Gear system dynamics modeling method containing time-varying backlash and bilateral impact

Abstract

The invention relates to the technical field of gear transmission, in particular to a dynamic modeling method for a gear system with time-varying backlash and bilateral impact, which comprises the following steps: acquiring a theoretical backlash of a gear pair; obtaining a time-varying gear backlash of the gear pair; acquiring bilateral meshing impact excitation of the gear pair; and constructing a gear system dynamic model. The method can be effectively used for evaluating the system nonlinear dynamic behavior considering the gear manufacturing error, the modification amount, the gear backlash and the meshing impact factor, and is helpful to clarify the action mechanism of the gear manufacturing error, the modification amount, the gear backlash and the bilateral meshing impact factor on the dynamic response of the gear transmission system; theoretical support is provided for noise reduction and service life prolonging of a gear transmission system.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and in particular to a method for dynamic modeling of a gear system containing time-varying tooth side clearance and double-sided impact. Background Art

[0002] In the gear system, manufacturing errors are inevitable, and gear modification is usually introduced to improve the meshing characteristics of the gear. However, the uncertainty of manufacturing errors will cause differences in the tooth surface errors of each gear tooth, which further makes the meshing stiffness and meshing error excitation of the gear pair have a long periodicity beyond the meshing period. It is generally believed that this long period is the rotation period of the gear or the chasing tooth pair period. Relative to the ideal error-free tooth surface, when the long-period meshing stiffness and meshing error act, the gear tooth deformation also produces growth periodicity accordingly. When the gear tooth deformation with long periodicity and the tooth surface error act together, the tooth side clearance during the meshing process of the gear pair will also produce long periodicity, that is, the tooth side clearance also has time-varying characteristics within a long period. The time-varying tooth side clearance will change the meshing state of the gear pair through coupling with the vibration displacement, causing the gear pair to produce three states: positive meshing, disengagement, and reverse meshing. During forward and reverse meshing, the gear pair will produce speed differences between the simultaneously meshing teeth due to gear tooth deformation and tooth surface errors, thereby generating forward or reverse meshing impacts. The time-varying tooth side clearance will make this meshing impact phenomenon very complicated, further complicating the vibration response of the gear system.

[0003] The problem of predicting the dynamic response of a gear system considering time-varying tooth backlash and bilateral meshing impact involves the nonlinear coupling of factors such as error, deformation, backlash and impact, which can more realistically reflect the vibration characteristics of the gear system and is of great significance for clarifying the mechanism of the effect of factors such as gear error and backlash on the vibration response of the system. That is, there is an urgent need for relevant mathematical models for the dynamic modeling method of gear systems containing time-varying tooth backlash and bilateral impact.

[0004] Therefore, it is necessary to provide a gear system dynamics modeling method with time-varying tooth side clearance and double-sided impact to solve the above problems. Summary of the invention

[0005] The invention provides a gear system dynamics modeling method including time-varying tooth side clearance and double-sided impact to solve the existing problems.

[0006] A gear system dynamics modeling method with time-varying tooth backlash and double-sided impact of the present invention adopts the following technical solution, including: Obtain the theoretical tooth side clearance of the gear pair under the factors of tooth thickness deviation and center distance deviation; Based on the theoretical backlash of the gear pair, the time-varying backlash of the gear pair under the gear manufacturing error, modification amount and its long periodicity factors is obtained; Obtain the bilateral meshing impact excitation of the gear pair under the time-varying tooth backlash factor; Based on the time-varying tooth backlash and bilateral meshing impact excitation of the gear pair, a dynamic model of the gear system is constructed.

[0007] Preferably, the expression of the theoretical tooth backlash of the gear pair is: In the formula, It is half of the theoretical tooth backlash of the gear pair; is the normal base circle pitch; is the normal base circle tooth thickness of the driving gear; is the normal base circle tooth thickness of the driven gear; is the base circle radius of the driving gear; is the base circle radius of the driven gear; is the gear meshing angle; is the base circle helix angle; .

[0008] Preferably, the expression of the normal base circle pitch is:

[0009] In the formula, is the end face modulus; is the end pressure angle.

[0010] Preferably, the expression of the normal base circle tooth thickness of the gear is:

[0011] In the formula, For gear The thickness of the base scallop of the French surface; is the normal modulus; is the tooth thickness deviation of the gear teeth; For gear The base circle radius; For gear The pitch circle radius; is the end pressure angle; where, =(1,2), When it is 1, it indicates the driving gear; When it is 2, it indicates the driven gear.

