Forming Gear Grinding Chip Parameter Calculation and Correction Method

Abstract

The present invention discloses a method for calculating and correcting the chip parameters of form grinding gears, which includes the following steps: Step 1: Construct a grinding kinematic model considering the direction of the tooth surface normal vector: 11) Calculate the abrasive grain motion trajectory: Calculate the abrasive grain motion trajectory during the grinding process; 12) Construct a gear grinding kinematic model: Solve the cutting paths of adjacent cutting abrasive grains, and establish a numerical model of the abrasive grain cutting trajectory and chip considering the superposition effect of the adjacent abrasive grain motion; Step 2: Calculate and correct the chip parameters of form grinding gears: 21) Chip geometry of form grinding gears: Solve the motion trajectory plane at the position with the maximum normal grinding depth of two adjacent abrasive grains to obtain the chip geometry of form grinding gears; 22) Calculate the chip cross-section and the undeformed chip thickness: Calculate the chip cross-section of form grinding gears based on the obtained chip geometry; Correct the undeformed chip thickness by using the equivalent cutting diameter and the chip cross-sectional area coefficient of form grinding gears.

Description

Technical Field

[0001] The present invention belongs to the technical field of grinding machining, and specifically relates to a method for calculating and correcting the chip parameters of form grinding of gears. Background Art

[0002] The grinding force affects the grinding heat, machine tool vibration, workpiece surface topography, and wheel wear, and is an important parameter for evaluating the grinding machining state. However, different from other machining methods such as turning and milling, in grinding, the abrasive grains cut with a negative rake angle, and a large number of abrasive grains that do not directly participate in material removal will still generate abrasive grain-workpiece contact forces, resulting in a more complex calculation process of the grinding force. Different from traditional surface / outer circle grinding, in form grinding of gears, there is an angle between the normal vector direction of the abrasive grains and the radial direction of the grinding wheel, and this angle changes with the involute angle position of the grinding surface, resulting in obvious changes in the chip geometric parameters. In addition, traditional grinding force models usually use the classical Hertz contact spherical model to calculate different grinding critical conditions, but due to the actual shape of the abrasive grains not being spherical, there are errors in the calculation results.

[0003] The chip is formed by the cutting of the abrasive grain movement trajectory and the workpiece tooth surface, and is a geometric body formed by the enclosure of the abrasive grain cutting path and the gear tooth surface. The chip shape and geometric parameters are the most important analysis and calculation parameters in the grinding process modeling, and are also important transition parameters in the modeling steps of machining process variables such as grinding force and grinding temperature. Therefore, the modeling of the grinding machining chip and the calculation of related parameters are an essential part of the grinding geometry-kinematics modeling. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for calculating and correcting the chip parameters of form grinding of gears. Based on the movement path of the form grinding abrasive grains, considering the influence of the special geometric shape of the gear on the cutting process, a chip model for form grinding machining is established, providing a basis for subsequent grinding force and tooth surface topography modeling.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] A method for calculating and correcting the chip parameters of form grinding of gears includes the following steps:

[0007] Step 1: Construct a grinding kinematic model considering the normal vector direction of the tooth surface

[0008] 11) Calculate the abrasive grain movement trajectory: Considering the influence of the normal vector direction of the abrasive grains on the calculation results, calculate the abrasive grain movement trajectory during the grinding process;

[0009] 12) Construct a gear grinding kinematic model considering adjacent cutting abrasive grains: According to the abrasive grain movement trajectory, solve the cutting paths of adjacent cutting abrasive grains respectively, and establish a numerical model of the abrasive grain cutting trajectory and chip of the machining process considering the superposition effect of adjacent abrasive grain movements;

[0010] Step 2: Calculate and correct the chip parameters of form grinding

[0011] 21) Chip geometry of form grinding: Based on the established kinematic model of gear grinding, solve the motion trajectory plane at the position with the maximum normal grinding depth of two adjacent abrasive grains to obtain the chip geometry of form grinding;

[0012] 22) Calculate the chip cross-section and the undeformed chip thickness

[0013] Calculate the chip cross-section of form grinding based on the obtained chip geometry;

[0014] Use the equivalent grinding diameter and the chip cross-section area coefficient of form grinding to correct the undeformed chip thickness.

[0015] Furthermore, in the above step 11), for the abrasive grain at any position point P on the grinding wheel surface, the abrasive grain number is n; the angle between the normal vector direction of the abrasive grain position and the radial direction of the grinding wheel results in different normal grinding depths and radial grinding depths of grinding:

[0016] a n = a r cosα p

[0017] where, a n is the normal cutting depth of the abrasive grain; a r is the radial cutting depth of the abrasive grain; α p is the angle between the normal direction of the abrasive grain and the radial direction of the grinding wheel;

[0018] In the established coordinate system TCS, the motion trajectory line of the nth abrasive grain on the grinding wheel is:

[0019] x gn = X wp

[0020] y gn = R p cosω + Y wp

[0021] z gn = R p sinω + Z wp

[0022] where, x gn , y gn , z gn are the motion trajectories of the nth abrasive grain respectively; R p is the grinding wheel rotation radius corresponding to the discrete segment of the abrasive grain position; ω is the grinding wheel rotation angle; X wp , Y wp , Z wpis the perpendicular point coordinate of the abrasive grain position to the axis of the grinding wheel, that is, the coordinate of the rotation center of the abrasive grain; the Z-axis of the coordinate system TCS is the axis of the gear workpiece, the Y-axis is the perpendicular intersection line of the axis of the gear workpiece and the axis of the grinding wheel, and the X-axis is perpendicular to the Y-axis and the Z-axis respectively;

[0023] The cutting trajectory of the abrasive grain inside the workpiece material is in the YZ plane, and due to the influence of the normal direction of the abrasive grain, the trajectory line of the cutting-out point of the abrasive grain is a curve on the tooth surface.

