Zero transmission error reverse compensation modification method based on contact ratio

Abstract

The invention discloses a zero transmission error reverse compensation modification method based on the overlap ratio, and belongs to the field of vibration noise suppression of a gear transmission system. Firstly, the geometric transmission error is designed according to the requirement for bearing the transmission error of the modified tooth surface; then, the modification amount of the tooth surface is calculated through a preset geometric transmission error; establishing a tooth surface modification optimization function with bearing transmission error fluctuation amplitude as a target; and a self-adaptive genetic algorithm is adopted to carry out optimization solution on gear tooth surface modification parameters taking the geometric transmission error as a target, and a tooth surface modification optimization result is obtained. According to the method, modification of the tooth surface is achieved by presetting the geometric transmission error of the modified tooth surface, and the method has universality, is suitable for transmission of gears with various contact ratios and has good engineering practical application value.

Description

Technical Field

[0001] The present invention broadly relates to the field of vibration noise suppression of gear transmission systems, and in particular to a zero transmission error reverse compensation shaping method based on overlap. Background Art

[0002] As modern industry continues to develop towards high speed and heavy load, the vibration and noise problems in gear transmission systems have attracted widespread attention from scholars at home and abroad, and various vibration and noise reduction design and control methods have emerged. Tooth surface modification, as an effective tooth surface vibration suppression method, has always been an important method for vibration suppression in the gear design stage. In the gear transmission process, the amplitude of the load transmission error fluctuation is one of the main sources of vibration and noise. Reducing the amplitude of the load transmission error fluctuation is of great significance for vibration and noise reduction in the gear transmission process.

[0003] The gear system will produce elastic deformation to varying degrees during power transmission, causing distortion of the gear tooth profile and tooth curve, forcing the gear to produce impact, vibration and eccentric load during the meshing process. Transmission error and meshing impact are the primary excitation sources that deteriorate the gear transmission performance. In order to reduce vibration and noise, scholars have achieved good vibration reduction effects by modifying the tooth profile and tooth curve of the gear teeth. However, traditional modification methods have a good improvement effect on cylindrical gears with small overlap, but they are far from meeting the needs for non-standard large tooth height coefficient cylindrical gears that are widely used today. Traditional tooth surface modification is mainly performed on the root, top, and both sides of the tooth direction, without considering the impact of the alternating conversion of the number of gears that are in contact at the same time during the gear transmission process. Since the overlap of non-standard large tooth height coefficient cylindrical gears exceeds 2, the original "two teeth-single tooth-two teeth" meshing process is transformed into "three teeth-two teeth-three teeth-two teeth-three teeth". At this time, the traditional cam modification design will find it difficult to track the changes in the number of tooth pairs involved in meshing, it will be difficult to compensate for the transmission error fluctuations of the gear pair with large overlap, and it will not be able to match the change law of the meshing area caused by the overlap.

[0004] Therefore, in order to further reduce the fluctuation amplitude of the load-bearing transmission error, a zero transmission error reverse compensation modification method based on overlap is proposed, and the tooth surface is modified by presetting the geometric transmission error of the modified tooth surface. The fluctuation amplitude of the load-bearing transmission error of the tooth surface modification curve (modified tooth surface geometric transmission error) and the conjugate tooth surface of the pair of gears (unmodified standard tooth surface) under the design load is equal in magnitude and opposite in direction. According to the above idea, a diagonal modification design is performed, and in theory, a load-bearing transmission error with a fluctuation amplitude of zero can be obtained, and it can cope with the meshing impact excitation under the full speed range. Summary of the invention

[0005] The purpose of the present invention is to provide a zero transmission error reverse compensation shaping method based on overlap, in order to achieve better vibration reduction and noise reduction effects, wherein the tooth surface is modified by pre-setting the geometric transmission error of the modified tooth surface, the modification amount of the tooth surface is calculated by the preset geometric transmission error, and a tooth surface modification optimization function with the bearing transmission error fluctuation amplitude as the target is further established, and an adaptive genetic algorithm is used to optimize and solve the gear tooth surface modification parameters with the geometric transmission error as the target to obtain the tooth surface modification optimization result.

