A gear wear uniformity identification method based on gearbox body vibration response

Abstract

The application provides a gear wear uniformity identification method based on gear box vibration response characteristics. The constraint relationship in each element of the gear box in the actual operation process is analyzed, the description mode of the system boundary condition is determined, and a rigid-flexible coupling model containing the gear box body and the gear transmission system is established. The dynamic meshing stiffness of the uniform and non-uniform wear gears is calculated by using a numerical calculation method, a system dynamics calculation model is constructed, the influence degree of different wear modes on the gear meshing stiffness and the wear amount is quantitatively evaluated, the gear meshing force and the box vibration response law under the uniform and non-uniform wear are obtained in combination with the rigid-flexible coupling model, a simulation test bench is built, the gear box vibration signals are collected and the features are extracted, and the wear uniformity identification is realized. The gear box dynamic model is established by using the rigid-flexible coupling method and the numerical calculation comprehensive method, the change of the meshing stiffness and the wear amount and the mutual influence of the shell and the transmission system are considered, and the gear wear uniformity can be accurately calculated.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology for mechanical transmission systems, specifically relating to a method for identifying the uniformity of gear wear during the dynamic transmission of internal excitation in a mechanical system. Background Technology

[0002] Gearboxes, as the most crucial power transmission system in an engine, are a key focus of mechanical dynamics research. Failure types in multi-stage gear transmission systems include tooth breakage, plastic deformation, and tooth surface contact fatigue wear. Among these, tooth surface contact fatigue wear accounts for the highest proportion (over 60%), and severe wear can lead to tooth breakage. Failure of critical components inevitably affects other mechanisms; if not prevented and eliminated in a timely manner, the probability of potential risks increases significantly, potentially leading to the collapse of the entire unit and causing catastrophic accidents. Therefore, effectively capturing the response changes caused by dynamic wear of gears is of great significance for ensuring the long-term safe operation of the unit.

[0003] Currently, research on the dynamic response of gear systems under continuous wear processes is relatively limited, and changes in gear dynamic characteristics caused by variations in the wear location of uniform and non-uniform gears are not considered. Therefore, given the unclear dynamic response law of gear systems due to tooth surface wear, this study, based on a rigid-flexible coupling model and combining numerical calculations and finite element analysis, investigates the influence of meshing stiffness and cumulative wear on the system's dynamic response under different wear modes. The study yields the variation law of gear meshing stiffness and the trend of dynamic characteristic changes under different wear fault states. Summary of the Invention

[0004] The purpose of this invention is to provide an effective method for identifying wear uniformity in the analysis of early wear fault diagnosis. Based on the gearbox vibration acceleration signal, the invention extracts the envelope feature frequency domain features, which can quantitatively and accurately evaluate the vibration response and wear uniformity of the internal excitation in the gear system. It can also be used for fault mechanism analysis and research, which is of great significance for fault tracing of mechanical systems.

[0005] The objective of this invention is achieved through the following technical solutions: First, the constraint relationships among the components of the gearbox during actual operation are analyzed to determine the description method of the system boundary conditions, and a rigid-flexible coupling model including the gearbox body and the gear transmission system is established. Then, numerical calculation methods are used to calculate the dynamic meshing stiffness of uniformly and non-uniformly worn gears, constructing a system dynamics calculation model to obtain a quantitative evaluation of the influence of different wear modes on gear meshing stiffness and wear amount. Combined with the rigid-flexible coupling model, the gear meshing force and gearbox vibration response laws under uniform and non-uniform wear are obtained. Finally, a simulation test bench is built to collect gearbox vibration signals and extract features to achieve gearbox wear uniformity identification.

[0006] A method for identifying gear wear uniformity based on gearbox vibration response, characterized by comprising the following steps:

[0007] 1) Establish a rigid-flexible coupled multibody dynamics simulation model of the gearbox transmission system: obtain the characteristic parameters and initial operating parameters of the transmission gearbox; determine the motion constraint relationship between each component and the description method of the gear / box boundary conditions based on the characteristic parameters and initial operating parameters; establish a rigid-flexible coupled multibody dynamics model of the gearbox transmission system based on the constraint relationship and the description method of each boundary.

[0008] 2) Calculate the dynamic meshing stiffness under uniform and non-uniform wear: The dynamic meshing stiffness of gears with uniform and non-uniform wear is calculated by analytical method to obtain the quantitative results of the influence of different wear modes on gear meshing stiffness and wear amount.

