A straight diagonal modification method for herringbone gears based on profile grinding

Abstract

A method for linear diagonal modification of herringbone gears based on profile grinding, which relates to the technical field of gear transmission. The present invention is to solve the problems of low machining accuracy and low machining efficiency existing in the existing linear diagonal modification method for herringbone gears. The present invention includes: obtaining a standard tooth tip modification area and a standard tooth root modification area; obtaining the projection helix angle of the tooth tip modification starting line and the projection helix angle corresponding to the tooth root modification starting line; modifying the amount of discrete coordinate points in the standard tooth tip modification area, and obtaining the position vector and normal vector of the target tooth tip modification tooth surface; obtaining the modification amount of discrete coordinate points in the standard tooth root modification area, and obtaining the position vector and normal vector of the target tooth root modification tooth surface; optimizing with the pressure angle, module, and helix angle as optimization variables to obtain the optimal pressure angle, module, and helix angle for tooth tip and tooth root modification, and using the obtained optimal parameters to perform diagonal modification on the herringbone gear. The present invention is used for linear diagonal modification of herringbone gears.

Description

Technical Field

[0001] The invention relates to the technical field of gear transmission, and in particular to a linear diagonal shaping method for herringbone gears based on forming grinding. Background Art

[0002] With the rapid development of industry, involute cylindrical gears have been widely and extensively used, and the requirements for gear performance such as high speed, heavy load and precision are increasing day by day. The herringbone gear is equivalent to two congruent but opposite helical gears. Due to its compact structure, axial forces can offset each other, good working stability and large bearing capacity, its importance in high-speed and heavy-load occasions such as ship power transmission is becoming more and more prominent. However, due to the various excitations such as prime mover, load, meshing impact, meshing stiffness, etc., it will inevitably cause vibration and noise, which is not conducive to the normal operation and safe operation of the equipment. Diagonal shaping is an effective way to reduce vibration and noise by only modifying the meshing and meshing part of the tooth surface, without or less repairing the middle part, by reducing the meshing impact excitation. The use characteristics of the application determine that the herringbone gear is generally a hardened tooth surface, which makes it have better pitting resistance, longer service life, stronger load-bearing capacity, and occupies less volume and weight when designing mechanical structures.

[0003] At present, the methods for achieving diagonal shaping and finishing of hardened gears mainly include shaving and grinding. However, the highest processing accuracy of shaving is level 6, the processing accuracy level is low, and there is a problem of difficulty in tool manufacturing. Grinding is mostly achieved through the QMK50 five-axis linkage gear grinding machine, but the accuracy is not high, and the grinding wheel and the workpiece are in point contact, so the processing efficiency is relatively low. Therefore, the current linear diagonal shaping method of hardened herringbone gears still has the problems of low processing accuracy and low processing efficiency. Summary of the invention

[0004] The purpose of the present invention is to solve the problems of low processing accuracy and low processing efficiency in the existing linear diagonal shaping method of herringbone gears, and propose a linear diagonal shaping method of herringbone gears based on forming grinding.

[0005] A linear diagonal modification method for herringbone gears based on profile grinding. The specific process is as follows:

[0006] Step 1: Determine the orientation of the tooth addendum and tooth root modification area of the herringbone gear according to the single-side gear tooth rotation direction and the left and right tooth surfaces, so as to obtain the standard tooth addendum modification area △ABC and the standard tooth root modification area △DEF;

[0007] Step 2: Obtain the standard tooth top modification area △ABC and the standard tooth root modification area △DEF according to step 1 to obtain the projection helix angle β of the tooth top modification starting line BC aThe projection helix angle β corresponding to the tooth root modification starting line EF f ;

[0008] Step 3: Based on β obtained in Step 2 a Obtain the modification amount of the discrete coordinate points in the standard tooth tip modification area, and obtain the position vector R a1 and the normal vector N a1 ;

[0009] Step 4: Based on β obtained in Step 2 f Obtain the modification amount of the discrete coordinate points in the standard tooth root modification area, and obtain the position vector R f1 and the normal vector N f1 ;

[0010] Step 5: Based on the position vector R a1 and the normal vector N a1 of the tooth tip target modification tooth surface obtained in Step 3, obtain the deviation E a of the actual modification tooth surface position vector corresponding to the discrete coordinate points in the standard tooth tip modification area in the direction of the target modification tooth surface normal vector. Taking the minimum sum of squares of E a as the optimization objective, and the pressure angle, module, and helix angle as the optimization variables, use the NSGA-II genetic algorithm for optimization to obtain the optimal pressure angle, module, and helix angle for tooth tip modification;

[0011] Step 6: Based on the position vector R f1 and the normal vector N f1 of the tooth root target modification tooth surface obtained in Step 4, obtain the deviation E f of the actual modification tooth surface position vector corresponding to the discrete coordinate points in the standard tooth root modification area in the direction of the target modification tooth surface normal vector. Taking the minimum sum of squares of E f as the optimization objective, and the pressure angle, module, and helix angle as the optimization variables, use the NSGA-II genetic algorithm for optimization to obtain the optimal pressure angle, module, and helix angle for tooth root modification;

[0012] Step 7: Perform diagonal modification on the herringbone gear according to the standard tooth surface parameters and the optimal pressure angle, module, and helix angle for tooth tip modification and tooth root modification obtained in Steps 5 and 6 to obtain the modified herringbone gear.

[0013] Furthermore, determining the orientations of the tooth tip and tooth root modification areas of the herringbone gear according to the single-side tooth helix direction and the left and right tooth surfaces in Step 1, so as to obtain the standard tooth tip modification area △ABC and the standard tooth root modification area △DEF, specifically includes the following steps:

[0014] Step 1: Determine the orientation of the tooth tip and tooth root modification regions of the herringbone gear according to the helix direction of the single-sided teeth and the left and right tooth surfaces:

[0015] First, take the triangular regions where the tooth root of the driving tooth engages and the tooth tip disengages as the single-sided tooth surface modification regions;

[0016] Then, determine the range of the tooth tip modification termination position and the range of the tooth root modification termination position within the tooth surface modification region, that is, the orientation of the tooth tip and tooth root modification regions of the herringbone gear;

[0017] The range of the tooth tip modification termination position is: the region range where the tooth tip is non-chamfered;

[0018] The range of the tooth root modification termination position is: the region range of the starting point where the tooth tip of the driven gear engages and contacts on the tooth surface of the driving gear;

[0019] Step 2: Based on the orientation of the tooth tip and tooth root modification regions of the herringbone gear determined in Step 1, obtain the standard tooth tip modification region △ABC according to the preset tooth tip modification height AB, and obtain the standard tooth root modification region △DEF according to the preset tooth root modification height DE;

[0020] Among them, BC is the boundary line between the standard tooth surface and the tooth tip modification tooth surface, and EF is the boundary line between the standard tooth surface and the tooth root modification tooth surface.

[0021] Furthermore, the step in Step 2 of obtaining the standard tooth tip modification region △ABC according to the preset tooth tip modification height AB and obtaining the standard tooth root modification region △DEF according to the preset tooth root modification height DE based on the orientation of the tooth tip and tooth root modification regions of the herringbone gear determined in Step 1 includes the following steps:

[0022] Step 2.1: Given the tooth tip modification height AB, establish a coordinate system z a O a x a , and obtain the x and z coordinate components of vertex B in the coordinate system z a O a x a :

[0023]

[0024] In the formula, x aB , z aB respectively represent the x and z coordinate components corresponding to point B in the coordinate system z a O a x a , W represents the tooth width, and AB is the modification height;

[0025] The coordinate z a O a x aThe origin O a is located at the intersection of the mid - section of the tooth width and the axis. The x a axis is along the radial direction of the mid - section of the tooth width, and the z a axis is located on the gear axis;

[0026] Step 122: Establish the gear moving coordinate system S a -x a y a z a , the rack cutter reference coordinate system S b -x b y b z b , the rack cutter moving coordinate system S d -x d y d z d , and obtain the position vector R d -x d y d z d of point B in the rack cutter moving coordinate system S d (u, l) and the normal vector N d (u, l). Then, use R d (u, l) and N d (u, l) to obtain the position vector a -x a y a z a of point B in the gear moving coordinate system S Normal vector

[0027]

[0028] R d (u, l)=M db (β)R0(u, l)

[0029] N d (u, l)=M db (β)N0(u, l)

[0030] In the formula, R0(u, l) and N0(u, l) respectively represent the position vector and the normal vector of point B in S b -x b y b z b . u and l are the tooth surface parameters of the rack cutter; R d (u, l) and N d (u, l) respectively represent the position vector and the normal vector of point B in S d -x d y d z dThe position vector and normal vector in, M db (β) represents the point B from S b -x b y b z b to S d -x d y d z d The coordinate transformation parameters of represents the point B from S d -x d y d z d to S a -x a y a z a The coordinate transformation parameters of is the gear machining rotation angle;

[0031] The moving coordinate system S of the gear a -x a y a z a In the coordinate system, the origin O a is located at the intersection of the middle cross-section of the tooth width and the axis. The x a axis is along the radius direction of the middle cross-section of the tooth width. The y a axis is located in the middle cross-section of the tooth surface and perpendicular to the x a axis. The z a axis is located on the gear axis;