[0006] The existing LTCA calculation program is fully utilized with the high efficiency and convenience of genetic algorithm. On this basis, combined with the relevant technical foundations of tooth surface three-dimensional shaping, a reasonable and efficient zero transmission error reverse compensation shaping preset geometric transmission error design calculation program based on overlap is compiled. Two examples are given, and the tooth surface modification design is completed based on the proposed tooth surface modification method.

[0007] The present invention selects the load transmission error fluctuation amplitude as the target, optimizes and modifies the pinion tooth surface, and uses an adaptive genetic algorithm to optimize and solve the gear tooth surface modification parameters with the geometric transmission error as the target, to obtain the tooth surface modification optimization result.

[0008] Beneficial effects of the present invention:

[0009] The present invention provides a zero transmission error reverse compensation shaping method based on overlap, in which the tooth surface is modified by presetting the geometric transmission error of the modified tooth surface. The influence of the overlap is taken into account in the shaping method, so that the shaping rule is consistent with the meshing zone change rule caused by the overlap, and the fluctuation amplitude of the load-bearing transmission error can be minimized. This method reduces vibration noise in the gear transmission process, improves the transmission quality, and has good practical engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 The schematic diagram of the design of the reverse compensation of the geometric transmission error based on the zero transmission error of the overlap ratio is shown;

[0011] Figure 2 A flow chart for designing geometric transmission error for reverse compensation modification of zero transmission error based on overlap;

[0012] Figure 3 To reverse compensate the machining coordinate relationship of the modified gear;

[0013] Figure 4 is the coordinate relationship of a pair of involute cylindrical helical gears meshing;

[0014] Figure 5 Optimize the process flow chart for tooth surface modification;

[0015] Figure 6Preset and optimize the geometric transmission error of the modified tooth surface for reverse compensation in Example 1;

[0016] Figure 7 Comparison of the fluctuation amplitude of the load transmission error before and after the gear pair modification in Example 1;

[0017] Figure 8 Preset and optimize the geometric transmission error of the modified tooth surface for reverse compensation in Example 2;

[0018] Fig. 9 Comparison of the fluctuation amplitude of the load transmission error before and after the gear pair modification in Example 2;

[0019] Fig.10 The three-dimensional mesh of the tooth surface modification amount for the inverse compensation modification optimized in Example 1;

[0020] Fig.11 The maximum curvature of the inverse compensation modified tooth surface at the meshing point optimized for Example 1;

[0021] Fig.12 The three-dimensional mesh of the tooth surface modification amount for the inverse compensation modification optimized in Example 2;

[0022] Fig.13 The maximum curvature of the inverse compensation modified tooth surface at the meshing point optimized for Example 2; Specific implementation plan

[0023] The present invention is further described below in conjunction with the accompanying drawings and embodiments, but the protection scope of the present invention is not limited thereto.

[0024] 1. Figure 1 This is a schematic diagram of the preset geometric transmission error design for the reverse compensation modification of zero transmission error based on overlap. Before designing the preset geometric transmission error, it is necessary to first obtain the load transmission error of the tooth surface before modification. Figure 1 Curve 1 in the figure is the load transmission error of the standard tooth surface gear pair under a certain design load, and curve 2 is the preset geometric transmission error of the reverse compensation modified tooth surface. The designed geometric transmission error and the load transmission error of the unmodified standard tooth surface under the design load have the same fluctuation amplitude and opposite direction. The design process of the preset geometric transmission error of the reverse compensation modification with zero transmission error based on overlap is as follows: Figure 2 shown.