[0012] Preferably, the expression of the gear meshing angle is:

[0013] In the formula, is the gear meshing angle; is the normal modulus; is the number of teeth of the driving gear; is the number of teeth of the driven gear; is the helix angle; is the center distance deviation of the gear pair.

[0014] Preferably, the steps of obtaining the time-varying tooth side clearance of the gear pair under the gear manufacturing error, the modification amount and its long periodicity factor are: According to the manufacturing errors and modification amounts corresponding to the working tooth surface and the non-working tooth surface of the gear, the static transmission errors corresponding to the working tooth surface and the non-working tooth surface of the gear under the cycle to the preset long period are obtained; The time-varying tooth backlash of the gear pair is obtained according to the theoretical tooth backlash of the gear pair, the static transmission error of the working tooth surface and the static transmission error of the non-working tooth surface.

[0015] Preferably, the step of obtaining the static transmission error corresponding to the working tooth surface and the non-working tooth surface of the gear under the preset long cycle is: Establish the meshing action surface of the working tooth surface of the gear pair and the meshing action surface of the non-working tooth surface; Arrange and number the contact lines and contact points of the meshing surfaces at equal intervals, and select the contact lines and contact points of the meshing gears at the same time according to the meshing principle and overlap; According to the manufacturing errors and modification amounts corresponding to the contact lines and contact points of the meshing gear teeth, the static transmission errors corresponding to the working tooth surface and the non-working tooth surface of the gear under the preset long cycle are obtained; Among them, the expression of the static transmission error of the working tooth surface of the gear under long period is:

[0016] Among them, the expression of the static transmission error of the non-working tooth surface of the gear under long period is:

[0017] In the formula, t A moment in a long period; For gears in long periods t Static transmission error of the working tooth surface at the moment; For gears in long periods t Static transmission error of the non-working tooth surface at the moment; For long period t At this moment, the first i The contact line j Manufacturing error of each contact point; For long period t At the moment, the first iThe contact line j Manufacturing error of each contact point; For long period t At this moment, the first i The contact line j The amount of modification for each contact point; For long period t At the moment, the first i The contact line j The amount of modification for each contact point; For long period t The first tooth surface of the non-working gear at the time i The contact line j Manufacturing error of each contact point; For long period t The first non-working tooth surface of the driven gear at the time i The contact line j Manufacturing error of each contact point; For long period t The first tooth surface of the non-working gear at the time i The contact line j The amount of modification for each contact point; For long period t The first non-working tooth surface of the driven gear at the time i The contact line j The amount of modification for each contact point.

[0018] Preferably, the expression of the time-varying tooth backlash of the gear pair is:

[0019] In the formula, It is half of the theoretical tooth backlash of the gear pair; For the gear pair in a long period t Half of the time-varying tooth backlash at time .

[0020] Preferably, the step of obtaining the bilateral meshing impact excitation of the gear pair is: According to the geometric relationship at the gear meshing line, the positions of the positive meshing impact point and the reverse meshing impact point of the gear pair are obtained; Obtaining the corresponding meshing impact speed according to the position of the meshing impact point; Obtain the bilateral meshing impact energy based on the meshing impact speed, the gear's moment of inertia and the gear's base circle radius; The maximum impact force generated by the bilateral meshing is obtained according to the bilateral meshing impact energy; Obtain the bilateral meshing impact excitation of the gear pair according to the maximum impact force; The bilateral meshing impact excitation includes: the impact generated by the positive meshing on the working tooth surface and the impact generated by the negative meshing on the non-working tooth surface.

[0021] Preferably, the expression of the gear system dynamics model with time-varying tooth backlash and double-sided impact is:

[0022] in, is the mass matrix of the gear system; is the damping matrix of the gear system; is the stiffness matrix of the gear system; is the load torque vector external to the gear system; The impact excitation generated by positive meshing; Impact excitation generated by reverse meshing; b t For the gear pair in a long period t Half of the time-varying backlash at time ; is the vibration acceleration of the gear in the direction of the meshing line; is the vibration speed of the gear in the direction of the meshing line; is the vibration displacement of the gear in the direction of the meshing line, and its expression is:

