A method and system for analyzing vibration characteristics of a helical bevel gear meshing system

Abstract

The application discloses a kind of oblique-toothed bevel gear meshing system vibration characteristic analysis method and system, the method includes the following steps: obtaining the system parameter of orthogonal oblique-toothed bevel gear pair;According to the system parameter of orthogonal oblique-toothed bevel gear pair, the meshing vibration force between gears is obtained;The influence matrix of meshing gear pair is calculated by decomposing the meshing vibration force between gears combined with shear force, bending moment and torque balance equation;The relationship formula of state vector of two ends of shaft section is established according to the mechanical characteristics of shaft section, and the influence matrix of shaft section is obtained;The influence matrix of shaft section and the influence matrix of meshing gear pair are multiplied in turn, and the dynamic equation of the whole system is established;The dynamic equation is solved, and all critical speeds in the working speed range of gear system are obtained, and the vibration mode corresponding to the critical speed of gear transmission system is solved using the critical speed of gear transmission system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of gear nonlinear vibration analysis, and particularly relates to a kind of helical bevel gear meshing system vibration characteristic analysis method and system. BACKGROUND

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] The orthogonal bevel gear is a major direction-changing transmission device, and the vehicle main reducer is a typical bevel gear meshing system, which is a major component of the drive train and also a major vibration source of the vehicle. The existing gear meshing system vibration analysis still stays in the finite element modal analysis and the statistical energy estimation in the frequency domain through Fourier transform. The finite element method or Fourier transform method is calculated roughly, cannot reflect the influence of gear system parameters on critical speed, and cannot guide the design.

[0004] The safe working area of the gear transmission system with complex structure in the whole angular frequency domain is limited and regular. The existing method cannot quantitatively analyze and divide it, and cannot conveniently change the gear parameters. The research and comparison of various forms of gear combinations can be carried out to analyze the vibration characteristics of the gear meshing system in detail in the research and development stage before mass production, and used to guide the optimization design.

[0005] The finite element method is a static calculation, which reflects the static vibration characteristics of the system, and cannot reflect the vibration characteristics caused by the speed of the whole system. The Fourier transform estimation method based on statistical energy spectrum analysis is biased towards using the calculation results to prove the effectiveness of the improvement measures, but cannot reflect the specific effect of the change of various parameters. SUMMARY

[0006] To overcome the shortcomings of the prior art, the present application provides a helical bevel gear meshing system vibration characteristic analysis method, which quantitatively calculates the vibration characteristics of the vehicle main reducer according to its structural characteristics, and is used to guide the parameter optimization and improve the vehicle vibration problem.

[0007] To achieve the above purpose, one or more embodiments of the present application provide the following technical solutions:

[0008] A helical bevel gear meshing system vibration characteristic analysis method, comprising the following steps:

[0009] Obtaining the system parameters of the orthogonal helical bevel gear pair;

[0010] Obtaining the meshing vibration force between gears according to the system parameters of the orthogonal helical bevel gear pair;

[0011] The influence matrix of the meshing gear pair is calculated by decomposing the meshing vibration force of the gear pair and combining the shear force, bending moment and torque balance equation;

[0012] The relationship of the state vectors at both ends of the shaft segment is established according to the mechanical properties of the shaft segment to obtain the influence matrix of the shaft segment;

[0013] The dynamic equation of the whole system is established by sequentially multiplying the influence matrix of the shaft segment and the influence matrix of the meshing gear pair;

[0014] The dynamic equation is solved to obtain all critical speeds in the working speed range of the gear system, and the vibration mode corresponding to each critical speed of the gear transmission system is obtained by using the critical speed of the gear transmission system.

[0015] According to the vibration mode corresponding to the critical speed of the gear transmission system, different vibration modes and characteristics of the meshing gear system are studied and summarized, so as to systematically guide the design of the gear system.

[0016] Further, the system state vector includes the generalized force and displacement vectors of the orthogonal helical and bevel gear pair.

[0017] Further, the meshing vibration force between gears is F=k*d, wherein k is the tooth stiffness, and d is the vibration displacement in the meshing force direction.