[0025] 2. The reverse compensation modification of the tooth surface obtained by the preset geometric transmission error can be achieved through the additional movement of the rack cutter during the gear processing process. Figure 3 In order to reversely compensate the machining coordinate relationship of the modified gear, an additional displacement ΔL is added 1 The tooth surface modification can be achieved. According to the gear meshing principle, the tooth surface equation can be expressed as (1).

[0026]

[0027] Where: subscript i = 1, 2 represents the small gear and large gear respectively, ΔL i is the additional displacement of the tool, [M]i,ti represents the transformation matrix from the coordinate system Sti to Si, [L]i,ti is the rotation sub-matrix, are the position vector and normal vector of the tooth surface, are the position vector and unit normal vector of the tool, ui, θi and l i are theoretical tooth surface parameters.

[0028] Figure 4 is the coordinate relationship of a pair of involute cylindrical helical gears meshing. The geometric contact analysis calculation formulas of the large and small gear tooth surfaces in the same coordinate system are (2) and (3).

[0029]

[0030] Where: [M] f,i (i=1,2) indicates the coordinate system S i To S f The transformation matrix, [L] f,i (i=1,2) is the rotation submatrix, are the turning angles of the small wheel and the large wheel respectively.

[0031] because Based on the gear tooth geometry contact analysis, five independent scalar equations can be obtained. is a known quantity, and solving the remaining five unknown quantities can obtain all the contact points of the two tooth surfaces, and then determine the geometric transmission error and the tooth surface contact path.

[0032] When a pair of standard involute gears rotate, the geometric transmission error is zero. Due to the influence of the error and tooth surface modification, the actual rotation angle of the driven gear deviates from the theoretical rotation angle, that is, a geometric transmission error occurs. The geometric transmission error calculation equation is (4).

[0033]

[0034] Where: N i (i=1,2) are the number of teeth on the small wheel and the large wheel respectively, are the initial rotation angles of the small wheel and the large wheel respectively.

[0035] Based on equations (2) and (3), five independent scalar equations can also be obtained, with the preset geometric transmission error is a known quantity. According to the geometric transmission error calculation equation (4), the small wheel angle and geometric transmission error Indicates the large wheel angle Take the small wheel angle Substitute it into the equation as a known quantity to determine the large wheel rotation angle

[0036] Based on the above description, through the preset geometric transmission error The additional displacement of the tool ΔL is obtained 1 , through ΔL 1 The tooth surface modification can be achieved, and the modification amount of the tooth surface is expressed as equation (5).

[0037]

[0038] Where: are the position vector and unit normal vector of the standard tooth surface of the small wheel, is the position vector of the modified tooth surface of the small wheel.

[0039] 3. Establish a tooth surface modification optimization function with the load transmission error fluctuation amplitude as the target, and the optimization variable is the geometric error of a certain instantaneous contact position. Establish the optimization function as shown in formulas (6) to (8).

[0040] Optimization variables:

[0041] Objective function: min f(x) = F ALTE (7)

[0042] Constraints: stQ min ≤x≤Q max (8)

[0043] Where: is the geometric error of a certain instantaneous contact position, n represents the number of contact lines from the tooth entering meshing to exiting meshing, To optimize the lower bound of the variable, is the upper bound value of the optimized variable, where It is the geometric transmission error at each contact position on the preset geometric transmission error curve, and is also the initial value of the optimization variable in the optimization process.

[0044] 4. Adopting adaptive genetic algorithm to optimize and solve the gear tooth surface modification parameters with geometric transmission error as the target, the tooth surface modification optimization result can be obtained. The tooth surface modification optimization process is as follows: Figure 5 shown.

[0045] To summarize the present invention, firstly, the geometric transmission error of the modified tooth surface is designed according to the requirement of the load-bearing transmission error; then, the modification amount of the tooth surface is calculated by the preset geometric transmission error; a tooth surface modification optimization function with the load-bearing transmission error fluctuation amplitude as the target is established; and an adaptive genetic algorithm is used to optimize and solve the gear tooth surface modification parameters with the geometric transmission error as the target to obtain the tooth surface modification optimization result.