[0023] In the formula, Indicates driving gear x The vibration displacement in the direction Indicates driving gear y The vibration displacement in the direction Indicates driving gear z The vibration displacement in the direction Indicates driven gear x The vibration displacement in the direction Indicates driven gear y The vibration displacement in the direction Indicates driven gear z Vibration displacement in direction; Indicates the driving gear winding x The vibration displacement of the rotation direction, Indicates the driving gear winding y The vibration displacement of the rotation direction, Indicates the driving gear winding z The vibration displacement of the rotation direction, Indicates the driven gear winding x The vibration displacement of the rotation direction, Indicates the driven gear winding y The vibration displacement of the rotation direction, Indicates the driven gear windingz Vibration displacement of rotation direction. is the helix angle of the gear base circle; , is the gear meshing angle, For installation phase angle.

[0024] The beneficial effects of the present invention are: By obtaining the theoretical tooth side clearance of the gear pair considering the tooth thickness deviation and the center distance deviation factors; based on the theoretical tooth side clearance of the gear pair, obtaining the long-period time-varying tooth side clearance of the gear pair under the gear manufacturing error, the shaping amount and its long-periodic factors; according to the geometric relationship at the gear meshing line, the positions of the positive and reverse meshing impact points of the gear pair are derived; according to the geometric position of the meshing impact point, the meshing impact velocity is determined, and the bilateral meshing impact excitation of the gear pair is further determined according to the impact kinetic energy; the dynamic model of the gear system containing long-period time-varying tooth side clearance and bilateral impact is established and solved. The present invention can be effectively used to evaluate the nonlinear dynamic behavior of the system considering the gear manufacturing error, shaping amount, tooth side clearance and meshing impact factors, which helps to clarify the mechanism of the gear manufacturing error, shaping amount, tooth side clearance and bilateral meshing impact factors on the dynamic response of the gear transmission system, and provides theoretical support for the noise reduction and life extension of the gear transmission system. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0026] Figure 1 It is a flow chart of a method for dynamic modeling of a gear system containing time-varying tooth backlash and double-sided impact according to the present invention; Figure 2 A schematic diagram of the meshing surface of a gear pair in an embodiment of the present invention; Figure 3 A schematic diagram of determining the position of the meshing impact point of a gear pair in an embodiment of the present invention; Figure 4 This is a schematic diagram of the vibration response results of a gear pair under different gear manufacturing errors solved by the modeling method of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] An embodiment of a gear system dynamics modeling method with time-varying tooth backlash and double-sided impact according to the present invention is as follows: Figure 1 As shown, including: S1, obtaining the theoretical tooth side clearance of the gear pair; Specifically, in this embodiment, the theoretical tooth side clearance of the gear pair under the factors of tooth thickness deviation and center distance deviation is considered, wherein the expression of the theoretical tooth side clearance of the gear pair under the factors of tooth thickness deviation and center distance deviation is:

[0029] In the formula, It is half of the theoretical backlash of the gear pair; is the normal base circle pitch; is the normal base circle tooth thickness of the driving gear; is the normal base circle tooth thickness of the driven gear; is the base circle radius of the driving gear; is the base circle radius of the driven gear; is the gear meshing angle; is the base circle helix angle; .

[0030] Among them, the expression of normal base circle pitch is:

[0031] In the formula, is the end face modulus; is the end pressure angle.

[0032] Among them, the expression of the normal base circle tooth thickness of the gear is:

[0033] In the formula, For gear The thickness of the base scallop of the French surface; is the normal modulus; is the tooth thickness deviation of the gear teeth; For gear The base circle radius; For gear The pitch circle radius; is the end pressure angle; where, =(1,2), When it is 1, it indicates the driving gear; When it is 2, it indicates the driven gear.

[0034] The expression of gear meshing angle is:

[0035] In the formula, is the gear meshing angle; is the normal modulus; is the number of teeth of the driving gear; is the number of teeth of the driven gear; is the helix angle; is the center distance deviation of the gear pair.