[0032] The S b -x b y b z b In the coordinate system, the origin O b is located at the intersection of the normal middle cross-section of the rack cutting tool and the pitch circle. The x b axis direction is along the normal middle cross-section of the tool and perpendicular to the gear axis direction. The y b axis is perpendicular to the tool surface. The z b axis is along the tool surface direction and perpendicular to the x b axis;

[0033] The S d -x d y d z d In the coordinate system, O b is translated along the negative y c axis by a m to obtain the origin O d The x d axis is along the gear radius direction. The y d axis is along the gear tangential direction. The z d axis is along the gear axis direction;

[0034] where a m = πm n / 4, and m n is the normal module of the standard gear;

[0035] Steps One, Two, and Three: Using the R d (u, l), N d (u, l) obtained in Step One and Two, establish the addendum meshing equation:

[0036]

[0037] In the formula, represents the coordinate component of the position vector corresponding to point B along the j-axis in the moving coordinate system S a -x a y a z a of the gear, R dj (u, l), N dj (u, l) respectively represent the coordinate components of the position vector and the normal vector corresponding to point B along the j-axis in the moving coordinate system S d -x d y d z d of the rack cutter, j = x, y, z, and r p1 represents the pitch circle radius, is the instantaneous machining rotation angle of the gear at point B;

[0038] Step One and Four: Substitute x aC = r a1 into the addendum meshing equation (3) established in Steps One, Two, and Three to obtain the rack cutter tooth surface parameters u and l, and then calculate z ac , and then use z ac to obtain the profile modification length AC, thereby obtaining the standard addendum profile modification area △ABC;

[0039] where x aC is the z coordinate component corresponding to point C in z a O a x a , r a1 is the addendum circle radius, are respectively the instantaneous machining rotation angles of the gear corresponding to point B and point C on the projection BC of the tooth surface contact line, and z aC is the z coordinate component corresponding to point C in z a O a x a ;

[0040] Step One and Five: Given the root profile modification height DE, obtain z aO a x a The x and z coordinate components of the coordinates of point E in the coordinate system are specifically as follows:

[0041]

[0042] Among them, x aE and z aE are respectively the x and z coordinate components corresponding to point E in the coordinate system z a O a x a ; r k1 is the radius of the root modification termination line;

[0043] Step 126: Obtain the root modification length DF based on the x and z coordinate components of the coordinates of point E obtained in Step 125, so as to obtain the standard root modification region △DEF.

[0044] Furthermore, the specific method of obtaining the modification length AC by using z ac in Step 124 is as follows:

[0045]

[0046] Furthermore, the specific method of obtaining the root modification length DF based on the x and z coordinate components of the coordinates of point E obtained in Step 125 in Step 126 is as follows:

[0047] First, obtain the position vector a -x a y a z a of point E in the gear moving coordinate system S and the normal vector ; obtain the position vector R' d -x d y d z d of point E in the rack cutter moving coordinate system S d (u, l) and the normal vector N' d (u, l);

[0048] Among them, the method of obtaining R' d (u, l), N' d (u, l) is the same as the method of obtaining R d (u, l), N d (u, l);

[0049] Then, R' d (u, l), N' dSubstitute \((u, l)\) and Equation (5) into the tooth root meshing equation to obtain the machining rotation angle corresponding to the tooth surface contact line \(EF\).

[0050] The method for obtaining the tooth root meshing equation is the same as that for obtaining the tooth tip meshing equation.

[0051] Then, substitute x aE = r k1 into the tooth root meshing equation to obtain the tooth root modification length \(DF\):

[0052]

[0053] where \(z\) aF is the \(z\)-coordinate component corresponding to point \(F\) in the coordinate system \(z\) a O a x a and \(x\) aE is the \(x\)-coordinate component corresponding to point \(E\) in \(z\) a O a x a . They are the instantaneous machining rotation angles of the gear corresponding to the projected points \(E\) and \(F\) of the tooth surface contact line respectively.

[0054] Furthermore, obtaining the projection helix angle \(\beta\) of the tooth tip modification starting line \(BC\) and the projection helix angle \(\beta\) of the tooth root modification starting line \(EF\) according to the standard tooth tip modification region \(\triangle ABC\) and the standard tooth root modification region \(\triangle DEF\) obtained in step 1 in step 2 a is specifically as follows: f

[0055] Step 2-1: Obtain the projection helix angle \(\beta\) of the tooth tip modification starting line \(BC\) according to the standard tooth tip modification region \(\triangle ABC\) obtained in step 1 a :

[0056] \(\beta\) a = arctan(AB / AC) (7)

[0057] where \(AB\) is the tooth tip modification height and \(AC\) is the tooth tip modification length.

[0058] Step 2-2: Obtain the projection helix angle \(\beta\) of the tooth surface contact line \(EF\) according to the standard tooth root modification region \(\triangle DEF\) obtained in step 1 f :

[0059] \(\beta\) f = arctan(DE / DF) (8)

[0060] where \(DE\) is the tooth root modification height and \(DF\) is the tooth root modification length.

[0061] ​Further, β obtained in step two in step three a Obtain the modification amount of the discrete coordinate points in the standard addendum modification area, and obtain the position vector R of the target addendum modified tooth surface according to the modification amount of the discrete coordinate points a1 and the normal vector N a1 , specifically:

[0062] Step 3-1: Establish a coordinate system z a2 O a2 x a2 , discretize the coordinates of the △ABC area numerically to obtain discrete coordinate points, and then obtain the modification amount E corresponding to each discrete coordinate point R ai (z ai ,x ai ): at :

[0063] First, discretize the coordinates of the △ABC area numerically to obtain the coordinates of each discrete point within the △ABC area;

[0064] The discrete points are obtained in the following way: in the △ABC area, take an equal number of equally spaced discrete coordinate points on each rotational projection line parallel to the addendum modification starting line BC, and the number of points is denoted as MI; take equally spaced discrete coordinate points on the modification length AC, and the number of points is denoted as MII;

[0065] Then, obtain the modification amount E corresponding to each discrete coordinate point R ai (z ai ,x ai ): at :

[0066]

[0067] Among them, R a2i (z a2i ,x a2i ) is the coordinate representation of R ai (z ai ,x ai ) in the z a2 O a2 x a2 coordinate system, AG = ACsin(β a ) is the perpendicular distance from point A to BC, x a2G represents the perpendicular distance from point O a2 to BC, y a is the preset maximum addendum modification amount, z ai is the z-axis coordinate of R ai , x ai is the x-axis coordinate of R ai ;

[0068] The coordinate system za2 O a2 x a2 The x-axis is in the normal direction of the starting line of the tip relief, and the z a2 axis and the z a2 axis forms an angle β with the positive semi-axis. O a1 is translated by r along the positive x a axis to obtain O a . The z p1 axis is located on the pitch circle; a2 a1

[0069] Step 3-2: According to the modification amount E corresponding to the discrete coordinate points in the △ABC area obtained in Step 3-1 at (u, l), obtain the position vector R of the target tip-modified tooth surface a1 and the normal vector N a1 :

[0070] R a1 = R a0 (u, l) + N a0 (u, l)E at (u, l) (10)

[0071]

[0072] where R a0 (u, l) is the position vector corresponding to the unmodified standard tooth surface, and N a0 is the normal vector corresponding to the unmodified standard tooth surface.

[0073] Furthermore, according to β obtained in Step 2 in Step 4 f , obtain the modification amount of the discrete coordinate points in the standard root relief area, and obtain the position vector R of the target root-modified tooth surface according to the modification amount of the discrete coordinate points f1 and the normal vector N f1 , which specifically includes the following steps:

[0074] Step 4-1: Establish a coordinate system z a3 O a3 x a3 . Discretize the coordinates of the △DEF area numerically to obtain discrete coordinate points, and then obtain the modification amount E corresponding to each discrete coordinate point R' ak (z ak , x ak ): ft :

[0075] First, discretize the coordinates of the △DEF area numerically to obtain the coordinates of each discrete point in the △DEF area;

[0076] ​​The discrete points are obtained as follows: In the △DEF region, an equal number of discrete coordinate points at equal intervals are taken on each rotational projection line parallel to the tooth root modification starting line EF, and the number of points is denoted as MIII; on the modification length DF, discrete coordinate points at equal intervals are taken, and the number of points is denoted as MIV.

[0077] Then, each discrete coordinate point R' is obtained. ak (z ak , x ak ) corresponding to the modification amount E ft :

[0078]

[0079] Among them, R' a3k (z a3k , x a3k ) is the coordinate representation of R' ak (z ak , x ak ) in the z a3 O a3 x a3 coordinate system. DH = DFsin(β f ) is the perpendicular distance from point D to EF, x a3H represents the perpendicular distance from point O a3 to EF, y f is the preset maximum tooth root modification amount, k = D, E, F,..., k is any discrete point within the tooth root modification region;

[0080] In the said coordinate system z a3 O a3 x a3 the x a3 axis is located in the normal direction of the tooth root modification starting line, the z a3 axis forms an angle of β a1 with the negative half-axis of z a , O a is translated along the positive x a axis by r p1 to obtain O a3 ;

[0081] Step Four Two. According to the modification amount E corresponding to the discrete coordinate points in the △ABC region obtained in Step Four One, ft the position vector R f1 and the normal vector N f1 of the tooth root target modified tooth surface are obtained;

[0082] Among them, the method for obtaining the position vector R f1 and the normal vector N f1 of the tooth root target modified tooth surface is the same as the method for obtaining the position vector R a1 and the normal vector Na1 is the same as the method.

