grinding, semi-finishing and fine grinding. Then, the first tooth groove can be fine-ground, the second tooth groove can be semi-finished, and the third tooth groove can be rough-ground at the same time, that is, the grinding of three tooth grooves can be carried out at the same time. If it is a combination of rough grinding + fine grinding + rough grinding + fine grinding, the grinding of four tooth grooves can be achieved at the same time, but when grinding, the fine grinding wheel at the back needs to skip the tooth grooves that have been finely ground. Similarly, by matching different combinations of grinding wheels, more tooth grooves can be ground simultaneously, but the fine grinding wheel at the back needs to skip the tooth grooves that have been finely ground.

[0039] It should be noted that this method can be applied to the simultaneous grinding of multiple tooth grooves on internal gears as well as the profile grinding of multiple tooth grooves on external gears. a Adjust to r 0+ r 1, r 0 is adjusted to the outer gear pitch radius, r 1 Adjust to the pitch radius of the fine grinding wheel, gear parameters P 1 is adjusted to the external gear spiral parameter, β Adjust to the external gear helix angle, and the other parameter meanings and formulas remain unchanged.

[0040] The working principle of the present invention is to use different rough grinding allowances and fine grinding allowances respectively, calculate the corresponding combined grinding wheel profile, and then use the grinding wheel dressing tool on the internal gear forming grinding wheel grinding machine to simultaneously dress the tooth profiles of the rough grinding wheel teeth and the fine grinding wheel teeth, and then grind the internal gear tooth surface, so as to achieve the purpose of simultaneous rough grinding and fine grinding of the internal gear forming grinding, thereby improving the grinding efficiency and grinding accuracy of the internal gear. The present invention is suitable for internal gears that are involute internal helical gears or involute internal spur gears, and when the helix angle is β When it is zero, it is an internal spur gear.

[0041] The beneficial effects of the present invention are:

[0042] (1) The present invention utilizes a combination of a rough grinding wheel and a fine grinding wheel to simultaneously perform rough grinding and fine grinding on multiple tooth grooves of an internal gear. Compared with the step-by-step grinding of conventional profile grinding, there is no need to replace the grinding wheel, and the grinding efficiency is higher.

[0043] (2) The present invention solves the corresponding grinding profile according to the grinding amount of rough grinding and fine grinding, and then grinds the tooth surface of the internal gear with the trimmed grinding wheel, so that the grinding accuracy of the tooth groove tooth surface is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings and the accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. Among them:

[0045] Figure 1 Schematic diagram of the working state of the workpiece and the combined grinding wheel according to an embodiment of the present invention.

[0046] Figure 2 Schematic diagram of the installation position of the combined grinding wheel and the grinding wheel shaft interface profile of an embodiment of the present invention.

[0047] Figure 3 This is a schematic structural diagram of a five-axis CNC internal gear forming grinding wheel grinding machine according to an embodiment of the present invention.

[0048] In the figure: first turntable 101, internal gear 102, second guide rail 103, second slide 104, first guide rail 105, first slide 106, third guide rail 107, third slide 108, second turntable 109, fine grinding wheel 110, rough grinding wheel 111, grinding wheel shaft 112, first tooth groove 200, second tooth groove 201, third tooth groove 202, shaft cross-section profile 300. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field fall within the scope of protection of the present invention.

[0050] The implementation process of the present invention is described in detail below in conjunction with the internal gear parameters and processing parameters in Table 1. In this embodiment, the internal gear is an involute internal helical gear.

[0051] Table 1 Gear parameters and processing parameters

[0052]

[0053] Based on the above parameters, calculate the remaining parameters of the internal gear:

[0054] Internal gear tooth half angle s 0=0.0393rad;

[0055] Internal gear pitch circle radius r 0=85.134mm;

[0056] Internal gear base circle radius r 0=79.387mm;

[0057] The angle between the internal gear and the combined grinding wheel S =1.2217rad(70°);

[0058] Internal gear helical parameters P 1=233.904mm;

[0059] The internal gear forming grinding wheel gear grinder used includes five CNC motions: the first slide 106 moves along the X direction of the first guide rail 105, the second slide 104 moves along the Y direction of the second guide rail 103, the third slide 108 moves along the Z direction of the third guide rail 107, the first turntable 101 drives the workpiece to rotate around the C axis, and the second turntable 109 drives the grinding wheel to rotate around the B axis. The five CNC motions are controlled by the internal gear forming grinding wheel gear grinder servo motor and CNC system. In addition, the internal gear forming grinding wheel gear grinder is also equipped with a high-speed motor to drive the grinding wheel shaft 112 to produce high-speed rotation, driving the combined grinding wheel to produce grinding motion. The internal gear forming grinding wheel gear grinder is also equipped with a grinding wheel dressing mechanism for dressing the axial cross-sectional profile of the combined grinding wheel.