[0009] 3) Characteristic analysis of gear meshing force / box vibration under uniform and non-uniform conditions: In step 1), the gear meshing contact element is input into the gear meshing stiffness transformation curve calculated in step 2) as the internal excitation; select vibration measurement points, generally selecting points close to the vibration source excitation as vibration measurement points, and monitor the meshing force / vibration acceleration signals before and after the application of the internal excitation force at the gear / box interface; the vibration measurement points are arranged on the interface above the speed-increasing gear / box axle hole, and the measured vibration acceleration signals are all in the direction of gravity;

[0010] 4) Acquisition of actual gearbox vibration signals and identification of gear wear uniformity: A simulation test bench is built to acquire gearbox vibration signals and extract features to achieve gearbox wear uniformity identification.

[0011] In step 1), the characteristic parameters include the geometric parameters and material properties of the gearbox's speed-increasing spur gear, shaft, and housing. The geometric parameters are obtained from the drawing files of the gear, shaft, and housing. The material properties include at least the material grade and mechanical properties of the gear, shaft, and housing. A three-dimensional model of the gearbox is established based on the geometric parameters in the drawing files. This three-dimensional model is then imported into multibody dynamics analysis software to establish a multibody dynamics model. All imported components are considered rigid bodies. Constraints are established between the components according to their kinematic relationships: a fixed constraint exists between the gear and its mating shaft; a rotational constraint exists between the shaft and the housing about the z-axis; and a fixed constraint exists between the housing and the ground. Bearing contact is added between the shaft and the housing to simulate bearing damping and stiffness. Based on Hertz contact theory, the expression for the normal contact force between the contacting components is as follows:

[0012]

[0013] In the formula, k is the contact stiffness coefficient; c is the damping coefficient; and δ is the contact penetration depth. is the derivative of the contact penetration depth; m1, m2, and m3 are the stiffness exponent, damping exponent, and dent exponent, respectively. Based on the materials of the shaft and body, contact parameters are selected according to relevant material contact parameters. Contact pairs are added between the meshing gears to simulate gear meshing constraints, and gear meshing stiffness is set. The target gear, transmission shaft, and gearbox are made flexible, while other components remain rigid. The key components are meshed using finite element software, preferably using a four-node tetrahedral element structure. A mass element is created at the center of the shaft hole, with the center node as the master node and points on the hole surface as slave nodes, creating a rigid connection. A flexible bearing containing model node, material, and element type information is imported into multibody dynamics software to replace the original rigid element, achieving rigid-flexible coupling. The rigid-flexible coupling model is then established. The model's driving form is torque around the drive shaft axial direction, and the load form is torsional damping around the power output gear.

[0014] In step 2), the formula for calculating the gear meshing stiffness considering wear uniformity is expressed as:

[0015]

[0016] In the above formula, k h For the contact stiffness of the driving wheel, k b1 k is the bending stiffness of the driving gear teeth. s1 k is the shear stiffness of the driving wheel teeth. a1 k is the axial compressive stiffness of the drive wheel. f1 k represents the elastic stiffness of the drive wheel base. b2 k is the bending stiffness of the passive gear teeth. s2 k is the shear stiffness of the passive wheel teeth. a2 k is the axial compressive stiffness of the passive wheel. f2 This refers to the elastic stiffness of the passive wheel base.

[0017] Where, k h The calculation formula is expressed as:

[0018]

[0019] In the above formula, E is the elastic modulus; ν is Poisson's ratio; and L is the tooth width.

[0020] The formulas for calculating kb, ks, and ka are expressed as follows:

[0021]

[0022]

[0023]

[0024] In the above formula, N is the number of teeth, hw To represent the amount of wear at the meshing point A on the tooth profile at coordinate x, R b Let α be the base circle radius of the gear tooth, α0 be the pressure angle at the perfect tooth profile, α be the pressure angle at the meshing point A, and α2 be half the angle occupied by the base circle of a single tooth of the driving gear. α1 is the angle at the point of contact of the perfect tooth profile, and α3 is the angle at point A of contact.

[0025] k f The calculation formula is expressed as:

[0026]

[0027]

[0028] In the above formula, u f S represents the distance between the intersection of the line of action and the line of symmetry of the gear teeth and the base circle. f L represents the arc length of a single tooth profile. * M * P * Q * These represent four parameters related to the number of gear teeth and the module. The calculation process for the stiffness of the driven gear is exactly the same as that for the driving gear. The values ​​of L*, M*, P*, and Q* can be obtained through polynomial fitting:

[0029]

[0030] The values ​​of Ai, Bi, Ci, Di, Ei, and Fi are shown in Table 2. fi =R r / R int R r R represents the radius of the tooth root circle. int θ represents the gear shaft bore diameter. f This indicates the angle occupied by the profile of a single tooth.

