Calculation method of tooth surface error based on grinding wheel wear

Abstract

The present invention discloses a tooth surface error calculation method based on grinding wheel wear. The geometric parameters of abrasive particles under different wear states are calculated through a micro-geometric model of abrasive particles, a tooth surface error calculation method based on grinding wheel wear is proposed, and the influence of grinding wheel wear on tooth profile deviation, helix deviation and pitch deviation is studied. Among them, the tooth profile inclination deviation is analyzed by the height difference of abrasive wear of abrasive particles with different grinding wheel radius; the helix deviation is analyzed by the height difference of abrasive wear of abrasive particles with the same grinding wheel radius and different rotation angle position measuring points; and because the tooth thickness of the preceding cutting wheel teeth is also affected by wear, the pitch deviation has no obvious influence relationship with the grinding wheel wear; that is, the tooth surface error calculation method based on grinding wheel wear of the present invention analyzes the grinding wheel wear at the micro-level of abrasive particles, and reveals the influence mechanism of grinding wheel wear on tooth surface error.

Description

Technical Field

[0001] The invention belongs to the technical field of grinding processing, and specifically relates to a tooth surface error calculation method based on grinding wheel wear. Background Art

[0002] Among various gear quality parameters, tooth surface error and morphology are the most important indicators, which affect the gear's transmission smoothness, wear resistance, fatigue strength, contact stiffness and other service performance. In terms of tooth surface error of form grinding, existing research on gear error is usually based on machine tool geometric error and motion error, by establishing a mapping relationship model between machine tool error and gear workpiece error, but this method ignores the influence of factors such as grinding wheel wear on gear manufacturing accuracy during processing. After the grinding wheel is worn, the normal protrusion height of the abrasive grains decreases, affecting the tooth surface error. Therefore, it is necessary to analyze the grinding wheel wear at the microscopic level of the abrasive grains based on the proposed quantitative expression and calculation method of grinding wheel wear to reveal the influence mechanism of grinding wheel wear on tooth surface error. Summary of the invention

[0003] In view of this, in order to solve the problem that the influence of grinding wheel wear on gear manufacturing accuracy is ignored in the prior art, an object of the present invention is to provide a method for calculating tooth surface error based on grinding wheel wear.

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

[0005] A method for calculating tooth surface error based on grinding wheel wear comprises the following steps:

[0006] Step 1: Construct the relationship between tooth surface error and grinding wheel wear, where:

[0007] The relationship between tooth profile inclination deviation and abrasive wear is:

[0008] f hα =h i (ε top ―ε bot )

[0009] In the formula, f hα is the tooth profile inclination deviation error term caused by grinding wheel wear; h i The protruding height of the abrasive grain; ε top and ε bot These are the measurement and calculation results of abrasive wear rate corresponding to tooth top and tooth root respectively;

[0010] The relationship between the total helical deviation and abrasive wear is:

[0011] F β_top =h i (max([ε top ])―min([εtop ]))

[0012] In the formula, F β_top is the total helix deviation error term of the tooth profile tooth tip position caused by grinding wheel wear; max([ε top ]) and min([ε top ]) are the maximum and minimum values ​​of the abrasive wear rate measurement calculation results at different measuring points on the tooth top;

[0013] For pitch deviation, grinding wheel wear will cause the tooth thickness to change, which will lead to a normal offset in the tooth profile curve of the gear. The relationship between the normal offset and abrasive wear is:

[0014] Δp n =h i ε

[0015] In the formula, Δp n is the normal offset of the gear teeth caused by the wear of the grinding wheel; ε represents the wear rate of the grinding wheel;

[0016] Step 2: Solve the tooth surface error based on the grinding wheel multi-information fusion model

[0017] 21) Construct a multi-information fusion model of grinding wheel;

[0018] 22) The multi-information fusion model of the grinding wheel is used to solve the tooth surface errors including the tooth profile inclination deviation, the total helix deviation and the normal offset of the tooth profile curve.

[0019] Further, in step 21), the steps of constructing the grinding wheel multi-information fusion model are as follows:

[0020] 211) Constructing a macro-geometric model of the grinding wheel grinding surface: using the conjugate contact relationship between the grinding wheel grinding surface and the workpiece grinding surface, using the workpiece grinding surface profile equation to obtain the grinding wheel grinding surface profile equation, and establishing the grinding wheel grinding surface macro-geometric model;

[0021] 212) Constructing a micro-geometric model of grinding wheel abrasive particles

[0022] 2121) Using the macro-geometric model of the grinding wheel grinding surface, a three-dimensional expression of the grinding wheel grinding surface profile is established, and the position of any abrasive grains on the grinding wheel grinding surface is expressed in three dimensions;

[0023] 2122) Expand the grinding wheel grinding surface into a two-dimensional annular plane along the axial side view, convert the three-dimensional expression of the grinding wheel grinding surface profile into a two-dimensional expression of the grinding wheel grinding surface side view, and express any abrasive grain position on the grinding wheel grinding surface in two dimensions; wherein, the difference between the radius of any point A on the two-dimensional annular plane and the inner circle radius of the two-dimensional annular plane is equal to the length of the curve segment located between point A and the inner end point of the curve intercepted by the plane passing through the grinding wheel grinding surface point A′ and the grinding wheel axis on the grinding wheel grinding surface, and any point A on the two-dimensional annular plane is obtained by expanding the point A′ on the grinding wheel grinding surface along the axial side view;

[0024] 2123) Expand the two-dimensional annular plane into an isosceles trapezoidal plane along the circumferential direction and perform numerical discretization, and convert the two-dimensional side view expression of the grinding wheel grinding surface into a grinding wheel matrix expression;

[0025] 213) Constructing the micro-geometric parameter model of grinding wheel abrasive

[0026] Elements are filled in the grinding wheel matrix according to the random distribution law of abrasive particles. The actual spatial position of the abrasive particles is expressed by the number of rows and columns of the elements in the grinding wheel matrix, and the height of the abrasive particles is expressed by the size of the elements.

[0027] Further, in step 211), the workpiece is an involute spur gear, the grinding surface of the involute spur gear is the tooth surface, and the grinding surface profile equation of the grinding wheel obtained by the tooth surface is:

[0028]

[0029] in: is the involute angle parameter, and are the upper and lower limits of the parameters respectively; r b is the radius of the gear base circle: r b =mzcosα

[0030] Where: m is the gear module, z is the number of gear teeth, and α is the pressure angle.

[0031] Further, in step 2121), the three-dimensional expression W1 of any abrasive grain position on the grinding surface of the grinding wheel is:

[0032]

[0033] in: is the gear involute angle parameter corresponding to the abrasive position; θ is the rotation angle parameter of the abrasive position on the circumference of the grinding wheel;

[0034] In step 2122), the two-dimensional expression W2 of the position of any abrasive grain on the grinding surface of the grinding wheel is:

[0035] W2=f(R,θ)

[0036] Where R is the radius of the abrasive particle in the two-dimensional annular plane; and:

[0037]

[0038] Where: Y D Y is the distance between the grinding wheel center and the origin of the gear coordinate system in the Y direction; end is the Y coordinate value of the tooth top; is the involute angle parameter corresponding to the starting point of the involute; and:

[0039]

[0040] in: is the involute angle parameter of the tooth top;

[0041] In the step 2123), the conversion relationship between the grinding wheel grinding surface side view two-dimensional expression W2 and the grinding wheel matrix expression W3 is:

[0042]

[0043] Where: i w and j w Respectively represent the number of rows and columns of the grinding wheel matrix; Δi w and Δj w are the row spacing and column spacing between adjacent abrasive particles, respectively, which are determined by the number of abrasive particles per unit area; δ(i w ) is the distance between the grinding wheel matrix element boundary and the maximum width position of the matrix; and:

[0044]

[0045] The maximum number of rows in the grinding wheel matrix is:

[0046] i wmax =1+r b (((z+2) / zcosα) 2 ―1) / 2Δi w

[0047] For the solved i wmax Perform rounding;

[0048] The maximum number of columns in the grinding wheel matrix is:

[0049]

[0050] For the solved j wmax Round up.

[0051] Further, in step 213), when filling elements in the grinding wheel matrix, from i w =1,jw =1 starts filling the matrix elements;

[0052] If satisfied:

[0053] δ(i w ) / Δj w ≤j w ≤j wmax ―2δ(i w ) / Δj w

[0054] Then there are abrasive particles at the position corresponding to the corresponding matrix element, otherwise there are no actual abrasive particles at the position corresponding to the corresponding matrix element.

[0055] Further, in step 22), the method steps of solving the tooth surface error by using the grinding wheel multi-information fusion model are as follows:

[0056] 221) according to the effective grinding area of ​​the grinding wheel in contact with the workpiece during grinding, extracting elements corresponding to the effective grinding area of ​​the grinding wheel from the grinding wheel matrix to form a grinding wheel grinding matrix;

[0057] 222) Before the grinding wheel is worn, the distribution law of the protruding height of the grinding wheel abrasive grains is fitted; after the grinding wheel is worn, the distribution law of the residual height of the grinding wheel abrasive grains is fitted;

[0058] 223) According to the distribution law of the protruding height of the grinding wheel abrasive grains, elements are filled in the grinding wheel grinding matrix to obtain the protruding height distribution matrix of the grinding wheel grinding abrasive grains; according to the distribution law of the residual height of the grinding wheel abrasive grains, elements are filled in the grinding wheel grinding matrix to obtain the residual height distribution matrix of the grinding wheel grinding abrasive grains;

[0059] 224) respectively solve the tooth profile inclination deviation, the total helix deviation and the normal offset of the tooth profile curve.