[0036] S2, obtaining the time-varying tooth side clearance of the gear pair; Specifically, in this embodiment, based on the theoretical tooth side clearance of the gear pair, the time-varying tooth side clearance of the gear pair under the gear manufacturing error, shaping amount and its long-periodic factors is considered; that is, the steps of obtaining the time-varying tooth side clearance of the gear pair under the gear manufacturing error, shaping amount and its preset long-periodic factors are: according to the manufacturing error and shaping amount corresponding to the working tooth surface and non-working tooth surface of the gear, obtain the long-period static transmission error corresponding to the working tooth surface and non-working tooth surface of the gear; according to the theoretical tooth side clearance of the gear pair, the long-period static transmission error of the working tooth surface and the long-period static transmission error of the non-working tooth surface, obtain the long-period time-varying tooth side clearance of the gear pair. Define the meshing cycle of the gear teeth from meshing in to meshing out as T 0 , then consider the long period of manufacturing error differences of each gear pair T 1 for:

[0037] In the formula, is the number of teeth of the driving gear of the meshing gear pair; is the number of teeth of the driven gear of the meshing gear pair, To find the greatest common divisor of the number of teeth of the driving gear and the driven gear.

[0038] In an exemplary embodiment, the steps of obtaining the long-period static transmission error corresponding to the working tooth surface and the non-working tooth surface of the gear are as follows: Figure 2 As shown in the figure, the meshing surface of the working tooth surface of the gear pair and the meshing surface of the non-working tooth surface are established, and the contact lines and contact points of the meshing surface are arranged and numbered at equal intervals. According to the meshing principle and overlap, the contact lines and contact points of the simultaneously meshing gears are selected. t At this moment, get the contact line i Upper contact pointj The manufacturing error of the working tooth surface of the driving gear and the driven gear on its meshing surface and the amount of shaping , and obtain the manufacturing error of the non-working tooth surface of the driving gear and the driven gear on its meshing surface and the amount of shaping When the actual tooth surface is convex compared to the ideal tooth surface, the deviation is a positive value, and when the actual tooth surface is concave compared to the ideal tooth surface, the deviation is a negative value, and the modification amount is always a negative value.

[0039] Among them, the expression of the static transmission error of the working tooth surface of the gear under long period is:

[0040] Among them, the expression of the static transmission error of the non-working tooth surface of the gear under long period is:

[0041] In the formula, t is a moment in a long cycle. Generally speaking, in a meshing cycle, the equal spacing is divided into n After trial calculation, in order to balance the solution accuracy and calculation efficiency, n The value can be between 50 and 100, so there are a moment; For gears in long periods t Static transmission error of the working tooth surface at the moment; For gears in long periods t Static transmission error of the non-working tooth surface at the moment; For long period t At this moment, the first i The contact line j Manufacturing error of each contact point; For long period t At the moment, the first i The contact line j Manufacturing error of each contact point; For long period t At this moment, the first i The contact line j The amount of modification for each contact point; For long period t At the moment, the first i The contact line j The amount of modification for each contact point; For long period t The first tooth surface of the non-working gear at the timei The contact line j Manufacturing error of each contact point; For long period t The first non-working tooth surface of the driven gear at the time i The contact line j Manufacturing error of each contact point; For long period t The first tooth surface of the non-working gear at the time i The contact line j The amount of modification for each contact point; For long period t The first non-working tooth surface of the driven gear at the time i The contact line j The amount of modification for each contact point.

[0042] In one exemplary embodiment, according to the theoretical tooth side clearance of the gear pair, the static transmission error of the working tooth surface, and the static transmission error of the non-working tooth surface, the time-varying tooth side clearance of the gear pair is obtained, that is, the expression of the long-period time-varying tooth side clearance of the gear pair is:

[0043] In the formula, It is half of the theoretical tooth side clearance of the gear pair. When the manufacturing error and the long periodicity of the modification are taken into account, it is assumed that the manufacturing errors of each gear tooth are different, and the static transmission error is e wt and e nt The determination cycle can be repeated until a long period, that is, the long-period static transmission error is obtained. e wt and e nt .

[0044] S3, obtaining the bilateral meshing impact excitation of the gear pair; In one exemplary embodiment, the steps for obtaining the bilateral meshing impact excitation of a gear pair are as follows: according to the geometric relationship at the gear meshing line, the positions of the positive meshing impact point and the reverse meshing impact point of the gear pair are obtained; according to the positions of the meshing impact points, the corresponding meshing impact speed is obtained; according to the meshing impact speed, the rotational inertia of the gear and the base circle radius of the gear, the bilateral meshing impact energy is obtained; according to the bilateral meshing impact energy, the maximum impact force generated by the bilateral meshing is obtained; according to the maximum impact force, the bilateral meshing impact excitation of the gear pair is obtained; wherein, the bilateral meshing impact excitation includes: the impact generated by the positive meshing on the working tooth surface and the impact generated by the reverse meshing on the non-working tooth surface.