[0060] A profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear, wherein the grinding wheel for grinding the internal gear 102 is a combined grinding wheel comprising a fine grinding wheel 110 and a rough grinding wheel 111; when the combined grinding wheel is used on an internal gear profile grinding machine to profile grind the tooth surface of the internal gear 102, the combined grinding wheel simultaneously performs rough grinding and fine grinding of different tooth grooves, comprising the following steps:

[0061] Step 1: Establish the tooth surface equation and three-dimensional model of the first tooth groove of the internal gear;

[0062] like Figure 1 to Figure 3 As shown, according to the rotation direction of the internal gear 102 during the grinding process, the installation positions of the fine grinding wheel 110 and the rough grinding wheel 111 are determined; according to the geometric parameters of the internal gear 102 and the outer diameter of the combined grinding wheel, the internal gear coordinate system is established. S 0( O 0: x 0, y 0, z 0) Grinding wheel coordinate system S 1 ( O 1: x 1, y 1, z 1) and the rough grinding wheel coordinate system S 2 ( O 2: x 2, y 2, z 2); x 0. x 1. x The 2 coordinate axes have the same direction, x 0. x The axial direction of the 1st coordinate axis points to the first tooth groove 200 of the internal gear, which is the tooth depth feed direction during grinding; y 1 and y 2 coordinate axes have the same direction; the z0 coordinate axis is y 1 axis and y The angle between the two coordinate axes is the internal gear helix angle; the internal gear coordinate system S Origin 0 O 0 is at the center of the inner gear and the coordinate system of the grinding wheel S 1's coordinate origin O 1 The distance between the centers is a ; In the internal gear coordinate system S 1, the final tooth surface equation of the first tooth groove 200 of the internal gear is established R 1 and tooth surface 3D model D 1; The tooth groove adjacent to the first tooth groove 200 of the internal gear is the second tooth groove 201, and the tooth groove adjacent to the second tooth groove 201 is the third tooth groove 202, and so on;

[0063] ,

[0064] The upper half “+” of the “±” symbol in the expression represents the end face involute of the left tooth surface at the first tooth groove 200, and the lower half “-” represents the end face involute of the right tooth surface; r b is the base circle radius of the internal gear; m is the involute angle; s 0 is the tooth half angle; matrix M g Expressed as:

[0065]

[0066] M g In the expression P 1 is the internal gear helical parameter, i is the rotation angle.

[0067] Step 2: Grind the first tooth groove 200 with the fine grinding wheel 110 and the second tooth groove 201 with the rough grinding wheel 111 in the initial grinding state; determine the grinding amount of the tooth surface fine grinding according to the total grinding amount of the internal gear 102 d 1 and coarse grinding amount d 2. According to the relative position of the first tooth groove 200 and the second tooth groove 201 and the rotation direction of the internal gear 102 during the tooth grinding process, determine the installation distance of the fine grinding wheel 110 and the rough grinding wheel 111 on the central axis d；

[0068] ;

[0069] In the formula z is the number of teeth on the internal gear, β is the helix angle of the internal helical gear, r 0 is the pitch circle radius of the internal helical gear.

[0070] Step 3: Fine grinding the tooth surface d 1 and the final 3D model of the internal gear tooth surface D 1 is superimposed to establish the tooth surface equation of the second tooth groove 201 of the internal gear corresponding to the rough grinding wheel 111 R 2 and the corresponding three-dimensional model of the tooth surface D 2;

[0071] .