[0060] Further, in the step 223), the method for solving the tooth profile inclination deviation is: extracting a row of elements corresponding to the tooth top and the tooth root from the grinding wheel grinding abrasive grain protrusion height distribution matrix to form a tooth top protrusion height distribution matrix before wear and a tooth root protrusion height distribution matrix before wear; extracting a row of elements corresponding to the tooth top and the tooth root from the grinding wheel grinding abrasive grain residual height distribution matrix to form a tooth top protrusion height distribution matrix after wear and a tooth root protrusion height distribution matrix after wear;

[0061] The abrasive wear rate corresponding to the tooth top is solved by using the tooth top protrusion height distribution matrix before wear and the tooth top protrusion height distribution matrix after wear:

[0062] ε top =mean(([h i_top ]―[h r_top ]) / [h i_top ])

[0063] In the formula, [h i_top ] represents the distribution matrix of tooth top protrusion height before wear; [h r_top ] represents the distribution matrix of tooth top protrusion height after wear; mean(·) represents the mean function; h i_top Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_top The protruding height of the abrasive particles corresponding to the tooth top after wear;

[0064] The abrasive wear rate corresponding to the tooth root is solved by using the tooth root protrusion height distribution matrix before wear and the tooth root protrusion height distribution matrix after wear:

[0065] ε bot =mean(([h i_bot ]―[h r_bot ]) / [h i_bot ])

[0066] In the formula, [h i_bot ] represents the distribution matrix of tooth top protrusion height before wear; [h r_bot ] represents the distribution matrix of tooth top protrusion height after wear; mean(·) represents the mean function; h i_bot Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_bot The protruding height of the abrasive particles corresponding to the tooth top after wear.

[0067] Further, in step 223), the total deviation of the helix is ​​calculated as follows:

[0068] Extract a row of elements corresponding to the tooth top from the grinding wheel grinding abrasive grain protrusion height distribution matrix to form the tooth top protrusion height distribution matrix before wear; extract a row of elements corresponding to the tooth top from the grinding wheel grinding abrasive grain residual height distribution matrix to form the tooth top protrusion height distribution matrix after wear;

[0069] The grinding wheel abrasive wear height distribution matrix is ​​obtained by the tooth top protrusion height distribution matrix before wear and the tooth top protrusion height distribution matrix after wear:

[0070] [h w_top ]=[h i_top ]―[h r_top ]

[0071] Among them, [h w_top ] represents the grinding wheel abrasive wear height distribution matrix; [h i_bot ] represents the distribution matrix of tooth top protrusion height before wear; [h r_bot ] represents the distribution matrix of tooth top protrusion height after wear; h i_top Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_topThe protruding height of the abrasive particles corresponding to the tooth top after wear; h w_top Indicates the abrasive wear height corresponding to the tooth top;

[0072] According to the grinding wheel abrasive wear height distribution matrix, the wear rate of each abrasive particle is solved:

[0073] ε i_top =(h i_top ―h r_top ) / h i_top

[0074] In the formula, ε i_top Indicates the wear rate of abrasive particles;

[0075] The wear rate of abrasive particles is used to obtain the distribution matrix of the wear rate of grinding wheel particles [ε top ], from the grinding wheel abrasive wear rate distribution matrix [ε top ] to extract the maximum value max([ε top ]) and the minimum value min([ε top ]) to obtain the total deviation of the helix.

[0076] Furthermore, the calculation method of the normal offset of the gear tooth profile curve is: using the grinding wheel grinding abrasive protrusion height distribution matrix and the grinding wheel grinding abrasive residual height distribution matrix to solve the grinding wheel wear rate:

[0077] ε=mean(([h i ]―[h r ]) / [h i ])

[0078] Where ε represents the grinding wheel wear rate; mean(·) represents the mean function; [h i ] represents the protruding height distribution matrix of grinding wheel abrasive grains; [h r ] represents the residual height distribution matrix of grinding wheel abrasive particles; h i Indicates the protruding height of the grinding wheel abrasive grains; h r Indicates the residual height of grinding wheel abrasive grains;

[0079] The normal offset of the gear tooth profile curve is obtained using the solved grinding wheel wear rate.

[0080] Furthermore, the method further includes step 225), looping through steps 222) to 224), and calculating an average value after multiple solutions.

[0081] The beneficial effects of the present invention are:

[0082] The present invention is based on a method for calculating tooth surface errors due to grinding wheel wear. The geometric parameters of abrasive particles under different wear states are calculated through a micro-geometric model of abrasive particles, a method for calculating tooth surface errors due to grinding wheel wear is proposed, and the influence of grinding wheel wear on tooth profile deviation, helix deviation and pitch deviation is studied. Among them, the tooth profile inclination deviation is analyzed by the height difference of abrasive wear of particles with different grinding wheel radii; the helix deviation is analyzed by the height difference of abrasive wear of particles with the same grinding wheel radius and different rotation angle positions; and since the tooth thickness of the preceding cutting wheel teeth is also affected by wear, the pitch deviation has no obvious influence relationship with the grinding wheel wear; that is, the method for calculating tooth surface errors due to grinding wheel wear of the present invention analyzes the grinding wheel wear at the micro-level of abrasive particles, and reveals the influence mechanism of grinding wheel wear on tooth surface errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0084] Figure 1 is a schematic diagram of the gear geometric error diagram;

[0085] Figure 2 This is the schematic diagram of the gear error caused by grinding wheel wear;

[0086] Figure 3 is the normal grinding depth of different parts of the grinding wheel;

[0087] Figure 4 This is a schematic diagram of the principle of tooth profile deviation caused by grinding wheel wear;

[0088] Figure 5 is the relationship between the difference in abrasion wear rate and the tooth profile inclination deviation;

[0089] Figure 6 This is a schematic diagram of the principle of spiral line deviation caused by grinding wheel wear;

[0090] Figure 7 is the relationship between the wear difference and the helix deviation;

[0091] Figure 8 Schematic diagram of grinding wheel wear and tooth pitch deviation;

[0092] Fig. 9 It is a schematic diagram of the grinding surface of the involute grinding wheel;

[0093] Fig.10 This is the process diagram of the conversion between the three-dimensional position information of the grinding wheel and the number of rows and columns of the matrix;

[0094] Fig.11 It is a schematic diagram of the three-dimensional expression of the grinding wheel;

[0095] Fig.12It is a schematic diagram of the conversion between the three-dimensional expression and the axial side view expression of the grinding wheel;

[0096] Fig.13 It is a schematic diagram of the conversion between the grinding wheel side view expression and the matrix expression;

[0097] Fig.14 Fill the step flow chart for the grinding wheel matrix element;

[0098] Fig.15 It is a schematic diagram of the wear particle position-height fusion matrix;

[0099] Fig.16 The decomposition and influence diagram of wear particle orientation vector;

[0100] Fig.17 Schematic diagram of abrasive grain orientation, local coordinate system and abrasive grain orientation circle on the involute;

[0101] Fig.18 Schematic diagram of the abrasive geometry with circular and triangular cross sections;

[0102] Fig.19 Schematic diagram of the main forms of abrasive wear;

[0103] Fig. 20 It is the geometric diagram of grinding wheel abrasive grains;

[0104] Fig.21 This is the calculation process diagram of abrasive wear rate;

[0105] Fig. 22 The measurement and fitting results of wear particle protrusion and residual height distribution;

[0106] Fig.23 It is the numerical distribution of abrasive protrusion height, residual height and wear height;

[0107] Fig.24 is the calculation result of each abrasive wear height;

[0108] Fig.25 The results of abrasion and wear rate are calculated multiple times. DETAILED DESCRIPTION

[0109] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0110] The tooth surface error calculation method based on grinding wheel wear in this embodiment includes the following steps.

[0111] Step 1: Construct the relationship between tooth surface error and grinding wheel wear.

[0112] After the grinding wheel is worn, the normal protrusion height of the abrasive grains decreases, affecting the tooth surface error. Therefore, it is necessary to analyze the grinding wheel wear at the microscopic level of the abrasive grains based on the proposed quantitative expression and calculation method of grinding wheel wear to reveal the mechanism of the influence of grinding wheel wear on the tooth surface error. According to the definition of gear geometric error in ISO1328-1:2013 (corresponding to the national standard GB / T 10095.1-2008), the main measurement parameters of gear geometric error are gear tooth profile deviation, gear helix deviation and gear pitch deviation, such as Figure 1 shown.

[0113] This embodiment classifies the sources of gear errors related to grinding wheel wear into three categories, such as Figure 2 As shown. The first category: Grinding wheel wear causes the theoretical cutting depth to decrease, causing the normal offset of the tooth profile curve. This normal offset can be regarded as the normal offset of the grinding wheel, which causes the normal grinding amount of the gear to change, causing the gear tooth thickness to change, and ultimately affecting the gear pitch deviation. The second category: Tooth profile inclination deviation caused by uneven wear of the grinding wheel grinding surface at different positions along the involute direction. The moving direction of the machine tool spindle column during processing is the radial direction of the gear. The nominal cutting depth entered when setting the processing parameters is the radial cutting depth, but the grinding wheel grinding surface is a complex curved surface, and the normal directions of each position on the surface are different. Therefore, the normal (actual) cutting depth of the grinding wheel grinding surface at different positions along the involute direction is different, resulting in different wear amounts at different positions of the grinding wheel, and ultimately leading to inclination deviation. The third category: Tooth profile shape deviation caused by micro deformation of the grinding wheel processing surface. When the grinding wheel is worn, due to the randomness of the size and position distribution of the grinding wheel abrasives, the wear conditions of different abrasives are different when the grinding wheel is worn. There is also the possibility of abrasives falling off or being damaged due to insufficient mechanical properties of the grinding wheel binder or the abrasives themselves, which causes uneven changes in the microscopic morphology of the grinding surface of the grinding wheel and causes shape deviation of the gear workpiece.

[0114] Based on the above analysis, the tooth profile deviation, helix deviation and pitch deviation caused by the grinding wheel are quantitatively calculated. That is, in this embodiment,

[0115] (1) Relationship between tooth profile inclination deviation and abrasive wear

[0116] The definition of gear tooth profile deviation in ISO1328-1:2013 (corresponding to the national standard GB / T 10095.1-2008) is: the amount by which the actual tooth profile deviates from the designed tooth profile, which is measured in the end plane and perpendicular to the direction of the involute tooth profile. In the profile grinding process, the shape of the contact line between the grinding wheel and the workpiece determines the gear tooth profile geometry at the moment of cutting. Therefore, the wear state of the grinding wheel will affect the gear tooth profile deviation. According to the principle of profile grinding, due to the different directions of the normal vectors at different positions on the tooth surface, the normal cutting depth will change, which can be solved by setting the grinding radial cutting depth and the normal vector direction:

[0117] a n =a r cosα p

[0118] In the formula, a n is the normal cutting depth of the abrasive; a r is the radial cutting depth of the abrasive; α p is the angle between the normal direction of the abrasive and the radial direction of the grinding wheel. This angle corresponds to the involute angle of the abrasive position. related:

[0119]

[0120] Calculate the normal cutting depth at different involute positions on the tooth surface. The results are as follows: Figure 3 shown.