[0046] Example

[0047] In order to verify the reverse compensation and shaping effect of the present invention, two groups of example calculations are carried out with the parameters in Table 1. Table 1 shows the parameters of two groups of cylindrical helical gear pairs.

[0048] Table 1

[0049]

[0050] Based on the example given in Table 1, Figure 6 This is the preset and optimization of the geometric transmission error of the reverse compensation modified tooth surface in Example 1. It can be seen from the figure that the preset geometric transmission error is designed to be equal to the load-bearing transmission error fluctuation amplitude of the conjugate tooth surface of the pair of gears under the design load, and the direction is opposite. The optimized geometric transmission error is slightly smaller than the preset geometric transmission error fluctuation amplitude and the change trend is consistent. The geometric transmission error of the standard tooth surface is almost zero, and the geometric transmission error of the optimized reverse compensation modified tooth surface shows a fluctuating trend.

[0051] Figure 7 A comparison of the load-bearing transmission error fluctuation amplitudes of the standard tooth surface, traditional modified tooth surface and reverse compensation modified tooth surface in Example 1 is given. Based on the optimized geometric transmission error, the load-bearing transmission error fluctuation amplitude is greatly reduced to almost zero, indicating that the tooth surface modification amount obtained by the zero transmission error reverse compensation modification method based on overlap basically achieves effective compensation for the gear tooth deformation in different meshing areas.

[0052] same, Figure 8-Figure 9 The preset and optimization of the geometric transmission error of the reverse compensation modified tooth surface in Example 2 are given, and the load-bearing transmission error fluctuation amplitudes of the standard tooth surface, the traditional modified tooth surface and the reverse compensation modified tooth surface are compared. Compared with Example 1, the overlap of Example 2 is larger. It can be seen from Examples 1 and 2 that the tooth surface modification amount obtained by the zero transmission error reverse compensation modification method based on overlap achieves effective compensation for the deformation of gear teeth in different meshing areas, indicating that the method proposed in the present invention to design the required geometric transmission error through the load-bearing transmission error of the standard tooth surface is feasible. The basic profile of the preset geometric transmission error curve determines the basic profile of the optimized geometric transmission error. Compared with the traditional modified tooth surface, the reverse compensation modified tooth surface has greater advantages.

[0053] Fig.10The three-dimensional mesh of the tooth surface modification amount of the reverse compensation modification example 1 is given in the figure. The modification amount is based on Figure 6 (c) is obtained by optimizing the geometric transmission error of the reverse compensation modification. The size of the geometric transmission error determines the size of the tooth surface modification amount. The fluctuation trend of the geometric transmission error determines the fluctuation trend of the three-dimensional mesh surface of the tooth surface modification amount. From the three-dimensional mesh diagram of the modification amount, it can be seen that the tooth surface modification amount along the instantaneous contact line is equal. The modified tooth surface is composed of a standard tooth surface and a modification amount surface. The present invention calculates the maximum curvature of the modified tooth surface at the contact point, such as Fig.11 As shown, the machinability and meshing performance of the modified tooth surface are checked.

[0054] Fig.12 The three-dimensional mesh of the tooth surface modification amount of inverse compensation modification in Example 2 is given. The modification amount is based on Figure 8 The optimized reverse compensation modification geometric transmission error in (c) is obtained. Similar to Example 1, the machinability and meshability of the modified tooth surface are checked by calculating the maximum curvature of the modified tooth surface at the contact point, as shown in Fig.13 As shown, the maximum curvatures of the modified tooth surfaces of Examples 1 and 2 at the contact points perpendicular to the instantaneous contact line are both greater than zero, indicating that the zero transmission error reverse compensation modification method based on overlap proposed in the present invention has good practical engineering application value.

