A method for calculating transmission error of helical gear considering modification amount

Abstract

This invention discloses a method for calculating the transmission error of helical gears considering profile modification. Based on solving the time-varying meshing stiffness and nonlinear profile modification of the helical gear, the transmission error is solved by establishing a multi-tooth load balance equation. The implementation steps are as follows: the helical gear is divided into multiple slice teeth along the tooth width direction, and the time-varying meshing stiffness of a single slice tooth is obtained; the meshing points of the helical gear tooth surface are discretized into r×s points along the end face and tooth direction, and the stiffness value of each meshing point is obtained; according to the variation law of the helical gear meshing line, the time-varying meshing stiffness of the multi-tooth helical gear under high overlap is solved; a mathematical model of profile modification is established along the end face of the helical gear, and the deformation of each meshing point of the gear is calculated; using the time-varying meshing stiffness of the multi-tooth helical gear and the deformation of each meshing point, the load balance equation of the helical gear is established, and the transmission error of the helical gear is solved.

Description

Technical Field

[0001] This invention relates to the field of mechanical dynamics, and in particular to a method for calculating the transmission error of helical gears that takes into account the amount of modification. Background Technology

[0002] Today, the new energy vehicle industry has become the mainstream of future development. New energy vehicles use drive motors to replace the engines in traditional cars, which makes the "masking effect" in traditional fuel vehicles disappear. The noise of the gear transmission device becomes prominent, which makes the overall comfort of the vehicle worse and affects the riding experience of the driver and passengers. Therefore, it is urgent to optimize vibration and noise. The optimization method mainly comes from profile modification. The main internal excitation sources of vibration and noise are stiffness and transmission error. Therefore, it is very important to optimize these two through profile modification. However, the traditional calculation method treats any position on the tooth as the same stiffness, which greatly reduces the calculation accuracy. Moreover, there is no accurate calculation method for the profile modification amount along the tooth profile and tooth direction. Therefore, this invention designs a transmission error calculation method that considers profile modification at any position on the tooth surface, which comprehensively improves the calculation accuracy of transmission error of profile modified helical gears. Summary of the Invention

[0003] In view of the above-mentioned problems in the existing technology, the technical problem to be solved by the present invention is: how to provide a high-precision method for calculating the transmission error of helical gears.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A method for calculating the transmission error of helical gears considering the amount of modification includes the following steps:

[0006] Step 1: Based on the helical gear model, a single helical tooth is divided into multiple slice teeth along the tooth direction;

[0007] Step 2, calculate the meshing stiffness k of the slicing teeth. total (α K );

[0008] Step 3: Discretize the helical gear end face into s meshing points, and calculate the meshing stiffness K corresponding to each meshing point. total (t), (t=1···s), then repeat the previous step along the tooth direction to divide the meshing tooth surface into r×s meshing points, and obtain the meshing stiffness of each point;

[0009] Step 4: Calculate the meshing stiffness K of the helical gear according to the variation law of the line of action. dc (i);

[0010] Step 5: Substitute the tooth profile modification parameters Ca and La to obtain the modification amount at the corresponding position on the tooth profile;

[0011] Step 6: Set the minimum deviation value of the total transmitted load, solve the tooth surface bearing contact equation based on the iterative method to obtain the transmission error of the helical gear, introduce the modification amount, and finally obtain the transmission error after modification.

[0012] Preferably, in step S2, the meshing stiffness k of the slicing teeth is calculated. total (α K The specific steps are as follows:

[0013] Calculation of meshing stiffness of the slicing teeth based on the potential energy method:

[0014] At this point, the bending-shear-radial compressive stiffness k b i k s i k a i Hertzian contact stiffness k h Wheel stiffness k f i They are represented as follows:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] In the formula, i = p, g; i = p represents the driving wheel, i = g represents the driven wheel, and k total Let be the meshing stiffness of a single gear, and F be the load acting on the single gear. For gear bending stiffness, For shear stiffness, For radial compressive stiffness, k h For Hertzian contact stiffness, R is the gear body stiffness, E is the elastic modulus of the gear material, and r is the gear body stiffness. b Let r be the radius of the base circle. f Let be the radius of the root circle, v be Poisson's ratio, b0 be the effective tooth width, α be the angle between the tangent point at different positions on the tooth profile and the X-axis, α1 be the angle between the meshing force and the Y-axis, α2 be the half angle corresponding to the base circle, α4 be the half angle corresponding to the root circle, and α5 be arccos(r). b / r f )+α4, α5 are the included angles on the X-axis corresponding to the root circle; Let be the distance between a point on the root circle of the gear tooth on the line of symmetry and the intersection of the line of action of the meshing force and the line of symmetry of the gear tooth. L is the arc length corresponding to a single tooth on the root circle. * M * ,P * Q * All represent coefficients, X i * Indicates coefficient L * M * ,P * Q * h f θ is the ratio of the root circle radius of the gear to the bore radius of the gear. f It is half of the central angle corresponding to the arc occupied by a single tooth;

