A modeling method, equipment, and medium for a lumped parameter model of a harmonic reducer.

Abstract

This invention discloses a modeling method, equipment, and medium for a lumped parameter model of a harmonic reducer. The method includes the following steps: analyzing the interaction between the flexible wheel and the outer ring of the thin-walled bearing to obtain their interaction model; establishing a lumped parameter model of the entire harmonic reducer; analyzing the rotation law of the outer ring of the thin-walled bearing and its influence on the fault impact time interval; establishing a mathematical model of the excitation when the thin-walled bearing has an impact-type fault, as the input to the lumped parameter model; and establishing and solving the motion differential equations. This invention can accurately simulate the characteristic frequencies of the thin-walled bearing in a harmonic reducer during a fault, explains the formation of the vibration response frequency distribution during harmonic transmission, and fills the research gap of lacking an effective mechanism model for the coupled vibration of multiple components in a harmonic reducer.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery fault diagnosis and signal processing, and more specifically, relates to a modeling method, equipment and medium for a lumped parameter model of a harmonic reducer. Background Technology

[0002] Harmonic reducers are widely used in aerospace, industrial robots, precision machining equipment, and medical equipment due to their high precision and transmission efficiency, large transmission ratio, and compact structure. Existing research mainly focuses on transmission accuracy, tooth profile optimization, flexspline deformation and stress distribution, and stiffness. Because of the complex structure of harmonic reducers and the incomplete understanding of their mechanisms, existing research on fault diagnosis mainly focuses on data-driven intelligent diagnosis.

[0003] Zhao et al. (Zhao, Z., etc., 2024. Dynamics modeling and fault diagnosis of flexible thin-walled elliptical bearings in harmonic reducers. Measurement 238, 115378. DOI: 10.1016 / j.measurement.2024.115378) established a dynamic model of thin-walled bearings using the finite element method, analyzed the stress distribution and motion characteristics, and studied the vibration response characteristics of thin-walled bearings under local faults. However, their study focused solely on thin-walled bearings and did not consider the influence of the entire harmonic reducer. Zheng Ziheng et al. (Zheng Ziheng, Ding Kang. Optimization method of harmonic reducer based on lumped parameter model [P]. Guangdong Province: CN202310412907.8, 2023-08-22.) established a lumped parameter method rigid body dynamic vibration model of the whole harmonic reducer and studied the frequency distribution law of vibration response under normal conditions. However, it regarded the thin-walled bearing outer ring and flexible wheel with clearance fit and relative motion as a whole, and lacked the common faults of harmonic reducers, which has certain limitations. Summary of the Invention

[0004] To address at least one of the problems existing in the prior art, this invention provides a modeling method, device, and medium for a lumped parameter model of a harmonic reducer considering impact-type faults in thin-walled bearings, providing mechanistic support for harmonic reducer fault diagnosis. By establishing a 12-DOF lumped parameter model of the harmonic reducer and a mathematical model of the excitation considering impact-type faults, the vibration response characteristics of the harmonic reducer under local faults (impact faults) are revealed through mechanism and simulation analysis. This fills the research gap in the lack of an effective mechanistic model for the coupled vibration of multi-component harmonic reducers and has certain engineering application value.

[0005] To achieve the objective of this invention, the present invention provides a modeling method for a lumped parameter model of a harmonic reducer considering impact-type faults in thin-walled bearings, comprising the following steps:

[0006] The interaction between the flexible gear and the outer ring of the thin-walled bearing is analyzed, and an interaction model between the flexible gear and the outer ring of the thin-walled bearing is obtained.

[0007] Establish a lumped parameter model of the harmonic reducer as a whole;

[0008] The rotation law of the outer ring of the thin-walled bearing and its influence on the fault impact time interval are analyzed, and the characteristic frequency of the thin-walled bearing of the harmonic reducer when a fault occurs is obtained.

[0009] A mathematical model for the excitation of thin-walled bearings under impact failure is established as the input to the lumped parameter model.

[0010] The motion differential equations are established and solved to obtain the vibration response signal.

[0011] Furthermore, the analysis of the interaction between the flexspline and the outer ring of the thin-walled bearing yields an interaction model between the flexspline and the outer ring of the thin-walled bearing, including:

[0012] Based on the variational principle of elastic dynamics, the elastic deformation w1(t,θ) generated when the flexible wheel meshes with the rigid wheel in the working state is calculated.

