A gear transmission error optimization method and system

Abstract

The present invention provides a method for optimizing the gear transmission error, which includes determining the meshing gear sets in the gear transmission system and the driving gear, driven gear and bearing of each group; setting characteristic parameters and their value ranges, where the characteristic parameters include gear micro-modification parameters, macro parameters and system parameters; determining a certain number of samples formed by each group of meshing gears according to the value ranges of the characteristic parameters; randomly sampling the samples of each group of meshing gears, constructing a corresponding sample matrix and importing it into the gear transmission error calculation model, calculating the first-order sensitivity index and total effect index of all characteristic parameters in each group of meshing gears, so as to further obtain the characteristic parameters to be optimized in each group of meshing gears; and optimizing and reducing the gear transmission error based on the characteristic parameters to be optimized. Implementing the present invention, the gear transmission error is optimized by comprehensively considering the gear micro-modification parameters, macro parameters and system parameters and their correlations, reducing the dimension of the optimization process. Since these parameters are closely related to gear manufacturing, the processing cost can be correspondingly reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and particularly to a method and system for optimizing gear transmission error. Background Art

[0002] Gear transmission error (TE) refers to the corresponding displacement difference between the actual meshing position and the theoretical meshing position on the gear meshing line, which leads to interference and collision between meshing gears and causes periodic vibration of the gear transmission system. As a comprehensive manifestation of factors such as error excitation, load excitation, and time-varying meshing stiffness excitation, it is generally considered that gear transmission error is the main excitation source causing vibration and noise of the gear transmission system.

[0003] In order to improve the gear transmission error in the gear transmission system, generally, the optimization design of gear micro-modification parameters and macro-parameters is carried out. However, the influence of system parameters on the vibration and noise of the transmission system is rarely considered. In addition, in the optimization of relevant parameters, due to the large number of parameters, the optimization of the characteristic parameters of the gear transmission system is not clear enough, and the correlation between the characteristic parameters and the transmission error is not analyzed, resulting in a high dimension in the optimization process of the characteristic parameters and low optimization efficiency.

[0004] Therefore, it is necessary to propose a new method for optimizing gear transmission error, which can effectively identify the gear micro-modification parameters, macro-parameters, and system parameters with greater influence on gear transmission error or obvious interaction as characteristic parameters, and optimize the gear transmission error with these characteristic parameters as the goal, thereby improving the design and development efficiency. Since these parameters are closely related to gear manufacturing, the processing cost can be reduced accordingly. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a method and system for optimizing gear transmission error, which optimizes gear transmission error by comprehensively considering the correlation of gear micro-modification parameters, macro-parameters, and system parameters, not only reducing the dimension of the optimization process but also improving the optimization efficiency.

[0006] To solve the above technical problem, the embodiments of the present invention provide a method for optimizing gear transmission error, and the method includes the following steps:

[0007] S1. Determine the meshing gear sets in the gear transmission system, as well as the driving wheel, driven wheel, and bearing in each set of meshing gears;

[0008] S2. Set the characteristic parameters and their value ranges. The characteristic parameters include gear micro-modification parameters, macro parameters, and system parameters. Among them, the gear micro-modification parameters include tooth profile crowning modification, tooth profile slope modification, tooth lead crowning modification, tooth lead slope modification, diagonal tooth lead bottom modification, and diagonal tooth lead top modification. The macro parameters include effective tooth width, helix angle, and modification coefficient. The system parameters include the position of the driven gear and the positions of the corresponding bearings of the driven gear.

[0009] S3. According to the value ranges of the characteristic parameters, determine a certain number of samples formed by each group of meshing gears. Among them, each sample is a set composed of all the characteristic parameter values.

[0010] S4. Randomly sample the samples of each group of meshing gears, construct the sample matrix of each group of meshing gears, and import the sample matrix of each group of meshing gears into a preset gear transmission error calculation model to calculate the first-order sensitivity index and total effect index of all the characteristic parameters in each group of meshing gears. Further, based on the first-order sensitivity index and total effect index of all the characteristic parameters in each group of meshing gears, determine the characteristic parameters to be optimized in each group of meshing gears.

[0011] S5. Optimize respectively according to the characteristic parameters to be optimized in each group of meshing gears to reduce the gear transmission error.

[0012] Among them, in the step S2, the value ranges of the tooth profile crowning modification, the tooth profile slope modification, the tooth lead crowning modification, the tooth lead slope modification, the diagonal tooth lead bottom modification, and the diagonal tooth lead top modification are all [-5, 5] μm.

[0013] Among them, in the step S2, the value range of the modification coefficient x is determined by multiple constraint conditions. Among them, the constraint conditions include the first constraint condition to the eighth constraint condition.

[0014] Among them, the first constraint condition is represented by formula (1), which is the condition to avoid undercutting during gear machining.

[0015]

[0016] The second constraint condition is represented by formulas (2)-(5), which are the conditions to obtain smooth and continuous transmission of gear meshing.

[0017]

[0018]

[0019]

[0020]

[0021] The third constraint condition is expressed by formulas (6)-(7), which is the condition to ensure the tooth tip strength of the gear;

[0022]

[0023]

[0024] The fourth constraint condition is expressed by formulas (8)-(11), which is the condition to avoid tooth surface wear and premature failure of the gear;

[0025] η ≤ 2.5 (8);

[0026]

[0027]

[0028]

[0029] The fifth constraint condition is expressed by formulas (12)-(15), which is the condition to resist the impact caused by the change of the center distance of the gear and store lubricating oil during the meshing process;

[0030] c ≥ 0.1m n (12);

[0031] c = r a1 + r f2 - a (13);

[0032]

[0033]

[0034] The sixth constraint condition is expressed by formula (16), which is the condition that there is no interference between the root of the small gear and the tip of the large gear;

[0035]

[0036] The seventh constraint condition is expressed by formula (17), which is the condition that there is no interference between the root of the large gear and the tip of the small gear;

[0037]

[0038] The eighth constraint condition is expressed by formula (18), which is the condition to achieve high-precision meshing;

[0039]