[0022] Establish α1 and α K The relationship transforms the meshing stiffness function into the corresponding pressure angle α at the meshing point. K A function of variables

[0023]

[0024]

[0025] In the formula, K total (α K () is about the pressure angle α K meshing stiffness;

[0026] Define α1 and α K The relationship is as follows:

[0027] α1=α K -(π / 2·z-(inv(α K )-inv(α t )));

[0028] Where, α t The z represents the face engagement angle, and z represents the number of teeth.

[0029] As a preferred embodiment, the specific steps for calculating the meshing stiffness at each point in step 3 are as follows:

[0030] Based on the slicing method, the tooth profile surface is divided into r spur gears, and the angle through which each equal part rotates is:

[0031] Δλ=(B / p) / r

[0032] Divide the angle rotated from the starting and ending positions into 's' parts, that is, divide the helical gear tooth profile on the end face from the tooth root to the tooth tip into 's' parts, and the angle rotated by each part is 's'.

[0033] Δω=|ω B2-ω B1 | / s

[0034] Let Δω = Δλ, then

[0035] Where, ω B2 ω represents the angle at which the end faces begin to mesh. B1 This indicates the angle at which the end face ends meshing, B represents the tooth width, and p represents the lead parameter;

[0036] Here, the continuous rotation time is discretized into several time points, where t is the meshing position number on the tooth profile during rotation, N1 is the point where the base circle of the driving gear is tangent to the line of meshing, and P′ is the node; the pressure angle α at point t is... K The expression for (t) is:

[0037] α K (t)=arctan(N1B2+B2B1·t / s) / N1O1

[0038] In the formula, t = 0, 1, 2...s, B2 represents the starting point of meshing on the front end face of the meshing plane, B1 represents the ending point of meshing on the front end face of the meshing plane, N1 represents the point of tangency between the meshing plane and the base circle of the driving wheel, and O1 represents the center of the driving wheel.

[0039] Combining this with the above equation, the expression for the meshing stiffness of the spur gear slices is transformed into a function of the discrete quantity t, yielding the stiffness of each slice tooth at different positions on the divided tooth profile:

[0040]

[0041] Preferably, in step 4, the meshing stiffness K is calculated. dc The specific steps for (i) are as follows:

[0042] The helical gear meshing line can be discretized into different meshing points, each distributed in a different colored meshing region. By accumulating the stiffness of the meshing points and combining it with the variation law of the meshing line, the time-varying meshing stiffness of a single tooth within one cycle is expressed as follows:

[0043]

[0044] In the formula, i represents the engagement time corresponding to the i-th meshing line when a single tooth is engaged;

[0045] The formula for the multi-tooth meshing stiffness over one cycle is as follows:

[0046]

[0047] Where: K dc (i) represents the formula for calculating the meshing stiffness of the five-tooth and four-tooth gears at time i within a cycle, where αm which corresponds to the rotation angle in the interval from the moment the front teeth start engaging to the moment the rear teeth start engaging;

[0048] α m =2·π / z

[0049] α z =ω B2 -(ω B1 -B / p).

[0050] Preferably, the specific steps for calculating the modification amount at the corresponding position on the tooth profile in step 5 are as follows:

[0051] The expression of tooth profile modification amount ε(t):

[0052]

[0053] wherein Ca represents the modification amount, La represents the modification length, r b represents the base circle radius, r g represents the root circle radius, r d represents the addendum circle radius.