[0024] Furthermore, in the step 12), to solve the complete cutting path of the nth abrasive grain, for the nth abrasive grain: assume that the involute angle corresponding to the position of the abrasive grain on the tooth surface is The orientation of the abrasive grain is the normal vector direction at this position. According to the involute equation of the tooth surface, determine the coordinates (X P , Y P , Z P ) of the abrasive grain position point:

[0025]

[0026] Z P = b n

[0027] where b n is the position of the nth abrasive grain in the tooth direction; r b is the base circle radius of the gear:

[0028] Discretize the protruding height of the abrasive grain. The position of each discrete segment is related to the discretization degree. Discretize the normal protruding height into m segments on average. Then, the discrete point coordinates of the kth discrete segment of the nth abrasive grain in the gear coordinate system are:

[0029]

[0030] Z n,k = Z P

[0031] In the formula, X n,k , Y n,k , Z n,k respectively represent the coordinate values of the kth discrete segment of the nth abrasive grain in the X, Y, and Z directions in the coordinate system; h i is the total protruding height of the abrasive grain; α p is the angle between the normal direction of the abrasive grain and the radial direction of the grinding wheel;

[0032] The rotation plane of the abrasive grain is the YZ plane of the gear coordinate system. The motion trajectory of the kth discrete segment during the grinding rotation is:

[0033] x n,k = X n,k

[0034] y n,k = (Y D - Y n,k ) cos ω n,k + Y D

[0035] z n,k = (Y D - Y n,k ) sin ω n,k + Z n,k

[0036] where x n,k , y n,k , z n,k respectively represent the coordinate values of the trajectory line of the k-th discrete segment of the n-th abrasive grain in the X, Y, and Z directions in the coordinate system; Y D is the distance between the grinding wheel and the gear center; ω n,k is the rotation angle parameter of the k-th discrete segment of the n-th abrasive grain;

[0037] Based on the involute basic parameter equation of the standard external involute spur cylindrical gear, the numerical solutions of the involute angle of the tooth profile at the cut-off point of the k-th discrete segment of the n-th abrasive grain and the rotation angle ω n,k_out of the abrasive grain are obtained;

[0038] The complete cutting path of the n-th abrasive grain over the entire protrusion height is obtained through the cut-off point of the k-th discrete segment and the cutting motion path.

[0039] Furthermore, based on the superposition effect of the adjacent abrasive grain movement, the cutting path of the (n + 1)-th abrasive grain adjacent to the n-th abrasive grain is solved;

[0040] There is a feeding motion in the axial direction between the (n + 1)-th abrasive grain and the n-th abrasive grain:

[0041] x n+1,k = x n,k

[0042] y n+1, k = y n,k

[0043] z n+1,k = z n,k + f n,k

[0044] where x n+1,k , y n+1,k , z n+1,k respectively represent the X, Y, and Z coordinate values of the k-th discrete segment trajectory of the (n + 1)-th abrasive grain; f n,k is the axial feed amount of the adjacent cutting abrasive grains corresponding to the k-th discrete segment;

[0045] The cutting positions of different discrete segments are different, and the total axial feed of the discrete segments is also different:

[0046]

[0047] In the formula, f n,k_out is the total axial feed corresponding to the cutting point of the k-th discrete segment of the n-th abrasive grain; ω n,k_out and ω n,m_out are the cutting position rotation angles of the k-th and m-th discrete segments of the n-th abrasive grain respectively; f n,m_out is the total axial feed corresponding to the cutting point of the m-th discrete segment of the n-th abrasive grain;

[0048] According to the total axial feed of each discrete segment, the feed matrix [f] of all discrete segments of the n-th abrasive grain can be obtained:

[0049]

[0050] In the formula, [f n,k is the feed matrix of the k-th discrete segment of the n-th abrasive grain;

[0051] The feed matrix [f n,k and the trajectory line matrix [z n,k of the n-th abrasive grain in the Z direction of the coordinate system space are matrices of the same type; the matrix [z n,k is established through the abrasive grain rotation angle matrix, and the feed matrix of any discrete segment k is:

[0052]

[0053] In the formula, length(·) represents the length of the array, that is, the larger value of the number of rows or columns of the matrix.

[0054] Furthermore, in step 21), according to the movement trajectories of the m-th discrete segments of the n-th abrasive grain and the (n + 1)-th abrasive grain respectively, connecting the trajectory points of the two abrasive grain discrete segments at the same rotation angle ω n,m is the boundary line segment on the chip side plane at this rotation angle; each rotation angle element in the discrete segment rotation angle matrix [ω n,m corresponds to a boundary line segment on the chip side plane at this rotation angle, and the equation of the side plane boundary line segment corresponding to the i-th rotation angle element value ω n,m in the rotation angle matrix [ω n,m_i is:

[0055] x sb,i = X n,m

[0056] y sb,i = Y n,m_out

[0057] z sb,i =t sb,i (z n+1,m_i -z n,m_i )+z n,m_i

[0058] In the formula, x sb,i , y sb,i , z sb,i are the X, Y, and Z coordinate values of the boundary line segments of the chip side plane corresponding to the rotation angle elements respectively; X n,m is the X coordinate value of the trajectory line of the m-th discrete segment of the n-th abrasive grain; Y n,m_out is the Y coordinate value of the cut-off point of the trajectory of the m-th discrete segment of the n-th abrasive grain; z n,m_i and z n+1,m_i are the Z coordinate values of the trajectory lines of the m-th discrete segment of the n-th abrasive grain and the m-th discrete segment of the (n + 1)-th abrasive grain at the rotation angle element ω n,m_i respectively; t sb,i is the parameter variable of the line segment, representing the length of the side plane section line;

[0059] In form grinding of gears, the movement trajectory of the n-th abrasive grain forms the upper surface of the chip, the movement trajectory of the (n + 1)-th abrasive grain forms the lower surface of the chip, and the feed movement between the two abrasive grains forms the side plane of the chip, which together with the gear tooth surface forms the chip geometry.

[0060] Furthermore, in the step 22), the chip is jointly composed of the upper surface, the lower surface, the side plane and the tooth surface, and the cross-sectional area of the chip is calculated according to the equations of each line segment of the chip cross-section as:

[0061]

[0062] l u_i =t ub_max

[0063] l b_i =t bb_max

[0064] In the formula, S cs_i is the cross-sectional area of the chip at the rotation angle element; l u_i and l b_i are the lengths of the upper surface section line and the lower bottom section line of the chip cross-section respectively. When the rotation angle element exceeds the critical position, l u_i is 0, and the cross-sectional shape is triangular; t sb_i is the length of the side plane section line; t ub_max and t bb_max are both parameter variables.