[0072] Step 4: According to the tooth surface equation R 1. R2 and the installation position of the corresponding fine grinding wheel 110 and the rough grinding wheel 111, respectively calculate the contact conditions between the tooth surface and the combined grinding wheel to obtain the corresponding contact line L 1 and L 2 coordinate point; the contact line between the tool and the helical surface of the workpiece should satisfy the common normal vector at the contact point between the tool rotation surface and the helical surface. n , and the relative motion velocity at this point should be perpendicular to the common normal, so the contact condition is:

[0073]

[0074] In the above formula, v 12 is the relative velocity at the contact point; n is the common normal vector at the contact point;

[0075] The contact condition equation between the combined grinding wheel and the tooth surface is:

[0076]

[0077] In the above formula x , y , z is the coordinate value of the contact point on the tooth surface equation; n x , n y , n z is the common normal vector n The coordinate components of .

[0078] Step 5: Use coordinate transformation to transform the contact line L 1 and L 2 coordinate points are converted to the grinding wheel coordinate system S 1 and rough grinding wheel coordinate system S 2, the axial cross-sectional profiles of the rough grinding wheel 111 and the fine grinding wheel 110 are obtained, and the profiles of the rough grinding wheel 111 and the fine grinding wheel 110 are smoothly connected to form a complete combined grinding profile; Figure 2 The axial cross-sectional profile 300 of the combined grinding wheel is shown in FIG; From the internal gear coordinate system S 0 to the grinding wheel coordinate system S The transformation matrix of 1 is:

[0079]

[0080] From the grinding wheel coordinate system S 1 to the rough grinding wheel coordinate system S The transformation matrix of 2 is:

[0081]

[0082] The axial cross-sectional profile 300 of the fine grinding wheel 110 and the rough grinding wheel 111 can be obtained at a certain point on the tooth profile. j Axial section profile coordinates R j and z j It is expressed as follows:

[0083]

[0084] In the above formula, x j , y j , z j is the coordinate value of a point j on the contact line solved according to the contact condition equation, R j It is the turning radius formed by the point on the contact line along the axis of the grinding wheel.

[0085] Step 6: Calculate the motion trajectory of the dressing roller based on the cross-sectional profile 300 of the combined grinding wheel shaft including the rough grinding wheel and the fine grinding wheel. Simultaneously, perform trimming on the profiles of the rough grinding wheel 111 and the fine grinding wheel 110 on a gear shaping grinding wheel grinding machine. Then, use the trimmed combined grinding wheel to grind the tooth surface of the internal gear 102.

[0086] First adjust the angle of the B axis of the internal gear forming grinding wheel gear grinding machine. For right-hand internal gears, Figure 3 As shown, the B-axis rotates the internal gear helix angle by 20 degrees in the positive direction, and the turntable 109 drives the combined grinding wheel to rotate by 20 degrees. Then, the rotation angle of the C-axis, the movement of the Y-axis, and the movement of the Z-axis are adjusted so that the fine grinding wheel 110 enters the tooth groove of the internal gear 102. At the same time, it is necessary to ensure that the center of the combined grinding wheel is lower than the upper end face of the internal gear 102, and the two side faces of the fine grinding wheel 110 are in contact with the left and right tooth surfaces of the tooth groove. The tooth groove is set as the first tooth groove 200. In the CNC system, the rotation angle of the C-axis, the value of the Y-axis, and the value of the Z-axis at this position are the linkage initial positions of the axes of the CNC internal gear forming grinding wheel gear grinding machine. The motion relationship between the rotation of the C-axis and the movement of the Z-axis is as follows:

[0087]

[0088] Among them, Z0 is the moving distance of the Z axis, and C0 is the rotation angle of the C axis;

[0089] Under the premise that the linkage relationship between the C-axis and the Z-axis remains unchanged, the first slide 106 is fed in the positive direction. According to the grinding allowance and process requirements, after multiple forming grinding movements, the X-axis is fed to the theoretical tooth depth position to complete the grinding of the first tooth groove 200 and the rough grinding of the second tooth groove 201.