[0018] Further, the accurate expression of the vibration displacement d in the meshing force direction of the two gears in the space Cartesian coordinate system is:

[0019]

[0020] wherein x i represents the X-direction component of the shaft center vibration displacement, R i represents the pitch circle radius, represents the torsion angle, y i represents the Y-direction component of the shaft center vibration displacement, δ j represents the conical angle, θ i represents the deflection angle, z i represents the Z-direction component of the shaft center vibration displacement, α represents the pressure angle, and β represents the helix angle, wherein i=A or B, and j=1 or 2.

[0021] Further, the decomposition of the meshing vibration force is as follows: a space Cartesian coordinate system is established with the meshing force action point as the origin, the Z-axis positive direction is directed to the large end of the driving gear A from the intersection of the two shafts, and the Y-axis positive direction is directed to the large end of the driven gear B; the self-rotation angular velocity of the driving gear is along the Z-axis negative direction, the self-rotation angular velocity of the driven gear is along the Y-axis positive direction; the linear velocity direction of the driving gear at the meshing point is the X-axis positive direction;

[0022] the conical top angle of the driving gear is δ1, the conical top angle of the driven gear is δ2, the shaft angle is ∑, and δ2=∑-δ1.

[0023] Further, the shear force, bending moment and torque balance equations are the differences of the shear force, bending moment and torque on both sides of the gear disc respectively.

[0024] Further, the shear force difference on both sides of the gear disc is the vector sum of the meshing vibration force and the radial component of the gear revolution centrifugal force;

[0025] The bending moment difference on both sides of the gear disc is the vector sum of the gear revolution inertia bending moment and the bending moment generated by the meshing vibration force;

[0026] The torque difference on both sides of the gear disc is the vector sum of the axial torque generated by the circumferential component of the meshing vibration force and the inertia torque generated by the gear revolution.

[0027] One or more embodiments provide a helical bevel gear meshing system vibration characteristic analysis system, comprising:

[0028] A system parameter acquisition module configured to acquire system parameters of the orthogonal helical bevel gear pair;

[0029] A vibration force calculation module configured to obtain the inter-gear meshing vibration force according to the system parameters of the orthogonal helical bevel gear pair;

[0030] A vibration force decomposition module configured to calculate the influence matrix of the meshing gear pair by decomposing the inter-gear meshing vibration force in combination with the shear force, bending moment and torque balance equations;

[0031] An influence matrix of the shaft segment is obtained according to the relationship between the state vectors at both ends of the shaft segment;

[0032] A dynamic equation construction module configured to multiply the influence matrix of the shaft segment and the influence matrix of the meshing gear pair in sequence to establish the dynamic equation of the entire system;

[0033] A vibration mode output module configured to solve the dynamic equation to obtain all critical speeds in the working speed range of the gear system, and to solve the vibration mode corresponding to the critical speed of the gear transmission system by using the critical speed of the gear transmission system.

[0034] One or more embodiments provide a computer device, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the steps of any one of the helical bevel gear meshing system vibration characteristic analysis methods described above.

[0035] One or more embodiments provide a computer readable storage medium having a computer program stored thereon, wherein the program is executed by a processor to implement the steps of any one of the helical bevel gear meshing system vibration characteristic analysis methods described above.

[0036] The above one or more technical solutions have the following beneficial effects:

[0037] (1) The present application can conveniently change gear parameters and compare and analyze the vibration characteristics of gear engagement system. In addition to being effective for single rotor system, it can quantitatively study different gear forms, arrangement modes and linkage states. The safe working area of a certain rotor system with fixed structure in the entire angular frequency domain is limited and regular. The calculation method and program of the present application can quantitatively analyze it, which is obviously superior to the calculation of finite element method and makes up for the defects of the previous fuzzy estimation of Fourier transform and static calculation of finite element method.

[0038] (2) The vibration characteristics of the gear system formed by gear engagement are much more complex than single rotor, and the system has more coupled critical speeds, which cannot be defined and measured by other calculation methods.

[0039] (3) The present application introduces the coefficient matrix of shaft section and organically integrates it with gear parameters.

[0040] (4) The present application calculates the inherent critical speed of the gear engagement system including vehicle main reducer and aero-engine. It makes up for the shortcomings of previous calculation methods and can obtain quantitative and accurate calculation results, and can be used to study the influence of various parameters on the inherent critical speed of the system to guide the design and make the vibration of the gear system controllable.

[0041] (5) The present method and software couple the gear system through the engagement vibration force containing gear specific parameters to solve the critical speed of the whole system, which is fast, non-divergent and accurate and stable. BRIEF DESCRIPTION OF DRAWINGS

[0042] The drawings accompanying the specification of the present application form a part thereof and serve to provide further understanding of the present application, the exemplary embodiments of which and its description serve to explain the present application and do not constitute an improper limitation thereof.