[0054] Preferably, the specific steps of said step 6 are as follows, the total load of five teeth is:

[0055] wherein F(x) is:

[0056]

[0057] obtaining the allowable deviation between the calculated total load and the actual total load of the given gear, and iteratively solving the transmission error of the helical gear in one meshing cycle; the specific steps are as follows:

[0058] in the above formula, for the contact point t, if δ>ε(t) is satisfied, the point is in contact, u(t) takes a positive value, otherwise u(t) takes 0;

[0059] 1) Let k=1, and give the initial value δ of transmission error (1) ;

[0060] 2) sequentially determine the magnitude of deformation δ (k) -ε(t) at each contact point i, if it is less than 0, set it to 0;

[0061] 3) obtain the total load F Z (k);

[0062] 4) determine whether |F Z (k)-F|<F0 holds; if not, let δ (k+1) =δ (k) -(F Z (k)-F) / k sIf k = k + 1, return to step 2); if true, the iteration stops and output δ = δ (k) ;

[0063] In the formula, k is the number of iterations, δ (k+1) For the propagation error in the (k+1)th step, δ (k) For the propagation error in the k-th step, F Z (k) represents the meshing force calculated in the k-th step, k s The average meshing stiffness of several gear teeth at a certain moment in a gear pair;

[0064] δ=u(t)+ε(t)

[0065] In the formula, u(t) is the deformation amount, δ is the transmission error after modification, and ε(t) is the modification amount at each contact point.

[0066] Compared with the prior art, the present invention has at least the following advantages:

[0067] By taking advantage of the different meshing stiffness at different positions on the tooth profile, and by superimposing the stiffness of different slice teeth according to the meshing line at different times, a time-varying high-precision meshing stiffness is obtained. Based on this, the transmission error obtained by solving the load balance equation also has high accuracy. Attached Figure Description

[0068] Figure 1 This is a flowchart of the present invention.

[0069] Figure 2 This is a schematic diagram illustrating the calculation parameters for the meshing stiffness of a single slice gear tooth.

[0070] Figure 3 This is a schematic diagram of the meshing process. Figure 3 (a) Schematic diagram of the end face meshing process. Figure 3 (b) is a schematic diagram of the meshing line of the tooth surface.

[0071] Figure 4 This is a graph showing the relationship between the meshing stiffness and the length of the line of action of a single tooth over one cycle. Figure 4 (a) indicates that the stiffness of the first segment increases with the increase of the length of the meshing line. Figure 4 (b) shows how the stiffness of the second segment changes when the length of the meshing line remains constant and only the position changes. Figure 4 (c) indicates that the stiffness of the third segment decreases as the length of the meshing line decreases.

[0072] Figure 5 This is a superimposed diagram of the lengths of the multi-tooth meshing lines.

[0073] Figure 6 This is a comparison chart of the multi-tooth meshing stiffness calculation model, the finite element model, and the national standard calculation method.

[0074] Figure 7 This is a schematic diagram of a single tooth slice and tooth profile modification of a helical gear.

[0075] Figure 8 This is a comparison chart of the results from the gear transmission error calculation model and the finite element model.

[0076] Figure 9 This is a comparison chart showing the gear transmission error before and after modification. Detailed Implementation

[0077] The present invention will now be described in further detail.

[0078] A method for calculating the transmission error of helical gears considering the amount of modification includes the following steps:

[0079] Step 1: Based on the helical gear model, a single helical tooth is divided into multiple slice teeth along the tooth direction.

[0080] Step 2, calculate the meshing stiffness k of the slicing teeth. total (α K The specific steps are as follows:

[0081] Calculation of meshing stiffness of the slicing teeth based on the potential energy method:

[0082] At this point, the bending-shear-radial compressive stiffness k b i k s i k a i Hertzian contact stiffness k h Wheel stiffness They are represented as follows:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] In the formula, i = p, g; i = p represents the driving wheel, i = g represents the driven wheel, and k total Let be the meshing stiffness of a single gear, and F be the load acting on the single gear. For gear bending stiffness, For shear stiffness, For radial compressive stiffness, kh For Hertzian contact stiffness, R is the gear body stiffness, E is the elastic modulus of the gear material, and r is the gear body stiffness. b Let r be the radius of the base circle. f Let be the radius of the root circle, v be Poisson's ratio, b0 be the effective tooth width, α be the angle between the tangent point at different positions on the tooth profile and the X-axis, α1 be the angle between the meshing force and the Y-axis, α2 be the half angle corresponding to the base circle, α4 be the half angle corresponding to the root circle, and α5 be arccos(r). b / r f )+α4, α5 are the included angles on the X-axis corresponding to the root circle; Let be the distance between a point on the root circle of the gear tooth on the line of symmetry and the intersection of the line of action of the meshing force and the line of symmetry of the gear tooth. L is the arc length corresponding to a single tooth on the root circle. * M * ,P * Q * All represent coefficients, X i * Indicates coefficient L * M * ,P * Q * h f θ is the ratio of the root circle radius of the gear to the bore radius of the gear. f It is half of the central angle corresponding to the arc occupied by a single tooth.