[0045] Exemplarily, according to the geometric relationship at the gear meshing line, the steps of obtaining the positions of the positive meshing impact point and the reverse meshing impact point of the gear pair are: that is, combining Figure 3 As shown in the figure, the positions of the positive and negative meshing impact points of the gear pair are calculated by using the triangle and Determine the impact point of the back meshing by the geometric relationship in P' Locations include: In the triangle The geometric relationship is:

[0046]

[0047]

[0048] in, r bi ( i =1, 2) is the base circle radius of the gear; is the gear pitch circle pressure angle; For the driving gear from the ideal positive meshing point P Move to the ideal back-meshing point P' Around the gear center O 1 The angle of rotation; is the geometric clearance angle when the driving gear is meshed in reverse; It is the geometric clearance angle of the driven gear when it is back-meshing. It refers to the deviation of the back-meshing point from the driven gear due to factors such as tooth surface manufacturing error, modification amount, and gear tooth deformation. P'' At the actual back-to-back meshing point P'' The ideal meshing point is opposite to the ideal P' Between gear center O 1 and O 2 The angle formed, k is the ratio of the base circle radius of the driving gear to the base circle radius of the driven gear, .

[0049] In the triangle The geometric relationship is:

[0050]

[0051]

[0052]

[0053] in,a is the actual center distance of the gear pair, , is the normal modulus, is the number of teeth of the driving gear, is the number of teeth of the driven gear, is the helix angle, is the center distance deviation of the gear pair; For the driven gear from the ideal positive meshing point P Move to the ideal back-meshing point P' Around the gear center O 2 The angle of rotation; For the gear pair in a long period t Half of the time-varying tooth backlash at time .

[0054] Exemplarily, the calculation methods of the forward impact excitation and the backward impact excitation are the same. The calculation steps of the impact excitation are given below by taking the backward meshing impact as an example: Calculate the gear back-meshing impact velocity based on the position of the meshing impact point :

[0055] in, is the angular velocity of the driving gear; is the rotational angular velocity of the driven gear; It is the reverse meshing point of the driving gear. P' Distance from the gear center of the driving gear O 1 distance; It is the back meshing point of the driven gear P' Distance from the gear center of the driven gear O 2 distance.

[0056] Impact energy of back engagement The expression is:

[0057] in, J 1 is the moment of inertia of the driving gear; J 2 is the moment of inertia of the driven gear.

[0058] The maximum impact force generated by the back-meshing impact energy is for:

[0059] in, At the back meshing pointP' The flexibility coefficient of a single meshing tooth of a gear pair.

[0060] The impact excitation is assumed to be a half-sine pulse excitation, and the impact excitation of the back meshing is calculated based on the maximum impact force. for:

[0061] in, is the circular frequency of the impact excitation; t b is the impact time, and its calculation formula is:

[0062] in, m e1 is the equivalent mass of the driving gear on the meshing line; m e2 is the equivalent mass of the driven gear on the meshing line. The calculation formula for the equivalent mass of the gear on the meshing line is:

[0063] in, ρ is the gear material density, b is the gear tooth width, r h1 is the radius of the shaft hole of the driving gear; r h2 is the shaft hole radius of the driven gear.

[0064] S4, construct the dynamic model of the gear system; Based on the time-varying tooth backlash and bilateral meshing impact excitation of the gear pair, a gear system dynamics model is constructed. Exemplary gear pair parameters are shown in Table 1.

[0065] Table 1

[0066] Preferably, the expression of the gear system dynamics model with time-varying tooth backlash and double-sided impact is:

[0067] in, is the mass matrix of the gear system; is the damping matrix of the gear system; is the stiffness matrix of the gear system; is the load torque vector external to the gear system; The impact excitation generated by positive meshing; Impact excitation generated by reverse meshing; b t For the gear pair in a long periodt Half of the time-varying backlash at time ; is the vibration acceleration of the gear in the direction of the meshing line; is the vibration speed of the gear in the direction of the meshing line; is the vibration displacement of the gear in the direction of the meshing line, and its expression is:

[0068] In the formula, Indicates driving gear x The vibration displacement in the direction Indicates driving gear y The vibration displacement in the direction Indicates driving gear z The vibration displacement in the direction Indicates driven gear x The vibration displacement in the direction Indicates driven gear y The vibration displacement in the direction Indicates driven gear z Vibration displacement in direction; Indicates the driving gear winding x The vibration displacement of the rotation direction, Indicates the driving gear winding y The vibration displacement of the rotation direction, Indicates the driving gear winding z The vibration displacement of the rotation direction, Indicates the driven gear winding x The vibration displacement of the rotation direction, Indicates the driven gear winding y The vibration displacement of the rotation direction, Indicates the driven gear winding z Vibration displacement of rotation direction. is the helix angle of the gear base circle; , is the gear meshing angle, For installation phase angle.