[0121] As can be seen from the figure, the normal grinding depth at the top of the grinding wheel is smaller, the abrasive wear at the top of the grinding wheel is smaller in the same processing time, and the remaining abrasive material is more. After the next feed, the tooth root position ground by the top of the grinding wheel is less affected by the grinding wheel wear, and more material is removed at the root of the gear tooth, and less material is left, resulting in gear tooth profile tilt deviation. The specific schematic diagram of the relationship between grinding wheel wear and tooth profile tilt deviation is as follows Figure 4 shown.

[0122] As can be seen from the figure, based on the relationship between the cutting section and the tooth profile section at a certain moment after the grinding wheel is worn, the gear tooth profile tilt deviation can be considered to be caused by uneven wear of different parts of the grinding wheel. The maximum height difference of abrasive wear is the tooth profile tilt deviation. When the worn grinding wheel is processed, the material residue at the top of the tooth is more than that at the root of the tooth, and the tilt direction of the tooth profile tilt deviation is the tooth top direction. Therefore, the tooth profile tilt deviation caused by grinding wheel wear can be expressed as:

[0123]

[0124] In the formula, f hα is the tooth profile inclination deviation error term caused by grinding wheel wear; is the normal residual height sequence of the abrasive particles at the tooth top position after wear; is the normal residual height sequence of the abrasive particles at the tooth root after wear; and are the involute angles corresponding to the tooth addendum and tooth root, respectively.

[0125] The residual height sequence of abrasive grains after wear is obtained based on the distribution frequency of the protruding height of abrasive grains after grinding wheel wear. In the sequence calculation, it will be affected by the random number generation, making the calculated residual height sequence random. Therefore, through the relationship between the protruding height of abrasive grains after grinding and the abrasive grain wear rate, the random sequence is converted into a constant value of the abrasive grain wear rate, and the influence of grinding wheel wear on the tooth profile inclination deviation is quantitatively calculated:

[0126] f hα =h i (ε top ―ε bot )

[0127] In the formula, f hα is the tooth profile inclination deviation error term caused by grinding wheel wear; h i The protruding height of the abrasive grain; ε top and ε bot These are the measurement and calculation results of the abrasive wear rate corresponding to the tooth top and tooth root respectively.

[0128] Based on the above analysis, the quantitative influence of the different abrasive wear rates of the top and bottom of the grinding wheel on the tooth profile inclination deviation is calculated, such as Figure 5 As shown. Figure 5 It can be seen that without considering the machine tool geometric error and machine tool motion error, there is a linear relationship between the tooth profile tilt deviation and the difference in wear rate between the top and bottom of the grinding wheel. The greater the protruding height of the abrasive before grinding, the greater the rate of change of the tooth profile tilt deviation with the wear rate difference. When the difference in wear rate between the top and bottom of the grinding wheel is 0, the tooth profile tilt deviation is 0, that is, when the wear conditions of the top and bottom of the grinding wheel are the same, the tooth profile curve should be a theoretical involute, and there is no tooth profile tilt deviation. However, in actual processing, in addition to grinding wheel wear, various factors such as machine tool geometric error, motion error, and machine tool vibration will affect the gear processing error.

[0129] (2) Relationship between total helical deviation and abrasive wear

[0130] The definition of helix deviation in ISO1328-1:2013 (corresponding to the national standard GB / T 10095.1-2008) is: the deviation of the actual helix measured in the tangent direction of the end face base circle from the designed helix. The gear helix is ​​generated by the deflection of the grinding wheel B axis and the feed motion of the grinding wheel. It is the error between the measured curve along the gear axial direction and the theoretical helix at the same involute angle position. According to the principle of profile grinding, the cutting of the gear helix in discrete sections of different cross sections corresponds to the abrasive cutting edges with different rotation angles of the same grinding wheel radius, such as Figure 6 As shown. Figure 6It can be seen that the cutting of the helix corresponds to the abrasive grains with the same grinding wheel radius and different rotation angles, and the cutting is carried out sequentially with the rotation and axial feed of the grinding wheel during the grinding process. Therefore, the total deviation of the gear helix is ​​affected by the wear difference of the abrasive grains with the same radius and different rotation angles on the grinding wheel.

[0131] Unlike the tooth profile inclination deviation, the cutting abrasives of the spirals at different cross-sectional positions have the same involute angle and different rotation angles. There is no problem of different normal cutting depths between these abrasives. At the same time, due to the large ratio of the grinding wheel linear speed to the axial feed speed, the same abrasive will be cut multiple times in the generation of the spiral. There is no regular pattern for the uneven wear of these abrasives, while the spiral inclination deviation has a clear direction definition. Therefore, in theory, the uneven wear of abrasives at the same radial position and different rotation angles of the grinding wheel will cause the total spiral deviation, but the spiral inclination deviation may produce small fluctuations, but there is no intuitive and obvious influence rule. According to the above analysis, the relationship between the total spiral deviation and the abrasive wear height is:

[0132]

[0133] In the formula, F β_top is the total helix deviation error term of the tooth profile tip position caused by grinding wheel wear; and They are the maximum and minimum values ​​of the normal residual height sequence of the abrasive particles after wear at the tooth top position, respectively.

[0134] Similar to the tooth profile inclination deviation, the random sequence is converted into a constant value of abrasive wear rate through the relationship between the protruding height of the abrasive after grinding and the abrasive wear rate, and the influence of grinding wheel wear on the total deviation of the helix is ​​quantitatively calculated:

[0135] F β_top =h i (max([ε top ])―min([ε top ]))

[0136] In the formula, F β_top is the total helix deviation error term of the tooth profile tooth tip position caused by grinding wheel wear; max([ε top ]) and min([ε top ]) are the maximum and minimum values ​​of the abrasive wear rate measurement calculation results at different measuring points on the tooth top;

[0137] According to the above analysis, the quantitative influence relationship of the difference of abrasive wear rate at the same involute position and different rotation angle measuring points on the total deviation of the helix is ​​calculated, such as Figure 7 As shown. Figure 7It can be seen that due to the random characteristics of the grinding wheel abrasives, there are differences in the geometric parameters of the abrasives such as the protruding height of the abrasives at the same grinding wheel radius and different angular positions, resulting in different wear and tear of the abrasives at different angular positions, which will cause the gear helix deviation. The total helix deviation is proportional to the height difference of the abrasives at the same grinding wheel radius and different angular positions. The larger the protruding height of the abrasives before wear, the faster the change speed of the height difference with wear. The increase in the wear rate will cause the error of some positions on the helix to increase, but there is no directionality in the tilt deviation, so in theory there is no correlation between the helix tilt deviation and the difference in the wear rate.

[0138] According to the above analysis, when measuring and calculating the wear of the grinding wheel, it is necessary not only to measure multiple measuring points at different radial positions of the grinding wheel, but also to measure multiple measuring points at the same radius and different rotation angle positions.

[0139] (3) Relationship between normal offset and abrasive wear

[0140] The definition of pitch deviation in ISO1328-1:2013 (corresponding to the national standard GB / T 10095.1-2008) is: the algebraic difference between the actual pitch and the theoretical pitch on a circle concentric with the gear axis and close to the middle of the tooth height on the end plane. The gear pitch deviation items mainly include the single pitch deviation f p , adjacent tooth pitch difference f u And the cumulative pitch deviation F p , where the adjacent tooth pitch difference and the cumulative pitch deviation are calculated through the single pitch deviation. Grinding wheel wear will cause the overall normal height distribution of the abrasive to decrease, thereby reducing the actual grinding depth. According to the principle of profile grinding, grinding wheel wear can be regarded as the offset of the grinding wheel in the normal direction, resulting in the normal offset of the tooth profile, such as Figure 8 As shown. Figure 8 It can be seen that the normal offset of a single tooth profile curve produces a pitch deviation, which is related to the abrasive wear height:

[0141] Δp n =h w

[0142] In the formula, h w Indicates the height of abrasive wear.

[0143] Since the pitch deviation is measured on a circle that is concentric with the gear axis and has a fixed diameter, which is close to the involute pitch circle, the normal deviation of the tooth profile does not need to consider the influence of different involute angle positions, and can be directly calculated based on the abrasive wear rate ε measured and calculated near the pitch circle:

[0144] Δp n =h i ε

[0145] In the formula, Δp n is the normal offset of the gear teeth caused by the wear of the grinding wheel; ε represents the wear rate of the grinding wheel;

[0146] It can be seen that the normal deviation of the tooth profile is related to the protruding height of the abrasive before grinding and the abrasive wear rate. However, it should be noted that the single pitch deviation f p It is calculated by the pitch of adjacent teeth and the theoretical pitch:

[0147] f p =Δp t

[0148] It can be seen from the formula that the gear pitch deviation and is calculated by measuring the pitch, not directly measuring the gear tooth thickness p n Therefore, according to the gear geometry, if the tooth thickness p of the previous gear tooth is n The tooth profile has shifted from the theoretical tooth profile to the actual tooth profile, that is, if the tooth thickness of the previous gear has changed:

[0149] p n―1 =p′ n―1 ―f p

[0150] In the formula, p n―1 is the actual tooth thickness of the previous gear tooth; p′ n-1 is the theoretical tooth thickness of the previous gear tooth.

[0151] At this time, even if the tooth thickness of the gear changes, the pitch deviation calculated by measurement will not be affected because the measurement reference position has changed. Therefore, for the pitch deviation, the wear of the grinding wheel will cause the tooth thickness of the gear to change, but it will not directly affect the measured pitch deviation result.