[0065] Furthermore, for the intercepted line segment of the chip cross-section on the tooth surface, at any instantaneous rotation angle ω cs :

[0066]

[0067] In the formula, x tb , y tb , z tb are the spatial coordinates of the cross-sectional line segment on the tooth surface respectively; t tb is a parameter variable, and t tb_min and t tb_max are the minimum and maximum values of the parameter variable respectively, and:

[0068] t tb_min = Y D - Y n,m , ω cs ∈(0, ω n,m_out )

[0069]

[0070] Solve to obtain the numerical solution of t tb_max ;

[0071] For the line segment on the upper surface of the chip, for any instantaneous rotation angle ω cs ∈(0, ω n,m_out ):

[0072]

[0073] In the formula, x ub , y ub , z ub are the spatial coordinates of the cross-sectional line segment on the upper surface of the chip respectively; t ub is a parameter variable; t ub_max are the maximum values of the parameter variable respectively. Combine x n,k , y n,k , z n,k in step 12) and x n+1,k , y n+1,k , z n+1,k , f n,k_out Solve the equation and combine x ub , y ub and z ub Solve the equation to obtain the numerical solution of t ub_max ;

[0074] For the line segment on the lower surface of the chip, for any instantaneous rotation angle ω cs ∈(0, ω n+1,m_out ):

[0075]

[0076] In the formula, x bb , y bb , zbb They are the spatial coordinates of the cross-section line segments on the upper surface of the chip; t bb is a parameter variable; t bb_max They are the maximum values of the parameter variables. By simultaneously solving the x in step 12) n,k , y n,k , z n,k and x n+1,k , y n+1,k , z n+1,k , f n,k_out and solving the equations, and the x in step 22) bb , y bb and z bb and solving the equations, the numerical solution of t bb_max is obtained.

[0077] Furthermore, in step 22), according to the classical theory of grinding machining, the maximum undeformed chip thickness is:

[0078]

[0079] In the formula, C is the number of abrasive grains per unit area; r is the ratio of the chip cross-section width to the thickness; v w is the grinding workpiece speed, and in form grinding of gears, it is the axial feed speed of the grinding wheel; v s is the grinding wheel linear speed; a p is the normal cutting depth of the abrasive grain; d e is the equivalent grinding diameter;

[0080]

[0081] In the formula, d s is the grinding wheel diameter; d w is the workpiece cutting position diameter;

[0082] For form grinding of gears, the cutting diameters at different positions in the involute direction of the tooth surface are different:

[0083] d s = 2(Y D - Y P )

[0084] d w = 2Y P

[0085] In the formula, Y D is the distance between the grinding wheel-gear center point in the Y direction; Y P is the Y-direction coordinate value of the grinding point P.

[0086] Furthermore, the abrasive grain is frustum-shaped, and the ratio r of the chip cross-section width to the thickness is:

[0087]

[0088] Wherein, L 1 , h i , α g are respectively the contact bottom diameter, protruding height and oblique angle of the abrasive grain; ξ is the chip cross-sectional area coefficient of form grinding gear teeth;

[0089] The ratio of the remaining height of the chip to the total height is a value that varies with the rotation angle of the abrasive grain. Then, the chip cross-sectional area coefficient ξ of form grinding gear teeth is:

[0090]

[0091] Wherein, f n,k_out is the total axial feed corresponding to the cut-off point of the k-th discrete segment of the n-th abrasive grain, f n,m_out is the total axial feed corresponding to the cut-off point of the m-th discrete segment of the n-th abrasive grain; m is the number of discrete segments obtained by evenly discretizing the abrasive grain in the normal protruding height.

[0092] The beneficial effects of the present invention are as follows:

[0093] The method for calculating and correcting the chip parameters of form grinding gear teeth of the present invention calculates the movement trajectory of the abrasive grains according to the form grinding gear teeth processing principle, constructs a kinematic model of form grinding gear teeth considering adjacent cutting abrasive grains, thereby obtaining the chip geometry of form grinding gear teeth, and then can calculate the chip cross-section of form grinding gear teeth based on the obtained chip geometry. At the same time, according to the characteristics of form grinding gear teeth, the equivalent cutting diameter and the chip cross-sectional area coefficient of form grinding gear teeth are used to correct the undeformed chip thickness; that is, the method for calculating and correcting the chip parameters of form grinding gear teeth of the present invention is based on the calculation of the movement path of form grinding gear teeth abrasive grains, considers the influence of the special geometry of the gear on the cutting process, establishes a chip model for form grinding gear teeth processing, and provides a basis for subsequent grinding force and tooth surface topography modeling by calculating the relevant geometric parameters of the chip. Description of the Drawings

[0094] In order to make the objectives, technical solutions and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0095] Figure 1 is a schematic diagram of the movement of the grinding wheel for form grinding gear teeth processing;

[0096] Figure 2 is a schematic diagram of the movement of the abrasive grains for form grinding gear teeth processing;

[0097] Figure 3 is the trajectory line of the cut-off point of the abrasive grain on the tooth surface;

[0098] Figure 4 is a schematic diagram of the grinding trajectory of the discrete segments of the abrasive grain;

[0099] Figure 5 is the chip geometry of form grinding gear teeth processing;

[0100] Figure 6 For the comparison of chip geometries between form grinding of gears and surface grinding

[0101] Figure 7 Schematic diagram of chip cross-section

[0102] Figure 8 Calculation results of abrasive grain cross-sectional area

[0103] Figure 9 Schematic diagram of undeformed chip in form grinding of gears

[0104] Figure 10 Variation of chip cross-section in form grinding of gears

[0105] Figure 11 Influence of different involute angle positions on maximum undeformed chip thickness

[0106] Figure 12 Influence of abrasive grain rake angle on maximum undeformed chip thickness

[0107] Figure 13 Relationship between different abrasive grain heights and undeformed depth of cut Specific implementation manner

[0108] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited are not intended to limit the present invention.

[0109] The method for calculating and correcting chip parameters in form grinding of gears in this embodiment includes the following steps.

[0110] Step 1: Construct a grinding kinematic model considering the direction of the tooth surface normal vector. The grinding wheel movement in the form grinding process of gears is relatively simple: after grinding a single tooth groove, the machine tool table rotates around the C-axis to the next station, and the single tooth groove cutting process is repeated until all tooth grooves of the gear are ground. Therefore, the calculation model and conclusion of a single processing cycle can be extended to the entire gear processing cycle.

[0111] 11) Calculate the abrasive grain movement trajectory: Considering the influence of the abrasive grain normal vector direction on the calculation results, calculate the abrasive grain movement trajectory during the grinding process.

[0112] During the cutting process of a single tooth groove, the machine tool movements mainly include the rotational movement of the grinding wheel around its own axis and the feed movement of the tool holder spindle along the gear axial direction, as shown in Figure 1 (a). Different from surface grinding, in form grinding of gears, the grinding wheel rotation radius of discrete segments at different involute positions is different, and the normal vector direction of the machining position is also different, as shown in Figure 1As shown in (b). In addition, there is an angle between the normal vector direction of the conjugate grinding surface of the form grinding wheel and the radial direction of the grinding wheel, and this angle changes with the involute angle of the grinding surface. This angle affects the chip shape and geometric parameters, resulting in the inapplicability of the surface grinding model to form grinding.