[0043] Figure 1 The whole analysis flowchart in the embodiment of the present application is shown in the figure;

[0044] Figure 2 The main reducer physical diagram in the embodiment of the present application is shown in the figure;

[0045] Figure 3 The engagement vibration force decomposition diagram of the orthogonal conical gear in the embodiment of the present application is shown in the figure;

[0046] Figures 4(a)-4(b) The gear disc shear force balance diagram in the embodiment of the present application is shown in the figure;

[0047] Figure 5 This is a torque diagram of the gear disk gyroscope described in an embodiment of the present invention;

[0048] Figures 6(a)-6(b) This is the bending moment balance diagram of the gear disk described in this embodiment of the invention;

[0049] Figure 7 This is the torque balance diagram of the gear disk described in the embodiment of the present invention;

[0050] Figures 8(a)-8(b) This refers to the positive definition of the shear force on the shaft segment described in this embodiment of the invention;

[0051] Figures 9(a)-9(b) This refers to the positive definition of the bending moment on the shaft segment described in this embodiment of the invention;

[0052] Figure 10 This is the positive definition of the deflection angle on the shaft segment in the embodiments of the present invention. Detailed Implementation

[0053] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0054] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0055] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0056] Example 1

[0057] like Figure 1 As shown in the figure, this embodiment discloses a method for analyzing the vibration characteristics of a helical bevel gear meshing system, including the following steps:

[0058] Step 1: Obtain the system parameters of the orthogonal helical bevel gear pair;

[0059] The gear system parameters include: gear mass, moment of inertia, polar moment, pitch circle radius, tooth stiffness, pressure angle, helix angle, cone angle, shaft length, shaft diameter, cross section moment of inertia of the shaft, Young's modulus of elasticity, and bearing stiffness.

[0060] The parameters include generalized force and displacement vectors of the orthogonal helical bevel gear pair, the generalized force includes shear force, bending moment, torque, and the displacement includes relative displacement of shaft center, deflection angle, torsion angle, etc.

[0061] In the embodiment, the positive direction of shear force and bending moment is different from the definition in material mechanics, the positive direction of force and torque along the coordinate axis is positive, and the bending moment and torque should strictly follow the right-hand rule.

[0062] The correct analysis of the gear coefficient matrix is the feature of the method, and the key is the decomposition of the meshing force and the accurate expression of the vibration displacement in the direction of the meshing force;

[0063] Step 2: Obtain the meshing vibration force between gears according to the generalized force and displacement vectors of the orthogonal helical bevel gear pair;

[0064] The meshing vibration force between gears is F=k*d, wherein k is the gear stiffness, and d is the vibration displacement in the direction of the meshing force.

[0065] The accurate expression of the vibration displacement d in the direction of the meshing force between the two gears is:

[0066]

[0067] The vibration displacement d in the direction of the meshing force is a superimposed quantity, x i represents the X-direction component of the shaft center vibration displacement, R i represents the pitch circle radius, represents the torsion angle, y i represents the Y-direction component of the shaft center vibration displacement, δ j represents the split cone angle, θ i represents the deflection angle, z i represents the Z-direction component of the shaft center vibration displacement, α represents the pressure angle, and β represents the helix angle, wherein i=A or B, and j=1 or 2.

[0068] The vibration displacement d in the direction of the meshing force is determined by the relative displacement of the two shaft centers, the deflection angle, and the torsion angle, and is also affected by the gear parameters, i.e., the pressure angle, the helix angle, the split cone angle, the pitch circle radius, etc.

[0069] Step 3: Calculate the meshing gear pair by decomposing the meshing vibration force and combining the shear force, bending moment, and torque balance equation.

[0070] Step 3-1: As shown in Figure 3 the decomposition of the meshing vibration force is as follows:

[0071] A rectangular coordinate system is established with the engagement force action point as the origin, and the Z-axis positive direction is defined as pointing from the intersection of the two shafts to the large end of the driving wheel A, and the Y-axis positive direction is defined as pointing to the large end of the driven wheel B; the driving wheel self-rotation angular velocity is along the z-axis negative direction, the driven wheel self-rotation angular velocity is along the Y-axis positive direction; the linear velocity direction of the driving wheel at the engagement point is the X-axis positive direction. The driving wheel cone top angle is δ1, the driven wheel cone top angle is δ2, the shaft angle is ∑, and δ2 = ∑ - δ1;

[0072] When ∑ = 90°, it is a normal transmission. The helix angle is defined as that, when viewed from the cone top, the tooth trace rotates counterclockwise from the small end to the large end, and the left-handed rotation is negative.