[0152] Step 2: Solve the tooth surface error based on the grinding wheel multi-information fusion model

[0153] 21) Constructing a multi-information fusion model for grinding wheels

[0154] 211) Construct a macro-geometric model of the grinding wheel grinding surface: Utilize the conjugate contact relationship between the grinding wheel grinding surface and the workpiece grinding surface, use the workpiece grinding surface profile equation to obtain the grinding wheel grinding surface profile equation, and establish the grinding wheel grinding surface macro-geometric model.

[0155] This embodiment takes an involute spur gear as an example, that is, the workpiece ground by the grinding wheel is an involute spur gear. Forming gear grinding is a typical line contact processing method, in which the grinding surface of the grinding wheel and the gear tooth surface are in full tooth height meshing conjugate contact, and each contact point between the grinding wheel and the workpiece tooth surface meets the conjugate contact condition:

[0156] n·v=0

[0157] Among them: n is the normal vector of the contact point, and v is the relative movement speed of the grinding wheel at the contact point to the workpiece surface.

[0158] The conjugate contact line between the grinding wheel and the gear can be regarded as the basic element of the grinding wheel and the workpiece at the same time. The grinding wheel grinding surface is formed by rotating the conjugate contact line around the grinding wheel axis. At the same time, the gear tooth surface is formed by translating the contact line along the gear helix line. Therefore, according to the conjugate grinding processing principle, the grinding wheel grinding surface profile can be deduced from the gear end face profile.

[0159] First, determine the gear end profile based on the gear design parameters. Taking the involute cylindrical gear as an example, the common design parameters include the normal module m n , number of teeth z, helix angle β, displacement coefficient x, gear width b, etc. The tooth profile curve can be regarded as a multi-end curve connected, including an involute segment, a tooth root transition arc segment, and a connecting segment of two adjacent teeth. This embodiment mainly studies the process of forming gear grinding. Therefore, the macroscopic modeling of the grinding wheel mainly considers the involute part, that is, the grinding surface profile of the grinding wheel. Taking the involute external meshing standard spur gear as an example, the parametric equation is determined according to the basic properties of the involute, and the grinding surface profile equation of the grinding wheel is obtained by the tooth surface:

[0160]

[0161] in: 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:

[0162] r b =mz cosα

[0163] Where: m is the gear module, z is the number of gear teeth, and α is the pressure angle.

[0164] Involute angle parameter The upper and lower limits can be determined according to the starting and ending points of the effective involute of the gear:

[0165]

[0166] Where: r Nf and r Na They are respectively the radii of the starting and ending points of the effective involute of the gear.

[0167] Usually, the effective involute end point is located on the gear tooth addendum circle, and the effective involute end point radius is the same as the tooth addendum circle radius. The effective involute start point position is determined according to the gear design meshing requirements. For standard meshing cylindrical gears, the effective involute start point is located on the tooth root circle, and the effective involute start point radius is the same as the tooth root circle radius. The calculation method of the tooth addendum circle and tooth root circle radius will not be repeated here, and you can refer to the relevant books on mechanical principles.

[0168] The cross-sectional profile is solved according to the involute parameter equation of the tooth profile, and the rotating surface obtained by rotating along the axis of the grinding wheel is the macroscopic shape of the grinding surface of the grinding wheel, such as Fig. 9 shown.

[0169] 212) Constructing a micro-geometric model of grinding wheel abrasive particles

[0170] Grinding wheel micro-modeling is the expression of the micro-geometric parameters of the grinding wheel abrasive particles, mainly including: abrasive particle position, abrasive particle height, abrasive particle shape, abrasive particle size, abrasive particle orientation, etc. The abrasive particles of the double-beveled grinding wheel for forming gear grinding are distributed on a three-dimensional surface, and the position information expression and calculation are more complicated. In addition, the abrasive particle geometric information is rich and has random characteristics, requiring a large amount of data to express the microscopic characteristics of the abrasive particles. Therefore, it is necessary to propose a more efficient and accurate method for expressing the information of grinding wheel abrasive particles to provide theoretical support for subsequent calculations.

[0171] Abrasive position modeling is an important part of expressing the microscopic modeling of the grinding wheel. The position matrix is ​​used to express the position of the abrasive in the grinding wheel space. The abrasive position in the traditional grinding wheel model usually uses three position matrices to represent the X, Y, and Z coordinate values ​​of the abrasive. Assuming that the length of each position matrix is ​​the total number of abrasives N, the spatial position coordinate distribution of the abrasive can be expressed by three [1×N] position matrices, or the three position matrices can be formed into a new [3×N] or [1×3N] position matrix by data splicing. This method is sensitive to the position and posture of the grinding wheel coordinate system. In subsequent calculations, the changes in the position and posture of the grinding wheel and the mutual conversion relationship between the grinding wheel and other coordinate systems in space need to be considered. At the same time, the abrasive spatial position matrix established by this method has low data utilization, large model data volume, and time-consuming calculation.

[0172] Therefore, this embodiment proposes a micro-geometric modeling method for abrasive grains of double-beveled grinding wheels for forming gear grinding, establishes an abrasive grain micro-information fusion matrix, calculates the position of the grinding wheel abrasive grains by the number of rows and columns of the matrix, and characterizes other geometric information of the abrasive grains by the corresponding matrix element size, so as to realize the simultaneous expression of multiple types of abrasive grain micro-information and improve the calculation efficiency. The number of matrix rows and columns corresponding to the spatial position of the abrasive grains is calculated as follows: Fig.10 shown.

[0173] 2121) Using the macro-geometric model of the grinding wheel grinding surface, a three-dimensional expression of the grinding wheel grinding surface profile is established, and the position of any abrasive grains on the grinding wheel grinding surface is expressed in three dimensions.

[0174] Specifically, according to the principle of profile grinding, the grinding wheel grinding surface profile is the same as the gear tooth profile. The three-dimensional expression of the grinding wheel grinding surface profile can be established by referring to the involute parameter equation, such as Fig.11 Therefore, for any abrasive grain at any position on the grinding surface of the grinding wheel, its three-dimensional expression W1 is:

[0175]

[0176] in: is the gear involute angle parameter corresponding to the abrasive position; θ is the rotation angle parameter of the abrasive position on the circumference of the grinding wheel.

[0177] Any abrasive grain position on the grinding surface of the grinding wheel can be expressed by three-dimensional expression, but the involute angle of the three-dimensional expression parameter of the grinding wheel There is a nonlinear relationship between the increment of and the radial distance increment between the grinding wheel abrasive grains and the axis. In the numerical model, when the involute angle increases uniformly, the spacing between the abrasive grains increases nonlinearly, which affects the calculation accuracy of the numerical model and cannot meet the requirements of the grinding wheel model for subsequent calculations. In addition, the three-dimensional geometric shape of the grinding wheel grinding surface is complex and difficult to directly convert into a plane matrix. Therefore, it is necessary to convert the three-dimensional expression of the grinding wheel W1 into the side view expression of the grinding wheel W2 through the geometric relationship of the grinding wheel grinding surface.

[0178] 2122) The grinding wheel grinding surface is unfolded into a two-dimensional annular plane along the axial side view, and the three-dimensional expression of the grinding wheel grinding surface profile is converted into a two-dimensional expression of the grinding wheel grinding surface side view, such as Fig.12 As shown, the position of any abrasive grain on the grinding surface of the grinding wheel is expressed in two dimensions; wherein, the difference between the radius of any point A on the two-dimensional annular plane and the inner circle radius of the two-dimensional annular plane is equal to the length of the curve segment between point A and the inner end point of the curve intercepted by the plane passing through point A′ on the grinding surface of the grinding wheel and the axis of the grinding wheel on the grinding surface of the grinding wheel, and any point A on the two-dimensional annular plane is obtained by unfolding point A′ on the grinding surface of the grinding wheel along the axial side view.

[0179] Depend on Fig.12 It can be seen that the transformation from three-dimensional geometric figures to two-dimensional plane figures can be achieved by unfolding the grinding wheel side view. The two-dimensional expression W2 of any abrasive grain position on the grinding surface of the grinding wheel is:

[0180] W2=f(R,θ)

[0181] Where R is the radius of the position of the abrasive particle in the two-dimensional annular plane;

[0182] In both the three-dimensional expression W1 and the side view expression W2 of the grinding wheel, the rotation angle parameter θ of the abrasive position on the circumference of the grinding wheel remains unchanged. Therefore, only the involute angle needs to be calculated. The conversion relationship between the radius R of the abrasive particle in the side view of the gear.

[0183] The radius R of any point in the side view of the grinding wheel can be calculated from the inner diameter of the grinding wheel:

[0184] R=R1+ΔR=R1+ΔS

[0185] Among them: ΔR is the distance between the abrasive position and the inner diameter of the grinding wheel in the side view expression; ΔS is the involute length distance between the abrasive point and the starting point of the effective involute in the three-dimensional expression of the grinding wheel; R1 is the inner diameter of the grinding wheel side view. According to the position relationship between the grinding wheel and the gear in the form grinding process:

[0186] R1=Y D ―Y end

[0187] Where Y D Y is the distance between the center of the grinding wheel and the origin of the gear coordinate system in the Y direction of the gear and grinding wheel coordinate system; end is the Y coordinate value of the effective involute end point of the gear in the gear coordinate system. The involute angle parameter of the tooth tip circle can be Substitute the involute equation into the calculation, according to the geometric characteristics of the involute gear:

[0188]

[0189] Where z is the number of gear teeth; α is the pressure angle of the upper end face of the gear pitch circle, usually 20°.

[0190] According to the involute parametric equation, the length increment of the involute is:

[0191]

[0192] In the formula, Incremental value for the involute angle parameter.

[0193] Combine the grinding wheel grinding surface profile equation and the involute length increment equation to solve the involute length of the grinding wheel grinding surface:

[0194]

[0195] In the formula, It is the involute angle parameter corresponding to the effective involute starting point.

[0196] From this we get:

[0197]

[0198] Where: Y D Y is the distance between the center of the grinding wheel and the origin of the gear coordinate system in the Y direction; end is the Y coordinate value of the tooth top; is the involute angle parameter corresponding to the starting point of the involute; and:

[0199]

[0200] in: is the involute angle parameter of the tooth addendum.