[0031] Table 2. Parameters Ai, Bi, Ci, Di, Ei, and Fi

[0032] Ai Bi Ci Di Ei Fi <![CDATA[L * ]]> <![CDATA[-5.754×10 -5 ]]> <![CDATA[-1.999×10 -3 ]]> <![CDATA[-2.302×10 -4 ]]> <![CDATA[-4.77×10 -3 ]]> 0.027 6.805 <![CDATA[M * ]]> <![CDATA[-60.11×10 -5 ]]> <![CDATA[28.1×10 -5 ]]> <![CDATA[-83.43×10 -4 ]]> <![CDATA[-9.926×10 -3 ]]> 0.162 0.909 <![CDATA[P * ]]> <![CDATA[-50.95×10 -5 ]]> <![CDATA[185.5×10 -5 ]]> <![CDATA[0.0538×10 -4 ]]> <![CDATA[53.3×10 -3 ]]> 0.29 0.924 <![CDATA[Q * ]]> <![CDATA[-6.204×10 -5 ]]> <![CDATA[9.0889×10 -5 ]]> <![CDATA[-4.096×10 -4 ]]> <![CDATA[7.8297×10 -3 ]]> -0.15 0.59

[0033] The dynamic meshing stiffness of uniformly and non-uniformly worn gears is calculated to obtain quantitative curves of the influence of different wear modes on gear meshing stiffness and wear amount.

[0034] In step 3), the dynamic equations of the gear transmission system model are expressed as follows:

[0035]

[0036] In the above formula, M is the system mass matrix; C is the system damping matrix; K(t) is the system stiffness matrix, which is time-varying;

[0037] x s is the static relative displacement vector; x is the dynamic displacement vector; e(t) is the gear composite error; P s It is a static load; Let x be the second derivative and the first derivative.

[0038] Further derivation of the above formula can be rewritten as: in, For the overall stiffness of gear meshing, we can finally obtain:

[0039]

[0040]

[0041] In the above formula, ΔK is the variable stiffness part of the gear meshing comprehensive stiffness; S(t) is the meshing impact excitation force; F(t) is the dynamic load. It is a linear differential equation, and the terms on the right-hand side can be divided into two parts: one part is ΔKe(t) which includes gear stiffness excitation and error excitation, and the other part is S(t) which includes gear meshing impact excitation force.

[0042] Therefore, gear stiffness excitation, transmission error excitation, and gear meshing impact excitation are the main factors affecting the vibration response of the transmission system. This invention focuses on the nonlinearity of gear stiffness changes due to gear wear and explores the analysis of gear meshing force and body vibration characteristics under uniform and non-uniform wear. In step 1), the gear meshing contact unit is input into the gear meshing stiffness transformation curve calculated in step 2) as the internal excitation; a point near the excitation source on the gearbox body is selected as the measuring point, and the meshing force and vibration acceleration signals at the same measuring point under uniform and non-uniform wear are collected. Then, the samples are uniformly subjected to Fourier transform to obtain the frequency domain signal feature values, thereby quantifying the characteristic values ​​of the gear dynamic meshing force / box vibration acceleration signal under uniform and non-uniform wear.

[0043] In step 4), a gearbox wear simulation fault test bench is built. The vibration signal of the actual gearbox body is collected by a vibration acceleration sensor. The collected signal is Fourier transformed to obtain the frequency domain signal. The frequency domain signal is compared with the characteristic value in the frequency domain signal of the gearbox body under uniform and non-uniform wear simulated by rigid-flexible coupling in step 3) to realize the identification of gearbox wear uniformity.

[0044] The present invention, by adopting the above technical solutions, has the following advantages: 1. The present invention considers the stiffness coupling and nonlinearity of gear units, and inputs internal excitation when the mechanical system is in a dynamic operating state. Therefore, it can better match the real mechanical system, quantify the vibration transmission of excitation force during the operation of the mechanical system, and ensure the accuracy of the model. 2. The present invention establishes a dynamic model of the gear transmission system including the gearbox body using a combination of finite element method and experimental method, considering the interaction between gear wear uniformity and the transmission system. Therefore, it more realistically reflects the real-time state of the mechanical system.

[0045] The method described in this invention is based on a combination of classical nonlinear theory and finite element method, possessing a reliable theoretical foundation and being easily implemented in various commonly used multibody dynamics environments, thus exhibiting high computational efficiency. For fault diagnosis of mechanical transmission systems, the most fundamental aspect is the analysis of fault mechanisms and vibration transmission. Through the method described in this invention, the vibration response and wear uniformity of internal excitation in the gear system can be quantitatively and accurately evaluated, enabling fault mechanism analysis and research, which is of great significance for tracing the source of mechanical system faults. Attached Figure Description

[0046] Figure 1 Method Flowchart

[0047] Figure 2 Schematic diagram of gearbox dynamics model

[0048] Figure 3 Schematic diagram of gear meshing stiffness model under wear conditions