[0013] Based on the characteristics of harmonic drive and the distortion characteristics of the flexible wheel, the elastic deformation of the flexible wheel under the combined action of the wave generator and the rigid wheel is obtained by fitting.

[0014] The deformation of the flexure when the outer ring of the thin-walled bearing interacts with it is obtained as w(t,θ)=w2(t,θ)-w1(t,θ), and the force exerted by the outer ring of the thin-walled bearing on the flexure is obtained as follows:

[0015] q r (t,θ)=max(w(t,θ),0)·K

[0016] q t (t,θ)=μ·q r (t,θ)

[0017] Where, q r (t,θ), q t (t, θ) represent the radial and tangential forces exerted by the outer ring of the thin-walled bearing on the flexure, respectively; t and θ represent the time and the angular coordinates of the flexure at different positions, respectively; K is the static stiffness of the flexure; μ is the coefficient of dynamic friction between the outer ring of the thin-walled bearing and the flexure.

[0018] Replace the interaction between the outer ring of the thin-walled bearing and the flexible wheel rotating with the wave generator, and the two ends of the long shaft, with the resultant forces in the horizontal, vertical, and torsional directions of the absolute coordinate system, respectively:

[0019]

[0020] in, This represents the range of the force acting at one end of the major axis of the ellipse; ω n R represents the input speed of the harmonic reducer; R represents the radius of the inner wall surface of the flexure before deformation.

[0021] Furthermore, the equivalent stiffness is:

[0022] k fox (t)=F x (t) / δ x (t)

[0023] k foy (t)=F y (t) / δ y (t)

[0024] k foξ (t)=M(t)·R / δ ξ (t)

[0025] k fox (t), k foy (t), k foξ (t) represents the equivalent stiffness in the horizontal, vertical, and torsional directions, respectively; δ i (t), i = x, y, ξ, is the projection of the average deformation of the flexure, calculated from the deformation of the flexure w(t, θ), onto the x-axis, y-axis, and torsional direction.

[0026] Furthermore, when establishing the overall lumped parameter model of the harmonic reducer, the interaction between the camshaft and the rigid wheel is considered. A lumped parameter model of the overall harmonic reducer is established with the equivalent cam-thin-walled bearing outer ring-flexible wheel-rigid wheel as the research object. The equivalent cam is the whole composed of the camshaft and the thin-walled bearing inner ring.

[0027] Furthermore, the analysis of the rotation law of the outer ring of the thin-walled bearing and the influence of the rotation law on the fault impact time interval includes:

[0028] The outer ring of the thin-walled bearing and the flexible gear are in clearance fit. The thin-walled bearing transmits torque from the input shaft to the output shaft, which together causes the outer ring of the thin-walled bearing to rotate significantly.

[0029] When analyzing local faults in thin-walled bearings, it is necessary to consider the frequency fluctuations caused by the rotation of the outer ring of the thin-walled bearing, with the outer ring rotation frequency as f. o Substituting into the calculation, the cage rotation frequency f r for:

[0030]

[0031] In the formula: d is the roller diameter, D is the mean diameter of the thin-walled bearing, α is the roller contact angle, and f is the roller diameter. n The input frequency of the harmonic reducer;

[0032] The characteristic frequencies of inner and outer ring failures in thin-walled bearings are:

[0033]

[0034] Among them, z n The number of rollers.

[0035] Furthermore, based on the rotation law of the outer ring, an impact excitation model is established for impact-type failures in the inner and outer rings of thin-walled bearings:

[0036]

[0037] Among them, a in (t), a out (t), a c (t) represent amplitude modulation using the input frequency, output frequency, and the difference between the cage frequency and the inner or outer ring frequency as the fundamental frequency, respectively; t impi This indicates the time interval of the fault impact, which is affected by the fault type and the rotation of the outer ring of the thin-walled bearing. This indicates that the nth pulse excitation occurs at a time equal to the sum of the time intervals of the previous n pulses; t represents time.