[0201] According to the above calculation, the involute angle parameter in the three-dimensional expression of the grinding wheel is Converted to the radius parameter R in the side view expression, the distance between adjacent abrasive grains changes from nonlinear growth in the three-dimensional expression to linear growth in the side view expression. At the same time, this transformation also realizes the transformation of the grinding wheel grinding surface from a complex curved surface to a circular annular plane.

[0202] 2123) The two-dimensional circular plane is unfolded into an isosceles trapezoidal plane along the circumferential direction and numerically discretized, and the two-dimensional side view expression of the grinding wheel grinding surface is converted into a grinding wheel matrix expression.

[0203] In order to further optimize the model and form a more efficient abrasive position information expression model, the grinding wheel side view expression is further expanded from the perspective of graphics and numerically discretized, and the grinding wheel side view expression W2 is converted into the grinding wheel matrix expression W3, as shown in Fig.13 In the matrix expression of the grinding wheel abrasive position information, any abrasive position variable is the row number i of the abrasive in the matrix. w and the number of columns j w :

[0204] W3=(i w ,j w )

[0205] The side view of the grinding wheel is a trapezoid after unfolding. First, according to the conservation principle of the length of the corresponding line segment before and after the side view of the grinding wheel is unfolded, the geometric dimensions of the trapezoid are calculated to determine the matrix boundary and the critical values ​​of the number of rows and columns of the matrix:

[0206] L bot =2πR1

[0207] L top =2πR2=Δj w (j wmax -1)

[0208] Where, L bot and L top Respectively represent the lengths of the two parallel sides of the trapezoid; Δj w j is the distance between adjacent rows of abrasive particles; wmaxis the maximum number of columns in the grinding wheel matrix; R2 is the outer diameter of the grinding wheel side view, through the grinding wheel geometric relationship:

[0209] R2=R1+ΔS total

[0210] In the formula, ΔS total is the total length of the involute of the grinding wheel grinding surface, which can be calculated based on the involute angle corresponding to the end point of the effective involute of the grinding wheel. In this way, we can get:

[0211]

[0212] Similarly, the height H of the grinding wheel matrix corresponds to the difference between the inner and outer diameters of the grinding wheel:

[0213] H=ΔR total =ΔS total =Δi w (i wmax ―1)

[0214] In the formula, Δi w is the distance between adjacent rows of abrasive particles; i wmax is the maximum number of rows in the grinding wheel matrix, and we can obtain wmax for:

[0215]

[0216] Since the calculation result may be a non-integer, and the number of rows and columns of the grinding wheel are integers, the maximum number of rows and columns obtained are rounded:

[0217]

[0218] The matrices in mathematical expressions are all "rectangular", while the matrix of the profile grinding wheel is a "trapezoidal" matrix. The inside of the "trapezoidal" is the grinding wheel abrasive grains, and the part between the "rectangular" and the "trapezoidal" is the part without abrasive grains, but due to the form of the matrix itself, this part is still unavoidable. Therefore, the boundary line between the "rectangular" and the "trapezoidal" is the dividing line between the grinding wheel matrix abrasive grain element area and the element-free area.

[0219] The abrasive grain with radius R in the side view of the grinding wheel corresponds to the i-th w The distance between the row element boundary and the "rectangular" matrix boundary is δ(i w )for:

[0220] δ(i w )=π(R2―R)

[0221] Finally, the number of rows and columns of the abrasive grain position in the grinding wheel matrix is ​​calculated according to the abrasive grain position radius parameter R in the grinding wheel side view matrix. In the grinding wheel matrix expression, R can be determined according to the number of rows of the abrasive grain position:

[0222] R=R1+(i w ―1)Δi w

[0223] In addition, according to the grinding wheel matrix geometry:

[0224] Δj w (j w ―1)=δ(i w )+Rθ

[0225] but:

[0226]

[0227] The expression of the number of rows and columns of any abrasive grains of the grinding wheel can be obtained:

[0228]

[0229]

[0230] The conversion relationship between the side view two-dimensional expression W2 of the grinding wheel grinding surface and the grinding wheel matrix expression W3 is obtained as follows:

[0231]

[0232] Where: i w and j w Respectively represent the number of rows and columns of the grinding wheel matrix; Δi w and Δj w are the row spacing and column spacing between adjacent abrasive particles, respectively, which are determined by the number of abrasive particles per unit area; δ(i w ) is the distance between the grinding wheel matrix element boundary and the maximum width position of the matrix.

[0233] Through the above-mentioned grinding wheel geometric parameter conversion relationship calculation, any set of parameters in the three-dimensional expression of the gear grinding wheel and θ can be solved in the grinding wheel matrix expression, realizing the three-dimensional expression of the grinding wheel The side view expression of the grinding wheel W2(R,θ) and the matrix expression of the grinding wheel W3(i w ,j w )’s mutual conversion.

[0234] 213) Construct a micro-geometric parameter model of grinding wheel abrasives: fill elements in the grinding wheel matrix according to the random distribution law of abrasives, express the actual spatial position of the abrasives with the number of rows and columns of elements in the grinding wheel matrix, and express the abrasive information with the size of elements, and the abrasive information includes the protruding height of the abrasives, the shape of the abrasives and the direction of the abrasives.

[0235] The expression of the grinding wheel matrix contains regions with or without elements. When constructing the grinding wheel matrix, it is necessary to distinguish the abrasive element and non-abrasive element regions according to the boundary calculation results of the side-view unfolded graph, and only fill the corresponding values ​​in the regions containing abrasive elements. The discrete element filling process is as follows: Fig.14 When filling elements in the grinding wheel matrix, from i w =1,j w =1 starts filling the matrix elements;

[0236] If satisfied:

[0237] δ(i w ) / Δj w ≤j w ≤j wmax ―2δ(i w ) / Δj w

[0238] Then there are abrasive particles at the position corresponding to the corresponding matrix element, otherwise there are no actual abrasive particles at the position corresponding to the corresponding matrix element.

[0239] Compared with the three-dimensional expression and side-view expression of the grinding wheel, the grinding wheel matrix expression directly uses the rows and columns of the grinding wheel matrix as parameter variables. The position information of the grinding wheel is converted from specific values ​​to the number of rows and columns of the grinding wheel matrix. The elements in the matrix can be used to express other abrasive information. By establishing the abrasive micro-information fusion matrix, the abrasive multi-information fusion expression is realized without increasing the original matrix size and data length, which improves the calculation efficiency of the model and provides theoretical support for subsequent calculations.

[0240] Due to the random characteristics of the grinding wheel, the microscopic geometric information such as the height and size of any abrasive grain is difficult to measure or calculate accurately. However, according to research, the normal height of the abrasive grains on the grinding wheel surface satisfies the Gaussian distribution. Therefore, the probability density of the height hi of any abrasive grain on the grinding wheel surface is expressed by the Gaussian probability density function:

[0241]

[0242] Where: h i is the protrusion height of any abrasive grain; a, μ and σ are the peak value of the Gaussian distribution curve, the protrusion height value corresponding to the peak value and the standard deviation, respectively, which are obtained by measuring the microscopic morphology of the working surface of the grinding wheel.

[0243] According to the Gaussian density function, a sequence of abrasive protrusion heights that obeys the distribution can be generated by mathematical methods. The total length of the sequence is the total number of abrasive particles. The element values ​​in the sequence represent any abrasive protrusion height, and the production of the element values ​​satisfies the Gaussian distribution.

[0244] According to the calculation and modeling of the abrasive position in the previous article, the number of rows and columns of the grinding wheel matrix represent the position of the abrasive, and the value of the element can represent other abrasive information. Therefore, on the basis of establishing the abrasive protrusion height sequence, taking the abrasive protrusion height as an example, an abrasive position-height fusion matrix is ​​established. In the process of establishing the abrasive height matrix, when filling elements according to the calculated abrasive area boundary, the established abrasive height sequence elements are filled into the abrasive area of ​​the grinding wheel matrix in sequence. At the same time, since the spacing between adjacent abrasives is uneven, there are also some unfilled areas in the abrasive element area. The abrasive spacing is distinguished by the size of the area, and then the height element value is assigned according to the abrasive protrusion height sequence, such as Fig.15 shown.

[0245] As can be seen from the figure, the element value in the abrasive position-height fusion matrix represents the protruding height of the abrasive. When there is no abrasive at any position, the element size corresponding to the matrix position is 0, thereby realizing the calculation of different abrasive spacing. The abrasive position and protruding height fusion matrix model establishes the basic properties of the grinding wheel abrasive, meeting the basic requirements of the grinding process calculation simulation model for the tool model.

[0246] However, for the calculation of grinding process and related parameters, other microscopic information such as abrasive grain orientation needs to be considered to achieve accurate modeling of grinding. Therefore, based on the model of arbitrary abrasive grain position and protrusion height, the abrasive grain orientation is calculated to supplement the microscopic geometric model of grinding wheel abrasive grains.

[0247] Any direction vector in space can be decomposed into two direction vectors located in mutually perpendicular planes. Therefore, the normal direction vector of the abrasive is decomposed into a plane parallel to the grinding wheel feed direction and a plane perpendicular to the grinding wheel feed direction, as shown in Fig.16 (a) is shown. The influence of the angle change on the plane perpendicular to the feed direction and the angle change on the cutting parameters are different. Taking the grinding force as an example, the influence of the angle of different planes on the direction of the grinding force is shown in Fig.16 (b) and Fig.16 (c) As shown. However, for the grinding wheel grinding process, the rotation of the grinding wheel around its own axis during the processing will also produce an angle change in the plane parallel to the feed direction, such as Fig.16 (d), and this angle changes frequently and is usually not considered when calculating the cutting force of grinding. Therefore, this embodiment only considers the orientation vector of the abrasive decomposition perpendicular to the feed direction. The angle between the orientation direction of the abrasive perpendicular to the feed direction of the grinding wheel and the normal direction of the grinding wheel plane at the abrasive position is defined as the abrasive orientation angle.