[0073]

[0074] The following considers the influence of the meshing vibration force on the shear force, bending moment and torque on both sides of the gear disc. Due to the whirl, the mass of the gear disc will generate a centrifugal force, which acts on the shaft together with the meshing force. Let Ω represent the rotation speed of the rotor, and when the vibration starts, Ω = ω, at this time the shaft is in small deflection deformation, that is, the small deformation whirl at the beginning of the precession.

[0075] Step 3-2: According to the shear force difference on both sides of the gear, the torque balance equation is obtained, which is the vector sum of the meshing vibration force and the radial component of the gear rotation centrifugal force, where m A and m B are the masses of the two gears, F Ax and F Bx are the X-direction components of the meshing vibration forces acting on the two gears, F Ay is the Y-direction component of the meshing vibration force acting on the driving wheel, and F Bz is the Z-direction component of the meshing vibration force acting on the driven wheel.

[0076]

[0077]

[0078]

[0079]

[0080] Figures 4(a)-4(b) Q R in the direction shown is the counterforce of the right disc to the disc, and the force of the disc to the right disc is the relationship between the action force and the counterforce, and the direction of the force of the disc to the right disc is still along the positive direction of the coordinate axis.

[0081] Wherein, Q L is the force of the left disc to the disc, mΩ 2 x and mΩ 2 y are two components of the inertial centrifugal force of the disc along the x and y axes, F x and Fy are two components of the meshing force.

[0082] Step 3-3: According to the bending moment difference of the gear plate on both sides, the balance equation of the bending moment is obtained, which is the vector sum of the gear revolution inertia bending moment and the bending moment generated by the meshing vibration force. Where I d A and I d B are the principal rotational inertia of the two gears, respectively. p A and I p B are the polar rotational inertia of the two gears, respectively.

[0083]

[0084]

[0085]

[0086]

[0087] Where the inertia bending moment generated by the gear vibration revolution angular velocity Ω is specifically:

[0088] A rectangular coordinate system is established as Figure 5 oζ, oξ1 and oη1 are three central inertia principal axes of the gear plate, and the fixed point rotation of the gear plate around the original symmetry axis is described by three Euler angles, first rotating around oy axis by μ(t) with angular velocity ; then rotating around oξ1 axis by ν(t) with angular velocity ; and then rotating around oζ axis by φ(t) with angular velocity ω. The angular velocity projection along oy axis onto oη1 axis is Since μ and ν are very small at the start of vibration, cosμ≈1, cosν≈1; sinμ≈μ, sinν≈ν. The angular momentum along oη1 axis is along oξ1 axis is and along oζ axis is I p ω, the projections onto ox and oy axes are:

[0089]

[0090]

[0091] Where the rotational inertia of the gear plate around oζ axis is I p , the rotational inertia around oξ1 and oη1 is I d , μ≈Θ Y cos(-Ωt)=θ y , ν≈Θ Xsin(-Ωt) = θ x .

[0092] where the bending moment generated by the meshing vibration force is specifically:

[0093] As Figures 6(a)-6(b) , according to the relative center of mass moment of momentum theorem, the derivation is the inertia moment. According to the D'Alembert principle, the inertia moment provides a negative moment to the shaft, and thus the inertia bending moment of the gear disc revolution to the shaft is obtained:

[0094]

[0095]

[0096] When the driving wheel A does synchronous positive precession, its rotational angular velocity is negative, and the precession angular velocity is also negative. At this time, the driven wheel B is counter-precession, and its rotational angular velocity is positive.

[0097] The bending moment difference on both sides of the gear disc is the vector sum of the gear revolution inertia bending moment and the bending moment generated by the meshing vibration force. According to this, the balance equation of the bending moment can be obtained.

[0098] Step 3-4: As Figure 7 indicated, the balance equation of the torque is obtained according to the torque difference on both sides of the gear disc, and the torque difference on both sides of the gear disc is the vector sum of the axial torque generated by the circumferential component of the meshing vibration force and the inertia torque generated by the gear revolution.