[0049] Figure 4 Trend of meshing stiffness under uniform wear conditions with different wear degrees

[0050] Figure 5 Trend of meshing stiffness variation under different wear degrees in non-uniform wear conditions

[0051] Figure 6 Frequency domain diagram of meshing force of uniformly worn gears

[0052] Figure 7 Frequency domain diagram of meshing force of gears with non-uniform wear

[0053] Figure 8 Frequency domain diagram of vibration acceleration of uniformly worn gear body

[0054] Figure 9 Frequency domain diagram of vibration acceleration and meshing force of gear body with non-uniform wear

[0055] Figure 10 Gearbox Simulation Test Bench

[0056] Figure 11 Time-frequency domain diagram of vibration signal at measuring point 1 under constant working conditions Detailed Implementation

[0057] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Specific examples of the invention are shown in the drawings; however, it should be understood that the invention can be implemented in various forms and should not be limited to the examples set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0058] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0059] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0060] like Figure 1 As shown, this invention proposes a method for identifying gear wear uniformity based on gearbox vibration response, characterized by the following steps:

[0061] 1) Establish a rigid-flexible coupling dynamic model of the gearbox transmission system: This includes obtaining the characteristic parameters and initial operating parameters of the multi-stage transmission gearbox; determining the motion constraint relationships between each component and the description method of the gear / box boundary conditions based on the characteristic parameters and initial operating parameters; and establishing a rigid-flexible coupling dynamic model of the gearbox transmission system based on the constraint relationships and the description method of each boundary.

[0062] In this embodiment, the characteristic parameters include the geometric structural parameters and material properties of the speed-increasing gears, bevel gears, herringbone gears, helical gears, shafts, and spur gears in the multi-stage gearbox. The geometric structural parameters are obtained from the drawing files of the gears, shafts, and the gearbox body. The material properties include at least the material grade and mechanical properties of the gears, shafts, and gearbox body, as shown in Tables 1 and 2. A three-dimensional model of the gearbox is created in Solidworks based on the geometric parameters in the drawing files. The three-dimensional model is then imported into the multibody dynamics analysis software Recurdyn to create a multibody dynamics model. All imported components are rigid bodies. Constraints are established between the components according to the kinematic relationships between them: a fixed constraint exists between the gear and its mating shaft; a rotational constraint about the z-axis exists between the shaft and the body; and a fixed constraint exists between the body and the ground. Bearing contact is added between the shaft and the body to simulate bearing damping and stiffness. Based on Hertz contact theory, the expression for the normal contact force between the contacting components is as follows:

[0063]

[0064] In the formula, k is the contact stiffness coefficient; c is the damping coefficient; and δ is the contact penetration depth. is the derivative of the contact penetration depth; m1, m2, and m3 are the stiffness exponent, damping exponent, and dent exponent, respectively. Contact parameters are selected based on the material of the contact elements, as shown in Table 3. According to Table 2, both the gearbox shaft and the machine body are made of steel, and lubricating oil is used at the contact points. Contact parameters are set according to the steel (oil-lubricated) - steel (oil-lubricated) parameter values ​​in Table 3. Contact pairs are added between the meshing gears to simulate gear meshing constraints, and the gear meshing stiffness is set. The target gear, including the speed-increasing spur gear, transmission shaft, and gearbox housing, was made flexible, while the remaining components remained rigid. The key components were meshed using the finite element software Ansys, employing a four-node tetrahedral element structure. A mass element was created at the center of the shaft hole, with the center node as the master node and points on the hole surface as slave nodes, creating a rigid connection. A flexible bearing containing model node, material, and element type information was imported into multibody dynamics software to replace the original rigid element, achieving rigid-flexible coupling. The rigid-flexible coupling model was then established. The model's driving force is torque around the drive shaft axial direction, and the load is torsional damping around the power output gear. The flexible gearbox components and the rigid-flexible coupling model are shown below. Figure 2 As shown.

[0065] Table 1. Gear parameters for each stage of the gearbox

[0066] Number of teeth Normal Module Pressure angle (°) Helix angle (°) Tooth width (mm) Bevel gear 1 16 6.25 —— —— —— bevel gear 2 24 6.25 —— —— —— Spur Gear 1 63 2 20 —— 40 Spur Gear 2 35 2 20 —— 40 Herringbone teeth 1 50 1.75 20 13 55 Herringbone teeth 2 50 1.75 20 13 55 Helical Gear 1 40 2 20 12 40 Helical Gear 2 48 2 20 12 40

[0067] Table 2 Main Technical Parameters of Gearbox

[0068] Main parameters Parameter details Drive power 22kW Gearbox speed range 0~3000rpm Gearbox torque range 300 N·m Overall gear ratio 1:1 Gear tooth surface hardness Hardened tooth surface HRC58~62 Gear materials 20CrMnTi Gear precision IT6~IT8 Shaft material 45 steel Box material gray cast iron