[0083] Further, the position vector R of the tooth tip target modified tooth surface obtained in step three in step five a1 and the normal vector N a1 Obtain the deviation E of the actual modified tooth surface position vector corresponding to the discrete coordinate points in the standard tooth tip modification area in the direction of the target modified tooth surface normal vector a , with E a The sum of squares is the optimization objective, and the pressure angle, modulus, and helix angle are the optimization variables. The NSGA-II genetic algorithm is used for optimization to obtain the optimal pressure angle, modulus, and helix angle of the tooth tip modification, including the following steps:

[0084] Step Five-One: Obtain the R after changing the modulus, pressure angle, and helix angle ai (z ai , x ai ) corresponding actual modified tooth surface position vector R a2 , and obtain R according to the following formula a2 The deviation E in the direction of the target modified tooth surface normal vector N a1 : l :

[0085] E l =(R a2x -R a1x )N 1x +(R a2y -R a1y )N a1y +(R a2z -R a1z )N a1z (13)

[0086] In the formula, R a1j represents the j-axis coordinate component in R a1 corresponding to S a -x a y a z a , R a2j represents the j-axis coordinate component in R a2 corresponding to S a -x a y a z a , N a1j represents the j-axis coordinate component in N a1 corresponding to S a -x a y a z a ; l ∈ [1, M] is the label of the discrete coordinate points in the tooth tip modification area, and M is the total number of discrete coordinate points in the tooth tip modification area;

[0087] Step 5-2: Obtain the optimization parameter range of the pinion of the herringbone gear, and perform optimization to solve for the optimal optimization parameter E with the minimum sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tip modification region △ABC a =[[E1,...E M T ;

[0088] where M = MI(MII - 1)+1;

[0089] In the optimization with the minimum sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tip modification region △ABC as the objective, the optimization variables include: module m' n , pressure angle α' n , helix angle β';

[0090] The objective function is:

[0091] where f1 is the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points at the tooth tip;

[0092] The constraint conditions are:

[0093]

[0094] where α' n min is the preset lower limit of the pressure angle, α' n max is the preset upper limit of the pressure angle, m' n min is the preset lower limit of the module, m' n max is the preset upper limit of the module, β'min is the preset lower limit of the helix angle, and β'max is the preset upper limit of the helix angle.

[0095] Furthermore, the position vector R f1 and the normal vector N f1 of the target root modification tooth surface obtained in Step 4 in Step 6 are used to obtain the deviation E f of the actual modification tooth surface position vector corresponding to the discrete coordinate points in the standard root modification region in the direction of the target modification tooth surface normal vector. With the minimum sum of the squares of E f as the optimization objective and the pressure angle, module, and helix angle as the optimization variables, the NSGA-II genetic algorithm is used for optimization to obtain the optimal pressure angle, module, and helix angle of the root modification, including the following steps:

[0096] Step 6-1: Obtain the position vector R ak (z ak ,x ak ) of the actual modification tooth surface corresponding to the changed module, pressure angle, and helix angle, and obtain R f2 according to the following formula f2 ​In the direction of the normal vector N of the target modified tooth surface f1 Deviation E t :

[0097] E t =(R f2x -R f1x )N f1x +(R f2y -R f1y )N f1y +(R f2z -R f1z )N f1z (16)

[0098] Wherein, R f1j represents the j-axis coordinate component in R f1 corresponding to S a -x a y a z a , R f2j represents the j-axis coordinate component in R f2 corresponding to S a -x a y a z a , N f1j represents the j-axis coordinate component in N f1 corresponding to S a -x a y a z a , t ∈ [1, N] is the label of the discrete coordinate points in the tooth root modification region, and N is the total number of discrete coordinate points in the tooth root modification region;

[0099] Step 6-2. Obtain the optimization parameter range of the pinion of the herringbone gear, and optimize and solve the optimal optimization parameter E with the minimum sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region △DEF f =[E1,...E N T ;

[0100] Wherein, N = MIII(MIV - 1)+1;

[0101] The constraint conditions and optimization variables in the optimization with the minimum sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region △DEF as the objective are the same as those in the optimization with the minimum sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth tip modification region as the objective;

[0102] The objective function in the optimization with the minimum sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region △DEF as the objective is: ​

[0103] Among them, f2 represents the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification area.

[0104] The beneficial effects of the present invention are as follows:

[0105] The present invention proposes to obtain three different formed grinding wheel profiles by changing the module, pressure angle, and helix angle, and then use form grinding to successively machine the standard tooth surface, crowned tooth surface, and root modified tooth surface, thereby realizing linear diagonal modification. The form grinding wheel adopted in the present invention is line contact grinding, which improves the grinding efficiency and is more suitable for hard tooth surface machining; the form grinding proposed in the present invention does not require a generating motion, so the machine tool requires fewer motions and there are fewer error sources, thus making the machining accuracy more stable. The present invention can be realized on an existing CNC cylindrical gear grinding machine, and grinding is achieved by changing different modules, pressure angles, and helix angles, improving the machining accuracy and efficiency. Description of the Drawings

[0106] Figure 1 is a schematic diagram of the diagonal modification position of a herringbone gear;

[0107] Figure 2 is a three-dimensional diagonal modification schematic diagram of the left tooth surface of a right-handed helical gear;

[0108] Figure 3 is a schematic diagram of the diagonal modification of the rotational projection plane of the left tooth surface of a right-handed helical gear;

[0109] Figure 4 is a schematic diagram of the coordinate transformation of the tooth surface generated by the rack cutting method;

[0110] Figure 5 is a flowchart for optimizing the sum of the squares of the tooth surface errors in the modification area;

[0111] Figure 6 is a schematic diagram of a CNC grinding machine grinding a herringbone gear;

[0112] Figure 7 is a flowchart for CNC form grinding of a diagonal modified herringbone gear;

[0113] Figure 8 is a schematic diagram of a herringbone gear with centering and positioning by hydraulic centers at both ends;

[0114] Figure 9 is an error diagram of the standard tooth surface and the actual modified tooth surface in the crowned area;

[0115] Figure 10 is an error diagram of the target modified tooth surface and the actual modified tooth surface in the crowned area;

[0116] Figure 11 is an error diagram of the standard tooth surface and the actual modified tooth surface in the root modified area;

[0117] Figure 12 It is the error diagram of the target modified tooth surface and the actual modified tooth surface in the tooth root modification area. Specific implementation mode

[0118] Specific implementation mode 1: The specific process of a herringbone gear straight diagonal modification method based on profile grinding is as follows:

[0119] Step 1. Determine the orientation of the tooth tip and tooth root modification areas of the herringbone gear according to the helix direction of the single-sided tooth and the left and right tooth surfaces, so as to obtain the standard tooth tip modification area △ABC and the standard tooth root modification area △DEF. The specific steps are as follows:

[0120] Step 1-1. Determine the orientation of the tooth tip and tooth root modification areas of the herringbone gear according to the helix direction of the single-sided tooth and the left and right tooth surfaces:

[0121] The present invention only considers the positive diagonal modification of the tooth surface at the engagement and disengagement ends. The herringbone gear has different helix directions on both sides, and the teeth are symmetric about the middle section parallel to the tooth end face, and the modification areas are also symmetric. The determination of the modification area orientation is related to the helix direction of the teeth and the left and right tooth surfaces. The schematic diagram of the modification position is as shown in the shaded part of the tooth groove. The single-sided tooth surface modification occurs in the triangular area where the driving tooth root engages and the tooth tip disengages. Determine the tooth tip modification termination position according to whether the tooth tip is chamfered. The present invention does not consider chamfering; determine the tooth root modification termination position under the condition of ensuring the minimum involute engagement length, that is, the starting point where the driven tooth tip engages and contacts the driving tooth surface. Figure 1 As shown in the shaded part of the tooth groove, the single-sided tooth surface modification occurs in the triangular area where the driving tooth root engages and the tooth tip disengages. Determine the tooth tip modification termination position according to whether the tooth tip is chamfered. The present invention does not consider chamfering; determine the tooth root modification termination position under the condition of ensuring the minimum involute engagement length, that is, the starting point where the driven tooth tip engages and contacts the driving tooth surface.