[0099]

[0100]

[0101] Step 3-5: According to the meshing vibration force combined with the shear force, the bending moment and the torque balance equation, the state vector of the meshing gear pair is calculated [Z A Z B ] T ;

[0102] where,

[0103] where, Z A is the state vector of the driving wheel, Z B is the state vector of the driven wheel. Q Ax is the X-direction component of the shear force on both sides of the driving wheel, M Ay is the Y-direction component of the bending moment on both sides of the driving wheel, Q Ay is the Y-direction component of the shear force on both sides of the driving wheel, M Ax is the X-direction component of the bending moment on both sides of the driving wheel, T A is the axial torque on both sides of the driving wheel, θ AyY component of the deflection angle generated by the driving wheel, x A X component of the displacement of the driving wheel's axis, θ Ax X component of the deflection angle generated by the driving wheel, y A Y component of the displacement of the driving wheel's axis, Axial torsion angle of the driving wheel. Q Bx X component of the shear force on both sides of the driven wheel, M Bz Z component of the bending moment on both sides of the driven wheel, Q Bz Z component of the shear force on both sides of the driven wheel, M Bx X component of the bending moment on both sides of the driven wheel, T B Axial torque on both sides of the driven wheel, θ Bz Z component of the deflection angle generated by the driven wheel, x B X component of the displacement of the driven wheel's axis, θ Bx X component of the deflection angle generated by the driven wheel, z B Z component of the displacement of the driven wheel's axis, Axial torsion angle of the driven wheel.

[0104] The generalized force includes shear force, bending moment, and torque, and the generalized displacement includes axial relative displacement, deflection angle, and torsion angle.

[0105] Step 4: Obtain the influence matrix of the shaft segment by establishing the relationship between the state vectors at both ends of the shaft segment according to the mechanical properties of the shaft segment;

[0106] The forward definition of the shear force, bending moment, and deflection angle of the shaft segment should also comply with the right-hand rule, which is different from the definition in material mechanics. The shear force in the direction shown in Figures 8(a)-8(b) is defined as positive; the bending moment in the direction shown in Figures 9(a)-9(b) is defined as positive, and the deflection angle in the direction shown in Figure 10 is defined as positive.

[0107] The relationship between the parameters at both ends of the shaft segment includes:

[0108]

[0109] In the formula, u 11 and u 12 are the deflections caused by unit shear force and bending moment, u 21 and u 22 are the rotation angles caused by unit shear force and bending moment. Among them, u 11 = l 3 / 3EJ, u 12 = u 21 = l 2 / 2EJ, u 22 = l / EJ.

[0110] Transforming, we obtain the equation group with only initial cross-section state parameters on the right side:

[0111]

[0112] Further, let w1 = u 12 l-u 11 , w2 = u 22 l-u 21 , we obtain the influence matrix of the shaft segment:

[0113]

[0114] If the shaft segment matrix is incorrect, according to the uncoupling critical speed value and the single-rotor counter-precession critical speed value, we can determine whether the shaft segment matrix is correct. If they are consistent, the shaft segment matrix is correct; otherwise, it is incorrect. According to the calculation results, the low-order critical speed value is highly sensitive to the shaft length, and rapidly decreases with the increase of the shaft length, which is completely consistent with the actual situation.

[0115] Step 5: Multiply the influence matrix of the shaft segment with the influence matrix of the meshing gear pair in sequence to establish the overall transfer matrix of the entire transmission system to obtain the dynamic equation;

[0116] The generalized displacement of all continuous points of the gear system is continuous, i.e., the dynamic equation group satisfies the displacement continuity condition,

[0117]

[0118] Extract the coefficients of the above displacement variables to form the contribution matrix:

[0119]

[0120]

[0121] Further, we obtain the coefficient matrix T C of the gear system;

[0122]

[0123] wherein, T 11 = T 22 = T 33 = T 44 = E, T 13 = T 21 = T 23 = T 24 = T 31 = T 41 = T 42 = T 43 = 0.

[0124] Step 6: According to the dynamic equation, all critical speeds in the working speed range of the gear system are obtained, and the critical speed of the gear transmission system is solved to further obtain the vibration mode corresponding to the critical speed of the gear transmission system.