[0038] Furthermore, the equations of motion are established, including:

[0039] Establish the dynamic differential equations of the equivalent cam formed by the camshaft and the inner ring of the thin-walled bearing:

[0040]

[0041] Establish the dynamic differential equation for the outer ring of the thin-walled bearing:

[0042]

[0043] Establish the dynamic differential equation of the flexible wheel:

[0044]

[0045] Establish the dynamic differential equation of the rigid wheel:

[0046]

[0047] Where, m w m o m f m cThese are the masses of the equivalent cam, the outer ring of the thin-walled bearing, the flexure, and the rigid wheel, respectively; I p p = w, o, f, c, which are the moments of inertia of the equivalent cam, the outer ring of the thin-walled bearing, the flexure, and the rigid wheel, respectively; x p p = w, o, f, c, representing the displacements of the equivalent cam, the thin-walled bearing outer ring, the flexure, and the rigid wheel along the x-axis, respectively; y p p = w, o, f, c, representing the displacements of the equivalent cam, the thin-walled bearing outer ring, the flexure, and the rigid wheel in the y-axis direction, respectively; θ p p = w, o, f, c, representing the rotational amounts of the equivalent cam, the thin-walled bearing outer ring, the flexure, and the rigid wheel in the torsional direction, respectively; c pq p = w, f, c, q = x, y, ξ, representing the damping of the equivalent cam, flexure, and rigid wheel in the x-axis, y-axis, and torsional directions, respectively; k pq p = w, f, c, q = x, y, ξ, which are the stiffnesses of the equivalent cam, flexure, and rigid wheel in the x-axis, y-axis, and torsional directions, respectively; k wcq q = x, y, representing the connection stiffness between the equivalent cam and the rigid wheel in the horizontal and vertical directions, respectively, and c wcq q = x, y, representing the damping between the equivalent cam and the rigid wheel in the horizontal and vertical directions, respectively; k woq q = x, y, ξ, representing the connection stiffness between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions, respectively; c woq q = x, y, ξ, representing the damping between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions; k foq q = x, y, ξ, representing the connection stiffness between the flexible wheel and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions, and c foq q = x, y, ξ, representing the damping between the flexible wheel and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions; k fcq q = x, y, ξ, representing the connection stiffness between the flexible wheel and the rigid wheel along the x-axis, y-axis, and torsional direction, and c fcq q = x, y, ξ, representing the damping between the flexible and rigid gears along the x-axis, y-axis, and torsional direction; F impx F impy T impξ This represents the projection of the impact excitation onto the x-axis, y-axis, and torsional direction; T in T represents the input torque of the camshaft. out Indicates the output torque transmitted by the rigid wheel; e f e c These represent the eccentricity of the flexible wheel and the eccentricity of the rigid wheel, respectively; e fop p = x, y, ξ, representing the displacement excitation of the eccentricity of the flexible wheel along the x-axis, y-axis, and torsional direction; e fcpp = x, y, ξ, representing the displacement excitation of the rigid wheel eccentricity in the x-axis, y-axis and torsional directions.

[0048] Furthermore, based on the established lumped parameter model, the Runge-Kutta method is used to solve the dynamic differential equations to obtain the vibration response signal of the system for simulation analysis.

[0049] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the aforementioned modeling method for a lumped parameter model of a harmonic reducer.

[0050] A computer-readable storage medium storing a computer program, characterized in that, when executed by a processor, the computer program implements the aforementioned modeling method for the lumped parameter model of a harmonic reducer.

[0051] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0052] (1) This invention takes into account the relative rotation and interaction characteristics and the fit state of the outer ring of the thin-walled bearing and the flexible wheel. It establishes the interaction model between the outer ring of the thin-walled bearing and the flexible wheel by calculating the deformation and force of the flexible wheel, so as to obtain a more complete lumped parameter model of harmonic transmission.

[0053] (2) This invention establishes a mathematical model of the impact interval fluctuation caused by the rotation of the outer ring of the thin-walled bearing and the existence of three amplitude modulation characteristics, laying a theoretical foundation for establishing a lumped parameter model of the harmonic reducer that considers impact-type faults.