[0113] Therefore, when establishing a grinding kinematic model applicable to form grinding, it is necessary to consider the influence of the normal vector direction of the abrasive grains on the calculation results. The kinematic modeling of grinding machining calculates the movement trajectories of the abrasive grains during the grinding process. The movement trajectories of any abrasive grain on the grinding wheel in the grinding wheel and gear coordinate systems are as Figure 2 shown.

[0114] For the abrasive grain at any position point P on the grinding wheel surface, assuming the number is n, the angle between the normal vector direction of the abrasive grain position and the radial direction of the grinding wheel results in different normal grinding depths and radial grinding depths of the grinding:

[0115] a n =a r cosα p (1)

[0116] In the formula, a n is the normal cutting depth of the abrasive grain; a r is the radial cutting depth of the abrasive grain; α p is the angle between the normal direction of the abrasive grain and the radial direction of the grinding wheel, and this angle is related to the involute angle corresponding to the abrasive grain position:

[0117]

[0118] According to the processing movement principle of the grinding wheel in form grinding, the movement trajectory line of the nth abrasive grain on the grinding wheel in the established coordinate system TCS:

[0119] x gn =X wp (3)

[0120] y gn =R p cosω+Y wp (4)

[0121] z gn =R p sinω+Z wp (5)

[0122] In the formula, x gn ,y gn ,z gn are the movement trajectories of the nth abrasive grain respectively; R p is the rotation radius of the grinding wheel corresponding to the discrete segment of the abrasive grain position; ω is the rotation angle of the grinding wheel; X wp ,Y wp ,Zwp is the perpendicular point coordinate of the abrasive grain position to the grinding wheel axis, that is, the rotation center of the abrasive grain. The Z-axis of the coordinate system TCS is the axis of the gear workpiece, the Y-axis is the perpendicular intersection line of the gear workpiece axis and the grinding wheel axis, and the X-axis is perpendicular to the Y-axis and the Z-axis respectively.

[0123] The cutting trajectory of the abrasive grain inside the workpiece material is in the YZ plane. However, due to the influence of the normal direction of the abrasive grain, the trajectory line of the abrasive grain cutting-out point is a curve on the tooth surface, as Figure 3 shown.

[0124] 12) Construct a gear grinding kinematic model considering adjacent cutting abrasive grains: According to the abrasive grain motion trajectory, solve the cutting paths of adjacent cutting abrasive grains respectively, and establish a numerical model of the abrasive grain cutting trajectory and chip in the machining process considering the superposition effect of adjacent abrasive grain motions.

[0125] Based on the forming gear grinding principle and machine tool motion analysis, establish a numerical model of the abrasive grain cutting trajectory and chip in the machining process considering the superposition effect of adjacent abrasive grain motions. For the nth abrasive grain: Assume that the involute angle corresponding to the position of the abrasive grain on the tooth surface is The abrasive grain orientation is the normal vector direction at this position, as Figure 4 shown.

[0126] According to the involute equation of the tooth surface, the coordinates (X P , Y P , Z P ) of the abrasive grain position point can be determined:

[0127]

[0128] Z P = b n (8)

[0129] In the formula, b n is the position of the nth abrasive grain in the tooth direction.

[0130] Discretize the protrusion height of the abrasive grain. The position of each discrete segment is related to the discretization degree. The normal protrusion height is evenly discretized into m segments. Then the discrete point coordinates of the kth discrete segment of the nth abrasive grain in the gear coordinate system are:

[0131]

[0132] Z n,k = Z P (11)

[0133] In the formula, X n,k , Y n,k , Z n,k respectively represent the coordinate values of the kth discrete segment of the nth abrasive grain in the X, Y, and Z directions in the coordinate system; hi is the total protruding height of the abrasive particles.

[0134] The rotation plane of the abrasive particle is the YZ plane of the gear coordinate system. Therefore, the motion trajectory of the kth discrete segment during the grinding rotation process is:

[0135] x n,k =X n,k (12)

[0136] y n,k =(Y D -Y n,k )cosω n,k +Y D (13)

[0137] z n,k =(Y D -Y n,k )sinω n,k +Z n,k (14)

[0138] In the formula, x n,k ,y n,k , z n,k They represent the coordinate values ​​of the kth discrete segment of the nth abrasive particle in the X, Y, and Z directions in the coordinate system respectively; D is the grinding wheel-gear center distance; ω n,k is the rotation angle parameter of the kth discrete segment of the nth abrasive particle.

[0139] It can be seen from the formula that the abrasive grain rotation radius of different discrete segments is different, and the corresponding rotation angle of each discrete segment cut-out point is different. The basic parameter equation of the involute of the standard spur gear with external meshing involute, formula (7), (10) and (13) can be combined to obtain the involute angle of the tooth profile at the cut-out point of the kth discrete segment of the nth abrasive grain: and abrasive grain rotation angle ω n,k_out However, since the calculation process involves the involute equation many times, there is no explicit solution for the calculation result. Therefore, the corresponding numerical solution is obtained by numerical method. Among them, the involute basic parameter equation of the involute external meshing standard spur gear is:

[0140]

[0141] In the formula, is the involute angle parameter, and are the upper and lower limits of the parameters respectively; r b is the base circle radius of the gear.

[0142] The complete cutting path of the full protrusion height of the nth abrasive grain can be calculated from the cut-off point of the kth discrete segment and the cutting motion path. Based on this result, the cutting path of the (n + 1)th abrasive grain adjacent to the nth abrasive grain is calculated. According to the principle of form grinding, there is a feed motion in the axial direction between the (n + 1)th abrasive grain and the nth abrasive grain:

[0143] x n+1,k =x n,k (15)

[0144] y n+1,k =y n,k (16)

[0145] z n+1,k =z n,k +f n,k (17)

[0146] Wherein, x n+1,k , y n+1,k , z n+1,k respectively represent the X, Y, and Z coordinate values of the kth discrete segment trajectory of the (n + 1)th abrasive grain; f n,k is the axial feed amount corresponding to the adjacent cutting abrasive grains at the kth discrete segment.