[0248] First, calculate the normal vector direction of any point on the grinding wheel surface. The grinding wheel used for profile grinding is a double-bevel grinding wheel, and its grinding surface is an involute surface. The normal vector direction at different positions is different, such as Fig.17As shown in (a), the tangential direction and normal direction at any position on the involute are calculated as:

[0249] γ n +γ k =π / 2

[0250]

[0251] We can get:

[0252]

[0253] Taking the triangular cross-section abrasive as an example, the motion trajectories of abrasives with different orientations are different during the grinding process, such as Fig.17 (b) As shown. According to the abrasive position and the normal vector direction of the grinding wheel at the abrasive position, the abrasive local coordinate system (LCSY) is established. It can be seen that the influence of the abrasive orientation on the normal and tangential grinding forces is as follows: Fig.17 (c) as shown.

[0254] The direction angle vector range of the abrasive grain is an arc with the abrasive grain position point as the center, the abrasive grain protrusion height as the radius, and the grinding wheel surface as the boundary, such as Fig.17 (d), the parametric equation of this arc is:

[0255]

[0256] In the formula, x oc and oc is the coordinate variable of the abrasive particle toward the circle in the X and Y directions; g and g h is the coordinate of the abrasive particle position, which is calculated by the involute angle corresponding to the abrasive particle position; i is the protruding height of the abrasive grains; is the parameter of the wear particle circle equation, and its critical range and It can be solved by simultaneously solving the involute equation and the equation of the abrasive particle's direction circle.

[0257] The critical value of the abrasive particle direction vector corresponding to the critical point of the abrasive particle circle is:

[0258]

[0259]

[0260]

[0261] In the formula, Indicates the abrasive grain orientation angle; x g ,y g is the coordinate point of the abrasive particle space position; and They are the coordinate values ​​of the two intersection points of a circle with the spatial position of the abrasive as the center and the protruding height of the abrasive as the radius and the involute of the tooth profile.

[0262] According to the above calculation, the calculation range of the abrasive particle orientation circle can be determined, and the orientation vector of the abrasive particle is the position of any point within the arc segment.

[0263] The real shape of abrasive particles is irregular and difficult to accurately express with simple geometric bodies. However, in order to achieve unified modeling of abrasive particles and facilitate expression and calculation, it is usually assumed that the shape of abrasive particles is some simple geometric bodies. Commonly used geometric bodies include sphere, cone, tetrahedron, truncated cone, prism, etc. The grinding process is the process of abrasive particles rotating around the axis of the grinding wheel. The geometric shape of abrasive particles is often expressed by the cross-sectional shape of abrasive particles. Therefore, on the basis of modeling the position, protrusion height, and orientation of abrasive particles, the shape of abrasive particles is further expressed and calculated, and the microscopic model of abrasive particles is supplemented, such as Fig.18 shown.

[0264] The cross section of a spherical abrasive particle is a circle, and the radius is the protruding height of the abrasive particle. Since the circle is an isotropic geometric figure, the orientation of the abrasive particle has no effect on the geometric modeling of the circle. Therefore, the geometric equations of the circular cross-section abrasive particles in various orientations are the same as those of the abrasive particle orientation circle, such as Fig.18 (a) As shown. The cross-sections of conical and tetrahedral abrasive grains are both isosceles triangles, and the vertices of the triangles are located on the abrasive grain orientation circle. The specific position is determined by the orientation angle, such as Fig.18 (b) In addition, the abrasive grain vertex angle also affects the geometric shape. The positions of the upper and lower edges of the cross section of abrasive grains with the same orientation will change with the vertex angle parameters, such as Fig.18 (c) as shown.

[0265] In this embodiment, it is assumed that the shape of the abrasive particles is conical and quadrangular pyramidal, the cross section of the abrasive particles is triangular, and the vertex of the triangle is located on the radius circle of the abrasive particles, and its position is determined by the orientation of the abrasive particles:

[0266] x tv =x g +h i cosθ i

[0267] y tv =y g +h i sinθ i

[0268] Among them, x tv and tv The vertex coordinates of the abrasive cross-section triangle; θ i is the orientation angle of any abrasive particle; h i is the protrusion height of any abrasive particle.

[0269] The upper boundary line of the triangular cross-section abrasive can be expressed by the abrasive vertex angle and the abrasive orientation direction:

[0270]

[0271] Where: x tt and tt are the coordinate values ​​of the boundary lines on the triangular cross section; t tt is the parameter variable of the upper boundary line equation, t tt_max t tt The maximum value of is the direction vector of the upper boundary line; and

[0272]

[0273] The lower boundary line of the triangular cross-section abrasive is represented by the abrasive vertex angle and the abrasive orientation direction:

[0274]

[0275] Where: x tb and tb are the coordinates of the lower boundary line of the triangular cross section; t tb is the parameter variable of the lower boundary line equation, t tb_max t tb The maximum value of is the direction vector of the lower boundary line, and:

[0276]

[0277] Where: θ v is the vertex angle of the triangular cross section.

[0278] In the grinding wheel abrasive modeling, each abrasive grain does not interfere with each other. The abrasive grains will form an independent space according to the abrasive grain direction circle. The upper and lower boundaries of the abrasive grain cross section should not exceed this area, otherwise it will be regarded as interference with adjacent abrasive grains and invalid abrasive grains. Fig.18 (e) and Fig.18 As shown in (f), when the vertex angle of the abrasive is too large or the orientation of the abrasive is too close to the critical orientation, the upper and lower boundary lines of the triangular cross section will exceed the effective range, forming invalid abrasives. The geometric relationship between the critical vertex angle value and the orientation of the abrasive needs to be guaranteed: the angle between the line connecting the upper and lower critical points of the abrasive circle to the vertex of the triangle and the line connecting the abrasive position point to the vertex of the triangle is not less than half of the vertex angle of the triangle. The cross-sections of truncated cone abrasives and prism-shaped abrasives are both isosceles trapezoids, which can be regarded as the situation where the vertex position of the isosceles triangle is worn. Its parameters are similar to the parameters of the triangular cross section and will not be repeated.

[0279] The grinding wheel multi-information fusion model can be used to measure the grinding wheel wear rate. Fig.19As shown, the abrasive grains of the grinding wheel are connected to other abrasive grains or the grinding wheel matrix through a binder. The wear of the grinding wheel during the grinding process mainly includes oxidation wear, adhesive wear, abrasive grain shedding, abrasive grain crushing and abrasive grain abrasion wear. Among the various wear forms of the grinding wheel, adhesive wear has a limited effect on the microscopic geometric parameters of the abrasive grains, abrasive grain shedding rarely occurs under normal working conditions, and abrasive grain crushing and fracture will improve the self-sharpening of the grinding wheel to a certain extent and restore the grinding performance of the grinding wheel, while abrasion wear dominates the wear of the grinding wheel and is the main factor affecting the surface quality of the workpiece. Therefore, this embodiment mainly studies the abrasion wear of the grinding wheel.

[0280] In order to quantitatively express the abrasive wear and tear, considering the random characteristics of the grinding wheel abrasives and the uncontrollable factors in the wear process, this embodiment makes the following assumptions: ① The abrasive wear and tear occurs in the axial direction of the abrasive cone; ② The geometric shape of the unworn part of the abrasive remains unchanged.

[0281] like Fig. 20 The bottom surface of the frustum abrasive is the contact surface between the abrasive and the workpiece during grinding. When the grinding wheel is worn, the height of the abrasive becomes smaller and the contact bottom surface becomes larger. The height of the abrasive before the grinding wheel is worn is the protrusion height, the remaining height after wear is defined as the residual height, and the height of the part removed by grinding is defined as the wear height. The abrasive wear rate ε is defined as the ratio of the abrasive wear height to the protrusion height of the abrasive before grinding:

[0282]

[0283] In the formula, h w Indicates the abrasive wear height, h i Indicates the protruding height of abrasive particles before wear, h r Represents the residual height of the abrasive grain after wear. The wear height of the abrasive grain is calculated by the protruding height of the abrasive grain before grinding and the residual height of the abrasive grain after grinding. In addition to the residual height of the abrasive grain, other geometric parameters can also be solved according to the abrasive wear conditions:

[0284] L2=L1+2h w tanα g

[0285] Where L2 is the diameter of the contact bottom surface after grinding, L1 represents the diameter of the initial wear plane of the abrasive before processing, which is generally 2%-3% of the protruding height of the abrasive before grinding, and α g Indicates the grinding front angle of the abrasive grain. w Expressed in terms of directly measurable height values:

[0286] L2=L1+2(h i ―h r )tanα g

[0287] It can be seen from the formula that the abrasive wear rate can be determined by measuring the residual height distribution of the grinding wheel after grinding; the geometric dimensions of the abrasive in the current wear state can be determined by the abrasive wear rate.

[0288] 22) The multi-information fusion model of the grinding wheel is used to respectively solve the tooth surface errors including the tooth profile inclination deviation, the total helix deviation and the normal offset of the tooth profile curve. In this embodiment, the method steps for solving the tooth surface error using the multi-information fusion model of the grinding wheel are as follows:

[0289] 221) According to the effective grinding area of ​​the grinding wheel in contact with the workpiece during grinding, elements corresponding to the effective grinding area of ​​the grinding wheel are extracted from the grinding wheel matrix to form a grinding wheel grinding matrix.

[0290] The effective grinding area of ​​the grinding wheel is the annular area located within the grinding surface of the grinding wheel, and the inner radius and outer radius of the effective grinding area of ​​the grinding wheel are:

[0291]

[0292]

[0293] Where: r′ Nf and r′ Na Respectively represent the inner radius and outer radius of the effective grinding area of ​​the grinding wheel; d Nf With d Na Respectively represent the diameters of the starting and ending points of the effective involute of the gear; Y D is the center distance between the gear and the grinding wheel in the radial direction;

[0294] The grinding wheel grinding matrix is ​​formed by extracting the grinding wheel matrix elements located between the inner circle radius and the outer circle radius of the effective grinding area of ​​the grinding wheel.

[0295] 222) Before the grinding wheel is worn, the distribution law of the protruding height of the grinding wheel abrasive is fitted; after the grinding wheel is worn, the distribution law of the residual height of the grinding wheel abrasive is fitted.