[0040] Among them, is the minimum number of teeth without undercut; is the addendum coefficient; z is the number of teeth; β is the helix angle; α t is the transverse pressure angle; ε α is the transverse contact ratio, z1 and z2 are the number of teeth of the driving gear and the driven gear respectively; α at1 , α at2 are the transverse pressure angles of the addendum circles of the driving gear and the driven gear respectively; α wt is the working pressure angle; m n is the normal module; x is the modification coefficient; d a is the addendum circle diameter; d b is the base circle diameter, and the subscript t takes values of 1 or 2 representing the driving gear and the driven gear respectively; s a is the tooth thickness of the addendum circle; r a is the addendum circle radius; α n , α t are the normal pressure angle and the transverse pressure angle respectively; r is the pitch circle radius; inv is the involute function; η is the sliding ratio at the meshing point between the driving gear and the driven gear of the gear set; c is the backlash; r f is the root circle radius; a is the actual center distance; x1 and x2 are the modification coefficients of the driving gear and the driven gear respectively.

[0041] Among them, in the step S2, the value range of the helix angle β is determined by the axial contact ratio, the pressure angle, the normal backlash of the gear, and the gear strength of the involute helical gear.

[0042] Among them, the axial contact ratio ε β of the involute helical gear is calculated by formula (19);

[0043]

[0044] The pressure angle α t is determined by formula (20);

[0045]

[0046] The normal backlash j bn of the gear is calculated by formulas (21)-(23);

[0047] j bt = e bt2 - s bt1 + 2(r bt1 + r bt2 ) * invα wt (21);

[0048] j bt = e bt1 - sbt2 +2(r bt1 +r bt2 )*invα wt (22);

[0049] j bn =j bt *cosβ b (23);

[0050] The gear strength includes the tooth root bending strength and the tooth surface contact fatigue strength, and is constrained by formulas (24)-(25);

[0051] σ H ≤σ HP (24);

[0052] σ F ≤σ FP (25);

[0053] where r bt is the base circle radius of the gear; e bt is the base circle tooth space width of the gear; s bt is the base circle tooth thickness of the gear; p bt is the normal base pitch of the gear end face; formula (21) is the normal side clearance of the gear end face tooth profile when the teeth of the driving gear are in the tooth spaces of the driven gear; formula (22) is the normal side clearance of the gear end face tooth profile when the teeth of the driven gear are in the tooth spaces of the driving gear; σ H , σ F are the calculated contact stress and the calculated tooth root stress respectively; σ HP , σ FP are the allowable contact stress and the allowable tooth root stress respectively.

[0054] wherein, in the step S2, the value range of the effective tooth width is ±10% of the effective tooth widths of the two meshing gears; the value range of the positions of the bearings is the positions that do not interfere with other parts.

[0055] wherein, the step S4 specifically includes:

[0056] Based on the Monte Carlo sampling method, in the samples of each group of meshing gears, the Sobol sequence sampling method is used for random sampling to construct a sample matrix of each group of meshing gears; wherein, the sample matrix is composed of n columns of sample parameter groups with different values, and each column of sample parameter groups is composed of s sampling samples; n is the number of characteristic parameters, which is a positive integer; s is the number of sampling times, which is a positive integer greater than 1;

[0057] The sample parameter groups of each column in the sample matrix of each group of meshing gears are sequentially imported into the gear transmission error calculation model for calculation, and the peak-to-peak values of the transmission errors of the meshing gears corresponding to the sample parameter groups of each column in the sample matrix of each group of meshing gears are obtained;

[0058] According to the peak-to-peak values of the transmission errors of the meshing gears corresponding to all the sample parameter groups of each column in the sample matrix of each group of meshing gears, the variances and partial variances of each characteristic parameter in the sample matrix of each group of meshing gears with respect to the peak-to-peak value of the transmission error are calculated, and based on the variances and partial variances of each characteristic parameter in the sample matrix of each group of meshing gears with respect to the peak-to-peak value of the transmission error, the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears are obtained;

[0059] Based on the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears, sorting is performed to determine the characteristic parameters to be optimized in each group of meshing gears.

[0060] An embodiment of the present invention also provides a gear transmission error optimization system, including;

[0061] A gear transmission structure recognition unit for determining the meshing gear groups in the gear transmission system, as well as the driving wheel, driven wheel and bearing in each group of meshing gears;

[0062] A characteristic parameter setting unit for setting the characteristic parameters and their value ranges, where the characteristic parameters include gear micro-modification parameters, macro parameters and system parameters; among them, the gear micro-modification parameters include profile crowning modification, profile slope modification, helix crowning modification, helix slope modification, diagonal helix bottom modification and diagonal helix top modification; the macro parameters include effective tooth width, helix angle and addendum modification coefficient; the system parameters include the position of the driven wheel and the positions of the respective bearings corresponding to the driven wheel;

[0063] A gear characteristic sample forming unit for determining a certain number of samples formed by each group of meshing gears according to the value ranges of the characteristic parameters; where each sample is a set composed of all the characteristic parameter values;

[0064] A characteristic parameter screening unit for randomly sampling the samples of each group of meshing gears, constructing the sample matrix of each group of meshing gears, and importing the sample matrix of each group of meshing gears into a preset gear transmission error calculation model to calculate the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears, and further determining the characteristic parameters to be optimized in each group of meshing gears based on the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears;

[0065] A characteristic parameter optimization unit for respectively optimizing according to the characteristic parameters to be optimized in each group of meshing gears to reduce the gear transmission error.

[0066] Implementing the embodiments of the present invention has the following beneficial effects:

[0067] Based on the value ranges of the gear micro-modification parameters, macro parameters, and system parameters in the characteristic parameters, the present invention forms samples. After random sampling, the first-order sensitivity index and total effect index of each characteristic parameter are calculated to determine the characteristic parameters to be optimized for optimization, so as to reduce the gear transmission error. Therefore, the correlation of the gear micro-modification parameters, macro parameters, and system parameters is comprehensively considered for gear transmission error optimization, which not only reduces the dimension of the optimization process but also improves the optimization efficiency. Since these parameters are closely related to gear manufacturing, the processing cost can be correspondingly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, obtaining other drawings based on these drawings still belongs to the scope of the present invention.