[0147] The cut-off positions of different discrete segments are different, and the total axial feed amounts of the discrete segments are also different:

[0148]

[0149] Wherein, f n,k_out is the total axial feed amount corresponding to the cut-off point of the kth discrete segment of the nth abrasive grain; ω n,k_out and ω n,m_out are respectively the cut-off position rotation angles of the kth and mth (last segment) discrete segments of the nth abrasive grain; f n,m_out is the total axial feed amount corresponding to the cut-off point of the mth discrete segment of the nth abrasive grain, which is related to the set processing parameters.

[0150] According to the total axial feed amounts of each discrete segment, the feed amount matrix [f] of all discrete segments of the nth abrasive grain can be obtained:

[0151]

[0152] Wherein, [f n,k is the feed amount matrix of the kth discrete segment of the nth abrasive grain.

[0153] In order to realize the calculation between matrices, the feed amount matrix [f n,k and the trajectory line matrix [z n,k of the nth abrasive grain in the Z direction of the coordinate system space are matrices of the same type. Matrix [z n,kIt is established through the abrasive grain rotation matrix. Therefore, the feed matrix for any discrete segment k is as follows:

[0154]

[0155] In the formula, length(·) represents the length of the array, that is, the larger value among the number of rows or columns of the matrix.

[0156] The cutting trajectory of adjacent cutting abrasive grains inside the gear is obtained according to the motion trajectory line of adjacent cutting abrasive grains and the boundary calculation result.

[0157] Step 2: Calculate and correct the chip parameters of form grinding

[0158] The chip shape and geometric parameters are the most important analysis and calculation parameters in the grinding process modeling, and also important transition parameters in the modeling steps of machining process variables such as grinding force and grinding temperature. Therefore, the modeling of grinding chips and the calculation of related parameters are an essential part of the grinding geometry-kinematics modeling. The chip is formed by the cutting of the abrasive grain cutting trajectory and the workpiece tooth surface, and is a geometric body formed by the enclosure of the abrasive grain cutting path and the gear tooth surface. Therefore, based on the calculation of the abrasive grain motion path in form grinding, considering the influence of the special geometric shape of the gear on the cutting process, a chip model for form grinding is established, and related geometric parameters are calculated to provide a basis for subsequent grinding force and tooth surface topography modeling.

[0159] 21) Chip geometry of form grinding: Based on the constructed gear grinding kinematic model, solve the motion trajectory plane at the position with the maximum normal grinding depth of two adjacent abrasive grains to obtain the chip geometry of form grinding.

[0160] The part between the motion trajectories of two abrasive grains and the tooth surface is the grinding chip. Therefore, according to the calculation of the abrasive grain motion trajectory in the previous text, the motion trajectory of the nth abrasive grain, the motion trajectory of the n + 1th abrasive grain, the tooth surface equation and the critical point coordinates are determined. It is only necessary to determine the last surface enclosed by the mth discrete segment trajectories of two abrasive grains, that is, the motion trajectory plane at the position with the maximum normal grinding depth of the nth abrasive grain and the n + 1th abrasive grain.

[0161] According to the motion trajectories of the mth discrete segments of the nth abrasive grain and the n + 1th abrasive grain respectively, connect the trajectory points of the two abrasive grain discrete segments at the same rotation angle ω n,m The trajectory point at this rotation angle is the boundary line segment on the chip side plane at this rotation angle. Each rotation angle element in the discrete segment rotation angle matrix [ω n,m corresponds to a boundary line segment on the chip side plane at this rotation angle. The equation of the boundary line segment on the side plane corresponding to the ith rotation angle element value ω n,m in the rotation angle matrix [ω n,m_i is as follows:

[0162] x sb,i= X n,m (21)

[0163] y sb,i = Y n,m_out (22)

[0164] z sb,i = t sb,i (z n+1,m_i - z n,m_i ) + z n,m_i (23)

[0165] In the formula, x sb,i , y sb,i , z sb,i are the X, Y, and Z coordinate values of the boundary line segments of the chip side plane corresponding to the respective corner elements; X n,m is the X coordinate value of the trajectory line of the m-th discrete segment of the n-th abrasive grain, calculated according to Equation (3.12); Y n,m_out is the Y coordinate value of the cut-out point of the trajectory of the m-th discrete segment of the n-th abrasive grain, calculated according to Equation (13); z n,m_i and z n+1,m_i are the Z coordinate values of the trajectory lines of the m-th discrete segment of the n-th abrasive grain and the m-th discrete segment of the (n + 1)-th abrasive grain at the corner element ω n,m_i ; t sb,i is the parameter variable of the line segment, and t sb,i ∈ [0, 1].

[0166] The calculation results of the chip geometry are as Figure 5 shown. In form grinding of gears, the movement trajectory of the n-th abrasive grain forms the upper surface of the chip, the movement trajectory of the (n + 1)-th abrasive grain forms the lower surface of the chip, and the feed movement between the two abrasive grains forms the chip side plane, which together with the gear tooth surface constitutes the chip geometry. From Figure 5 it can be seen that the cross-sectional shape of the chip changes with the rotation angle of the abrasive grain. Most of the cross-sectional shapes of the grinding chips are right trapezoids, and the cross-sectional shape is a right triangle after the abrasive grain movement exceeds the critical position. The critical position is the cut-out point of the movement trajectory of the n-th abrasive grain.

[0167] Compared with the chip model of traditional surface grinding, as Figure 6 shown, the chip geometry in form grinding of gears is more complex, and the cross-sectional shape changes with the movement of the abrasive grain. It can be regarded as the part of the surface grinding chip that is cut and separated by the gear tooth surface and retained.

[0168] The above calculations prove the influence of the special geometry of the tooth surface on the grinding process and also reflect the necessity of considering the special cutting process in form grinding of gears.

[0169] 22) Calculate the chip cross-section and the undeformed chip thickness

[0170] (1) Calculation of the chip cross section of the profiled gear based on the obtained chip geometry

[0171] According to the calculation and analysis of chip geometry, the chip is composed of the upper surface, lower surface, side plane and tooth surface, and each section needs to be calculated segmentally.

[0172] For the cut section of the tooth surface, any instantaneous rotation angle ω cs :

[0173]

[0174] In the formula, x tb ,y tb 、z tb are the spatial coordinates of the cross-section line segments on the tooth surface; t tb is the parameter variable, t tb_min and t tb_max They are the minimum and maximum values ​​of the parameter variables:

[0175] t tb_min =Y D -Y n,m ,ω cs ∈(0,ω n,m_out ) (25)

[0176]

[0177] x in the simultaneous equations (12)-(18) n,k ,y n,k 、z n,k and x n+1,k ,y n+1,k 、z n+1,k 、f n,k_out Solve the equation and x in equation (24) tb ,y tb and z tb Solve the equation to solve for t in equation (26) tb_max , which is similar to the solution method of the cut-out point angle in the previous article, and the calculation result is a numerical solution.