[0090] Establish α1 and α K The relationship transforms the meshing stiffness function into the corresponding pressure angle α at the meshing point. K It is a function of the variable so that α can be represented later using gear parameters. K .

[0091]

[0092]

[0093] In the formula, K total (α K () is about the pressure angle α K The meshing stiffness.

[0094] Define α1 and α K The relationship is as follows:

[0095] α1=α K -(π / 2·z-(inv(α K )-inv(α t )));

[0096] Where, α tThe 'z' represents the face engagement angle, and 'z' represents the number of teeth.

[0097] Step 3: Discretize the helical gear end face into s meshing points, and calculate the meshing stiffness K corresponding to each meshing point. total (t), (t=1···s), then repeat the previous step along the tooth direction to divide the meshing tooth surface into r×s meshing points, and obtain the meshing stiffness of each point. The specific steps are as follows:

[0098] The time-varying meshing stiffness of a single tooth is calculated based on the corresponding stiffness at various positions on the tooth surface. For helical gears, the meshing process is shown in Figure (3b). The line of action on a single driving gear continuously lengthens from A1A2 to B1B1". From the end face, the meshing process of the helical gear has ended, but in the tooth profile direction, the line of action continues to move, shortening from B1B1" to C1C2. Throughout the meshing process, the rotation angle of the gear axis changes from ω B2 to ω B1 -B / p, (considering |ω) B2 -ω B1 |>B / p). Where B is the tooth width and p is the lead parameter.

[0099] P = P z / (2·π)

[0100] P z =π·d / cotβ

[0101] In the formula P z denoted as lead, d as pitch circle diameter, and β as helix angle.

[0102] ω B1 =π / 2+α t -atan(N1B1 / r b1 )-N1B1 / r b1 +α B1

[0103] ω B2 =π / 2+α t -atan(N1B2 / r b1 )-N1B2 / r b1 +α B2

[0104] In the formula α t θ is the end face meshing angle. B2 θ B2 The development angles of points B2 and B1 are α and α, respectively. B1 α B2 The pressure angles are B2 and B1, respectively; the base circle radius of the drive wheel is rb1; ω B1 ω B2 This represents the rotational position of points B1 and B2.

[0105] To obtain the meshing stiffness corresponding to the line of action at different times, it is necessary to first calculate the meshing stiffness value corresponding to each meshing point on the line of action. Based on the above slicing method, the tooth profile surface is divided into r spur gears along the B2B2' direction, and the angle rotated through each equal part is:

[0106] Δλ=(B / p) / r

[0107] Divide the angle rotated from the starting and ending positions (B2 to B1) into 's' parts. This means dividing the helical gear tooth profile on the end face from the tooth root to the tooth tip into 's' parts, with each part rotating through an angle of 's'.

[0108] Δω=|ω B2 -ω B1 | / s

[0109] Let Δω = Δλ, then

[0110] Where, ω B2 ω represents the angle at which the end faces begin to mesh. B1 This indicates the angle at which the end face ends meshing, B represents the tooth width, and p represents the lead parameter.

[0111] The position of the meshing point on the end face of the helical gear also changes with the rotation angle. Here, the continuous rotation time is discretized into several time points, where t is the sequence number of the meshing position on the tooth profile during rotation. The solid line represents the driving gear, the dashed line represents the driven gear, N1 is the point where the base circle of the driving gear is tangent to the line of meshing, and P′ is the node. The pressure angle α at point t K The expression for (t) is:

[0112] α K (t)=arctan(N1B2+B2B1·t / s) / N1O1

[0113] In the formula, t = 0, 1, 2...s, B2 represents the starting point of meshing on the front end face of the meshing plane, B1 represents the ending point of meshing on the front end face of the meshing plane, N1 represents the point of tangency between the meshing plane and the base circle of the driving wheel, and O1 represents the center of the driving wheel.

[0114] Combining this with the above equation, the expression for the meshing stiffness of the spur gear slices is transformed into a function of the discrete quantity t, yielding the stiffness of each slice tooth at different positions on the divided tooth profile:

[0115]

[0116] It is approximated that the change in meshing stiffness from the tooth root to the tooth tip of each spur gear is the same. As shown in Figure (3b), the different colored areas represent the meshing stiffness values ​​at different positions on the tooth profile surface.