[0069] Table 3 Contact parameters of relevant materials

[0070] Material 1 Material 2 k / (N / mm) c / (N·s / mm) <![CDATA[m1]]> <![CDATA[m2]]> <![CDATA[m3]]> δ / mm Steel (drying) Steel (drying) 100000.000 50.000 1.5-2.5 0-1 2 0-5 Steel (Oil-lubricated) Steel (Oil-lubricated) 100000.000 50.000 1.5-2.5 0-1 2 0-5 Steel (Oil-lubricated) Steel (drying) 100000.000 50.000 1.5-2.5 0-1 2 0-5 Aluminum (dry) Steel (drying) 35000.000 28.000 1.5-2.5 0-1 2 0-5 Aluminum (dry) Steel (Oil-lubricated) 35000.000 28.000 1.5-2.5 0-1 2 0-5 Aluminum (oil-lubricated) Steel (drying) 35000.000 28.000 1.5-2.5 0-1 2 0-5 Aluminum (oil-lubricated) Steel (Oil-lubricated) 35000.000 28.000 1.5-2.5 0-1 2 0-5

[0071] 2) Calculate the dynamic meshing stiffness under uniform and non-uniform wear: The dynamic meshing stiffness of gears with uniform and non-uniform wear is calculated by analytical method to obtain a quantitative evaluation of the influence of different wear modes on gear meshing stiffness and wear amount.

[0072] The formula for calculating gear meshing stiffness considering wear uniformity is expressed as follows:

[0073]

[0074] In the above formula, k h For the contact stiffness of the driving wheel, k b1 k is the bending stiffness of the driving gear teeth. s1 k is the shear stiffness of the driving wheel teeth. a1 k is the axial compressive stiffness of the drive wheel. f1 k represents the elastic stiffness of the drive wheel base. b2 k is the bending stiffness of the passive gear teeth. s2 k is the shear stiffness of the passive wheel teeth. a2 k is the axial compressive stiffness of the passive wheel. f2 This refers to the elastic stiffness of the passive wheel base.

[0075] Where, k h The calculation formula is expressed as:

[0076]

[0077] In the above formula, E is the elastic modulus; ν is Poisson's ratio; and L is the tooth width.

[0078] The formulas for calculating kb, ks, and ka are expressed as follows:

[0079]

[0080]

[0081]

[0082] In the above formula, N is the number of teeth, h w To represent the amount of wear at the meshing point A on the tooth profile at coordinate x, R b Let α be the base circle radius of the gear tooth, α0 be the pressure angle at the perfect tooth profile, α be the pressure angle at the meshing point A, and α2 be half the angle occupied by the base circle of a single tooth of the driving gear. α1 is the angle at the point of contact of the perfect tooth profile, and α3 is the angle at point A of contact.

[0083] k f The calculation formula is expressed as:

[0084]

[0085]

[0086] In the above formula, u f S represents the distance between the intersection of the line of action and the line of symmetry of the gear teeth and the base circle. f L represents the arc length of a single tooth profile. * M * P * Q * These represent four parameters related to the number of gear teeth and the module. The calculation process for the stiffness of the driven gear is exactly the same as that for the driving gear. The values ​​of L*, M*, P*, and Q* can be obtained through polynomial fitting:

[0087]

[0088] The values ​​of Ai, Bi, Ci, Di, Ei, and Fi are shown in Table 4. fi =R r / R int R r R represents the radius of the tooth root circle. int Gear

[0089] Table 4. Parameters Ai, Bi, Ci, Di, Ei, and Fi

[0090]

[0091]

[0092] In this embodiment, two different working conditions are set: uniform wear and non-uniform wear. The speed is 1200 r / min and the load is 90 N·m. Three different wear clearance levels are set: normal wear, moderate wear, and severe wear. The meshing stiffness of the gear is calculated when the wear thickness is 30 μm, 60 μm, and 90 μm, respectively. The number of cycles for non-uniform wear is calculated to be 10. 5 10 6 10 7 Changes in post-meshing stiffness.

[0093] Figure 4 , Figure 5The graphs show the changes in gear meshing stiffness under uniform and non-uniform wear conditions. In the early stage of slight wear, the gear wear thickness is small, and its meshing stiffness curve is almost close to that of the healthy state. As the wear depth increases and the wear thickness increases, the meshing stiffness of the uniformly worn gear decreases overall. Furthermore, the degree of decrease in meshing stiffness increases with the increase in cumulative wear, indicating that the change in meshing stiffness is more pronounced when the gear wear is severe. In the case of non-uniform wear, as the wear depth increases and the wear amount increases, the overall meshing stiffness of the gear is lower than that of the healthy state. Moreover, with the increase in cumulative wear, the overall decrease in stiffness increases, except for the stiffness in the single tooth area. The changes in the later stage are more sensitive than those in the early stage, and the rate of decrease in gear meshing stiffness increases with the increase in wear amount.