[0054] (3) This invention reveals the vibration response characteristics of the harmonic reducer when there is a local fault through mechanism and simulation analysis, filling the research gap of the lack of an effective mechanism model for the multi-component coupled vibration of the harmonic reducer. Attached Figure Description

[0055] Figure 1 This is a flowchart of a modeling method for a lumped parameter model of a harmonic reducer considering impact-type faults of thin-walled bearings, provided by an embodiment of the present invention.

[0056] Figure 2 This is a schematic diagram of the experimental platform constructed in an embodiment of the present invention.

[0057] Figure 3 This is a lumped parameter model diagram of the harmonic reducer established in the embodiments of the present invention.

[0058] Figure 4 This is a schematic diagram of the frequency variation curves of the outer ring of a thin-walled bearing under different working conditions, obtained from measurements in an embodiment of the present invention.

[0059] Figure 5 This is the simulated signal spectrum obtained by using the proposed method in this embodiment of the invention.

[0060] Figure 6 This is the demodulated spectrum of the simulated signal obtained using the proposed method in this embodiment of the invention.

[0061] Figure 7 This is a spectrum diagram of the signal measured in the experiment of this embodiment of the invention.

[0062] Figure 8 This is the demodulation spectrum of the signal measured in the experiment of this embodiment of the invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Please see Figure 1 The present invention provides a modeling method for a lumped parameter model of a harmonic reducer considering impact-type faults of thin-walled bearings, comprising the following steps:

[0065] S1. Analyze the interaction between the flexure and the outer ring of the thin-walled bearing to obtain the interaction model between the flexure and the outer ring of the thin-walled bearing.

[0066] Step S1 specifically includes the following sub-steps:

[0067] S11. Based on the variational principle of elastic dynamics, calculate the elastic deformation w1(t,θ) generated when the selected flexible wheel with a fixed bottom (such as a top hat type flexible wheel) meshes with the rigid wheel in the working state.

[0068] S12. Based on the characteristics of harmonic drive and the distortion characteristics of the flexible wheel, the elastic deformation of the flexible wheel under the combined action of the wave generator and the rigid wheel is fitted to obtain w2(t,θ).

[0069] S13. The deformation of the flexure when the outer ring of the thin-walled bearing interacts with the flexure is obtained as w(t,θ)=w2(t,θ)-w1(t,θ), and then the force exerted by the outer ring of the thin-walled bearing on the flexure is obtained:

[0070] q r (t,θ)=max(w(t,θ),0)·K

[0071] q t(t,θ)=μ·q r (t,θ)

[0072] Where t and θ represent time and the angular coordinates of different positions of the flexure, respectively, and q r (t,θ), q t (t,θ) represent the radial and tangential forces exerted by the outer ring of the thin-walled bearing on the flexure, respectively; K is the static stiffness of the flexure; and μ is the coefficient of dynamic friction between the outer ring of the thin-walled bearing and the flexure.

[0073] Replace the interaction between the outer ring of the thin-walled bearing and the flexible wheel rotating with the wave generator, and the two ends of the long shaft, with the resultant forces in the horizontal, vertical, and torsional directions of the absolute coordinate system, respectively:

[0074]

[0075] The equivalent stiffness is calculated as follows:

[0076] k fox (t)=F x (t) / δ x (t)

[0077] k foy (t)=F y (t) / δ y (t)

[0078] k foξ (t)=M(t)·R / δ ξ (t)

[0079] in, This indicates the range of the force acting at one end of the major axis of the ellipse; k fox (t), k foy (t), k foξ (t) represents the equivalent stiffness in the horizontal, vertical, and torsional directions, respectively, and δ i (t), i = x, y, ξ, are the projections of the average deformation of the flexible wheel, calculated from the deformation w(t, θ), onto the x-axis, y-axis, and torsional direction; R represents the radius of the inner wall of the flexible wheel before deformation; ω n This indicates the input speed of the harmonic reducer.

[0080] S2. Establish a lumped parameter model of the harmonic reducer as a whole.

[0081] Based on step S1, and combining existing research, and considering the interaction between the camshaft and the rigid wheel, a lumped parameter model of the harmonic reducer as a whole is established, taking the equivalent cam (the integral structure consisting of the camshaft and the inner ring of the thin-walled bearing) – the outer ring of the thin-walled bearing – the flexible wheel – the rigid wheel as the research object, as follows: Figure 3 As shown.