[0069] Figure 1 It is a flowchart of a method for optimizing gear transmission error provided by an embodiment of the present invention;

[0070] Figure 2 It is a convergence trend diagram of the sensitivity index of characteristic parameters in the application scenario of a method for optimizing gear transmission error provided by an embodiment of the present invention;

[0071] Figure 3 It is a comparison diagram of the effects of the first-order sensitivity index and total effect index of 14 characteristic parameters of the transmission system under the input torques of 10 Nm, 20 Nm, and 30 Nm for gear set 1 in the application scenario of a method for optimizing gear transmission error provided by an embodiment of the present invention;

[0072] Figure 4 It is a comparison diagram of the effects of the first-order sensitivity index and total effect index of 14 characteristic parameters of the transmission system under the input torques of 10 Nm, 20 Nm, and 30 Nm for gear set 2 in the application scenario of a method for optimizing gear transmission error provided by an embodiment of the present invention;

[0073] Figure 5 It is a comparison diagram of the effects of the first-order sensitivity index and total effect index of 14 characteristic parameters of the transmission system under the input torques of 10 Nm, 20 Nm, and 30 Nm for gear set 3 in the application scenario of a method for optimizing gear transmission error provided by an embodiment of the present invention;

[0074] Figure 6Schematic diagram of a gear transmission error optimization system provided by an embodiment of the present invention. Specific embodiments

[0075] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0076] As Figure 1 shown, in an embodiment of the present invention, a gear transmission error optimization method is proposed, and the method includes the following steps:

[0077] Step S1: Determine the meshing gear sets in the gear transmission system, as well as the driving wheels, driven wheels and bearings in each set of meshing gears;

[0078] Step S2: Set the characteristic parameters and their value ranges. The characteristic parameters include gear micro-modification parameters, macro parameters and system parameters. Among them, the gear micro-modification parameters include profile crowning modification, profile taper modification, helix crowning modification, helix taper modification, diagonal helix bottom modification and diagonal helix top modification; the macro parameters include effective tooth width, helix angle and modification coefficient; the system parameters include the position of the driven wheel and the positions of the respective bearings corresponding to the driven wheel;

[0079] Step S3: According to the value ranges of the respective characteristic parameters, determine a certain number of samples formed by each set of meshing gears. Among them, each sample is a set composed of all the characteristic parameter values;

[0080] Step S4: Randomly sample the samples of each set of meshing gears, construct a sample matrix for each set of meshing gears, and import the sample matrix of each set of meshing gears into a preset gear transmission error calculation model to calculate the first-order sensitivity index and total effect index of all the characteristic parameters in each set of meshing gears, and further determine the characteristic parameters to be optimized in each set of meshing gears based on the first-order sensitivity index and total effect index of all the characteristic parameters in each set of meshing gears;

[0081] Step S5: Optimize respectively according to the characteristic parameters to be optimized in each set of meshing gears to reduce the gear transmission error.

[0082] Specifically, in step S1, the specific process is to analyze the meshing gear sets in the gear transmission system, as well as the driving wheels, driven wheels and bearings in each set of meshing gears, including specifically the number of meshing gear sets, the positions of the driving wheels, the positions of the driven wheels, the number of bearings corresponding to the driven wheels and the positions of each bearing.

[0083] In step S2, the specific process is, first, to set the characteristic parameters, and this characteristic parameter needs to comprehensively consider gear micro-modification parameters, macro parameters and system parameters, etc.

[0084] (a) The selection of gear micro-modification parameters includes profile crowning modification, profile slope modification, helix crowning modification, helix slope modification, diagonal helix bottom modification, and diagonal helix top modification, etc.

[0085] (b) If the goal is to reduce the transmission error of the driven gear, when optimizing the design of the gear macro parameters, the following design requirements need to be met:

[0086] (b1) The transmission ratio of the driven gear is obtained through calculation of matching with the motor power, and it is a set of design parameters to ensure the vehicle runs in the best state. That is, the number of teeth of the driven gear is not used as an optimization parameter, but the gear module and pressure angle are both selected as standard values;

[0087] (b2) Changing the gear parameters will surely affect the overall strength of the driven gear. Therefore, when optimizing the gear macro parameters, it is necessary to ensure that the strength of the optimized gear meets the design requirements;

[0088] (b3) The transmission efficiency of the meshing gears in the optimized transmission system needs to meet certain requirements;

[0089] (b4) Regarding the modification coefficient, when the center distance is fixed, if the gear parameters do not change, the sum of the modification coefficients can be determined, and only the distribution of the modification coefficients between the driving gear and the driven gear needs to be optimized. The value of the modification coefficient is very crucial. If it is selected improperly, undercutting will occur, reducing the gear strength and causing premature failure of the gear, etc.

[0090] Therefore, the macro parameters selected are the effective tooth width b, helix angle β, and modification coefficient x, etc.

[0091] (c) The system parameters selected are the position of the driven gear and the positions of the corresponding bearings of the driven gear, etc. It should be noted that the bearings, as important components in the transmission system, are generally used in pairs and are located at both ends of the shaft respectively, playing a certain role in support and positioning.

[0092] Secondly, set the value ranges of each characteristic parameter as follows:

[0093] (I) The gear micro-modification parameters can be designed according to actual needs. In one embodiment, the value ranges of profile crowning modification, profile slope modification, helix crowning modification, helix slope modification, diagonal helix bottom modification, and diagonal helix top modification are all [-5, 5] μm.

[0094] (II.1) The value range of the modification coefficient is determined by multiple constraint conditions; among them, the constraint conditions include the first constraint condition to the eighth constraint condition.

[0095] (II.11) The first constraint condition is expressed by formula (1), which is the condition to avoid undercutting during gear machining;

[0096]

[0097] Among them, is the minimum number of teeth without undercutting; is the addendum coefficient; z is the number of teeth; β is the helix angle.