[0122] Step 1-2. Based on the orientation of the tooth tip and tooth root modification areas of the herringbone gear determined in Step 1-1, given the modification height on the tooth tip and tooth root end faces, and then respectively determine the dividing lines between the standard tooth surface and the tooth tip modified tooth surface and the tooth root modified tooth surface, so as to determine the standard tooth tip modification area △ABC and the standard tooth root modification area △DEF:

[0123] For the convenience of description, take Figure 2 the left tooth surface of the right-handed tooth as an example for analysis. Given the modification height on the tooth tip and tooth root end faces, respectively determine the dividing lines between the standard tooth surface and the tooth tip modified tooth surface and the tooth root modified tooth surface, and then determine the modification lengths of the tooth tip and tooth root, so as to determine the modification area;

[0124] Step 1-2-1. Given the tooth tip modification height AB, establish a coordinate system z a O a x a , and obtain the x and z coordinate components of vertex B in the coordinate system z a O a x a :

[0125] Adopt the diagonal modification method with the same modification amount along the contact line. The three-dimensional modification schematic diagram of diagonal modification and the modification schematic diagram of the rotating projection plane are respectively as Figure 2 , Figure 3 shown. In Figure 3 , △ABC and △DEF respectively represent the tip and root modification regions. AB and DE represent the modification heights on the tooth end face. BC and EF represent the rotating projections of the tooth surface contact line, that is, the modification starting lines. AC and DF represent the modification lengths on the modification termination lines. W represents the tooth width. Point G is the intersection point of the perpendicular line from point A to BC, and point H is the intersection point of the perpendicular line from point D to EF. The origin O a is located at the intersection of the tooth width middle section and the axis. Take the x a axis as the radius direction along the tooth width middle section, and the z a axis is located on the gear axis; the origin O a is translated r a along the positive direction of the x p1 axis to obtain O a1 , O a2 , O a3 . The x a1 axis is located on the tooth width middle section, the z a1 axis is located on the pitch circle, the x a2 axis is located in the normal direction of the tip modification starting line, the included angle between the z a2 axis and the positive half-axis of z a1 is β a . The x a3 axis is located in the normal direction of the root modification starting line, the included angle between the z a3 axis and the negative half-axis of z a1 is β a . r a1 represents the tip circle radius, r p1 represents the pitch circle radius, r k1 represents the root modification termination line radius. O a1 , O a2 , O a3 are the same point.

[0126] Given the modification height AB on the tooth tip end face, then the x and z coordinate components of point B in the z a O a x a coordinate system are:

[0127]

[0128] In the formula, x ai , z ai (i = A, B, C …) respectively represent Figure 3 in the coordinate system z a O a x aThe x and z coordinate components corresponding to point i, W represents the tooth width, AB is the modification height, and i is a discrete point within the tip relief area.

[0129] Step 122: Establish the dynamic coordinate system S of the gear a -x a y a z a , the reference coordinate system S of the rack cutter b -x b y b z b , the dynamic coordinate system S of the rack cutter d -x d y d z d , let Figure 2 z a O a x a In the coordinate system, point B corresponds to Figure 4 In the dynamic coordinate system S of the gear a -x a y a z a The position vector and normal vector are respectively R B , N B , which can be calculated from equation (2):

[0130]

[0131] R d (u, l) = M db (β)R0(u, l)

[0132] N d (u, l) = M db (β)N0(u, l)

[0133] In the formula, R0(u, l) and N0(u, l) represent the position vector and normal vector of point B in Figure 3 The reference coordinate system S of the rack cutter b -x b y b z b , u and l are the tooth surface parameters of the rack cutter; R d (u, l), N d (u, l) represent the position vector and normal vector of point B in the dynamic coordinate system S of the rack cutter d -x d y d z d , M db (β) represents the transformation of point B from the reference coordinate system S of the rack cutter b -x b y b z bTo the moving coordinate system S of the rack cutter d -x d y d z d Coordinate transformation Indicates that point B is from the moving coordinate system S of the rack cutter d -x d y d z d To the moving coordinate system S of the gear a -x a y a z a Coordinate transformation Is the rotation angle of gear machining

[0134] The moving coordinate system S of the gear a -x a y a z a In the coordinate system, the origin O a Is located at the intersection of the middle section of the tooth width and the axis. The x a Axis is along the radial direction of the middle section of the tooth width. The y a Axis is located in the middle section of the tooth surface and perpendicular to the x a Axis. The z a Axis is located on the gear axis

[0135] The S b -x b y b z b In the coordinate system, the origin O b Is located at the intersection of the normal middle section of the rack cutter and the pitch circle. The x b Axis direction is along the normal middle section of the tool and perpendicular to the gear axis direction. The y b Axis is perpendicular to the tool surface. The z b Axis is along the tool surface and perpendicular to the x b Axis

[0136] The S d -x d y d z d In the coordinate system, the origin O b Is translated along the negative direction of the y c Axis by a m To obtain the origin O d Where a m = πm n / 4. The x d Axis is along the gear radius direction. The y d Axis is along the gear tangential direction. The z d Axis is along the gear axis direction. m n Is the normal module of the standard gear

[0137] Steps 1, 2, and 3: Substitute R d (u, l), N d (u, l) and Equation (2) into the meshing equation (3) to solve for the instantaneous machining rotation angle of the gear corresponding to point B where is an expression regarding u and l. By solving the first two equations in Equation (3), the rack cutter tooth surface parameters u and l can be obtained, and then this equation has a solution:

[0138]

[0139] In the formula, (j = x, y, z) represents the position vector coordinate components of point B along the x, y, and z axes in the gear moving coordinate system S a -x a y a z a R dj (u, l), N dj (u, l) (j = x, y, z) respectively represent the position vector and normal vector coordinate components of point B along the x, y, and z axes in the rack cutter moving coordinate system S d -x d y d z d ; is the gear machining rotation angle of point B;

[0140] Steps 1 and 4: In the Figure 3 z a O a x a coordinate system, according to the fact that the gear machining rotation angles corresponding to points B and C on the projection BC of the tooth surface contact line are approximately the same, and the z coordinate component of point C corresponding to the z a O a x a is the same as the addendum circle radius, that is x aC = r a1 , substitute it into the addendum meshing equation (3) to solve for the unknowns u and l, and then find z ac , and then use z ac to obtain the modification length AC:

[0141]

[0142] Steps 1 and 5: Given the modification height DE on the root end face, in the Figure 3 z a O a x a coordinate system, the x and z coordinate components of the coordinates of point E:

[0143]

[0144] Among them, x ak , z ak (k = D, E, F, …) respectively represent Figure 3 the x and z coordinate components corresponding to point k in the coordinate system z a O a x a where k is a discrete point in the root fillet modification region;

[0145] Step 126: Obtain the root fillet modification length DF based on the x and z coordinate components of the E-point coordinates obtained in Step 125, thereby determining the root fillet modification region △DEF. Specifically:

[0146] First, obtain the position vector and normal vector of point E in Figure 4 the gear moving coordinate system S a -x a y a z a based on the x and z coordinate components of the E-point coordinates obtained in Step 125

[0147] Among them, R' d (u, l), N' d (u, l) can be calculated and expressed by Equation (2);

[0148] R' d (u, l), N' d (u, l) represent the position vector and normal vector of point E in Figure 4 the rack cutter moving coordinate system S d -x d y d z d ;

[0149] Then, substitute R' d (u, l), N' d (u, l) and Equation (5) into the meshing equation (3) to solve the machining rotation angle corresponding to the tooth surface contact line EF

[0150] Then, based on the fact that the machining rotation angle of any point on EF is the same and the x coordinate of the root fillet modification termination point F in Figure 3 z a O a x a the coordinate system is the same as the root fillet modification starting radius, that is x aE = r k1 , substitute it into the meshing equation (3) to solve for z aF , then the modification length DF is:

[0151]

[0152] Among them, z aF is the z coordinate component corresponding to point F in the coordinate system z a O a x a in the x coordinate component corresponding to point E in the x aE is z a O a x a in the x coordinate component corresponding to point E in the x They are the instantaneous machining rotation angles of the gear corresponding to points E and F on the projection EF of the flank contact line respectively.

[0153] Step 2: Obtain the projection helix angle β of the addendum modification starting line and the projection helix angle β corresponding to the flank contact line EF according to the standard addendum modification region △ABC and the standard dedendum modification region △DEF obtained in Step 1 a and the projection helix angle β corresponding to the flank contact line EF f , including the following steps:

[0154] Step 2-1: To facilitate the calculation of the modification length of the addendum region along the normal direction of the contact line, approximately determine the projection helix angle β of the addendum modification starting line a :

[0155] β a = arctan(AB / AC) (7)

[0156] Step 2-2: To facilitate the calculation of the modification length of the dedendum modification region along the normal direction of the contact line, approximately determine the projection helix angle β corresponding to the flank contact line EF f :

[0157] β f = arctan(DE / DF) (8)

[0158] Step 3: Obtain the modification amount of the discrete coordinate points in the standard addendum modification region according to β obtained in Step 2 a and obtain the position vector R a1 and the normal vector N a1 of the target addendum modified tooth surface according to the modification amount of the discrete coordinate points:

[0159] Step 3-1: Establish the coordinate system z a2 O a2 x a2 , given the maximum addendum modification amount y a , discretize the coordinates of the △ABC region numerically, and the schematic diagram is as shown in Figure 3As shown. On each rotational projection line parallel to the starting line BC of the tip relief, an equal number of discrete coordinate points are taken at equal intervals, and the number of points is denoted as MI; on the relief length AC, discrete coordinate points are taken at equal intervals, and the number of points is denoted as MII. Calculate the relief amount of the △ABC region based on the distance between the discrete coordinate points and the tip dividing line. Let R ai (z ai ,x ai )(i = A, B, C, …) represent a discrete coordinate point in the △ABC region, then the relief amount E at corresponding to this point is:

[0160]

[0161] In the formula, R a2i (z a2i ,x a2i )(i = A, B, C, …) is the coordinate representation of R ai (z ai ,x ai ) in the z a2 O a2 x a2 coordinate system. The perpendicular distance from point A to BC is AG = ACsin(β a ), x a2G represents the perpendicular distance from point O a2 to BC, z ai is the z-axis coordinate of R ai , and x ai is the x-axis coordinate of R ai .