[0178] For a line segment on the upper surface of the chip, any instantaneous rotation angle ω cs ∈(0,ω n,m_out ):

[0179]

[0180] In the formula, x ub ,y ub 、z ub are the spatial coordinates of the cross-section line segments on the upper surface of the chip; t ub is a parameter variable; t ub_maxThey are the maximum values of the parameter variables. By simultaneously solving x in equations (12)-(18) in step 12) n,k , y n,k , z n,k and x n+1,k , y n+1,k , z n+1,k , f n,k_out Solve the equation and calculate its numerical solution using equation (27).

[0181] It should be noted that when ω cs > ω n,m_out , the cross-section of the abrasive grain is a triangular cross-section, and there is no upper surface of the chip at this time.

[0182] For the line segment on the lower surface of the chip, for any instantaneous rotation angle ω cs ∈(0, ω n+1,m_out ):

[0183]

[0184] where x bb , y bb , z bb are the spatial coordinates of the cross-section line segment on the upper surface of the chip respectively; t bb is the parameter variable; t bb_max are the maximum values of the parameter variables. By simultaneously solving x in equations (12)-(18) in step 12) n,k , y n,k , z n,k and x n+1,k , y n+1,k , z n+1,k , f n,k_out Solve the equation and calculate its numerical solution using equation (28).

[0185] In addition, the calculation of the chip side plane can be expressed by equations (21)-(23). According to the analysis and calculation of the cross-section line segments of the chip cross-section on the four boundary surfaces of the chip, the formed gear grinding chip cross-section can be obtained, as Figure 7 shown.

[0186] Calculate the chip cross-sectional area according to the equations of each line segment of the chip cross-section. Although the chip cross-section shape is divided into a right trapezoid and a triangle before and after the critical position, both can be solved by the same calculation method:[[]]

[0187]

[0188] where S cs_i is the chip cross-sectional area under the rotation angle element; l u_i and l b_iThey are the upper surface intercept line length and the lower bottom intercept line length of the chip cross-section respectively. When the corner element exceeds the critical position, l u_i is 0, and the cross-sectional shape is triangular; t sb_i is the length of the side plane line segment.

[0189] According to the parametric equations of the intercepted line segments of each cross-section, the upper and lower cross-section intercept line lengths can be determined:

[0190] l u_i = t ub_max (30)

[0191] l b_i = t bb_max (31)

[0192] Calculate the cross-sectional area of the abrasive grains varying with the rotation angle during cutting for different protruding heights of the abrasive grains, as Figure 8 shown. It can be seen from Figure 8 that the cross-sectional area of the abrasive grains first increases and then decreases with the increase of the rotation angle of the abrasive grains. The inflection point position corresponds to the critical position of the chip rotation angle. When the rotation angle is greater than the cutting-out rotation angle of the abrasive grains, the cross-sectional area of the abrasive grains becomes 0. The growth rate of the cross-sectional area before the critical position is slower than the decrease rate of the cross-sectional area after the critical position. The greater the height of the abrasive grains, the larger the cutting-out point angle, and the smaller the cross-sectional area maximum value.

[0193] (2) Modify the undeformed chip thickness by using the equivalent grinding diameter and the formed gear grinding chip cross-sectional area coefficient.

[0194] According to the classical theory of grinding machining, the chip is generated by the movement of two adjacent cutting abrasive grains, as Figure 9 (a) shown. The principle of chip generation in formed gear grinding is the same, but due to the angle between the normal direction of the abrasive grains and the radial direction of the grinding wheel, the cutting geometric parameters are changed, as Figure 9 (b) shown.

[0195] According to the classical theory of grinding machining, the maximum undeformed chip thickness is:

[0196]

[0197] In the formula, C is the number of abrasive grains per unit area, which is determined according to the measurement results of the grinding wheel surface topography; r is the ratio of the width to the thickness of the chip cross-section; v w is the grinding workpiece speed, which is the axial feed speed of the grinding wheel in formed gear grinding; v s is the grinding wheel linear speed; a p is the normal cutting depth of the abrasive grains; d e is the equivalent grinding diameter:

[0198]

[0199] In the formula, d sis the grinding wheel diameter; d w is the diameter of the workpiece cutting position. For form grinding of gears, the cutting diameters at different positions in the involute direction of the tooth surface are different:

[0200] d s = 2(Y D - Y P )(34)

[0201] d w = 2Y P (35)

[0202] In the formula, Y D is the distance between the center point of the grinding wheel - gear in the Y direction; Y P is the coordinate value of the grinding point P in the Y direction.

[0203] For the frustum - shaped abrasive grain model adopted in this embodiment, the ratio r of the chip cross - section width to the thickness is:

[0204]

[0205] In the formula, L 1 , h i , α g are respectively the contact bottom diameter, protrusion height and bevel angle of the abrasive grain, which are determined according to the measurement results of the grinding wheel; ξ is the chip cross - sectional area coefficient for form grinding of gears.

[0206] According to the calculation and comparison of the chip geometry for surface grinding and form grinding of gears, the chip shape generated by form grinding is more complex, and the influence of the chip cross - sectional area coefficient ξ needs to be considered, as Figure 10 shown.

[0207] It can be seen from the figure that the ratio of the remaining height of the chip to the total height is a value that changes with the rotation angle of the abrasive grain:

[0208]

[0209] Based on the above analysis and calculation, the relationship between the maximum undeformed chip thickness in form grinding of gears, the machining parameters, the involute position of the gear, and the abrasive grain parameters is solved, as Figure 11 and Figure 12 shown. It can be seen from Figure 11 - 12 that the change in the maximum undeformed chip thickness at different involute angle positions on the tooth surface is not significant, mainly because the grinding wheel diameter is large. If the difference between the grinding wheel diameter and the full tooth height of the gear is small, the influence of different involute positions on the tooth surface on the calculation results is more obvious. In addition, the larger the grinding wheel diameter and the larger the ratio of the grinding wheel linear speed to the axial feed speed, the smaller the maximum undeformed chip thickness.

[0210] The cutting depth of all abrasive grains on the grinding wheel is not equal to the maximum undeformed chip thickness, and only a very small number of abrasive grains will produce this chip thickness. Due to the random characteristics of the grinding wheel, the protrusion heights of different abrasive grains are different, and the undeformed cutting-in amounts obtained by the abrasive grains according to their own protrusion heights will also be different, as Figure 13 shown.