[0098] (II.12) The second constraint condition is expressed by formulas (2)-(5), which is the condition to obtain smooth and continuous transmission of gear meshing, adopting the PD 6457:1970 standard;

[0099]

[0100]

[0101]

[0102]

[0103] Among them, α t is the transverse pressure angle; ε α is the transverse contact ratio, z1 and z2 are the numbers of teeth of the driving gear and the driven gear respectively; α at1 , α at2 are the transverse pressure angles of the addendum circles of the driving gear and the driven gear respectively; α wt is the working pressure angle; m n is the normal module; x is the modification coefficient; d a is the addendum circle diameter; d b is the base circle diameter, and the subscript t takes values of 1 or 2 representing the driving gear and the driven gear respectively.

[0104] (II.13) The third constraint condition is expressed by formulas (6)-(7), which is the condition to ensure the tooth tip strength of the gear, ensuring that the tooth thickness of the addendum circle cannot be too thin;

[0105]

[0106]

[0107] Among them, s a is the tooth thickness of the addendum circle; r a is the addendum circle radius; α n , α t are the normal pressure angle and the transverse pressure angle respectively; r is the pitch circle radius; inv is the involute function.

[0108] (II.14) The fourth constraint condition is expressed by formulas (8)-(11), which are conditions to avoid tooth surface wear and premature gear failure, and it is necessary to ensure that the gear sliding ratio is less than or equal to 2.5;

[0109] η ≤ 2.5 (8);

[0110]

[0111]

[0112]

[0113] Among them, η is the sliding ratio between the driving gear and the driven gear of the gear set at the meshing point.

[0114] (II.15) The fifth constraint condition is expressed by formulas (12)-(15), which are conditions to resist the impact caused by the change of the gear center distance and to store lubricating oil during the meshing process. The backlash needs to satisfy c ≥ 0.1m n ;

[0115] c ≥ 0.1m n (12);

[0116] c = r a1 +r f2 -a (13);

[0117]

[0118]

[0119] Among them, c is the backlash; r f is the root circle radius; a is the actual center distance.

[0120] (II.16) The sixth constraint condition is expressed by formula (16), which is the condition to prevent interference between the root of the small gear and the tip of the large gear, and to prevent interference of the transition curve when the two meshing gears are working;

[0121]

[0122] (II.17) The seventh constraint condition is expressed by formula (17), which is the condition to prevent interference between the root of the large gear and the tip of the small gear, and to prevent interference of the transition curve when the two meshing gears are working;

[0123]

[0124] (II.18) The eighth constraint condition is expressed by formula (18), which is the condition to achieve high-precision meshing;

[0125]

[0126] Among them, x1 and x2 are the modification coefficients of the driving gear and the driven gear respectively.

[0127] Through the above constraints (II.11)-(II.18), when the addendum circle diameter remains unchanged, the value ranges of the modification coefficients of different gears under different constraints can be calculated.

[0128] (II.2) The helix angle β has a certain influence on the contact ratio and the total length of the meshing line of the helical gear, and its change also determines whether the driven gear can mesh normally. At this time, its value range is determined by the axial contact ratio, the pressure angle, the normal backlash of the gear, and the gear strength of the involute helical gear.

[0129] (II.21) The axial contact ratio ε of the involute helical gear β is calculated by formula (19);

[0130]

[0131] (II.22) The base circle of the gear remains unchanged, and the pressure angle α t changes with the change of the helix angle β. At this time, the pressure angle α t is determined by formula (20);

[0132]

[0133] (II.23) The normal backlash j of the gear bn plays an important role in lubricating the meshing gears. It can reduce the heat generated during gear meshing and also avoid phenomena such as jamming during gear meshing. At this time, the normal backlash j of the gear bn is calculated by formulas (21)-(23);

[0134] j bt = e bt2 - s bt1 + 2(r bt1 + r bt2 ) * invα wt (21);

[0135] j bt = e bt1 - s bt2 + 2(r bt1 + r bt2 ) * invα wt (22);

[0136] j bn = j bt * cosβ b (23);

[0137] Among them, r bt is the base circle radius of the gear; e bt is the base circle tooth space width of the gear; s bt is the base circle tooth thickness of the gear; p bt is the normal base pitch of the gear face; Formula (21) is the normal side clearance of the gear face profile when the teeth of the driving gear are in the tooth spaces of the driven gear; Formula (22) is the normal side clearance of the gear face profile when the teeth of the driven gear are in the tooth spaces of the driving gear.

[0138] (II.24) The gear strength includes the tooth root bending strength and the tooth surface contact fatigue strength, and is constrained by Formulas (24)-(25);

[0139] σ H ≤σ HP (24);

[0140] σ F ≤σ FP (25);

[0141] Among them, σ H , σ F are the calculated contact stress and the calculated tooth root stress respectively; σ HP , σ FP are the allowable contact stress and the allowable tooth root stress for use respectively.

[0142] (II.3) The effective tooth width b of the driven gear is related to the load-bearing capacity of the gear meshing. If the effective tooth width b is too narrow, it will cause insufficient gear strength, resulting in unreasonable design and premature failure of the gear. The wider the effective tooth width b, the greater the load-bearing capacity, but the unevenness of the load distribution in the tooth direction will also increase, which will increase the fluctuation of the transmission error. Considering the limited variation space of the effective tooth width b and avoiding interference with other adjacent parts, when defining the value range of the effective tooth width b of the meshing gears, take ±10% of the effective tooth widths of the two meshing gears as the variation space for sensitivity analysis, that is, the value range of the effective tooth width b is ±10% of the effective tooth widths of the two meshing gears.

[0143] (III) Among the system parameters, the value range of the position of each bearing is the position that does not interfere with other parts.

[0144] In step S4, first, according to the characteristic parameters and their value ranges in step S3, based on the Monte Carlo sampling method, in the samples of each group of meshing gears, the Sobol sequence sampling method is used for random sampling to construct a sample matrix of each group of meshing gears; among them, the sample matrix is composed of n columns of sample parameter groups with different numerical values, and each column of sample parameter groups is composed of s sampling samples; n is the number of characteristic parameters, which is a positive integer; s is the number of sampling times, which is a positive integer greater than 1;

[0145] For example, the number of characteristic parameters is n, and all characteristic parameters are randomly sampled independently twice within the value range. The number of sampling times is s, and a total of two n×s matrices are constructed, namely matrix A and matrix B. Each row of the matrix represents a combination of n characteristic parameters.