[0162] Step Three Two: According to the relief amount E at corresponding to the discrete coordinate points in the △ABC region obtained in Step Three One, solve the position vector R a1 and the normal vector N a1 of the target relief tooth surface at the tip:

[0163] The solution process of the target relief tooth surface at the tip is as follows: Combine the discrete coordinate points R ai (z ai ,x ai )(i = A, B, C, …) in the △ABC region with equations (1) to (3) to solve the position vector R a0 (u, l) and the normal vector N a0 of the non-relieved standard tooth surface. Calculate the relief amount E at according to equations (4), (7), and (9), and solve the position vector R a1 and the normal vector N a1 of the target relief tooth surface at the tip according to equations (10) and (11):

[0164] R a1 = Ra0 (u, l) + N a0 (u, l)E at (u, l)(10)

[0165]

[0166] Step 4. According to β obtained in Step 2 f Obtain the modification amount of the discrete coordinate points in the standard tooth root modification area, and obtain the position vector R of the tooth root target modification tooth surface according to the modification amount of the discrete coordinate points f1 and the normal vector N f1 :

[0167] Analyze the tooth root modification area, and the principle is the same as that for determining the tooth tip. Given the maximum tooth root modification amount y f , discretize the coordinates of the △DEF area numerically, and the schematic diagram is as shown in Figure 3 . Take an equal number of equally spaced discrete coordinate points on each rotation projection line parallel to the tooth root modification starting line EF, and record the number of points as MIII; take equally spaced discrete coordinate points on the modification length DF, and record the number of points as MIV. Calculate the modification amount of the △DEF area according to the distance between the discrete coordinate points and the tooth root demarcation line. Let R' ak (z ak , x ak )(k = D, E, F, …) represent a discrete coordinate point in the △DEF area, then the modification amount E corresponding to this point is ft :

[0168]

[0169] In the formula, R' a3k (z a3k , x a3k )(k = D, E, F …) is the coordinate representation of R' ak (z ak , x ak ) in the z a3 O a3 x a3 coordinate system. The vertical distance DH from point D to EF is DH = DFsin(β f ), and the vertical distance from point O a3 to EF is x a3H .

[0170] The solution process of the tooth root target modification tooth surface is as follows: Combine the discrete coordinate points in the △DEF modification area and solve the position vector R corresponding to the tooth root target modification tooth surface using formulas (1) to (3), (5) to (6), (8), (10), (11), (12) f1 and the normal vector N f1 .

[0171] Step 5. According to the position vector R of the tooth tip target modified tooth surface obtained in Step 3 a1 and the normal vector N a1 obtain the deviation E of the actual modified tooth surface position vector corresponding to the discrete coordinate points in the standard tooth tip modified area in the direction of the target modified tooth surface normal vector a , taking the minimum sum of squares of E a as the optimization objective, taking the pressure angle, module, and helix angle as optimization variables, and using the NSGA-II genetic algorithm for optimization to obtain the optimal solution for tooth tip modification:

[0172] For diagonal modification, the shapes of the rotation projection surfaces of the tooth tip and tooth root modification areas are triangular. The essence of using a formed grinding wheel to achieve diagonal modification is to obtain different grinding wheel profiles by optimizing the three parameters of the module, pressure angle, and helix angle, so that the actual modified tooth surface after grinding approximates the target modified tooth surface, thereby achieving diagonal modification. By changing the pressure angle, the actual modified height on the tooth end surface of the modified area approximates the target modified height. By changing the helix angle, the actual modified length of the modification termination line in the modified area approximates the modified length at the tooth tip modification termination position. By changing the module, pressure angle, and helix angle, the actual modified tooth surface approximates the target modified tooth surface. The specific implementation process of tooth profile modification is as follows:

[0173] Step 5-1. First, given the value range of the optimization parameters according to theoretical analysis and optimization experience. Since the pressure angle should increase when machining the crowned tooth surface, take the standard parameters as the lower bound and add an appropriate value as the upper bound. The upper and lower bound values of the module and helix angle change bidirectionally with the standard parameters. Secondly, give the initial values of the three optimization parameters according to the basic parameters of the standard tooth surface of the gear to be machined; solve R after changing the module, pressure angle, and helix angle in combination with Eqs. (1) to (3) ai (z ai ,x ai )(i = A, B, C,...) corresponding to the position vector R of the actual modified tooth surface a2 , and calculate the deviation E of R a2 in the direction of the target modified tooth surface normal vector N a1 : l :

[0174] E l =(R a2x -R a1x )N 1x +(R a2y -R a1y )N a1y +(R a2z -R a1z )N a1z (13)

[0175] In the formula, R a1j (j = x, y, z) represents the position vector R a1Corresponding to S a -x a y a z a The x, y, and z axis coordinate components in R a2j (j = x, y, z) represents the position vector R a2 Corresponding to S a -x a y a z a The x, y, and z axis coordinate components in N a1j (j = x, y, z) represents the position vector N a1 Corresponding to S a -x a y a z a The x, y, and z axis coordinate components, where l ∈ [1, M] is the label of the discrete coordinate points in the tip relief region, and M is the total number of discrete coordinate points in the tip relief region.

[0176] Step Four Two: After giving the basic parameters, modification parameters, and optimization parameter ranges of the herringbone gear pinion, optimize and solve for the best optimization parameters with the goal of minimizing the sum of the squared tooth surface errors corresponding to the discrete coordinate points in the tip relief region △ABC, denoted as E a = [E1,...E M T (M = MI(MII - 1) + 1);

[0177] The optimization model is as follows:

[0178] Optimization variables: module m' n , pressure angle α' n , helix angle β';

[0179] Objective function:

[0180]

[0181] In the formula, f1 represents the sum of the squared tooth surface errors corresponding to the discrete coordinate points at the tooth tip.

[0182] Constraint conditions:

[0183]

[0184] Among them, α' n min is the lower limit of the pressure angle, α' n max is the upper limit of the pressure angle, m' n min is the lower limit of the module, m' n max is the upper limit of the module, β'min is the lower limit of the helix angle, β'max is the upper limit of the helix angle, and the upper and lower limits of the parameters are set according to experience;

[0185] α'​n min, α' n max, m' n min, m' n max, β'min, β'max are the optimization parameter ranges of the pinion of the herringbone gear;

[0186] The value range of the design variables for this optimization is continuous. Compared with traditional optimization methods, the NSGA-II genetic algorithm has the characteristics of good convergence, high computational efficiency, and high robustness. Therefore, the NSGA-II genetic algorithm is adopted.

[0187] Step Six: According to the position vector R f1 and the normal vector N f1 of the tooth root target modified tooth surface obtained in Step Four, obtain the deviation E of the actual modified tooth surface position vector corresponding to the discrete coordinate points in the standard tooth root modification area in the direction of the normal vector of the target modified tooth surface f , and use the minimum sum of squares of E f as the optimization objective, and use the pressure angle, module, and helix angle as the optimization variables, and adopt the NSGA-II genetic algorithm to optimize to obtain the optimal solution of tooth root modification:

[0188] Step Six-One: First, given the value range of the optimization parameters according to theoretical analysis and optimization experience. Since the pressure angle should be reduced when machining the root-modified tooth surface, take the standard parameter as the upper bound and subtract an appropriate value as the lower bound, and the upper and lower bound values of the module and helix angle change bidirectionally with the standard parameter; secondly, give the initial values of the three optimization parameters according to the basic parameters of the standard tooth surface of the gear to be machined; combine equations (1) to (3) to solve R' ak (z ak , x ak )(k = D, E, F, …) corresponding to the position vector R f2 of the actual modified tooth surface, and calculate R f2 in the direction of the normal vector N f1 of the target modified tooth surface and the deviation E t :

[0189] E t = (R f2x - R f1x )N f1x + (R f2y - R f1y )N f1y + (R f2z - R f1z )N f1z (16)

[0190] In the formula, R f1j (j = x, y, z) represents the position vector R f1 corresponding to S a-x a y a z a The x, y, and z axis coordinate components, R f2j (j = x, y, z) represents the position vector R f2 Corresponding to S a -x a y a z a The x, y, and z axis coordinate components, N f1j (j = x, y, z) represents the normal vector N f1 Corresponding to S a -x a y a z a The x, y, and z axis coordinate components, t ∈ [1, N] is the label of the discrete coordinate points within the tooth root modification region, and N is the total number of discrete coordinate points within the tooth root modification region;

[0191] Step 6-2: Given the basic parameters, modification parameters, and optimization parameter ranges of the gear, optimize with the goal of minimizing the sum of the squares of the tooth surface errors f2 corresponding to the discrete coordinate points in the standard tooth root modification region, denoted as E f = [E1,...E N T (N = MIII(MIV - 1) + 1), the optimization variables, constraint conditions, and optimization algorithm are the same as those when optimizing the tooth surface with tooth tip modification, only the objective function is different:

[0192]

[0193] In the formula, f2 represents the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region.