[0090] Then, the position of the X axis is kept unchanged, and the third slide 108 moves along the negative Z direction of the third guide rail 107, while keeping the motion relationship between the rotation of the C axis and the movement of the Z axis unchanged. The combined grinding wheel exits the tooth groove of the internal gear, and the linkage relationship between the C axis and the Z axis is released. The first turntable 101 drives the internal gear 102 to rotate in the positive direction around the C axis. , rotate the second tooth groove 201 of the internal gear to the position of the first tooth groove 200, and then maintain the linkage relationship between the C axis and the Z axis to fine-grind the second tooth groove 201 and roughly grind the third tooth groove 202 at the same time; then, perform form grinding on the remaining tooth grooves of the internal gear 102 in turn until the grinding of all tooth surfaces of the internal gear 102 is completed.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are within the scope of protection of the pending claims of the present invention.

Claims

1. A profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear, characterized in that: The grinding wheel for grinding internal gears is a combination grinding wheel including a fine grinding wheel and a rough grinding wheel. When the combination grinding wheel is used on an internal gear forming grinding wheel grinding machine to perform profile grinding on the tooth surface of the internal gear, the combination grinding wheel simultaneously performs rough grinding and fine grinding of different tooth grooves, including the following steps: Step 1: Establish the tooth surface equation and three-dimensional model of the first tooth groove of the internal gear; According to the rotation direction of the internal gear during the grinding process, the installation positions of the fine grinding wheel and the rough grinding wheel are determined; the internal gear coordinate system S0 (O0: x0, y0, z0), the fine grinding wheel coordinate system S1 (O1: x1, y1, z1) and the rough grinding wheel coordinate system S2 (O2: x2, y2, z2) are established; the directions of the x0, x1 and x2 coordinate axes are the same, and the axial directions of the x0 and x1 coordinate axes point to the first tooth groove of the internal gear, which is the tooth depth feed direction during grinding; the directions of the y1 and y2 coordinate axes are the same; the angle between the z0 coordinate axis and the y1 coordinate axis and the y2 coordinate axis is the internal gear helix angle; the origin O0 of the internal gear coordinate system S0 is at the center of the internal gear circle, and the distance between it and the coordinate origin O1 of the fine grinding wheel coordinate system S1 is the center distance a; in the internal gear coordinate system S1, the final tooth surface equation R1 and the tooth surface three-dimensional model D1 of the first tooth groove of the internal gear are established; the tooth groove adjacent to the first tooth groove of the internal gear is the second tooth groove; Step 2: The grinding of the first tooth groove by the fine grinding wheel and the grinding of the second tooth groove by the rough grinding wheel are recorded as the grinding starting state; according to the total grinding amount of the internal gear, the grinding amount δ1 of the fine grinding and the grinding amount δ2 of the rough grinding are determined; Step 3: Superimpose the tooth surface fine grinding amount δ1 with the final tooth surface three-dimensional model D1 of the internal gear to establish the tooth surface equation R2 and the corresponding tooth surface three-dimensional model D2 of the second tooth groove of the internal gear corresponding to the rough grinding wheel; Step 4: According to the tooth surface equations R1 and R2 and the installation positions of the corresponding fine grinding wheel and rough grinding wheel, solve the coordinate points of the contact lines L1 and L2 between the tooth surface at the first tooth groove and the tooth surface at the second tooth groove and the combined grinding wheel respectively; Step 5: Convert the coordinate points of the contact lines L1 and L2 to the fine grinding wheel coordinate system S1 and the rough grinding wheel coordinate system S2 respectively, obtain the axial cross-sectional profiles of the rough grinding wheel and the fine grinding wheel, and smoothly connect the profiles of the rough grinding wheel and the fine grinding wheel to form a complete combined grinding profile; Step 6: The profiles of the rough grinding wheel and the fine grinding wheel are trimmed simultaneously according to the obtained combined grinding wheel profile, and then the tooth surface of the internal gear is ground with the trimmed combined grinding wheel.

2. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 1, characterized in that: In step 1, the fine grinding wheel and the rough grinding wheel are coaxially installed along the grinding wheel axis direction, and the center distance a between the coordinate origin O0 of the internal gear coordinate system S0 and the origin O1 of the fine grinding wheel coordinate system S1 in the direction of the internal gear axis x0 is r0-r1, where r0 is the pitch circle radius of the internal gear and r1 is the pitch circle radius of the fine grinding wheel; The rotation direction of the internal gear is viewed from the positive direction of the z0 axis of the internal gear to the negative direction. When the internal gear rotates clockwise, the rough grinding wheel is installed along the negative direction of the z1 axis. If the internal gear rotates counterclockwise, the rough grinding wheel is installed along the positive direction of the z1 axis.

3. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 1, characterized in that: In step 2, the installation distance d between the fine grinding wheel and the rough grinding wheel on the central axis is determined according to the relative positions of the first tooth groove and the second tooth groove and the rotation direction of the internal gear during the gear grinding process; d= （1）； In formula (1), β is the helix angle of the internal gear, r0 is the pitch radius of the internal gear, and z is the number of teeth of the internal gear.

4. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 1, characterized in that: In step 1, the final tooth surface equation R1 of the first tooth groove is expressed as: （2）； In formula (2), the "+" in the "±" sign corresponds to the end face involute of the left tooth surface of the first tooth space, and the "-" in the "±" sign corresponds to the end face involute of the right tooth surface of the first tooth space. b is the base circle radius of the internal gear; μ is the involute angle; σ0 is the tooth gap half angle; matrix M g Expressed as, （3）； In formula (3), the matrix M g The "+" in "±" and the "-" in "∓" correspond to the tooth surface of the right-hand internal gear; the matrix M g The "-" and " The "+" in the "" symbol corresponds to the left-handed internal gear tooth surface; P1 is the internal gear helical parameter, and θ is the rotation angle.

5. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 4, characterized in that: In step 3, the tooth surface equation R2 at the second tooth groove is expressed as: （4）； In formula (4), r0 is the pitch radius of the internal gear, r b is the base circle radius of the internal gear, z is the number of teeth of the internal gear, M g is the matrix M g .

6. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 5, characterized in that: In step 4, the calculated distribution of the contact lines L1 and L2 satisfies the tooth surface contact condition: （5）； In formula (5), (x, y, z) are the coordinates of the tooth surface contact point obtained according to the tooth surface equation R1 of the first tooth groove of the internal gear or the tooth surface equation R2 of the second tooth groove, (n x , n y , n z ) are the three components of the tooth surface normal vector at the contact point of the internal gear tooth surface, P1 is the internal gear helix parameter, Σ is the angle between the grinding wheel axis and the internal gear axis, z is the number of internal gear teeth; a=r0-r1, r0 is the pitch circle radius of the internal gear, and r1 is the pitch circle radius of the fine grinding wheel.

7. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 1, characterized in that: In step 5, the transformation matrix from the internal gear coordinate system S0 to the grinding wheel coordinate system S1 is: （6）； The transformation matrix from the internal gear coordinate system S0 to the rough grinding wheel coordinate system S2 is: （7）； In the above formula, Σ is the angle between the grinding wheel axis and the internal gear axis, z is the number of internal gear teeth, β is the internal gear helix angle; a=r0-r1, r0 is the internal gear pitch radius, and r1 is the pitch radius of the fine grinding wheel.

8. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 7, characterized in that: After the complete combined grinding wheel profile is obtained in step 5, coordinate transformation is performed. The coordinates of the tooth surface contact lines L1 and L2 calculated in step 4 are transformed into the fine grinding wheel coordinate system S1 and the rough grinding wheel coordinate system S2 to obtain the coordinates of the axial cross-section profiles of the fine grinding wheel and the rough grinding wheel.

9. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 1, characterized in that: In step six, when grinding the tooth surface of the internal gear with the dressed combined grinding wheel, first adjust the relative position of the fine grinding wheel and the first tooth groove of the internal gear, starting from the initial contact position of the fine grinding wheel and the rough grinding wheel with the tooth surface of the internal gear, according to the total grinding allowance, feed multiple times along the x0 coordinate axis direction of the internal gear, and gradually feed to the final grinding position of the internal gear, then keep the feed position of the combined grinding wheel unchanged, and grind the tooth surfaces corresponding to the remaining tooth grooves of the internal gear according to the motion relationship of the formed grinding until the grinding of all tooth surfaces of the internal gear is completed.

10. The profile grinding method for simultaneously grinding multiple tooth grooves of an internal gear according to claim 1, characterized in that: The combined grinding wheel includes one or more rough grinding gears and fine grinding gears; according to processing requirements, the grinding wheel materials of the rough grinding wheel and the fine grinding wheel are the same or different, and the grinding wheel grits of the rough grinding wheel and the fine grinding wheel are different.

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