[0055] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent implementation methods or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

Claims

1. A zero transmission error reverse compensation shaping method based on overlap, characterized in that: Firstly, the geometric transmission error of the modified tooth surface is designed according to the requirements of the load-bearing transmission error; then the modification amount of the tooth surface is calculated by the preset geometric transmission error; a tooth surface modification optimization function with the load-bearing transmission error fluctuation amplitude as the target is established; and an adaptive genetic algorithm is used to optimize and solve the gear tooth surface modification parameters with the geometric transmission error as the target, and the tooth surface modification optimization result is obtained; The specific process of the method comprises the following steps: Step 1: Generate the finite element mesh of the small wheel and the large wheel tooth surface according to the basic parameters of the gear pair and the load torque, perform TCA calculation (gear geometric contact analysis) on the modified front tooth surface of the large and small wheels, calculate the mesh flexibility coefficient of the tooth surface of the small wheel and the large wheel, solve the load transmission error of the modified front tooth surface through LTCA (gear load contact analysis), and then design a geometric transmission error with the same amplitude and opposite direction as the actual tooth surface load transmission error fluctuation. The geometric transmission error of the modified tooth surface fluctuates according to different overlaps and has universality; Step 2: Calculate the modification amount of the tooth surface, and design the reverse compensation modification tooth surface according to the preset geometric transmission error. The modification tooth surface can be achieved through the additional movement of the rack cutter during the gear processing process. The additional displacement of the tool is obtained through the preset geometric transmission error, and the tooth surface is modified through the additional displacement of the tool; Step 3: Establish an optimization function with the amplitude of the load transmission error fluctuation as the target, optimize the pinion tooth surface, perform load contact analysis on the modified tooth surface, obtain the load transmission error and design the geometric transmission error, generate the modified tooth surface of the pinion based on the preset geometric transmission error, complete the TCA calculation based on the modified tooth surface of the small wheel and the standard tooth surface of the large wheel, solve the tooth surface normal flexibility matrix, and use LTCA to solve the load transmission error and load transmission error amplitude of the modified tooth surface; Step 4: Adopt an adaptive genetic algorithm to optimize and solve the gear tooth surface modification parameters with geometric transmission error as the target, and obtain the optimization results of the load-bearing transmission error and the load-bearing transmission error amplitude.

2. The zero transmission error reverse compensation shaping method based on overlap according to claim 1 is characterized in that: The gear tooth surface equation is: Where: subscript i = 1, 2 represents the small gear and large gear respectively, ΔL i Additional displacement for the tool, [M] i,ti Indicates that from the coordinate system S ti To S i The transformation matrix, [L]i,ti is the rotation submatrix, and are the position vector and normal vector of the tooth surface, and is the position vector and unit normal vector of the tool, u i ,θ i and l i are theoretical tooth surface parameters. The calculation formula for gear geometric contact analysis is: Where: [M] f,i (i=1,2) indicates the coordinate system S i To S f The transformation matrix, [L] f,i (i=1,2) is the rotation submatrix, and are the turning angles of the small wheel and the large wheel respectively. Select small wheel angle Substituting as known quantities, the geometric transmission error and the tooth surface contact path are determined. The additional displacement ΔL1 of the tool is obtained by the preset geometric transmission error. The tooth surface modification can be achieved by ΔL1. The tooth surface modification amount is expressed as: Where: and are the position vector and unit normal vector of the standard tooth surface of the small wheel, is the position vector of the modified tooth surface of the small wheel.

3. The zero transmission error reverse compensation shaping method based on overlap according to claim 1 is characterized in that: The expression of the optimization function is as follows: Optimization variables: Objective function: min f(x) = F ALTE Constraints: stQ min ≤x≤Q max In the formula, is the geometric error of a certain instantaneous contact position, n represents the number of contact lines in the entire process from the gear teeth entering the meshing to exiting the meshing, F ALTE is the minimum load transmission error fluctuation amplitude, To optimize the lower bound of the variable, is the upper bound value of the optimized variable, where It is the geometric transmission error at each contact position on the preset geometric transmission error curve, and is also the initial value of the optimization variable in the optimization process.

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