[0194] The flowchart for minimizing the sum of the squares of the errors of the optimized tooth tip modification tooth surface and tooth root modification tooth surface is as Figure 5 shown. The smaller the sum of the squares of the tooth surface errors, the closer the actual modified tooth surface is to the target modified tooth surface.

[0195] Step 7: According to the optimal pressure angle, module, helix angle, and standard tooth surface parameters obtained in Step 5 and Step 6, perform diagonal modification on the herringbone gear:

[0196] The formation grinding of the herringbone gear tooth surface includes 4 basic motions as Figure 6 shown, the rotational motion of the forming grinding wheel spindle C, the radial motion of the forming grinding wheel tool rest table along the Y-axis relative to the workpiece spindle, the rotational motion of the workpiece spindle A, and the axial motion of the workpiece table along the workpiece on the X-axis. The present invention only describes the processing technological process for realizing the diagonal modification of the herringbone gear teeth, and the flowchart is as Figure 7 shown. The specific steps are as follows:

[0197] ​① Prepare a herringbone gear workpiece with sufficient grinding allowance processed by a hob before grinding. The positioning method is centering and positioning with hydraulic centers at both ends, as shown in Figure 8 . After the centers at both ends of the machine tool and the center holes of the herringbone gear are centered and positioned, the two are fixed through the self-locking nuts of the chucks. The center on the right side of the machine tool is a fixed shaft, and the center on the left side is a rotating shaft. Since the center hole on the end face of the gear blank will generate burrs on the surface after rubbing against the fixed center on the right side, the center hole and the center need to be polished with sandpaper after each processing to ensure the smoothness of both, thereby ensuring the machining accuracy of the gear.

[0198] ② Input three groups of parameters corresponding to the standard tooth surface, crowned tooth surface, and root-relieved tooth surface of the herringbone gear to be ground on the numerical control panel of the numerical control machine tool. The basic parameters of the herringbone gear corresponding to the standard tooth surface include module, pressure angle, helix angle, helix direction, normal modification coefficient, tooth width, and number of teeth. Compared with the standard tooth surface, the crowned tooth surface and the root-relieved tooth surface are only different in module, pressure angle, and helix angle.

[0199] Among them, the module, pressure angle, and helix angle of the tooth tip crowning and tooth root relief are the optimal parameters obtained in Step 6;

[0200] ③ Select the grinding wheel radius and perform dressing before grinding. Select a suitable grinding wheel radius to ensure that there is no interference with the teeth on the other side of the herringbone tooth when retracting the tool in the herringbone tooth relief groove. Before each processing, the profile of the grinding wheel needs to be dressed with a diamond roller according to the input parameters of the herringbone gear. The dressing ratio is 0.7, the dressing speed is 300 mm / min, and the dressing amount per time is 0.02 mm. Select an appropriate number of dressing times according to the actual situation.

[0201] ④ Grinding wheel tool setting. Ensure that the axis of the C-axis of the grinding wheel spindle and the outer end face of the right-handed tooth are in the same plane. Rotate the helix angle of the grinding wheel by β angle around the B-axis. By adjusting the angle of the A-axis of the workpiece spindle and the moving distance of the Y-axis of the radial movement axis of the grinding wheel headstock, make the profile of the grinding wheel completely coincide with the tooth surface of the gear tooth groove, thereby completing the tool setting.

[0202] ⑤ Grinding parameter setting. Input the length of the 5-tooth common normal corresponding to the final grinding size on the machine tool panel. The grinding includes three stages: rough grinding, semi-finishing grinding, and finishing grinding. The grinding method is selected as double-sided grinding, and the stroke number is selected according to the grinding feed rate. During rough grinding, the rotational speed of the grinding wheel spindle is 2000 r / min, and the single radial feed is 0.03 mm; during semi-finishing grinding, the rotational speed of the grinding wheel spindle is 1500 r / min, and the single radial feed is 0.025 mm; during semi-finishing grinding, the rotational speed of the grinding wheel spindle is 1200 r / min, and the single radial feed is 0.025 mm.

[0203] ⑥Grinding sequence setting. First, grind the standard tooth surface, and accurately record the rotation angle value of the workpiece spindle C-axis in the machine tool coordinate system when the grinding wheel tool setting is completed. When grinding the crowned tooth surface and the relieved tooth surface, it is necessary to keep the rotation angle of the workpiece spindle C-axis the same as that when grinding the standard tooth surface.

[0204] ⑦Changing the grinding direction. After all the right-handed teeth are ground, grind the left tooth surface in the same way, only changing the grinding direction input parameter on the machine tool panel to left-handed, and other parameters remain the same.

[0205] ⑧Tooth surface error detection. After grinding, conduct error detection at the measurement center to check whether the tooth surface accuracy and profile modification meet the design requirements.

[0206] Example:

[0207] The basic parameters of the herringbone gear pair are as follows: the left teeth of the pinion are right-handed and the right teeth are left-handed, the left teeth of the gear are left-handed and the right teeth are right-handed, the normal module is 5 mm, the modification coefficient is 0, the number of teeth of the pinion is 30, the number of teeth of the gear is 72, the normal pressure angle is 20°, the pitch circle helix angle is 33.273°, and the tooth width of one side of the teeth is 40 mm.

[0208] (1) Optimization example of the tooth tip part

[0209] Take MI = 9, MII = 10, the modification height AB = 3.93 mm, the maximum modification amount y a = 30 μm, 200 populations, 40 generations of genetic algebra, and the probabilities of crossover and mutation operations are set to 0.9 and 0.1 respectively according to experience. The optimization parameter range is set as: m n min = 4.8 mm, m n max = 5.2 mm, αmin = 20°, αmax = 21°, βmin = 32.6°, βmax = 34°. The optimization results are: m n = 4.99961 mm, α = 20.6469°, β = 33.4274°, f1min = 4.05831×10 -6 . The error diagrams of the standard tooth surface and the actual modified tooth surface in the tooth tip modification area are as Figure 9 shown, and the error diagrams of the target modified tooth surface and the actual modified tooth surface in the tooth tip modification area are as shown in Figure 10.

[0210] It can be found from Figures 9 - 10 that the maximum error of the actual tooth surface is 1 μm, which occurs on the end face of the modification starting point. The maximum modification amount at the tooth tip is 30 μm, and after calculation, the target modification height is 0.1253 mm larger than the actual modification height, and the target modification length is 0.2106 mm larger than the actual modification length, meeting the design requirements.

[0211] (2) Optimization example of the tooth root part

[0212] Take MIII = 9, MIV = 10, the modification height DF = 3 mm, and the maximum modification amount y f = 30 μm, 200 populations, 30 generations of genetic algebra, and the crossover and mutation operation probabilities are set to 0.9 and 0.1 respectively according to experience. Optimization parameter settings: m n min = 4.8 mm, m n max = 5.2 mm, αmin = 19°, αmax = 20°, βmin = 32.6°, βmax = 34°. The optimization results are: m n = 5.01109 mm, α = 19.7686°, β = 33.2137°, f2min = 8.02391×10 -6 . The error diagram of the standard tooth surface and the actual modified tooth surface in the tooth root modification area is as shown in Figure 11 Figure 12, and the error diagram of the target modified tooth surface and the actual modified tooth surface in the tooth root modification area is as shown in Figure 12.

[0213] From Figures 11 - 12 it can be seen that the maximum error of the actual tooth surface is 1 μm, which occurs on the end face of the modification starting point. The maximum modification amount at the tooth tip is 30 μm. After calculation, the target modification height is 0.1422 mm smaller than the actual modification height, and the target modification length is 0.1986 mm smaller than the actual modification length, meeting the design requirements.