[0211] As can be seen from the figure, the relationship between the cutting depth changes caused by different abrasive grain protrusion heights is:

[0212] t i =t imax -h ima +h i (38)

[0213] It can be seen from the formula that the cutting depths of different abrasive grains are different and are related to the protrusion height of the abrasive grains themselves. Therefore, the measurement results of the abrasive grain protrusion height distribution have an impact on the frequency distribution of the cutting depth of all abrasive grains.

[0214] The above-described embodiments are only preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for calculating and correcting the chip parameters of form grinding Characterized in that: It includes the following steps: Step 1: Construct a grinding kinematic model considering the direction of the tooth surface normal vector 11) Calculate the abrasive grain motion trajectory: Considering the influence of the abrasive grain normal vector direction on the calculation results, calculate the abrasive grain motion trajectory during the grinding process; 12) Construct a form grinding kinematic model considering adjacent cutting abrasive grains: According to the abrasive grain motion trajectory, solve the cutting paths of adjacent cutting abrasive grains respectively, and establish a numerical model of the abrasive grain cutting trajectory and chip considering the superposition effect of adjacent abrasive grain motions in the machining process; Step 2: Calculate and correct the chip parameters of form grinding 21) Chip geometry of form grinding: Based on the constructed form grinding kinematic model, solve the motion trajectory plane at the position with the maximum normal grinding depth of two adjacent abrasive grains, and obtain the chip geometry of form grinding; 22) Calculate the chip cross-section and the undeformed chip thickness Calculate the chip cross-section of form grinding based on the obtained chip geometry; Use the equivalent grinding diameter and the chip cross-section area coefficient of form grinding to correct the undeformed chip thickness.

2. The method for calculating and correcting the chip parameters of form grinding according to claim 1, Characterized in that: In the step 11), for the abrasive grains at any position point P on the grinding wheel surface, the abrasive grain number is n; the angle between the normal vector direction of the abrasive grain position and the radial direction of the grinding wheel results in different normal grinding depths and radial grinding depths during grinding: a n = a r cosα p where a n is the normal cutting depth of the abrasive grain; a r is the radial cutting depth of the abrasive grain; α p is the angle between the normal direction of the abrasive grain and the radial direction of the grinding wheel; In the established coordinate system TCS, the motion trajectory line of the nth abrasive grain on the grinding wheel is: x gn = X wp y gn = R p cosω + Y wp z gn = R p sinω + Z wp where x gn , y gn , z gn are the motion trajectories of the nth abrasive grain respectively; R p is the grinding wheel rotation radius corresponding to the discrete section of the abrasive grain position; ω is the grinding wheel rotation angle; X wp , Y wp , Z wp are the coordinates of the perpendicular point of the abrasive grain position to the axis of the grinding wheel, that is, the coordinates of the rotation center of the abrasive grain; the Z-axis of the coordinate system TCS is the axis of the gear workpiece, the Y-axis is the perpendicular intersection line of the axis of the gear workpiece and the axis of the grinding wheel, and the X-axis is perpendicular to the Y-axis and the Z-axis respectively; The cutting trajectory of the abrasive grain inside the workpiece material is in the YZ plane, and due to the influence of the abrasive grain normal direction, the trajectory line of the abrasive grain cutting-out point is a curve on the tooth surface.

3. The method for calculating and correcting the chip parameters of form grinding according to claim 2, Characterized in that: In the said step 12), to solve the complete cutting path of the nth abrasive grain, for the nth abrasive grain: Assume that the involute angle corresponding to the position of the abrasive grain on the tooth surface is The orientation of the abrasive grain is the normal vector direction at this position. Determine the coordinates (X P , Y P , Z P ) of the abrasive grain position point according to the involute equation of the tooth surface: Z P = b n where b n is the position of the nth abrasive grain in the tooth axial direction; r b is the base circle radius of the gear: Discretize the protruding height of the abrasive grain. The position of each discrete segment is related to the degree of discretization. The normal protruding height is evenly discretized into m segments, and the discrete point coordinates of the kth discrete segment of the nth abrasive grain in the gear coordinate system are: Z n,k = Z P wherein, X n,k , Y n,k , Z n,k respectively represent the coordinate values of the k-th discrete segment of the n-th abrasive grain in the X, Y, and Z directions in the coordinate system; h i is the total protrusion height of the abrasive grain; α p is the angle between the normal direction of the abrasive grain and the radial direction of the grinding wheel; The rotation plane of the abrasive grain is the YZ plane of the gear coordinate system, and the motion trajectory of the kth discrete segment during the grinding rotation is: x n,k = X n,k y n,k = (Y D - Y n,k ) cos ω n,k + Y D z n,k = (Y D - Y n,k ) sin ω n,k + Z n,k where x n,k , y n,k , z n,k respectively represent the coordinate values in the X, Y, and Z directions of the trajectory line of the k-th discrete segment of the n-th abrasive grain in the coordinate system; Y D is the center distance between the grinding wheel and the gear; ω n,k is the rotation angle parameter of the k-th discrete segment of the n-th abrasive grain; Based on the involute basic parameter equation of the standard external involute spur gear, the numerical solutions of the involute angle of the cut-off point of the k-th discrete segment of the n-th abrasive grain and the abrasive grain rotation angle ω are obtained. and the abrasive grain rotation angle ω n,k_out are obtained. Obtain the complete cutting path of the nth abrasive grain over the entire protruding height through the cutting-out point of the kth discrete segment and the cutting motion path.

4. The method for calculating and correcting the chip parameters of form grinding according to claim 3, Characterized in that: Based on the superposition effect of adjacent abrasive grain motions, solve the cutting path of the (n + 1)th abrasive grain adjacent to the nth abrasive grain; There is a feeding motion in the axial direction between the (n + 1)th abrasive grain and the nth abrasive grain: x n+1,k = x n,k y n+1,k = y n,k z n+1,k = z n,k + f n,k where x n+1,k , y n+1,k , z n+1,k respectively represent the X, Y, and Z coordinate values of the k-th discrete segment trajectory of the (n + 1)-th abrasive grain; f n,k is the axial feed of adjacent cutting abrasive grains corresponding to the k-th discrete segment; The cutting-out positions of different discrete segments are different, and the total axial feeding amounts of the discrete segments are also different: where f n,k_out is the total axial feed corresponding to the cut-off point of the k-th discrete segment of the n-th abrasive grain; ω n,k_out and ω n,m_out are the cut-off position rotation angles of the k-th and m-th discrete segments of the n-th abrasive grain respectively; f n,m_out is the total axial feed corresponding to the cut-off point of the m-th discrete segment of the n-th abrasive grain; According to the total axial feeding amounts of each discrete segment, obtain the feeding amount matrix [f] of all discrete segments of the nth abrasive grain: where, [f n,k is the feed matrix of the k-th discrete segment of the n-th abrasive grain; The feed matrix [f n,k and the trajectory line matrix [z n,k of the nth abrasive grain in the Z direction of the coordinate system space are matrices of the same type; the matrix [z n,k is established through the abrasive grain rotation angle matrix, and the feed matrix for any discrete segment k is: In the formula, length(·) represents the length of the array.