[0146]

[0147]

[0148] Replace the i-th column of matrix A in formula (1-1) with the i-th column of matrix B in formula (1-2), and keep the rest unchanged, then the new formula (1-3) matrix C can be obtained. i Perform the transformation in the same way and keep the rest unchanged to obtain the new formula (1-4) matrix C. i′ The expression is as follows:

[0149]

[0150]

[0151] Secondly, import each column of sample parameter groups in the sample matrix of each group of meshing gears into a pre-set gear transmission error calculation model for calculation, and obtain the peak-to-peak values of the transmission errors corresponding to each column of sample parameter groups in the sample matrix of each group of meshing gears.

[0152] For example, the gear transmission error calculation model adopts a single-column matrix weight calculation model. Import matrix C i′ in into the single-column matrix weight calculation model to obtain the peak-to-peak values of the transmission errors corresponding to each column of sample parameter groups.

[0153] Then, according to the peak-to-peak values of the transmission errors corresponding to all columns of sample parameter groups in the sample matrix of each group of meshing gears, calculate the variance and various partial variances of each characteristic parameter in the sample matrix of each group of meshing gears with respect to the peak-to-peak value of the transmission error, and based on the variance and various partial variances of each characteristic parameter in the sample matrix of each group of meshing gears with respect to the peak-to-peak value of the transmission error, obtain the first-order sensitivity index and the total effect index of all characteristic parameters in each group of meshing gears. Among them, the first-order sensitivity index (main effect sensitivity index) is used to evaluate the degree of influence of a single characteristic parameter on the transmission error; the total effect index (full effect sensitivity index) represents the degree of influence of a certain input characteristic parameter and the interaction between this parameter and other characteristic parameters on the transmission error.

[0154] Finally, based on the first-order sensitivity indices and total effect indices of all characteristic parameters in each group of meshing gears, sorting is performed to determine the characteristic parameters to be optimized in each group of meshing gears. For example, the characteristic parameter with the largest difference between the first-order sensitivity index and the total effect index can be selected as the characteristic parameter to be optimized.

[0155] In step S5, according to the characteristic parameters to be optimized in each group of meshing gears, optimization is carried out respectively to reduce the gear transmission error.

[0156] For example, the differences between the first-order sensitivity indices and the total effect indices of the tooth profile crowning modification and the effective tooth width are relatively large, indicating that these two characteristic parameters have a strong interaction effect. When formulating an optimization combination scheme for characteristic parameters, different input working conditions need to be considered, and at the same time, a method combining gear microparameters and macroparameters needs to be considered to carry out effective optimization of characteristic parameters to achieve a more ideal effect.

[0157] As Figures 2 to 5 shown, the application scenario of a gear transmission error optimization method in an embodiment of the present invention is further described as follows:

[0158] (1) Parameter selection

[0159] Considering reasons such as the convenience of implementing the modification method and the economy of later processing and manufacturing, all tooth surface micro-modifications are applied to the driving gear. First, calculate the maximum modification amounts of different modification methods for the three groups of gears, and at the same time, in combination with the direction of the tooth surface micro-modification, select the value range of the micro-modification parameters to be [-5, 5] μm, and the other macroparameters and system parameters are selected as shown in Table 1 below.

[0160]

[0161]

[0162] (2) Calculate sensitivity

[0163] Based on Matlab, a calculation program is written, the dimension, value range, sampling method, etc. of the characteristic parameters are set, and then RomaxDesigner is called for data exchange and simulation. Matlab automatically reads the input file and output file of RomaxDesigner to calculate the first-order sensitivity index and total effect index of each characteristic parameter.

[0164] (21) Selection of the optimal number of samples for sensitivity analysis

[0165] To analyze the accuracy of the calculated sensitivity index and ensure the reliability of the calculation results, this paper verified the rationality of selecting the sample size m for the sensitivity analysis of characteristic parameters. With the same sample size, 3 independent samplings were carried out, and the calculations were performed separately. The changes in the differences between the average value of the sensitivity index of the characteristic parameters and the standard upper deviation and standard lower deviation were observed. The smaller the difference, the more uniform the sampling, and the sample size conforms to the sampling quantity. For the sample size m, 15, 30, 45... 145 were used to calculate the first-order sensitivity index and the total effect index. The total data sample n = (D + 2)m, where D is the number of characteristic parameters. According to the total sample size, the corresponding number of calculations was 210, 420, 630... 2030 times. The convergence trend of the sensitivity index is as Figure 2 shown.

[0166] Figure 2 In Figure 2 , among the 14 sensitivity characteristic parameters of a set of meshing gears, the sensitivity indexes of 3 randomly selected characteristic parameters were analyzed and compared. Among them, 1 - 6 represent the microscopic modification parameters of the transmission system (tooth profile crowning modification, tooth profile slope modification, tooth direction crowning modification, tooth direction slope modification, diagonal tooth direction bottom modification, diagonal tooth direction top modification), 7 - 9 represent the macroscopic parameters (effective tooth width, helix angle, addendum modification coefficient), and 10 - 14 represent the system parameters (the position of the driven gear and the positions of 4 bearings corresponding to each set of driven gears), that is, there are 4 bearings in this set of meshing gears.

[0167] From Figure 2 it can be seen that because the sampling data is random each time, the sensitivity indexes calculated for each characteristic parameter with the same sample size also vary. When the sample size m = 115 - 145, the difference between the actual value and the average value of the sensitivity index fluctuates within 0.05 (0.05 is the sensitivity threshold), and the upper and lower values of the variance fluctuate within 0.02. The sensitivity indexes of each characteristic parameter tend to converge. Thus, it can be seen that when the sample size m = 150 is selected in this paper, the calculated sensitivity index is stable and reliable.

[0168] (22) Develop an optimization plan according to the sensitivity analysis results

[0169] For three different gear sets, sensitivity analysis was carried out, and corresponding plans were developed according to the results.