[0117] Step 4: Calculate the meshing stiffness K of the helical gear according to the variation law of the line of action. dc (i) The specific steps are as follows:

[0118] The helical gear meshing line can be discretized into different meshing points, each distributed in a different colored meshing region. By accumulating the stiffness of the meshing points and combining it with the variation law of the meshing line, the time-varying meshing stiffness of a single tooth within one cycle is expressed as follows:

[0119]

[0120] In the formula, i represents the meshing time corresponding to the i-th meshing line when a single tooth meshes. As shown in Figure (3b), there are a total of r+s-1 meshing lines (A1A2-C1C2). Each meshing line corresponds to a moment. These r+s-1 moments are divided into three segments: from point A1 to H, from point H to B1, and from B1” to C2. These correspond to the three cases in the formula: i≤r, r<i≤s, and s<i≤r+s, respectively. These correspond to the three cases in Figure (4). In the first figure, the stiffness increases as the meshing line length increases. In the second figure, the stiffness first increases and then decreases as the rotation angle changes when the meshing line length remains constant. In the third figure, the stiffness decreases as the meshing line length decreases.

[0121] The time-varying meshing stiffness of multiple teeth is calculated based on the time-varying meshing stiffness of a single tooth. During the meshing process of helical gears, there is alternating meshing of multiple teeth. This paper takes a helical gear pair with an overlap ratio of 4 to 5 as an example. It is formed by alternating meshing of four and five teeth. The length of the meshing line of multiple teeth is superimposed on the basis of the single tooth, as shown in Figure (5). Similarly, the meshing stiffness is also superimposed on this basis. Based on the formation diagram of the length of the meshing line of multiple teeth, it can be seen that the length of the meshing line at each corner is different, and the multi-tooth meshing stiffness diagram at each corner is formed by superimposing the stiffness of four or five teeth. Different line types represent different teeth. The intersection of the vertical dashed line and the point between them in the figure indicates that there are several contact lines on different teeth at different positions when the gears are meshing at a certain moment.

[0122] Multi-tooth meshing stiffness is based on α m As a periodic function, the formula for the multi-tooth meshing stiffness within one period is derived as follows:

[0123]

[0124] Where: K dc (i) represents the formula for calculating the meshing stiffness of the five-tooth and four-tooth gears at time i within a cycle, where α m The angle corresponding to the interval from when the front teeth begin to mesh to when the rear teeth begin to mesh;

[0125] α m =2π / z

[0126] α z =ωB2 -(ω B1 -B / p).

[0127] The time-varying meshing stiffness value of the large overlap helical gear obtained in this paper based on the slicing method is not only related to the length of the meshing line, but also considers the change of meshing stiffness when each meshing point on the meshing line is located at different positions on the tooth profile. Compared with the meshing stiffness calculated by the ISO-6336 method, it can more accurately reflect the meshing stiffness value of the gear during meshing, and it is in high agreement with the finite element simulation results. This is of great significance for the subsequent gear modification and vibration reduction research in this paper. The comparison results of the multi-tooth meshing stiffness of the main reduction helical gear obtained by the ISO-6336 method and the method in this paper are shown in Figure (6).

[0128] Step 5: Substitute the tooth profile modification parameters Ca and La to obtain the modification amount at the corresponding position on the tooth profile. The specific steps are as follows: This invention takes tooth tip modification in tooth profile modification as an example, and the modification curve is a parabolic modification curve; the tooth profile is modified within the allowance range of the tooth profile shape, where the shaded part is the part to be removed, as shown in Figure (7). Expression for tooth profile modification amount ε(t):

[0129]

[0130] Where Ca represents the shaping amount, La represents the shaping length, and r b The base circle radius, r g The radius of the tooth root circle, r d Indicates the radius of the tooth tip circle.

[0131] Step 6: Set the minimum deviation value of the total transmitted load, solve the tooth surface bearing contact equation based on the iterative method to obtain the transmission error of the helical gear, introduce the modification amount, and finally obtain the transmission error after modification. The specific steps are as follows:

[0132] During the loading process of a helical gear, contact deformation will occur at each meshing point on the meshing line. The product of the meshing stiffness at each point and the amount of deformation under load is the total load on the gear. The calculation formula is as follows (taking a five-tooth gear as an example):

[0133] The total load of the five teeth is:

[0134]

[0135] Where F(x) is

[0136]

[0137] The permissible deviation between the total load calculated for a given gear and the actual total load is used to iteratively determine the transmission error of the helical gear over one meshing cycle. The specific steps are as follows:

[0138] In the above formula, for the contact point t, if δ>ε(t) is satisfied, the point is in contact, u(t) takes a positive value, otherwise u(t) takes 0.