[0296] Similar to the protrusion height before grinding, the distribution frequency of the residual height of the abrasive particles after grinding obeys a certain distribution. The abrasive wear height can be solved by the protrusion height before grinding and the residual height after grinding. However, the direct calculation between the probability density functions of the protrusion height before grinding and the residual height after grinding needs to consider the independence of the two events, and the independence of the height of the grinding wheel abrasive particles before and after grinding is difficult to directly prove. Therefore, according to the height distribution and the total number of abrasive particles, the abrasive particle protrusion height sequence and the abrasive particle residual height sequence matrix are established respectively. The abrasive wear height is solved by calculating the corresponding elements in the matrix sequence, avoiding the discussion of the independence between the probability density functions. The calculation process is as follows: Fig.21 shown.

[0297] In order to explain the entire calculation process and steps more clearly, a set of data measured in the experiment is used as an example to calculate the wear rate. The abrasive height distribution of the grinding wheel grinding surface before and after wear is measured, and the Gaussian curve is used to fit the measurement results and calculate the fitting residual, such as Fig. 22 As shown. The Gaussian distribution fitting effect of the protrusion height distribution before grinding and the residual height distribution after grinding is good, and the fitting coefficient R2 is 0.997 and 0.995 respectively. The residual value is very small, which proves the effectiveness of using the Gaussian probability density function to fit the abrasive height. That is, the protrusion height of the grinding wheel abrasive grains obeys the Gaussian distribution:

[0298]

[0299] Where: h i is the protrusion height of any abrasive grain; a, μ and σ are the peak value of the Gaussian distribution curve, the protrusion height value corresponding to the peak value and the standard deviation, respectively, which are obtained by measuring the microscopic morphology of the working surface of the grinding wheel.

[0300] The residual height of the grinding wheel abrasive grains follows the Gaussian distribution:

[0301]

[0302] Where: h r is the residual height of any abrasive particle.

[0303] 223) According to the distribution law of the protruding height of the grinding wheel abrasive grains, elements are filled in the grinding wheel grinding matrix to obtain the protruding height distribution matrix of the grinding wheel abrasive grains; according to the distribution law of the residual height of the grinding wheel abrasive grains, elements are filled in the grinding wheel grinding matrix to obtain the residual height distribution matrix of the grinding wheel abrasive grains.

[0304] 224) respectively solve the tooth profile inclination deviation, the total helix deviation and the normal offset of the tooth profile curve.

[0305] Specifically, in this embodiment, the method for solving the tooth profile inclination deviation is: extracting a row of elements corresponding to the tooth top and the tooth root from the grinding wheel grinding abrasive grain protrusion height distribution matrix to form the tooth top protrusion height distribution matrix before wear and the tooth root protrusion height distribution matrix before wear; extracting a row of elements corresponding to the tooth top and the tooth root from the grinding wheel grinding abrasive grain residual height distribution matrix to form the tooth top protrusion height distribution matrix after wear and the tooth root protrusion height distribution matrix after wear.

[0306] The abrasive wear rate corresponding to the tooth top is solved by using the tooth top protrusion height distribution matrix before wear and the tooth top protrusion height distribution matrix after wear:

[0307] ε top =mean(([h i_top ]-[h r_top ]) / [h i_top ])

[0308] In the formula, [h i_top ] represents the distribution matrix of tooth top protrusion height before wear; [h r_top ] represents the distribution matrix of tooth top protrusion height after wear; mean(·) represents the mean function; h i_top Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_top The protruding height of the abrasive particles corresponding to the tooth top after wear;

[0309] The abrasive wear rate corresponding to the tooth root is solved by using the tooth root protrusion height distribution matrix before wear and the tooth root protrusion height distribution matrix after wear:

[0310] ε bot =mean(([h i_bot ]―[h r_bot ]) / [h i_bot ])

[0311] In the formula, [h i_bot ] represents the distribution matrix of tooth top protrusion height before wear; [h r_bot ] represents the distribution matrix of tooth top protrusion height after wear; mean(·) represents the mean function; h i_bot Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_bot The protruding height of the abrasive particles corresponding to the tooth top after wear.

[0312] Using the solved ε top and ε bot , substitute:

[0313] f hα =h i (ε top ―ε bot )

[0314] The tooth profile inclination deviation caused by grinding wheel wear is obtained.

[0315] In this embodiment, the calculation method of the total deviation of the spiral line is: extract a row of elements corresponding to the tooth top from the grinding wheel grinding abrasive grain protrusion height distribution matrix to form the tooth top protrusion height distribution matrix before wear; extract a row of elements corresponding to the tooth top from the grinding wheel grinding abrasive grain residual height distribution matrix to form the tooth top protrusion height distribution matrix after wear.

[0316] The grinding wheel abrasive wear height distribution matrix is ​​obtained by the tooth top protrusion height distribution matrix before wear and the tooth top protrusion height distribution matrix after wear:

[0317] [h w_top ]=[h i_top ]―[h r_top ]

[0318] Among them, [h w_top ] represents the grinding wheel abrasive wear height distribution matrix; [h i_bot ] represents the distribution matrix of tooth top protrusion height before wear; [h r_bot ] represents the distribution matrix of tooth top protrusion height after wear; h i_top Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_top The protruding height of the abrasive particles corresponding to the tooth top after wear; h w_top Indicates the abrasive wear height corresponding to the tooth top;

[0319] According to the grinding wheel abrasive wear height distribution matrix, the wear rate of each abrasive particle is solved:

[0320] ε i_top =(h i_top ―h r_top ) / h i_top

[0321] In the formula, ε i_top Indicates the wear rate of abrasive particles;

[0322] The wear rate of abrasive particles is used to obtain the distribution matrix of the wear rate of grinding wheel particles [ε top ], from the grinding wheel abrasive wear rate distribution matrix [ε top ] to extract the maximum value max([ε top ]) and the minimum value min([ε top ]) to obtain the total deviation of the helix.

[0323] Specifically, the max([ε top ]) and min([ε top ])Substitute:

[0324] F β_top =h i (max([ε top ])―min([ε top ]))

[0325] The total deviation of the helix caused by grinding wheel wear is obtained.

[0326] In this embodiment, the normal offset of the gear tooth profile curve is calculated by using the grinding wheel grinding abrasive protrusion height distribution matrix and the grinding wheel grinding abrasive residual height distribution matrix to solve the grinding wheel wear rate:

[0327] ε=mean(([h i ]―[h r ]) / [h i ])

[0328] Where ε represents the wear rate of the grinding wheel; mean(·) represents the mean function; [hi ] represents the protruding height distribution matrix of grinding wheel abrasive grains; [h r ] represents the residual height distribution matrix of grinding wheel abrasive particles; h i Indicates the protruding height of the grinding wheel abrasive grains; h r Indicates the residual height of grinding wheel abrasive grains.

[0329] In order to simplify the calculation, this embodiment assumes that the total number of abrasive grains does not change before and after grinding. Therefore, the total number of abrasive grains on the grinding wheel is represented by the number of grinding wheels measured before grinding:

[0330] d g =15.2M ―1

[0331] Where, d g It represents the average diameter of the abrasive particles in mm, and M represents the total number of abrasive particles in the area.

[0332] The elements in each sequence are classified according to the numerical interval and the total number of wear particles in each interval is counted, such as Fig.23 As shown. It can be seen from the figure that the maximum value in the protrusion height sequence before grinding is about 90μm, and the highest frequency intervals are 30-40μm and 40-50μm. In contrast, the maximum value in the residual height sequence after grinding is 60μm, and the highest frequency interval is 20-40μm. The distribution of values ​​in the protrusion height sequence before grinding is relatively more even, while the values ​​in the residual height sequence after grinding are more concentrated. Except for the highest frequency interval, the frequencies of other intervals are less than half of the highest interval frequency. Therefore, after grinding, the size of the abrasive particles tends to be below a certain threshold, the number of abrasive particles exceeding the critical value drops sharply, and the number of abrasive particles in the interval near the critical value will be more than before grinding.

[0333] At the same time, when generating the respective sequences, it cannot be guaranteed that each element value in the protrusion height sequence is greater than the corresponding value in the residual height sequence. The elements in the wear and tear sequence obtained by subtracting the two sequences will have negative values. This element only represents the calculated value in the statistical probability, not the actual value of the wear and tear, and does not affect the calculation of the wear and tear rate. The calculation results are as follows: Fig.24 As shown. Fig.25 It can be seen that under this working condition, the abrasive wear is 17.2μm and the wear rate ε is 36.7%. In addition, in order to minimize the impact of randomness in data generation, the same algorithm is used to repeat the calculation multiple times and calculate the average value, such as Fig.25 shown.

[0334] The normal offset of the gear tooth profile curve is obtained by using the solved grinding wheel wear rate. Specifically, substitute the solved ε into:

[0335] Δp n =h i ε

[0336] The normal deviation of the tooth profile curve caused by grinding wheel wear is obtained.

[0337] Step 225), loop through steps 222) to 224), calculate the average value after multiple solutions to reduce the error generated when generating random numbers.