[0170] (221) Gear set 1

[0171] For each characteristic parameter of the transmission system and its corresponding value range, calculate the sensitivity of each characteristic parameter to the transmission error. Considering the variable working conditions of the driven wheel of the transmission system, with different torques as boundary conditions, when each characteristic parameter is at an input torque of 10 Nm, 20 Nm, 30 Nm, and a rotational speed of 10,000 r / min, calculate the first-order sensitivity index and total effect index of the target value transmission error, as Figure 3 shown. Figure 3 In, the sensitivity index obtained by calculating the characteristic parameter is represented by a bar chart, which can conveniently and intuitively show the influence of the interaction between each characteristic parameter on the transmission error.

[0172] The magnitude of the sensitivity index can be expressed as: the degree of change in the transmission error caused by the change of the characteristic parameter of the transmission system. From the sensitivity index analysis of gear set 1 at different torques by Figure 3 it can be obtained that with the change of torque, the sensitivity index of each characteristic parameter keeps changing, but shows a certain upward or downward trend. This indicates that the change of torque affects the degree of influence of the characteristic parameter on the transmission error.

[0173] From Figure 3 it can be known that for the gear micro-modification parameters: profile crowning modification (parameter 1), profile slope modification (parameter 2), helix crowning modification (parameter 3), diagonal helix tip modification (parameter 6), the contribution rate of the sensitivity index to the transmission error is relatively obvious. The difference between the first-order sensitivity index and the total effect index of the diagonal helix root modification (parameter 5) is relatively obvious; for the gear macro-parameters: effective tooth width (parameter 7), the sensitivity index to the transmission error is relatively large, that is, it has a strong influence on the transmission error. For the system parameters: the position of the meshing gear pair (parameter 11) and the positions of the 4 bearings corresponding to each meshing gear pair (parameters 11, 12, 13, 14), the influence on the transmission error is relatively weak. At different torques, the difference between the first-order sensitivity index and the total effect index of each characteristic parameter is not large, indicating that the interaction between the characteristic parameters is relatively small. When optimizing the parameters, the optimization can be carried out in sequence according to the magnitude of the influence index of the characteristic parameter.

[0174] (222) Gear set 2

[0175] When each characteristic parameter is at an input torque of 10 Nm, 20 Nm, 30 Nm, and a rotational speed of 10,000 r / min, calculate the first-order sensitivity index and total effect index of the target value transmission error, as Figure 4 shown. Figure 4 In, the sensitivity index obtained by calculating the characteristic parameter is represented by a bar chart, which can conveniently and intuitively show the influence of the interaction between each characteristic parameter on the transmission error.

[0176] The magnitude of the sensitivity index can be expressed as: the degree of change in the transmission error caused by the change in the characteristic parameters of the transmission system. The sensitivity index analysis of the gear set 2 under different torques is as follows Figure 4 It can be obtained that with the change of torque, the sensitivity indices of each characteristic parameter are constantly changing, but show a certain upward or downward trend. This indicates that the change of torque affects the influence degree of the characteristic parameters on the transmission error.

[0177] From Figure 4 it can be known that for the micro-modification parameters: the total effect index of the profile slope modification (parameter 2) and the diagonal tooth direction bottom modification (parameter 5) is relatively high, and the difference between the first-order sensitivity index and the total effect index is relatively large, indicating that there is a strong interaction between the characteristic parameters, which means that a comprehensive scheme considering various combinations of micro-modification parameters needs to be considered when formulating an optimization scheme for the transmission error. For the macro parameters: the sensitivity index of the effective tooth width (parameter 7) to the transmission error is relatively large, while the sensitivity indices of the addendum modification coefficient (parameter 9) and the helix angle (parameter 8) to the transmission error are relatively small, and the first-order sensitivity index is less than 0.05. For the system parameters: the influence degree of the gear position (parameter 11) and the positions of the four bearings corresponding to each pair of gears (parameters 11, 12, 13, 14) on the transmission error is relatively weak.

[0178] (223) Gear set 3

[0179] When each characteristic parameter is under the input torques of 10 Nm, 20 Nm, 30 Nm and the rotational speed of 10000 r / min, the first-order sensitivity index and the total effect index of the target value transmission error are calculated, as Figure 5 shown. Figure 5 In it, the sensitivity indices obtained by calculating the characteristic parameters are represented by a bar chart, which can conveniently and intuitively show the influence of the interaction between the characteristic parameters on the transmission error.

[0180] The magnitude of the sensitivity index can be expressed as: the degree of change in the transmission error caused by the change in the characteristic parameters of the transmission system. The sensitivity index analysis of the gear set 3 under different torques is as follows Figure 5 It can be obtained that with the change of torque, the sensitivity indices of each characteristic parameter are constantly changing, but show a certain upward or downward trend. This indicates that the change of torque affects the influence degree of the characteristic parameters on the transmission error.

[0181] From Figure 5It can be seen that the sensitivity indices of the gear micro-modification parameters: tooth profile crowning modification (parameter 3), tooth profile slope modification (parameter 4), diagonal tooth profile bottom modification (parameter 5) are relatively large, and the influence on the transmission error is relatively obvious; for the gear macroscopic parameters, the sensitivity index of the effective tooth width (parameter 7) has a relatively large influence on the transmission error. As the input torque increases, the influence degree of the effective tooth width (parameter 7) on the transmission error also increases, while the influence degree of the tooth profile crowning modification (parameter 3) on the transmission error decreases. For the system parameters, the influence degrees of the gear position (parameter 11) and the positions of the four bearings corresponding to each pair of gears (parameters 11, 12, 13, 14) on the transmission error are relatively small. The differences between the first-order sensitivity indices and the total effect indices of the tooth profile crowning modification (parameter 3) and the effective tooth width (parameter 7) are relatively large, indicating that these two characteristic parameters have strong interaction effects. When formulating an optimization combination plan for characteristic parameters, different input working conditions need to be considered, and at the same time, a method combining gear micro-parameters and macro-parameters needs to be considered to effectively optimize the characteristic parameters and achieve a more ideal effect.