[0139] 1) Let k=1, and give the initial transmission error δ (1) ;

[0140] 2) Sequentially determine the magnitude of deformation δ (k) -ε(t) at each contact point i, if the value is less than 0, set it to 0;

[0141] 3) Obtain the total load F Z (k);

[0142] 4) Determine whether |F Z (k)-F|<F0 (F0 is an allowable small value) holds. If not, let δ (k+1) =δ (k) -(F Z (k)-F) / k s , k=k+1, return to step 2); if it holds, terminate the iteration, output δ=δ (k) ;

[0143] In the formula, k is the number of iterations, δ (k+1) is the transmission error of the (k+1)th step, δ (k) is the transmission error of the k-th step, F Z (k) is the meshing force calculated in the k-th step, k s is the average meshing stiffness of several tooth slices of the gear pair at a certain moment;

[0144] The transmission error generated by the helical gear during transmission is related to the initial backlash, the load deformation of the gear, the gear modification amount, the tooth surface error, etc. It is assumed that the tooth surface error is very small relative to the macro structure of the gear, the influence caused by assembly issues is not considered, and each normal direction does not change after contact.

[0145] δ=u(t)+ε(t)

[0146] In the formula, u(t) is the deformation amount, δ is the transmission error after modification, and ε(t) is the modification amount at each contact point. The initial clearance is ignored herein.

[0147] Combined with a set of gear parameters with a contact ratio between 4 and 5, a comparison diagram of the transmission error obtained by the calculation method of the present invention and the transmission error obtained by finite element simulation when there is no modification (that is, let ε(t)=0) is shown in Figure (8). After introducing the modification amount Ca=6um and La=9mm, the transmission error is shown in Figure (9), and its amplitude is significantly reduced.

[0148] Number of teeth 53 48 Modulus 2.25 Pressure angle (°) 14.5 Helix angle (°) 27 Tooth width (mm) 23.6 24 Tooth tip circle diameter (mm) 141.6 129.2 Tooth root circle diameter (mm) 129.43 117 Aperture (mm) 95 36.8 displacement coefficient 0.3144 0.1456 Material 20CrMoH Young's modulus (GPa) 207

[0149]

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating the transmission error of helical gears considering the amount of modification, characterized in that, Includes the following steps: Step 1: Based on the helical gear model, a single helical tooth is divided into multiple slice teeth along the tooth direction; Step 2: Calculate the meshing stiffness of the slicing teeth. ; Step 3: Discretize the helical gear end face into s meshing points, and calculate the meshing stiffness corresponding to each meshing point. Then repeat the previous step along the tooth direction to divide the meshing tooth surface into r×s meshing points to obtain the meshing stiffness of each point; Step 4: Calculate the meshing stiffness of the helical gear according to the variation law of the line of meshing. ; Step 5: Substitute the tooth profile modification parameters Ca and La to obtain the modification amount at the corresponding position on the tooth profile; The specific steps for calculating the modification amount at the corresponding position on the tooth profile in step 5 are as follows: Tooth profile modification amount expression: ； Where Ca represents the amount of shaping and La represents the length of shaping. Indicates the base circle radius. Indicates the radius of the tooth root circle. Indicates the radius of the tooth tip circle. Indicates meshing force and The included angle of the axis, This represents the half-angle corresponding to the base circle. This represents the half-angle corresponding to the root circle of the tooth; Step 6: Set the minimum deviation value of the total transmitted load, solve the tooth surface bearing contact equation based on the iterative method to obtain the transmission error of the helical gear, introduce the modification amount, and finally obtain the transmission error after modification.