5. The method for calculating and correcting the chip parameters of form grinding according to claim 4, Characterized in that: In the step 21), according to the movement trajectories of the m-th discrete segments of the n-th abrasive grain and the (n + 1)-th abrasive grain respectively, connecting the trajectory points of the two abrasive grain discrete segments at the same rotation angle ω n,m the obtained trajectory point is the boundary line segment on the chip side plane at this rotation angle; Discrete segment rotation matrix [ω n,m . Each rotation element corresponds to a boundary segment of the chip side plane at that rotation angle. Then, for the i-th rotation element value ω n,m in the rotation matrix [ω n,m_i , the equation of the corresponding side plane boundary segment is: x sb,i = X n,m y sb,i = Y n,m_out z sb,i = t sb,i (z n+1,m_i - z n,m_i ) + z n,m_i where x sb,i , y sb,i , z sb,i are the X, Y, and Z coordinate values of the boundary segment of the chip side plane corresponding to the corner element; X n,m is the X coordinate value of the trajectory line of the m-th discrete segment of the n-th abrasive grain; Y n,m_out is the Y coordinate value of the cut-out point of the trajectory of the m-th discrete segment of the n-th abrasive grain; z n,m_i and z n+1,m_i are the Z coordinate values of the trajectory lines of the m-th discrete segment of the n-th abrasive grain and the m-th discrete segment of the (n + 1)-th abrasive grain when the corner element is ω n,m_i ; t sb,i is the parameter variable of the line segment, representing the length of the side plane intercept line; During form grinding, the movement trajectory of the nth abrasive grain forms the upper surface of the chip, the movement trajectory of the (n + 1)th abrasive grain forms the lower surface of the chip, and the feed movement between the two abrasive grains forms the side plane of the chip, which together with the gear tooth surface constitutes the chip geometry.

6. The method for calculating and correcting the form grinding chip parameters according to claim 5, characterized in that: in the step 22), the chip is jointly composed of an upper surface, a lower surface, a side plane and a tooth surface, and the cross-sectional area of the chip is calculated according to the equations of each line segment of the chip cross-section as: l u_i ＝t ub_max l b_i ＝t bb_max Where S cs_i is the chip cross-sectional area under the corner element; l u_i and l b_i are respectively the lengths of the upper surface intercept line and the lower bottom intercept line of the chip cross-section. When the corner element exceeds the critical position, l u_i is 0 and the cross-sectional shape is triangular; t sb_i is the length of the side plane intercept line; t ub_max and t bb_max are both parameter variables.

7. The method for calculating and correcting the form grinding chip parameters according to claim 6, characterized in that: For the intercepted line segment of the chip cross-section on the tooth surface, the instantaneous rotation angle ω at any time cs : where x tb , y tb , z tb are the spatial coordinates of the cross-sectional line segment on the tooth surface, respectively; t tb is a parameter variable, and t tb_min and t tb_max are the minimum and maximum values of the parameter variable, respectively, and: t tb_min = Y D -Y n,m , ω cs ∈(0, ω n,m_out ) The numerical solution of t is obtained tb_max ; For the line segment on the upper surface of the chip, the arbitrary instantaneous rotation angle ω cs ∈(0, ω n,m_out ): where x ub , y ub , z ub are the spatial coordinates of the cross-section line segment on the upper surface of the chip respectively; t ub is a parameter variable; t ub_max are the maximum values of the parameter variables respectively. By simultaneously solving the equations with x n,k , y n,k , z n,k and x n+1,k , y n+1,k , z n+1,k , f n,k_out and solving the equations with x ub , y ub and z ub in step 22), the numerical solution of t ub_max is obtained; For the line segment on the lower surface of the chip, the arbitrary instantaneous rotation angle ω cs ∈(0, ω n+1,m_out ): where x bb , y bb , z bb are the spatial coordinates of the cross-sectional line segment on the upper surface of the chip; t bb is a parameter variable; t bb_max are the maximum values of the parameter variable respectively. By simultaneously solving the equations with x n,k , y n,k , z n,k in step 12) and x n+1,k , y n+1,k , z n+1,k , f n,k_out and then solving the equations with x bb , y bb and z bb in step 22), the numerical solution of t bb_max is obtained.

8. The method for calculating and correcting the form grinding chip parameters according to claim 6, characterized in that: in the step 22), according to the classical theory of grinding machining, the maximum undeformed chip thickness is: Where C is the number of abrasive grains per unit area; r is the ratio of the width to the thickness of the chip cross-section; v w is the grinding workpiece speed, and in form grinding of gears, it is the axial feed speed of the grinding wheel; v s is the grinding wheel linear speed; a p is the normal cutting depth of the abrasive grain; d e is the equivalent grinding diameter; where d s is the grinding wheel diameter; d w is the workpiece cutting position diameter; For form grinding, the cutting diameters at different positions in the involute direction of the tooth surface are different: d s = 2(Y D - Y P ) d w = 2Y P where Y D is the distance of the center point of the grinding wheel - gear in the Y direction; Y P is the coordinate value of the grinding point P in the Y direction.

9. The method for calculating and correcting the form grinding chip parameters according to claim 8, characterized in that: the abrasive grain is frustum-shaped, and the ratio r of the width to the thickness of the chip cross-section is: where L 1 , h i , α g are respectively the contact bottom diameter, protruding height and bevel angle of the abrasive grain; ξ is the chip cross-sectional area coefficient of form grinding gear teeth; the ratio of the remaining height to the total height of the chip is a value that changes with the rotation angle of the abrasive grain, then the chip cross-sectional area coefficient ξ of the gear grinding is: In the formula, m is the number of discrete segments of the average dispersion of the abrasive grain in the normal protruding height.

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