[0182] The above analysis shows that for different gear sets, the influence degrees of characteristic parameters on the transmission error are different at different torques. Due to different gear parameters, the influence degrees of their micro-modification parameters on the transmission error are also different. The sensitivity index of the macroscopic parameter effective tooth width (parameter 7) increases with the increase of the input torque, indicating that the influence degree of the tooth width change on the transmission error has the same change trend as the input torque. The influence of the modification coefficient (parameter 9) and the helix angle (parameter 8) on the transmission error is relatively small. Since the movable ranges of the system parameters of the gear position and the bearing position are relatively small, the analyzed sensitivity is poor, that is, the influence degree on the transmission error is weak. Therefore, when optimizing the characteristic parameters with the goal of reducing the transmission error, the system parameters can be not used as optimization parameters, so as to streamline the optimization model and improve the calculation efficiency.

[0183] As Figure 6 shown, in an embodiment of the present invention, a gear transmission error optimization system is provided, including;

[0184] A gear transmission structure identification unit 110, configured to determine the meshing gear sets in the gear transmission system, as well as the driving wheel, driven wheel and bearings in each set of meshing gears;

[0185] A characteristic parameter setting unit 120, configured to set characteristic parameters and their value ranges, where the characteristic parameters include gear micro-modification parameters, macroscopic parameters and system parameters; among them, the gear micro-modification parameters include tooth profile crowning modification, tooth profile slope modification, tooth profile crowning modification, tooth profile slope modification, diagonal tooth profile bottom modification and diagonal tooth profile top modification; the macroscopic parameters include effective tooth width, helix angle and modification coefficient; the system parameters include the position of the driven wheel and the positions of the respective bearings corresponding to the driven wheel;

[0186] A gear feature sample forming unit 130 is configured to determine a certain number of samples formed by each set of meshing gears according to the value ranges of the respective feature parameters; wherein, each sample is a set composed of all feature parameter values.

[0187] A feature parameter screening unit 140 is configured to randomly sample the samples of each set of meshing gears, construct a sample matrix of each set of meshing gears, and import the sample matrix of each set of meshing gears into a preset gear transmission error calculation model to calculate the first-order sensitivity index and the total effect index of all feature parameters in each set of meshing gears, and further determine the feature parameters to be optimized in each set of meshing gears based on the first-order sensitivity index and the total effect index of all feature parameters in each set of meshing gears.

[0188] A feature parameter optimization unit 150 is configured to perform optimization respectively according to the feature parameters to be optimized in each set of meshing gears to reduce the gear transmission error.

[0189] Implementing the embodiments of the present invention has the following beneficial effects:

[0190] Based on the value ranges of the gear micro-modification parameters, macro parameters, and system parameters in the feature parameters, the present invention forms samples. After random sampling, the first-order sensitivity index and the total effect index of each feature parameter are calculated to determine the feature parameters to be optimized for optimization, so as to reduce the gear transmission error. Thus, the correlation of the gear micro-modification parameters, macro parameters, and system parameters is comprehensively considered for gear transmission error optimization, which not only reduces the dimension of the optimization process but also improves the optimization efficiency. Since these parameters are closely related to gear manufacturing, the processing cost can be correspondingly reduced.

[0191] It should be noted that in the above system embodiments, the included respective units are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be realized; in addition, the specific names of the respective functional units are only for the convenience of mutual distinction and are not used to limit the protection scope of the present invention.

[0192] Those of ordinary skill in the art can understand that all or part of the steps in implementing the method of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium, such as ROM / RAM, disk, optical disc, etc.

[0193] The above-disclosed is only a preferred embodiment of the present invention, and of course, it cannot be used to limit the scope of the rights of the present invention. Therefore, equivalent changes made according to the claims of the present invention still fall within the scope covered by the present invention.

Claims

1. A method for optimizing gear transmission error, characterized in that, The method includes the following steps: S1. Determine the meshing gear sets in the gear transmission system, as well as the driving gears, driven gears and bearings in each set of meshing gears; S2. Set the characteristic parameters and their value ranges. The characteristic parameters include gear micro-modification parameters, macro parameters and system parameters. Among them, the gear micro-modification parameters include tooth profile crowning modification, tooth profile slope modification, tooth direction crowning modification, tooth direction slope modification, diagonal tooth direction bottom modification and diagonal tooth direction top modification; the macro parameters include effective tooth width, helix angle and modification coefficient; the system parameters include the position of the driven gear and the positions of the respective bearings corresponding to the driven gear; S3. Determine the samples formed by each set of meshing gears according to the value ranges of the respective characteristic parameters. Among them, each sample is a set composed of all the characteristic parameter values; S4. Randomly sample the samples of each set of meshing gears, construct the sample matrix of each set of meshing gears, and import the sample matrix of each set of meshing gears into a preset gear transmission error calculation model to calculate the first-order sensitivity index and total effect index of all the characteristic parameters in each set of meshing gears, and further determine the characteristic parameters to be optimized in each set of meshing gears based on the first-order sensitivity index and total effect index of all the characteristic parameters in each set of meshing gears; S5. Optimize respectively according to the characteristic parameters to be optimized in each set of meshing gears to reduce the gear transmission error.

2. The gear transmission error optimization method according to claim 1, wherein In the step S2, the value ranges of the tooth profile crowning modification, the tooth profile slope modification, the tooth direction crowning modification, the tooth direction slope modification, the diagonal tooth direction bottom modification and the diagonal tooth direction top modification are all [-5, 5] μm.

3. The gear transmission error optimization method according to claim 1, characterized in that In the step S2, the value range of the modification coefficient is determined by a plurality of constraint conditions. Among them, the constraint conditions include the first constraint condition to the eighth constraint condition.