Claims

1. A straight diagonal modification method for herringbone gears based on profile grinding, characterized in that The specific process of the method is as follows: Step 1: Determine the orientation of the tooth tip and tooth root modification regions of the herringbone gear according to the helix direction of the single-sided teeth and the left and right tooth surfaces, so as to obtain the standard tooth tip modification region △ABC and the standard tooth root modification region △DEF. Specifically: Step 1-1: Determine the orientation of the tooth tip and tooth root modification regions of the herringbone gear according to the helix direction of the single-sided teeth and the left and right tooth surfaces: First, take the triangular regions where the driving tooth root engages and the tooth tip disengages as the single-sided tooth surface modification regions; Then, determine the range of the tooth tip modification termination position and the range of the tooth root modification termination position within the tooth surface modification region, that is, the orientation of the tooth tip and tooth root modification regions of the herringbone gear; The range of the tooth tip modification termination position is: the region range where the tooth tip is non-chamfered; The range of the tooth root modification termination position is: the region range of the starting point where the driven tooth tip meshes and contacts on the driving tooth surface; Step 1-2: Based on the orientation of the tooth tip and tooth root modification regions of the herringbone gear determined in Step 1-1, obtain the standard tooth tip modification region △ABC according to the preset tooth tip modification height AB, and obtain the standard tooth root modification region △DEF according to the preset tooth root modification height DE; Among them, BC is the boundary line between the standard tooth surface and the tooth tip modification tooth surface, and EF is the boundary line between the standard tooth surface and the tooth root modification tooth surface; Step 2: Obtain the projection helix angle β of the tooth tip modification starting line BC and the projection helix angle β corresponding to the tooth root modification starting line EF according to the standard tooth tip modification area △ABC and the standard tooth root modification area △DEF obtained in Step 1 a f ;​ Step 3. According to β obtained in Step 2 a Obtain the modification amount of the discrete coordinate points in the standard addendum modification area, and obtain the position vector R of the target addendum modified tooth surface according to the modification amount of the discrete coordinate points a1 and the normal vector N a1 ; Step 4. According to β obtained in Step 2 f Obtain the modification amount of the discrete coordinate points in the standard tooth root modification area, and obtain the position vector R of the target modified tooth surface of the tooth root according to the modification amount of the discrete coordinate points f1 and the normal vector N f1 ; Step 5. According to the position vector R of the tooth tip target modified tooth surface obtained in Step 3 a1 and the normal vector N a1 obtain the deviation E of the position vector of the actual modified tooth surface corresponding to the discrete coordinate points in the standard tooth tip modification area in the direction of the normal vector of the target modified tooth surface a . Taking the minimum sum of squares of E a as the optimization objective, and taking the pressure angle, module, and helix angle as the optimization variables, use the NSGA-II genetic algorithm for optimization to obtain the optimal pressure angle, module, and helix angle of the tooth tip modification; Step 6: Based on the position vector R of the tooth root target modified tooth surface obtained in Step 4 f1 and the normal vector N f1 obtain the deviation E of the position vector of the actual modified tooth surface corresponding to the discrete coordinate points in the standard tooth root modification area in the direction of the normal vector of the target modified tooth surface f , taking the minimum sum of squares of E f as the optimization objective, taking the pressure angle, modulus, and helix angle as the optimization variables, and using the NSGA-II genetic algorithm for optimization to obtain the optimal pressure angle, modulus, and helix angle for tooth root modification; Step 7: Perform diagonal modification on the herringbone gear according to the standard tooth surface parameters and the optimal pressure angle, module, and helix angle of the tooth tip modification and tooth root modification obtained in Step 5 and Step 6 to obtain the modified herringbone gear.

2. A straight diagonal modification method for herringbone gears based on profile grinding according to claim 1, characterized in that: The step in Step 1-2 of obtaining the standard tooth tip modification region △ABC according to the preset tooth tip modification height AB and obtaining the standard tooth root modification region △DEF according to the preset tooth root modification height DE based on the orientation of the tooth tip and tooth root modification regions of the herringbone gear determined in Step 1-1 includes the following steps: Step 121: Given the addendum modification height AB, establish the coordinate system z a O a x a , and obtain the x and z coordinate components of vertex B in the coordinate system z a O a x a : where x aB , z aB respectively represent the x and z coordinate components corresponding to the midpoint B of the coordinate system z a O a x a , W represents the tooth width, and AB is the modification height; The coordinate z a O a x a The origin O a is located at the intersection of the mid-section of the tooth width and the axis, the x a axis is along the radial direction of the mid-section of the tooth width, and the z a axis is located on the gear axis; Step 122: Establish the moving coordinate system S of the gear a -x a y a z a , the reference coordinate system S of the rack cutter b -x b y b z b , the moving coordinate system S of the rack cutter d -x d y d z d , obtain the position vector R of point B in the moving coordinate system S of the rack cutter d -x d y d z d and the normal vector N d (u, l), and then use R d (u, l) and N d (u, l) to obtain the position vector of point B in the moving coordinate system S of the gear d (u, l) and N a -x a y a z a and the normal vector where \(R_0(u, l)\) and \(N_0(u, l)\) respectively represent the position vector and the normal vector of point B in S b -x b y b z b , \(u\) and \(l\) are the parameters of the rack cutter tooth surface; \(R\ d (u, l)\) and \(N\ d (u, l)\) respectively represent the position vector and the normal vector of point B in S d -x d y d z d , \(M\ db (β)\) represents the coordinate transformation parameter of point B from S b -x b y b z b to S d -x d y d z d , represents the coordinate transformation parameter of point B from S d -x d y d z d to S a -x a y a z a , is the rotation angle of gear machining; The gear moving coordinate system S a -x a y a z a In the coordinate system, the origin O a is located at the intersection of the mid-section of the tooth width and the axis. The x a axis is along the radial direction of the mid-section of the tooth width. The y a axis is located in the mid-section of the tooth surface and perpendicular to the x a axis. The z a axis is located on the gear axis; The said S b -x b y b z b In the coordinate system, the origin O b is located at the intersection point of the normal middle section of the rack cutting tool and the pitch circle. The x b axis direction is along the direction of the normal middle section of the tool and perpendicular to the axis of the gear. The y b axis is perpendicular to the surface of the tool. The z b axis is along the direction of the surface of the tool and perpendicular to the x b axis; The said S d -x d y d z d In the coordinate system, O b is translated along the negative y c axis by a m to obtain the origin O d , where the x d axis is along the radius direction of the gear, the y d axis is along the tangential direction of the gear, and the z d axis is along the axis direction of the gear; where a m = πm n / 4, and m n is the normal module of the standard gear; Steps One, Two, and Three: Utilize R obtained in Step One, Two, and Two d (u, l), N d (u, l), Establish the addendum meshing equation: In the formula, represents the coordinate component of the position vector corresponding to point B along the j-axis in the moving coordinate system S of the gear a -x a y a z a ; R dj (u, l), N dj (u, l) respectively represent the coordinate components of the position vector and the normal vector corresponding to point B along the j-axis in the moving coordinate system S of the rack cutter d -x d y d z d ; j = x, y, z; r p1 represents the pitch radius, is the instantaneous machining rotation angle of the gear at point B; Steps 1, 2, and 4: Substitute x aC = r a1 into the addendum meshing equation (3) established in Steps 1, 2, and 3 to obtain the rack cutter tooth surface parameters u and l, and then find z ac , and then use z ac to obtain the modification length AC, thereby obtaining the standard addendum modification region △ABC; Among them, x aC is z a O a x a The z - coordinate component corresponding to point C in a1 where r is the addendum circle radius, are the instantaneous machining rotation angles of the gear corresponding to points B and C on the projection BC of the tooth surface contact line respectively, and z aC is z a O a x a the z - coordinate component corresponding to point C in Step 125: Given the root modification height DE, obtain the x and z coordinate components of the coordinates of point E in the a O a x a coordinate system, specifically: where x aE , z aE are the x and z coordinate components corresponding to point E in the coordinate system z a O a x a , and r k1 is the radius of the root modification termination line; Step 1-2-6: Obtain the tooth root modification length DF according to the x and z coordinate components of the E point coordinates obtained in Step 1-2-5, so as to obtain the standard tooth root modification region △DEF.

3. A linear diagonal modification method for herringbone gears based on profile grinding according to claim 2, characterized in that: In the first, second, and fourth steps, the use of z ac Obtaining the modified length AC specifically is as follows:

4. A linear diagonal modification method for herringbone gears based on profile grinding according to claim 3, characterized in that: The specific method in Step 1-2-6 of obtaining the tooth root modification length DF according to the x and z coordinate components of the E point coordinates obtained in Step 1-2-5 is: First, obtain the x and z coordinate components of the E-point coordinates obtained in step 125 to obtain the position vector of point E in the gear moving coordinate system S a -x a y a z a and the normal vector The position vector of point E in the rack cutter moving coordinate system S d -x d y d z d and the normal vector N'(u, l); d (u, l) and the normal vector d (u, l); Among them, obtaining R' d (u, l), N' d (u, l) and the method of obtaining R d (u, l), N d (u, l) are the same; Then, substitute R' d (u, l), N' d (u, l) and Equation (5) into the tooth root meshing equation to obtain the machining rotation angle corresponding to the tooth surface contact line EF Among them, the method for obtaining the tooth root meshing equation is the same as the method for obtaining the tooth tip meshing equation; Then, substitute x aE = r k1 into the tooth root engagement equation to obtain the tooth root modification length DF: where z aF is the z - coordinate component corresponding to point F in the coordinate system z a O a x a and x aE is the x - coordinate component corresponding to point E in the z a O a x a coordinate system. They are the instantaneous machining rotations of the gear corresponding to the projected points E and F of the flank contact line respectively.

5. A straight diagonal modification method for herringbone gears based on profile grinding according to claim 4, characterized in that: Obtaining the projection helix angle β of the addendum modification starting line BC and the projection helix angle β corresponding to the dedendum modification starting line EF according to the standard addendum modification region △ABC and the standard dedendum modification region △DEF obtained in the first step in the second step a Specifically, it is as follows: f and the projection helix angle β corresponding to the dedendum modification starting line EF Step 2-1: Obtain the projection helix angle β of the tooth tip modification starting line BC according to the standard tooth tip modification area △ABC obtained in Step 1 a : β a = arctan(AB / AC) (7) Among them, AB is the tooth tip modification height, and AC is the tooth tip modification length; Step 22: Obtain the projection helix angle β corresponding to the tooth surface contact line EF according to the standard tooth root modification region △DEF obtained in Step 1 f : β f = arctan(DE / DF) (8) Among them, DE is the tooth root modification height, and DF is the tooth root modification length.