[0082] S3. Analyze the rotation law of the outer ring of the thin-walled bearing and the influence of the rotation law on the fault impact time interval, and obtain the characteristic frequency when the thin-walled bearing of the harmonic reducer fails.

[0083] This step specifically includes the following sub-steps:

[0084] S31. The outer ring of the thin-walled bearing and the flexible wheel are in clearance fit. As the core transmission component, the thin-walled bearing will inevitably transmit torque from the input shaft to the output shaft, which together causes the outer ring to rotate significantly.

[0085] S32. Set up a harmonic drive test bench, install an industrial endoscope, and observe and measure the rotation law of the thin-walled bearing outer ring of the harmonic reducer.

[0086] In some embodiments of the present invention, the harmonic drive experimental platform constructed is as follows: Figure 2 As shown, the servo motor is connected to the harmonic reducer via a coupling, and the output of the harmonic reducer is equipped with a load. An endoscope is used to acquire images, with a resolution of 1920×1080 and a frame rate of 30fps. An accelerometer is used to acquire vibration acceleration, and the sampling frequency of the vibration acceleration data is 25600Hz.

[0087] The harmonic reducer consists of a camshaft, thin-walled bearings, a flexible gear, and a rigid gear. The flexible gear is fixed, and the rigid gear provides the output. The flexible gear and rigid gear have 200 and 202 teeth respectively, with a speed ratio of 101. The thin-walled bearing has 21 rollers, a roller diameter of 4 mm, a bearing pitch diameter of 36.74 mm, and a roller contact angle of 0°. The experimental conditions are shown in Table 1.

[0088] Table 1. Operating Parameters of the Example

[0089]

[0090] In some embodiments of the present invention, the obtained frequency variation curves of the outer ring of the thin-walled bearing under different operating conditions are as follows: Figure 4 As shown.

[0091] S33. When analyzing local faults (such as impact faults) in thin-walled bearings, it is necessary to consider the frequency fluctuations caused by the rotation of the outer ring of the thin-walled bearing, using the outer ring rotation frequency as f. o Substituting into the calculation, the cage rotation frequency f r for:

[0092]

[0093] In the formula: d is the roller diameter, D is the mean diameter of the thin-walled bearing, α is the roller contact angle, and f is the roller diameter. n This is the input frequency of the harmonic reducer.

[0094] The characteristic frequencies of failure in the inner and outer rings of thin-walled bearings are:

[0095]

[0096] Among them, z n This represents the number of rollers. It is evident that the outer ring of a thin-walled bearing rotating in the same direction as the camshaft will cause the fault characteristic frequency to fluctuate within a specific range below the theoretical value. Correspondingly, 1 / f ni and 1 / f no That is, the time interval between fault impacts can also fluctuate.

[0097] S4. Establish a mathematical model of the excitation when a thin-walled bearing has an impact-type fault, and use it as the input of the lumped parameter model.

[0098] This step specifically includes:

[0099] Based on the observed outer ring rotation pattern in the experiment, an impact excitation model is established for impact-type faults in the inner and outer rings of thin-walled bearings:

[0100]

[0101] Among them, a in (t), a out (t), a c (t) represent amplitude modulation using the input frequency, output frequency, and the difference between the cage frequency and the inner or outer ring frequency as the fundamental frequency, respectively; t impi This indicates the time interval of the fault impact, which is affected by the fault type and the rotation of the outer ring of the thin-walled bearing. This indicates that the nth pulse excitation occurs at a time equal to the sum of the time intervals of the previous n pulses.

[0102] S5. Establish and solve the differential equations of motion to obtain the vibration response signal of the system and realize simulation analysis.