[0069] It should be noted that some calculation results of the nonlinear dynamic model of the gear system with time-varying tooth backlash and double-sided impact are shown in Figure 4 As shown, Figure 4 a is the vibration displacement response result diagram of gear accuracy level 4; Figure 4 b is the vibration displacement response result diagram of gear accuracy level 5; Figure 4 c is the vibration displacement spectrum of gear accuracy level 4; Figure 4 d is the vibration displacement spectrum of gear accuracy level 5; Figure 4 e is the vibration displacement velocity phase diagram of gear accuracy level 4; Figure 4f is the vibration displacement velocity phase diagram of gear accuracy level 5. Figure 4 It can be seen that the gear manufacturing error increases (the gear accuracy level decreases), the fluctuation of the system vibration displacement response caused by the time-varying tooth side clearance and bilateral meshing impact increases, more high-amplitude low-frequency vibration components appear in the spectrum, and the phase diagram trajectory becomes more complicated.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for dynamic modeling of a gear system with time-varying tooth backlash and double-sided impact, characterized in that: include: Obtain the theoretical tooth side clearance of the gear pair under the factors of tooth thickness deviation and center distance deviation; Based on the theoretical backlash of the gear pair, the time-varying backlash of the gear pair under the gear manufacturing error, modification amount and its long periodicity factors is obtained; Obtain the bilateral meshing impact excitation of the gear pair under the time-varying tooth backlash factor; Based on the time-varying tooth backlash and bilateral meshing impact excitation of the gear pair, a dynamic model of the gear system is constructed.

2. A gear system dynamics modeling method with time-varying tooth backlash and double-sided impact according to claim 1, characterized in that: The expression of the theoretical tooth backlash of a gear pair is: In the formula, It is half of the theoretical backlash of the gear pair; is the normal base circle pitch; is the normal base circle tooth thickness of the driving gear; is the normal base circle tooth thickness of the driven gear; is the base circle radius of the driving gear; is the base circle radius of the driven gear; is the gear meshing angle; is the base circle helix angle; .

3. A gear system dynamics modeling method with time-varying tooth backlash and double-sided impact according to claim 2, characterized in that: The expression of normal base circle pitch is: In the formula, is the end face modulus; is the end pressure angle.

4. The method for dynamic modeling of a gear system with time-varying tooth backlash and double-sided impact according to claim 2, characterized in that: The expression of the normal base circle tooth thickness of the gear is: In the formula, For gear The thickness of the base scallop of the French surface; is the normal modulus; is the tooth thickness deviation of the gear teeth; For gear The base circle radius; For gear The pitch circle radius; is the end pressure angle; where, =(1,2), When it is 1, it indicates the driving gear; When it is 2, it indicates the driven gear.

5. The method for dynamic modeling of a gear system with time-varying tooth backlash and double-sided impact according to claim 2, characterized in that: The expression of gear meshing angle is: In the formula, is the gear meshing angle; is the normal modulus; is the number of teeth of the driving gear; is the number of teeth of the driven gear; is the helix angle; is the center distance deviation of the gear pair.

6. The method for dynamic modeling of a gear system with time-varying tooth backlash and double-sided impact according to claim 1, characterized in that: The steps to obtain the time-varying backlash of a gear pair under gear manufacturing errors, modification amounts, and their long-periodic factors are: According to the manufacturing errors and modification amounts corresponding to the working tooth surface and the non-working tooth surface of the gear, the static transmission errors corresponding to the working tooth surface and the non-working tooth surface of the gear under the cycle to the preset long period are obtained; The time-varying tooth backlash of the gear pair is obtained according to the theoretical tooth backlash of the gear pair, the static transmission error of the working tooth surface and the static transmission error of the non-working tooth surface.