2. The method for calculating the transmission error of helical gears considering the modification amount as described in claim 1, characterized in that, The meshing stiffness of the slicing teeth is calculated in step S2. The specific steps are as follows: Calculation of meshing stiffness of the slicing teeth based on the potential energy method: At this point, the bending-shear-radial compressive stiffness , , Hertzian contact stiffness Wheel stiffness They are represented as follows: In the formula, , ; Indicates the driving wheel. Indicates the driven wheel, For the meshing stiffness of a single gear, The load acting on a single gear, For gear bending stiffness, For shear stiffness, For radial compressive stiffness, For Hertzian contact stiffness, For gear body stiffness, The elastic modulus of the gear material. The radius of the base circle, The radius of the tooth root circle, Poisson's ratio, For effective tooth width, For the corresponding tangent points at different positions on the tooth profile and The included angle of the axis, For meshing force and The included angle of the axis, The half angle corresponding to the base circle. The half-angle corresponding to the root circle of the tooth. , For the tooth root circle corresponding to The included angle of the axis; Let be the distance between a point on the root circle of the gear tooth on the line of symmetry and the intersection of the line of action of the meshing force and the line of symmetry of the gear tooth. This represents the arc length corresponding to a single tooth on the root circle. , , , All represent coefficients. Represents coefficients , , , , This is the ratio of the root circle radius of the gear to the bore radius of the gear. It is half of the central angle corresponding to the arc occupied by a single tooth; Establish and The relationship transforms the meshing stiffness function into the corresponding pressure angle at the meshing point. A function of variables In the formula, Regarding the pressure angle meshing stiffness; definition and The relationship is as follows: ； in, Indicates the end face engagement angle. Indicates the number of teeth.

3. The method for calculating the transmission error of helical gears considering the modification amount as described in claim 2, characterized in that, The specific steps for calculating the meshing stiffness at each point in step 3 are as follows: Based on the slicing method, the tooth profile surface is divided into r spur gears, and the angle through which each equal part rotates is: The angles rotated through the starting and ending positions are divided into... The helical gear tooth profile is divided into sections on the end face from the tooth root to the tooth tip. Each portion is rotated at an angle of , make ,but in, This indicates the angle at which the end faces begin to mesh. This indicates the angle at which the end faces end of engagement. Indicates tooth width. Indicates the lead parameter; Here, the continuous rotation time is discretized into several time points. These are the meshing position numbers on the tooth profile during rotation. The point where the base circle of the driving wheel is tangent to the line of meshing. For the node; the pressure angle at point t. The expression is: In the formula , Indicates the starting point of engagement of the front face on the meshing plane. This indicates the point where the front face of the meshing plane terminates in meshing. This indicates the point of tangency between the meshing plane and the base circle of the driving wheel. Represents the center of the active wheel; Combining with the above equation, the expression for the meshing stiffness of the spur gear slice is transformed into a discrete quantity. The function is used to obtain the stiffness of each slice tooth at different positions on the divided tooth profile: 。 4. The method for calculating the transmission error of helical gears considering the modification amount as described in claim 3, characterized in that, Step 4 involves calculating the meshing stiffness. The specific steps are as follows: The helical gear meshing line is discretized into different meshing points, each distributed in a different colored meshing region. The stiffness of the meshing points is accumulated, and combined with the variation law of the meshing line, the time-varying meshing stiffness of a single tooth in one cycle is expressed as follows: In the formula Indicates the first tooth in single-tooth meshing The engagement moment corresponding to each engagement line; The formula for the multi-tooth meshing stiffness over one cycle is as follows: In the formula: This is a formula for calculating the meshing stiffness of the five-tooth and four-tooth gears at time i within a cycle, where... The angle corresponding to the interval from when the front teeth begin to mesh to when the rear teeth begin to mesh; 。 5. The method for calculating the transmission error of helical gears considering the modification amount as described in claim 4, characterized in that, The specific steps of step 6 are as follows: The total load of the five teeth is: ,in for: The permissible deviation between the total load calculated for a given gear and the actual total load is used to iteratively determine the transmission error of the helical gear over one meshing cycle. The specific steps are as follows: In the above formula, for contact point t, if the following conditions are met... At that time, the point of contact, Take a positive value, otherwise Set to 0; 1) Order Given an initial value for the propagation error ; 2) Determine each contact point sequentially. Deformation If the value of is less than 0, set it to 0. 3) Calculate the total load ; 4) Judgment Is it true? If not, let , Return to step 2); If true, the iteration stops, and the output is... ; In the formula, k is the number of iterations. To propagate the error at step k+1, For the propagation error in the k-th step, To calculate the meshing force in step k, k s The average meshing stiffness of several gear teeth at a certain moment in a gear pair; In the formula, This is the amount of deformation. This refers to the transmission error after reshaping. This refers to the shaping amount at each contact point.

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