4. The gear transmission error optimization method according to claim 3, wherein, The first constraint condition is represented by formula (1), which is the condition to avoid undercutting during gear machining; The second constraint condition is represented by formulas (2)-(5), which are the conditions to obtain smooth and continuous transmission of gear meshing; The third constraint condition is represented by formulas (6)-(7), which are the conditions to ensure the tooth tip strength of the gear; The fourth constraint condition is represented by formulas (8)-(11), which are the conditions to avoid tooth surface wear and premature failure of the gear; η ≤ 2.5 (8); The fifth constraint condition is represented by formulas (12)-(15), which are the conditions to resist the impact caused by the change of the gear center distance and to store lubricating oil during the meshing process; c≥0.1m n (12); c = r a1 + r f2 − a(13); The sixth constraint condition is represented by formula (16), which is the condition that there is no interference between the root of the small gear and the tip of the large gear; The seventh constraint condition is represented by formula (17), which is the condition that there is no interference between the root of the large gear and the tip of the small gear; The eighth constraint condition is represented by formula (18), which is the condition to achieve high-precision meshing; Among them, is the minimum number of teeth without undercut; is the addendum coefficient; z is the number of teeth; β is the helix angle; α t is the transverse pressure angle; ε α is the transverse contact ratio, z1 and z2 are the number of teeth of the driving gear and the driven gear respectively; α at1 , α at2 are the transverse pressure angles of the addendum circles of the driving gear and the driven gear respectively; α wt is the working pressure angle; m n is the normal module; x is the modification coefficient; d a is the addendum circle diameter; d b is the base circle diameter, and the subscript t takes values in the range of 1 or 2, representing the driving gear and the driven gear respectively; s a is the tooth thickness of the addendum circle; r a is the addendum circle radius; α n 、α t are the normal pressure angle and the transverse pressure angle respectively; r is the pitch circle radius; inv is the involute function; η is the sliding ratio between the driving gear and the driven gear of the gear set at the meshing point; c is the clearance; r f is the root circle radius; a is the actual center distance; x1 and x2 are the modification coefficients of the driving gear and the driven gear respectively.

5. The gear transmission error optimization method according to claim 4, wherein, In the step S2, the value range of the helix angle β is determined by the axial contact ratio, pressure angle, normal backlash of the involute helical gear and gear strength.

6. The gear transmission error optimization method according to claim 5, characterized in that The axial contact ratio ε of the involute helical gear β is calculated by formula (19); The pressure angle α t is determined by formula (20); The normal backlash j of the gear bn is calculated by formulas (21)-(23); j bt = e bt2 - s bt1 + 2(r bt1 + r bt2 ) * invα wt (21); j bt = e bt1 − s bt2 + 2(r bt1 + r bt2 ) * invα wt (22); j bn = j bt * cosβ b (23); The gear strength includes the tooth root bending strength and the tooth surface contact fatigue strength, which are constrained by Formulas (24)-(25); σ H ≤σ HP (24); σ F ≤σ FP (25); where r bt is the base circle radius of the gear; e bt is the base circle tooth space width of the gear; s bt is the base circle tooth thickness of the gear; p bt is the normal base pitch on the tooth profile of the gear end face; Equation (21) is the normal side clearance of the tooth profile on the gear end face when the tooth of the driving gear is in the tooth space of the driven gear; Equation (22) is the normal side clearance of the tooth profile on the gear end face when the tooth of the driven gear is in the tooth space of the driving gear; σ H , σ F are the calculated contact stress and the calculated tooth root stress respectively; σ HP , σ FP are the allowable contact stress and the allowable tooth root stress for use respectively.

7. The gear transmission error optimization method according to claim 6, wherein In the step S2, the value range of the effective tooth width is ±10% of the effective tooth widths of the two meshing gears; the value range of the positions of the bearings is the positions that do not interfere with other parts.

8. The gear transmission error optimization method according to claim 1, characterized in that The step S4 specifically includes: Based on the Monte Carlo sampling method, in the samples of each group of meshing gears, the Sobol sequence sampling method is used for random sampling to construct a sample matrix of each group of meshing gears; wherein, the sample matrix is composed of n sets of sample parameters with different numerical values in columns, and each column of sample parameter sets is composed of s sampling samples; n is the number of characteristic parameters, which is a positive integer; s is the number of sampling times, which is a positive integer greater than 1; The sample parameter sets in each column of the sample matrix of each group of meshing gears are sequentially imported into the gear transmission error calculation model for calculation, and the peak-to-peak values of the transmission errors of the meshing gears corresponding to the sample parameter sets in each column of the sample matrix of each group of meshing gears are obtained; According to the peak-to-peak values of the transmission errors of the meshing gears corresponding to all the sample parameter sets in each column of the sample matrix of each group of meshing gears, the variances and partial variances of each characteristic parameter on the peak-to-peak value of the transmission error are calculated for the sample matrix of each group of meshing gears, and based on the variances and partial variances of each characteristic parameter on the peak-to-peak value of the transmission error in the sample matrix of each group of meshing gears, the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears are obtained; Based on the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears, sorting is performed to determine the characteristic parameters to be optimized in each group of meshing gears.

9. A gear transmission error optimization system, characterized in that, Including; A gear transmission structure identification unit for determining the meshing gear sets in the gear transmission system, as well as the driving wheel, the driven wheel and the bearings in each group of meshing gears; A characteristic parameter setting unit for setting the characteristic parameters and their value ranges, where the characteristic parameters include gear micro-modification parameters, macro parameters and system parameters; among them, the gear micro-modification parameters include tooth profile crowning modification, tooth profile taper modification, tooth direction crowning modification, tooth direction taper modification, diagonal tooth direction bottom modification and diagonal tooth direction top modification; the macro parameters include effective tooth width, helix angle and modification coefficient; the system parameters include the position of the driven wheel and the positions of the respective bearings corresponding to the driven wheel; A gear characteristic sample forming unit for determining the samples formed by each group of meshing gears according to the value ranges of the characteristic parameters; wherein, each sample is composed of a set of all the characteristic parameter values; A characteristic parameter screening unit for randomly sampling the samples of each group of meshing gears, constructing a sample matrix of each group of meshing gears, and importing the sample matrix of each group of meshing gears into a preset gear transmission error calculation model, calculating the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears, and further determining the characteristic parameters to be optimized in each group of meshing gears based on the first-order sensitivity index and the total effect index of all the characteristic parameters in each group of meshing gears; A feature parameter optimization unit is used to perform optimization separately according to the feature parameters to be optimized in each group of meshing gears. Since these parameters are closely related to gear manufacturing, the processing cost can be reduced accordingly.

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