7. A gear system dynamics modeling method with time-varying tooth backlash and double-sided impact according to claim 6, characterized in that: The steps for obtaining the static transmission errors corresponding to the working tooth surface and the non-working tooth surface of the gear under the preset long cycle are as follows: Establish the meshing action surface of the working tooth surface of the gear pair and the meshing action surface of the non-working tooth surface; Arrange and number the contact lines and contact points of the meshing surfaces at equal intervals, and select the contact lines and contact points of the meshing gears at the same time according to the meshing principle and overlap; According to the manufacturing errors and modification amounts corresponding to the contact lines and contact points of the meshing gear teeth, the static transmission errors corresponding to the working tooth surface and the non-working tooth surface of the gear under the preset long cycle are obtained; Among them, the expression of the static transmission error of the working tooth surface of the gear under long period is: Among them, the expression of the static transmission error of the non-working tooth surface of the gear under long period is: In the formula, the subscript t Indicates a moment in a long period; For gears in long periods t Static transmission error of the working tooth surface at the moment; For gears in long periods t Static transmission error of the non-working tooth surface at the moment; For long period t At this moment, the first i The contact line j Manufacturing error of each contact point; For long period t At the moment, the first i The contact line j Manufacturing error of each contact point; For long period t At this moment, the first i The contact line j The amount of modification for each contact point; For long period t At the moment, the first i The contact line j The amount of modification for each contact point; For long period t The first tooth surface of the non-working gear at the time i The contact line j Manufacturing error of each contact point; For long period t The first non-working tooth surface of the driven gear at the time i The contact line j Manufacturing error of each contact point; For long period t The first tooth surface of the non-working gear at the time i The contact line j The amount of modification for each contact point; For long period t The first non-working tooth surface of the driven gear at the time i The contact line j The amount of modification for each contact point.

8. A gear system dynamics modeling method with time-varying tooth backlash and double-sided impact according to claim 7, characterized in that: The expression of the time-varying backlash of a gear pair is: In the formula, It is half of the theoretical backlash of the gear pair; b t For the gear pair in a long period t Half of the time-varying tooth backlash at time .

9. The method for dynamic modeling of a gear system with time-varying tooth backlash and double-sided impact according to claim 1, characterized in that: The steps to obtain the bilateral meshing impact excitation of a gear pair are: According to the geometric relationship at the gear meshing line, the positions of the positive meshing impact point and the reverse meshing impact point of the gear pair are obtained; Obtaining the corresponding meshing impact speed according to the position of the meshing impact point; Obtain the bilateral meshing impact energy based on the meshing impact speed, the gear's moment of inertia and the gear's base circle radius; The maximum impact force generated by the bilateral meshing is obtained according to the bilateral meshing impact energy; Obtain the bilateral meshing impact excitation of the gear pair according to the maximum impact force; The bilateral meshing impact excitation includes: the impact generated by the positive meshing on the working tooth surface and the impact generated by the negative meshing on the non-working tooth surface.

10. The method for dynamic modeling of a gear system with time-varying tooth backlash and double-sided impact according to claim 1, characterized in that: The expression of the dynamic model of the gear system with time-varying tooth backlash and double-sided impact is: in, is the mass matrix of the gear system; is the damping matrix of the gear system; is the stiffness matrix of the gear system; is the load torque vector external to the gear system; The impact excitation generated by positive meshing; Impact excitation generated by reverse meshing; b t For the gear pair in a long period t Half of the time-varying backlash at time ; is the vibration acceleration of the gear in the direction of the meshing line; is the vibration speed of the gear in the direction of the meshing line; is the vibration displacement of the gear in the direction of the meshing line, and its expression is: In the formula, Indicates driving gear x The vibration displacement in the direction Indicates driving gear y The vibration displacement in the direction Indicates driving gear z The vibration displacement in the direction Indicates driven gear x The vibration displacement in the direction Indicates driven gear y The vibration displacement in the direction Indicates driven gear z Vibration displacement in direction; Indicates the driving gear winding x The vibration displacement of the rotation direction, Indicates the driving gear winding y The vibration displacement of the rotation direction, Indicates the driving gear winding z The vibration displacement of the rotation direction, Indicates the driven gear winding x The vibration displacement of the rotation direction, Indicates the driven gear winding y The vibration displacement of the rotation direction, Indicates the driven gear winding z Vibration displacement of rotation direction. is the helix angle of the gear base circle; , is the gear meshing angle, For installation phase angle.

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