[0125] The coefficient matrix of the gear system is solved, the characteristic value is obtained, and the characteristic vector is obtained according to the characteristic value, that is, the ratio of the generalized displacement, that is, the vibration mode.

[0126] When the working speed of the system reaches the critical speed, the vibration displacement vector group of the gear system will gradually increase with a certain proportion (vibration mode) over time, forming resonance.

[0127] Compared with a single rotor, the gear meshing system has more coupled critical speeds, which is reflected in that due to the existence of axial orthogonality and gear split cone angle, the meshing vibration force changes the vibration characteristics of the gear in the axial and circumferential directions, that is, the bending and torsional vibration characteristics, and the whole system generates new coupled critical speeds.

[0128] The gear meshing stiffness changes continuously within a certain range with the change of load, so that the coupled critical frequency is no longer a frequency point but a frequency band distribution, so the critical speed distribution of the gear meshing system is much more complex than that of a single rotor, and it is more prone to vibration. For an asymmetric rotor meshing system, the coupled frequency will be multiplied, and if it is transmitted through multiple shafts, the critical speed of the whole system will be distributed discretely in a wide range, and will present a frequency band characteristic at each discrete point with the continuous change of the meshing stiffness. Different gear forms, arrangement methods and linkage states show different characteristics. Therefore, in the whole angular frequency domain, the safe working area of a rotor system with a fixed structure is limited and regular. The application can be used to guide parameter optimization design, which cannot be achieved by other calculation methods, and the prior art only generally verifies whether an improvement measure is effective.

[0129] The above can easily change the gear parameters, and various forms of gear combinations can be studied and compared. The vibration characteristics of the gear meshing system can be analyzed in detail in the research and development stage before mass production, and used to guide optimization design. In these aspects, the method is obviously superior to the finite element method, which is a static calculation and reflects the static vibration characteristics of the system, and cannot reflect the vibration characteristics caused by the speed of the whole system. It is also superior to the Fourier transform estimation method based on statistical energy spectrum analysis of the vibration characteristics of the gear system in the past, which focuses on using the calculation results to prove the effectiveness of the improvement measures, but cannot reflect the specific effect of the change of various parameters. The method couples the gear system through the meshing vibration force containing the specific parameters of the gear, compiles a multi-degree-of-freedom solving program, and further obtains the critical speed of the whole system, which is fast, non-oscillating, numerically stable and accurate.

[0130] Embodiment Two

[0131] The embodiment provides a vibration characteristic analysis system of a helical bevel gear meshing system, comprising:

[0132] a system parameter acquisition module configured to acquire system parameters of the orthogonal helical bevel gear pair;

[0133] a vibration force calculation module configured to obtain meshing vibration force between gears according to the system parameters of the orthogonal helical bevel gear pair;

[0134] a vibration force decomposition module configured to calculate an influence matrix of the meshing gear pair by decomposing the meshing vibration force between gears in combination with shear force, bending moment and torque balance equations;

[0135] an influence matrix of the shaft section is obtained by establishing a relationship between state parameters at two ends of the shaft section according to the mechanical characteristics of the shaft section;

[0136] a dynamic equation construction module configured to multiply the influence matrix of the shaft section and the influence matrix of the meshing gear pair in sequence to establish a dynamic equation of the whole system;

[0137] a vibration mode output module configured to solve the dynamic equation to obtain all critical speeds in a working speed range of the gear system, and solve a vibration mode corresponding to the critical speed of the gear transmission system by using the critical speed of the gear transmission system.

[0138] Embodiment Three

[0139] The embodiment of the present specification provides a computer device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the program to realize the steps of the vibration characteristic analysis method of the helical bevel gear meshing system in embodiment one.

[0140] Embodiment Four

[0141] The embodiment of the present specification provides a computer readable storage medium, which stores a computer program, and the program is characterized in that the program is executed by a processor to realize the steps of the vibration characteristic analysis method of the helical bevel gear meshing system in embodiment one.

[0142] Those skilled in the art should understand that the above-mentioned modules or steps of the present application can be realized by a general computer device, alternatively, they can be realized by program codes executable by a computing device, so that they can be stored in a storage device and executed by a computing device, or they can be respectively manufactured into individual integrated circuit modules, or a plurality of modules or steps among them can be manufactured into a single integrated circuit module to realize. The present application is not limited to any specific combination of hardware and software.

[0143] The above merely provides the preferred embodiments of the present application, but is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the principles and technical solutions of the present application shall fall into the protection scope of the present application.