6. A linear diagonal modification method for herringbone gears based on profile grinding according to claim 5, characterized in that: β obtained in step three according to step two a Obtain the modification amount of the discrete coordinate points in the standard tip relief area, and obtain the position vector R of the target tip relief tooth surface according to the modification amount of the discrete coordinate points a1 and the normal vector N a1 , specifically as follows: Step 3.1: Establish a coordinate system z a2 O a2 x a2 , discretize the coordinates of the △ABC region numerically to obtain discrete coordinate points, and then obtain the cultivation amount E corresponding to each discrete coordinate point R ai (z ai ,x ai ), where at : First, discretize the coordinates of the △ABC region numerically to obtain the coordinates of each discrete point within the △ABC region; The discrete points are obtained in the following way: In the △ABC region, take an equal number of equally spaced discrete coordinate points on each rotation projection line parallel to the tooth tip modification starting line BC, and the number of points is denoted as MI; take equally spaced discrete coordinate points on the modification length AC, and the number of points is denoted as MII; Then, obtain each discrete coordinate point R ai (z ai ,x ai ) corresponding to the cultivation amount E at : wherein, R a2i (z a2i , x a2i ) is the coordinate representation of R ai (z ai , x ai ) in the z a2 O a2 x a2 coordinate system, AG = ACsin(β a ) is the perpendicular distance from point A to BC, x a2G represents the perpendicular distance from point O a2 to BC, y a is the preset maximum amount of tip relief, z ai is the z-axis coordinate of R ai , x ai is the x-axis coordinate of R ai ; The coordinate system z a2 O a2 x a2 In x a2 axis is in the normal direction of the starting line of tip relief, z a2 axis and z a1 The included angle between the positive semi-axis is β, O a Along x a axis in the positive direction is translated by r p1 to obtain O a2 , z a1 axis is located on the pitch circle; Step 32: Obtain the modification amount E corresponding to the discrete coordinate points in the △ABC area obtained in Step 31 at (u, l) Obtain the position vector R of the target modified tooth surface at the tooth tip a1 and the normal vector N a1 : R a1 = R a0 (u, l) + N a0 (u, l)E at (u, l) (10) wherein, R a0 (u, l) is the position vector corresponding to the unmodified standard tooth surface, and N a0 is the normal vector corresponding to the unmodified standard tooth surface.

7. A linear diagonal modification method for herringbone gears based on profile grinding according to claim 6, characterized in that: β obtained in step 4 according to step 2 f Obtain the modification amount of the discrete coordinate points in the standard tooth root modification area, and obtain the position vector R of the target modified tooth surface of the tooth root according to the modification amount of the discrete coordinate points f1 and the normal vector N f1 , specifically including the following steps: Step 4.1: Establish a coordinate system z a3 O a3 x a3 , discretize the coordinates of the △DEF region numerically to obtain discrete coordinate points, and then obtain each discrete coordinate point R' ak (z ak , x ak ) corresponding cultivation amount E ft : First, discretize the coordinates of the △DEF region numerically to obtain the coordinates of each discrete point in the △DEF region; The discrete points are obtained in the following way: In the △DEF region, take an equal number of equally spaced discrete coordinate points on each rotation projection line parallel to the tooth root modification starting line EF, and the number of points is denoted as MIII; take equally spaced discrete coordinate points on the modification length DF, and the number of points is denoted as MIV; Then, obtain each discrete coordinate point R' ak (z ak ,x ak ) corresponding cultivation amount E ft : wherein, R' a3k (z a3k , x a3k ) is the coordinate representation of R' ak (z ak , x ak ) in the z a3 O a3 x a3 coordinate system, DH = DFsin(β f ) is the perpendicular distance from point D to EF, x a3H represents the perpendicular distance from point O a3 to EF, y f is the preset maximum root modification amount, k = D, E, F, …, k is any discrete point within the root modification region; The coordinate system z a3 O a3 x a3 In x a3 axis is located in the normal direction of the starting line of the tooth root modification, z a3 axis and z a1 The included angle between the negative half-axis is β a , O a Translate along the positive direction of the x a axis by r p1 to obtain O a3 ; Step 42: Obtain the modification amount E corresponding to the discrete coordinate points in the △ABC area obtained in Step 41 ft Obtain the position vector R of the target modified tooth surface at the tooth root f1 and the normal vector N f1 ; Among them, the method for obtaining the position vector R f1 and the normal vector N f1 is the same as the method for obtaining the position vector R a1 and the normal vector N a1 of the target modified tooth surface at the tooth tip.

8. A method for linear diagonal modification of herringbone gears based on profile grinding, as claimed in claim 7, wherein: The position vector R of the tooth tip target modified tooth surface obtained according to Step 3 in Step 5 a1 and the normal vector N a1 Obtain the deviation E of the actual modified tooth surface position vector corresponding to the discrete coordinate points in the standard tooth tip modification area in the direction of the target modified tooth surface normal vector a , with E a Taking the minimum sum of squares as the optimization objective, and taking the pressure angle, module, and helix angle as the optimization variables, the NSGA-II genetic algorithm is used for optimization to obtain the optimal pressure angle, module, and helix angle of the tooth tip modification, including the following steps: Step 5.1: Obtain the position vector R of the actual modified tooth surface corresponding to the changed module, pressure angle, and helix angle ai (z ai ,x ai ), and obtain R according to the following formula a2 , and obtain the deviation E of R in the direction of the normal vector N of the target modified tooth surface a2 : a1 l : E l = (R a2x - R a1x )N 1x + (R a2y - R a1y )N a1y + (R a2z - R a1z )N a1z (13) where R a1j denotes R a1 corresponding to S a -x a y a z a is the j-axis coordinate component in, R a2j denotes R a2 corresponding to S a -x a y a z a is the j-axis coordinate component in, N a1j denotes N a1 corresponding to S a -x a y a z a is the j-axis coordinate component in, l ∈ [1, M] is the label of the discrete coordinate points in the tip relief region, and M is the total number of discrete coordinate points in the tip relief region; Step 52: Obtain the optimization parameter range of the pinion of the herringbone gear, and perform optimization to solve for the best optimization parameter E with the goal of minimizing the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tip modification region △ABC a = [E1,...E M T ;​ Wherein, M = MI(MII - 1)+1; The optimization variables in the optimization aiming at minimizing the sum of squares of tooth surface errors corresponding to the discrete coordinate points in the standard tip modification region △ABC include: module m' n , pressure angle α' n , helix angle β'; The objective function is: Wherein, f1 is the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points at the tooth tip; The constraint conditions are: where α' n min is the preset lower limit of the pressure angle, α' n max is the preset upper limit of the pressure angle, m' n min is the preset lower limit of the module, m' n max is the preset upper limit of the module, β'min is the preset lower limit of the helix angle, and β'max is the preset upper limit of the helix angle.

9. A method for linear diagonal modification of herringbone gears based on profile grinding according to claim 8, characterized in that: The position vector R of the tooth root target modified tooth surface obtained according to Step 4 in Step 6 f1 and the normal vector N f1 Obtain the deviation E of the actual modified tooth surface position vector corresponding to the discrete coordinate points in the standard tooth root modification area in the direction of the target modified tooth surface normal vector f , with E f Taking the minimum sum of squares as the optimization objective, and taking the pressure angle, module, and helix angle as the optimization variables, use the NSGA-II genetic algorithm for optimization to obtain the optimal pressure angle, module, and helix angle for tooth root modification, including the following steps: Step 6.1: Obtain R' after changing the module, pressure angle, and helix angle ak (z ak ,x ak ) corresponding position vector R of the actual modified tooth surface f2 , and obtain R according to the following formula f2 Deviation E in the direction of the normal vector N of the target modified tooth surface f1 : t : E t = (R f2x - R f1x )N f1x + (R f2y - R f1y )N f1y + (R f2z - R f1z )N f1z (16) wherein, R f1j represents R f1 corresponding to S a -x a y a z a is the j-axis coordinate component in f2j Table R f2 corresponding to S a -x a y a z a is the j-axis coordinate component in f1j represents N f1 corresponding to S a -x a y a z a where t ∈ [1, N] is the label of the discrete coordinate points in the tooth root modification region, and N is the total number of discrete coordinate points in the tooth root modification region; Step 62: Obtain the optimization parameter range of the pinion of the herringbone gear. Optimize and solve for the best optimization parameter E with the goal of minimizing the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region △DEF f = [E1,...E N T ;​ Wherein, N = MIII(MIV - 1)+1; The constraint conditions and optimization variables in the optimization with the objective of minimizing the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region △DEF are the same as those in the optimization with the objective of minimizing the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth tip modification region; The objective function in the optimization with the goal of minimizing the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region △DEF is as follows: Wherein, f2 represents the sum of the squares of the tooth surface errors corresponding to the discrete coordinate points in the standard tooth root modification region.

Images