[0338] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for calculating tooth surface error based on grinding wheel wear, characterized in that: The steps include: Step 1: Construct the relationship between tooth surface error and grinding wheel wear, where: The relationship between tooth profile inclination deviation and abrasive wear is: f hα =h i (e top —he bot ) In the formula, f hα is the tooth profile inclination deviation error term caused by grinding wheel wear; h i The protruding height of the abrasive grain; ε top and ε bot These are the measurement and calculation results of abrasive wear rate corresponding to tooth top and tooth root respectively; The relationship between the total helical deviation and abrasive wear is: F β_top =h i (max([e top ])―min([e top ])) In the formula, F β_top is the total helix deviation error term of the tooth profile tooth tip position caused by grinding wheel wear; max([ε top ]) and min([ε top ]) are the maximum and minimum values ​​of the abrasive wear rate measurement calculation results at different measuring points on the tooth top; For pitch deviation, grinding wheel wear will cause the tooth thickness to change, which will lead to a normal offset in the tooth profile curve of the gear. The relationship between the normal offset and abrasive wear is: Δp n =h i e In the formula, Δp n is the normal offset of the gear teeth caused by grinding wheel wear; ε represents the wear rate of the grinding wheel; Step 2: Solve the tooth surface error based on the grinding wheel multi-information fusion model: 21) Construct a multi-information fusion model of grinding wheel; 22) The multi-information fusion model of the grinding wheel is used to solve the tooth surface errors including the tooth profile inclination deviation, the total helix deviation and the normal offset of the tooth profile curve; The method steps for solving tooth surface error using the grinding wheel multi-information fusion model are as follows: 221) according to the effective grinding area of ​​the grinding wheel in contact with the workpiece during grinding, extracting elements corresponding to the effective grinding area of ​​the grinding wheel from the grinding wheel matrix to form a grinding wheel grinding matrix; 222) Before the grinding wheel is worn, the distribution law of the protruding height of the grinding wheel abrasive grains is fitted; after the grinding wheel is worn, the distribution law of the residual height of the grinding wheel abrasive grains is fitted; 223) According to the distribution law of the protruding height of the grinding wheel abrasive grains, elements are filled in the grinding wheel grinding matrix to obtain the protruding height distribution matrix of the grinding wheel grinding abrasive grains; according to the distribution law of the residual height of the grinding wheel abrasive grains, elements are filled in the grinding wheel grinding matrix to obtain the residual height distribution matrix of the grinding wheel grinding abrasive grains; 224) respectively solve the tooth profile inclination deviation, the total helix deviation and the normal offset of the tooth profile curve; 225) loops through steps 222) to 224) and calculates the average value after multiple solutions.

2. The tooth surface error calculation method based on grinding wheel wear according to claim 1, characterized in that: In the step 21), the construction method of the grinding wheel multi-information fusion model is as follows: 211) Constructing a macro-geometric model of the grinding wheel grinding surface: using the conjugate contact relationship between the grinding wheel grinding surface and the workpiece grinding surface, using the workpiece grinding surface profile equation to obtain the grinding wheel grinding surface profile equation, and establishing the grinding wheel grinding surface macro-geometric model; 212) Constructing a micro-geometric model of grinding wheel abrasive particles 2121) Using the macro-geometric model of the grinding wheel grinding surface, a three-dimensional expression of the grinding wheel grinding surface profile is established, and the position of any abrasive grains on the grinding wheel grinding surface is expressed in three dimensions; 2122) Expand the grinding wheel grinding surface into a two-dimensional annular plane along the axial side view, convert the three-dimensional expression of the grinding wheel grinding surface profile into a two-dimensional expression of the grinding wheel grinding surface side view, and express any abrasive grain position on the grinding wheel grinding surface in two dimensions; wherein, the difference between the radius of any point A on the two-dimensional annular plane and the inner circle radius of the two-dimensional annular plane is equal to the length of the curve segment located between point A and the inner end point of the curve intercepted by the plane passing through the grinding wheel grinding surface point A′ and the grinding wheel axis on the grinding wheel grinding surface, and any point A on the two-dimensional annular plane is obtained by expanding the point A′ on the grinding wheel grinding surface along the axial side view; 2123) Expand the two-dimensional annular plane into an isosceles trapezoidal plane along the circumferential direction and perform numerical discretization, and convert the two-dimensional expression of the grinding wheel grinding surface from the side view into a grinding wheel matrix expression; 213) Constructing the micro-geometric parameter model of grinding wheel abrasive Elements are filled in the grinding wheel matrix according to the random distribution law of abrasive particles. The actual spatial position of the abrasive particles is expressed by the number of rows and columns of the elements in the grinding wheel matrix, and the height of the abrasive particles is expressed by the size of the elements.

3. The method for calculating tooth surface error based on grinding wheel wear according to claim 2, characterized in that: In the step 211), the workpiece is an involute spur gear, the grinding surface of the involute spur gear is the tooth surface, and the grinding surface profile equation of the grinding wheel obtained by the tooth surface is: in: 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: <h2 style=";text-align:left;direction:ltr">r<h2 style=";text-align:left;direction:ltr"> b <h2 style=";text-align:left;direction:ltr"> (mzcosα) Where: m is the gear module, z is the number of gear teeth, and α is the pressure angle.

4. The method for calculating tooth surface error based on grinding wheel wear according to claim 3, characterized in that: In the step 2121), the three-dimensional expression W1 of any abrasive grain position on the grinding surface of the grinding wheel is: in: is the gear involute angle parameter corresponding to the abrasive position; θ is the rotation angle parameter of the abrasive position on the circumference of the grinding wheel; In step 2122), the two-dimensional expression W2 of the position of any abrasive grain on the grinding surface of the grinding wheel is: W2=f(R,θ) Where R is the radius of the abrasive particle in the two-dimensional annular plane; and: Where: Y D Y is the distance between the grinding wheel center and the origin of the gear coordinate system in the Y direction; end is the Y coordinate value of the tooth top; is the involute angle parameter corresponding to the starting point of the involute; and: in: is the involute angle parameter of the tooth top; In the step 2123), the conversion relationship between the grinding wheel grinding surface side view two-dimensional expression W2 and the grinding wheel matrix expression W3 is: Where: i w and j w Respectively represent the number of rows and columns of the grinding wheel matrix; Δi w and Δj w are the row spacing and column spacing between adjacent abrasive particles, respectively, which are determined by the number of abrasive particles per unit area; δ(i w ) is the distance between the grinding wheel matrix element boundary and the maximum width position of the matrix; and: The maximum number of rows in the grinding wheel matrix is: i wmax =1+r b (((z+2) / zcosα) 2 ―1) / 2Δi w For the solved i wmax Perform rounding; The maximum number of columns in the grinding wheel matrix is: For the solved j wmax Round up.

5. The method for calculating tooth surface error based on grinding wheel wear according to claim 4, characterized in that: In the step 213), when filling elements in the grinding wheel matrix, from i w =1,j w =1 starts filling the matrix elements; If satisfied: d(i w ) / Δj w ≤j w ≤j wmax ―2δ(i w ) / Δj w Then there are abrasive particles at the position corresponding to the corresponding matrix element, otherwise there are no actual abrasive particles at the position corresponding to the corresponding matrix element.

6. The method for calculating tooth surface error based on grinding wheel wear according to claim 1, characterized in that: In the step 223), the method for solving the tooth profile inclination deviation is: extracting a row of elements corresponding to the tooth top and the tooth root from the grinding wheel grinding abrasive grain protrusion height distribution matrix to form a tooth top protrusion height distribution matrix before wear and a tooth root protrusion height distribution matrix before wear; extracting a row of elements corresponding to the tooth top and the tooth root from the grinding wheel grinding abrasive grain residual height distribution matrix to form a tooth top protrusion height distribution matrix after wear and a tooth root protrusion height distribution matrix after wear; The abrasive wear rate corresponding to the tooth top is solved by using the tooth top protrusion height distribution matrix before wear and the tooth top protrusion height distribution matrix after wear: ε top =mean(([h i_top ]―[h r_top ]) / [j i_top ]) In the formula, [h i_top ] represents the distribution matrix of tooth top protrusion height before wear; [h r_top ] represents the distribution matrix of tooth top protrusion height after wear; mean(·) represents the mean function; h i_top Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_top The protruding height of the abrasive particles corresponding to the tooth top after wear; The abrasive wear rate corresponding to the tooth root is solved by using the tooth root protrusion height distribution matrix before wear and the tooth root protrusion height distribution matrix after wear: ε bot =mean(([h i_bot ]―[h r_bot ]) / [h i_bot ]) In the formula, [h i_bot ] represents the distribution matrix of tooth top protrusion height before wear; [h r_bot ] represents the distribution matrix of tooth top protrusion height after wear; mean(·) represents the mean function; h i_bot Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_bot The protruding height of the abrasive particles corresponding to the tooth top after wear.

7. The method for calculating tooth surface error based on grinding wheel wear according to claim 1, characterized in that: In step 223), the total deviation of the helix is ​​calculated as follows: Extracting a row of elements corresponding to the tooth top from the grinding wheel grinding abrasive grain protrusion height distribution matrix to form the tooth top protrusion height distribution matrix before wear; extracting a row of elements corresponding to the tooth top from the grinding wheel grinding abrasive grain residual height distribution matrix to form the tooth top protrusion height distribution matrix after wear; The grinding wheel abrasive wear height distribution matrix is ​​obtained by the tooth top protrusion height distribution matrix before wear and the tooth top protrusion height distribution matrix after wear: [h w_top ]=[hi _top ]―[h r_top ] Among them, [h w_top ] represents the grinding wheel abrasive wear height distribution matrix; [h i_bot ] represents the distribution matrix of tooth top protrusion height before wear; [h r_bot ] represents the distribution matrix of tooth top protrusion height after wear; h i_top Indicates the protruding height of the abrasive grain before wear corresponding to the tooth top; h r_top The protruding height of the abrasive particles corresponding to the tooth top after wear; h w_top Indicates the abrasive wear height corresponding to the tooth top; According to the grinding wheel abrasive wear height distribution matrix, the wear rate of each abrasive particle is solved: ε i_top =(h i_top ―h r_top ) / h i_top In the formula, ε i_top Indicates the wear rate of abrasive particles; The wear rate of abrasive particles is used to obtain the distribution matrix of the wear rate of grinding wheel particles [ε top ], from the grinding wheel abrasive wear rate distribution matrix [ε top ] to extract the maximum value max([ε top ]) and the minimum value min([ε top ]) to obtain the total deviation of the helix.

8. The method for calculating tooth surface error based on grinding wheel wear according to claim 1, characterized in that: The calculation method of the normal offset of the gear tooth profile curve is: the grinding wheel abrasive protrusion height distribution matrix and the grinding wheel abrasive residual height distribution matrix are used to solve the grinding wheel wear rate: ε=mean(([h i ]―[h r ]) / [h i ]) Where ε represents the grinding wheel wear rate; mean(·) represents the mean function; [h i ] represents the protruding height distribution matrix of grinding wheel abrasive grains; [h r ] represents the residual height distribution matrix of grinding wheel abrasive particles; h i Indicates the protruding height of the grinding wheel abrasive grains; h r Indicates the residual height of grinding wheel abrasive grains; The normal offset of the gear tooth profile curve is obtained using the solved grinding wheel wear rate.

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