[0094] 3) Characteristic analysis of gear meshing force / box vibration under uniform and non-uniform conditions: In step 1), the gear meshing contact unit is input into the gear meshing stiffness transformation curve calculated in step 2) as the internal excitation; the gearbox body near the excitation source is selected as the measuring point, and the meshing force and vibration acceleration signals of the same measuring point under uniform and non-uniform wear are collected. Then, the samples are uniformly subjected to Fourier transform to obtain the frequency domain signal, thereby quantifying the characteristic values ​​of gear dynamic meshing force / box vibration acceleration signal under uniform and non-uniform wear.

[0095] In this embodiment, under constant operating conditions of 1200 rpm and 90 N·m load, the time-frequency domain analysis of the meshing force of uniformly and non-uniformly worn gears and the vibration acceleration signals of the machine body is performed. The original signal of the tested gear is subjected to FFT transformation to obtain the spectrum, as shown below. Figures 6-9 As shown, under both uniform and non-uniform wear, the meshing force has relatively high amplitudes at 320Hz, 640Hz, 840Hz, and 960Hz. 320Hz is the meshing frequency of the bevel gear, 640Hz is twice the meshing frequency of the bevel gear, and 840Hz is the meshing frequency of the worn spur gear, gradually decreasing thereafter. Under uniform wear, the vibration acceleration signal of the gearbox body reaches its peak at approximately 320Hz, 400Hz, and 610Hz, with significant amplitude fluctuations with frequency, peaking at approximately 320Hz, and then gradually decreasing. Overall, the amplitude shows a trend of first increasing and then decreasing with increasing frequency. Under non-uniform wear, the vibration acceleration signal of the gearbox body is dominated by the meshing frequency fm = 840Hz, with 2fm and 3fm frequencies also present. The noise in the frequency domain diagram gradually increases, and the fluctuations under non-uniform wear are greater than those under uniform wear. The vibration response of uniformly worn gears is basically consistent with the frequency domain composition under healthy conditions. As the cumulative wear of the gears increases, the vibration impact increases, and it gradually tends to stabilize with frequency changes.

[0096] 4) Gearbox vibration signal acquisition and gear wear uniformity identification: A simulation test bench is set up and gearbox vibration signals are acquired. The acquired signals are Fourier transformed to obtain frequency domain signals, which are compared with the characteristic values ​​of gearbox vibration signals under uniform and non-uniform wear in step 3). If the frequency domain components of the actual signal are consistent with the frequency domain components of the gearbox vibration signal under uniform wear, it is considered that the gear wear is uniform, thus realizing gearbox wear uniformity identification.

[0097] In this embodiment, Figure 10 This represents a gearbox simulation test bench. Accelerometers are used to mount vibration sensors in both the radial and axial directions to monitor the vibration of each stage of the gearbox transmission system. Measurement points 1-5 are radial measurement points, and measurement points 6 and 7 are axial measurement points. On the test bench, a method of accelerated wear is employed where a soft-toothed gear meshes with a hard-toothed gear. The spur gear (driving gear) closest to measurement point 1 in the experimental gearbox is replaced with a soft-toothed gear. Under constant operating conditions of 1200 rpm and a load of 120 N·m, wear is gradually applied starting from the new gear. To illustrate the impact of gear wear evolution on the vibration signal, a representative measurement point—measurement point 1—is selected for analysis. The vibration signal characteristics of the experimental gearbox and the control gearbox at the corresponding measurement point are compared. Measurement point 1 is the radial vibration measurement point for the soft-toothed gear. Under stable operating conditions (n ​​= 1200 rpm), the vibration signal at measurement point 1 of the experimental gearbox is subjected to FFT transformation to obtain the spectrum, as shown below. Figure 11 As shown. The frequency components with higher amplitudes include 319Hz, 638.6Hz, 838.1Hz, 1916Hz, and 2246Hz, among which 638.6Hz has the most significant amplitude, followed by the 838.1Hz frequency domain component. 638.6Hz is the second harmonic of the bevel gear meshing frequency, 838.1Hz is the meshing frequency of the worn spur gear, 1916Hz is the meshing frequency of the gears on shafts 4 and 5, and 2246Hz is the seventh harmonic of the bevel gear meshing frequency. These are consistent with the frequency domain components of the gearbox body vibration acceleration signal under uniform wear obtained in step 3), which are 320Hz, 400Hz, and 610Hz. The amplitude fluctuations are quite significant, peaking at 320Hz and then gradually decreasing. This contradicts the overall trend of the amplitude initially increasing and then decreasing with frequency. Furthermore, it aligns with the characteristic values ​​of gearbox vibration signals under non-uniform wear, where the dominant frequency is the meshing frequency fm = 840Hz, accompanied by significant impacts, and the presence of harmonics and extraneous frequencies with gradually increasing impacts. This matches the characteristics of non-uniform wear faults, and the deviation from the dominant meshing frequency is within 1%. Therefore, the gearbox gear wear is in a non-uniform state at this time.