[0144] The above merely provides the preferred embodiments of the present application, but is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the principles and technical solutions of the present application shall fall into the protection scope of the present application.

Claims

1. A method of analyzing vibration characteristics of a helical gear meshing system, characterized by, The method comprises the following steps: obtaining system parameters of the orthogonal helical bevel gear pair; obtaining meshing vibration force between gears according to the system parameters of the orthogonal helical bevel gear pair; Vibrational displacement in the direction of the meshing force of two gears d The exact expression for this is: wherein represents the abscissa, represents the pitch radius, represents the torsion angle, represents the ordinate, represents the sector angle, represents the deflection angle, represents the Z-component of the axial vibration displacement, represents the pressure angle, represents the helix angle, wherein = A or B, = 1 or 2; calculating an influence matrix of the meshing gear pair by decomposing the meshing vibration force and combining shear force, bending moment and torque balance equations; the decomposition of the meshing vibration force is as follows: taking the meshing force action point as the origin, establishing a rectangular coordinate system, with the intersection of the two shafts pointing to the large end of the driving gear as the positive direction of the Z axis and the large end of the driven gear as the positive direction of the Y axis; the self-rotation angular velocity of the driving gear is along the negative direction of the Z axis, and the self-rotation angular velocity of the driven gear is along the positive direction of the Y axis; the linear velocity direction of the driving gear at the meshing point is the positive direction of the X axis; The cone top angle of the driving wheel is The cone top angle of the driven wheel is The shaft angle is , ; establishing a relationship between state vectors at both ends of the shaft section according to the mechanical properties of the shaft section to obtain an influence matrix of the shaft section; and multiplying the influence matrix of the shaft section and the influence matrix of the meshing gear pair in sequence to establish a dynamic equation of the whole system; solving the dynamic equation to obtain all critical speeds within the working speed range of the gear system, and solving the vibration mode corresponding to the critical speed of the gear transmission system by using the critical speed of the gear transmission system.

2. A method of analyzing the vibration characteristics of a helical gear system as set forth in claim 1, characterized in that, The system parameters include generalized force and displacement vectors of the orthogonal helical bevel gear pair.

3. A method of analyzing the vibration characteristics of a helical gear system as set forth in claim 1, characterized in that, The inter-gear meshing vibration force is wherein, is the gear stiffness, is the vibration displacement in the direction of the gear meshing force.

4. A method of analyzing the vibration characteristics of a helical gear system as set forth in claim 1, wherein The shear force, bending moment and torque balance equations are respectively the shear force, bending moment and torque differences on both sides of the gear disc.

5. A method of analyzing the vibration characteristics of a helical gear system as set forth in claim 1, characterized in that, The shear force difference on both sides of the gear disc is the vector sum of the meshing vibration force and the radial component of the gear revolution centrifugal force; The bending moment difference on both sides of the gear disc is the vector sum of the gear revolution inertia bending moment and the bending moment generated by the meshing vibration force; The torque difference on both sides of the gear disc is the vector sum of the torque along the axial direction generated by the circumferential component of the meshing vibration force and the inertia torque generated by the gear revolution.

6. A helical bevel gear meshing system vibration characteristic analysis system, which adopts the vibration characteristic analysis method according to any one of claims 1-5, characterized in that: a system parameter acquisition module configured to obtain system parameters of the orthogonal helical bevel gear pair; a vibration force calculation module configured to obtain meshing vibration force between gears according to the system parameters of the orthogonal helical bevel gear pair; a vibration force decomposition module configured to calculate an influence matrix of the meshing gear pair by decomposing the meshing vibration force and combining shear force, bending moment and torque balance equations; an influence matrix of a shaft section is obtained according to a relationship between state vectors at both ends of the shaft section; a dynamic equation construction module configured to multiply the influence matrix of the shaft section and the influence matrix of the meshing gear pair in sequence to establish a dynamic equation of the whole system; a vibration mode output module configured to solve the dynamic equation to obtain all critical speeds within the working speed range of the gear system, and solve the vibration mode corresponding to the critical speed of the gear transmission system by using the critical speed of the gear transmission system.

7. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the helical bevel gear meshing system vibration characteristic analysis method according to any one of claims 1-5.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the steps of the helical bevel gear meshing system vibration characteristic analysis method according to any one of claims 1-5.

Images