[0098] Using the above methods, the dynamic meshing force of the worn gear pairs and the vibration acceleration signals of key points in the gearbox body were finally obtained. The changing trends of time-varying meshing stiffness, dynamic meshing force, and vibration acceleration signals of key points in the gearbox body under different wear states were analyzed in detail, and the simulation results were compared with experimental results. Under simulated fault experiments, different degrees of impact appeared in both the time and frequency domain characteristics, and the vibration became more pronounced as the wear progressed, verifying the fault characteristics of the simulation model. Furthermore, the simulation results can provide a large amount of effective data to compensate for the deficiencies of actual fault data, providing data support for the development of digital analysis methods and possessing potential value in the field of digital twins.

[0099] In summary, this invention is suitable for calculating the dynamic characteristics of gearboxes. By considering the influence of wear, a dynamic model of the gear transmission system, including the gearbox housing, is established using a combination of finite element method and experimental methods. Considering the interaction between gear wear uniformity and the transmission system, it can accurately and efficiently calculate the dynamic characteristics of gear meshing stiffness considering wear. The method employed in this invention is based on a combination of classical nonlinear theory and finite element method, possessing a reliable theoretical foundation and being easily implemented in various commonly used multibody dynamics environments, resulting in high computational efficiency. For fault diagnosis of mechanical transmission systems, the most fundamental aspect is the analysis of fault mechanisms and vibration transmission. Through the method described in this invention, the vibration response and wear uniformity of internal excitation in the gear system can be quantitatively and accurately evaluated, enabling fault mechanism analysis and research, which is of great significance for tracing the source of faults in mechanical systems.

[0100] The above embodiments are only used to further illustrate the purpose, technical solution and beneficial effects of the present invention, and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying gear wear uniformity based on gearbox vibration response, characterized in that, Includes the following steps: 1) Establish a rigid-flexible coupled multibody dynamics simulation model of the gearbox transmission system: obtain the characteristic parameters and initial operating parameters of the transmission gearbox; determine the motion constraint relationship between each component and the description method of the gear / box boundary conditions based on the characteristic parameters and initial operating parameters; establish a rigid-flexible coupled multibody dynamics model of the gearbox transmission system based on the constraint relationship and the description method of each boundary. 2) Calculate the dynamic meshing stiffness under uniform and non-uniform wear: The dynamic meshing stiffness of gears with uniform and non-uniform wear is calculated by analytical method to obtain the quantitative results of the influence of different wear modes on gear meshing stiffness and wear amount. 3) Characteristic analysis of gear meshing force / box vibration under uniform and non-uniform conditions: In step 1), the gear meshing contact element is input into the gear meshing stiffness transformation curve calculated in step 2) as the internal excitation; select vibration measurement points, generally selecting points close to the vibration source excitation as vibration measurement points, and monitor the meshing force / vibration acceleration signals before and after the application of the internal excitation force at the gear / box interface; the vibration measurement points are arranged on the interface above the speed-increasing gear / box axle hole, and the measured vibration acceleration signals are all in the direction of gravity; 4) Acquisition of actual gearbox vibration signals and identification of gear wear uniformity: A simulation test bench is built to acquire gearbox vibration signals and extract features to identify gearbox wear uniformity.

2. The method for identifying gear wear uniformity based on gearbox vibration response according to claim 1, characterized in that: In step 1), the characteristic parameters include the geometric structural parameters and material properties of the gearbox's speed-increasing spur gear, shaft, and body. The geometric structural parameters are obtained from the drawing files of the gear, shaft, and body. The material properties include at least the material grade and mechanical properties of the gear, shaft, and body. A three-dimensional model of the gearbox is established based on the geometric parameters in the drawing files. The three-dimensional model is imported into multibody dynamics analysis software to establish a multibody dynamics model. All imported components are rigid bodies. Constraints are established between the components according to the kinematic relationships between them: a fixed constraint between the gear and its mating shaft, a rotational constraint about the z-axis between the shaft and the body, and a fixed constraint between the body and the ground. Bearing contact is added between the shaft and the body to simulate bearing damping and stiffness. Based on Hertz contact theory, the normal contact force f between the contacting components is... n The expression is as follows: In the formula, k is the contact stiffness coefficient; c is the damping coefficient; This refers to the contact penetration depth. The derivative of the contact penetration depth; , , These are the stiffness index, damping index, and dent index, respectively. Contact pairs are added between meshing gears to simulate gear meshing constraints, and gear meshing stiffness is set. The target gear, transmission shaft, and gearbox are made flexible, while other components remain rigid. The key components are meshed using finite element software, employing a four-node tetrahedral element structure. A mass element is created at the center of the shaft hole, with the center node as the master node and points on the hole surface as slave nodes, creating a rigid connection. Flexible bearings containing model node, material, and element type information are imported into multibody dynamics software to replace the original rigid elements, achieving rigid-flexible coupling. The rigid-flexible coupling model is then established, with the model's driving form being torque around the drive shaft axial direction and the load form being torsional damping around the power output gear.

3. The method for identifying gear wear uniformity based on gearbox vibration response according to claim 1, characterized in that: In step 2), the gear meshing stiffness k, considering wear uniformity, is... t The calculation formula is expressed as follows: ； In the above formula, k h For the contact stiffness of the driving wheel, k b1 k is the bending stiffness of the driving gear teeth. s1 k is the shear stiffness of the driving wheel teeth. a1 k is the axial compressive stiffness of the drive wheel. f1 k is the elastic stiffness of the drive wheel base. b2 k is the bending stiffness of the passive gear teeth. s2 k is the shear stiffness of the passive wheel teeth. a2 k is the axial compressive stiffness of the passive wheel. f2 The elastic stiffness of the passive wheel base; Where, k h The calculation formula is expressed as: In the above formula, E is the elastic modulus; ν is Poisson's ratio; and L is the tooth width. k b k s k a The calculation formulas are expressed as follows: ; ; In the above formula, N is the number of teeth, and h w To represent the amount of wear at the meshing point A on the tooth profile at coordinate x, R b Let α be the base circle radius of the gear tooth, α0 be the pressure angle at the perfect tooth profile, α be the pressure angle at the meshing point A, and α2 be half the angle occupied by the base circle of a single tooth of the driving gear. α1 is the angle of the perfect tooth profile engagement point, and α3 is the angle of engagement point A. ; k f The calculation formula is expressed as: ; In the above formula, u f S represents the distance between the intersection of the line of action and the line of symmetry of the gear teeth and the base circle. f L represents the arc length of a single tooth profile. * M * P * Q * These represent four parameters related to the number of gear teeth and the module; the stiffness calculation process for the driven gear is completely consistent with that for the driving gear; the values ​​of L*, M*, P*, and Q* can be obtained through polynomial fitting: A i B i C i D i E i F i h is a coefficient fi =R r / R int R r R represents the radius of the tooth root circle. int θ represents the gear shaft bore diameter. f Indicates the angle occupied by the profile of a single tooth; The dynamic meshing stiffness of uniformly and non-uniformly worn gears is calculated to obtain quantitative curves of the influence of different wear modes on gear meshing stiffness and wear amount.

4. The method for identifying gear wear uniformity based on gearbox vibration response according to claim 1, characterized in that: In step 3), the dynamic equations of the gear transmission system model are expressed as follows: In the above formula, ; ; ; ； ； ； ； ； Further derivation of the above formula can be rewritten as: in, , for Ultimately, we can obtain: ; In the above formula, ; ; ; This is a linear differential equation, and the terms on the right-hand side can be divided into two parts: one part contains gear stiffness excitation and error excitation. The other part includes the gear meshing impact excitation force. ; In step 1), the gear meshing contact unit is input into the rigid-flexible dynamic model. In step 2), the gear meshing stiffness transformation curve is calculated as the internal excitation. The gearbox body near the excitation source is selected as the measurement point. The meshing force and vibration acceleration signals of the same measurement point under uniform and non-uniform wear are collected. Then, the Fourier transform of the samples is performed uniformly to obtain the frequency domain signal feature values, thereby quantifying the characteristic values ​​of the gear dynamic meshing force / box vibration acceleration signal under uniform and non-uniform wear.

5. The method for identifying gear wear uniformity based on gearbox vibration response according to claim 1, characterized in that: In step 4), a gearbox wear simulation fault test bench is built. The actual gearbox vibration signal is collected by a vibration acceleration sensor. The collected signal is Fourier transformed to obtain the frequency domain signal. The frequency domain signal is compared with the characteristic value of the gearbox body vibration signal under uniform and non-uniform wear in step 3). If the frequency domain component of the actual signal is consistent with the frequency domain component of the gearbox body vibration signal under uniform wear, it is considered that the gear wear is uniform. Otherwise, it is considered non-uniform.

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