[0103] This step specifically includes:

[0104] S51. Establish the dynamic differential equation of the equivalent cam formed by the camshaft and the inner ring of the thin-walled bearing:

[0105]

[0106] S52. Establish the dynamic differential equation of the outer ring of the thin-walled bearing:

[0107]

[0108] S53. Establish the dynamic differential equation of the flexible wheel:

[0109]

[0110] S54. Establish the dynamic differential equation of the rigid wheel:

[0111]

[0112] Where, m w m o m f m c These are the masses of the equivalent cam, the outer ring of the thin-walled bearing, the flexure, and the rigid wheel, respectively; I p p = w, o, f, c, which are the moments of inertia of the equivalent cam, the outer ring of the thin-walled bearing, the flexure, and the rigid wheel, respectively; x p p = w, o, f, c, representing the displacements of the equivalent cam, the thin-walled bearing outer ring, the flexure, and the rigid wheel along the x-axis, respectively; y p p = w, o, f, c, representing the displacements of the equivalent cam, the thin-walled bearing outer ring, the flexure, and the rigid wheel in the y-axis direction, respectively; θ p p = w, o, f, c, representing the rotational amounts of the equivalent cam, the thin-walled bearing outer ring, the flexure, and the rigid wheel in the torsional direction, respectively; c pq p = w, f, c, q = x, y, ξ, representing the damping of the equivalent cam, flexure, and rigid wheel in the x-axis, y-axis, and torsional directions, respectively; k pq p = w, f, c, q = x, y, ξ, which are the stiffnesses of the equivalent cam, flexure, and rigid wheel in the x-axis, y-axis, and torsional directions, respectively; k wcq q = x, y, representing the connection stiffness between the equivalent cam and the rigid wheel in the horizontal and vertical directions, respectively, and c wcq q = x, y, representing the damping between the equivalent cam and the rigid wheel in the horizontal and vertical directions, respectively; k woq q = x, y, ξ, representing the connection stiffness between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions, respectively; c woq q = x, y, ξ, representing the damping between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions; k foq q = x, y, ξ, representing the connection stiffness between the flexible wheel and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions, and c foq q = x, y, ξ, representing the damping between the flexible wheel and the outer ring of the thin-walled bearing in the x-axis, y-axis, and torsional directions; k fcq q = x, y, ξ, representing the connection stiffness between the flexible wheel and the rigid wheel along the x-axis, y-axis, and torsional direction, and c fcq q = x, y, ξ, representing the damping between the flexible and rigid gears along the x-axis, y-axis, and torsional direction; F impx F impy T impξ This represents the projection of the impact excitation onto the x-axis, y-axis, and torsional direction; T in T represents the input torque of the camshaft.out Indicates the output torque transmitted by the rigid wheel; e f e c These represent the eccentricity of the flexible wheel and the eccentricity of the rigid wheel, respectively; e fop p = x, y, ξ, representing the displacement excitation of the eccentricity of the flexible wheel along the x-axis, y-axis, and torsional direction; e fcp p = x, y, ξ, representing the displacement excitation of the rigid wheel eccentricity in the x-axis, y-axis and torsional directions.

[0113] S55. Based on the established lumped parameter model, the Runge-Kutta method is used to solve the dynamic differential equations to obtain the vibration response signal of the system and realize simulation analysis.

[0114] In some embodiments of the present invention, a computer device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement a modeling method for a lumped parameter model of a harmonic reducer considering impact-type faults of thin-walled bearings, as provided in the foregoing embodiments.

[0115] In some embodiments of the present invention, a computer-readable storage medium is also provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements a modeling method for a lumped parameter model of a harmonic reducer considering impact-type faults of thin-walled bearings, as provided in the foregoing embodiments.

[0116] In some embodiments of the present invention, the spectrum of the simulated signal obtained by the present invention is as follows: Figure 5 As shown, the demodulation spectrum is as follows Figure 6 As shown, the spectrum and demodulated spectrum of the corresponding experimental signal are as follows: Figure 7 and Figure 8 As shown, the agreement at the characteristic frequency is clearly high. Comparison with experimental signals verifies the accuracy of the method and related conclusions of this invention, demonstrating that this invention can provide a theoretical basis for the condition monitoring and fault diagnosis of harmonic reducers.

[0117] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall fall within the protection scope of the present invention.

Claims

1. A modeling method for a lumped parameter model of a harmonic reducer, characterized in that, Includes the following steps: The interaction between the flexible gear and the outer ring of the thin-walled bearing is analyzed, and an interaction model between the flexible gear and the outer ring of the thin-walled bearing is obtained. Establish a lumped parameter model of the harmonic reducer as a whole; The rotation law of the outer ring of the thin-walled bearing and its influence on the fault impact time interval are analyzed, and the characteristic frequency of the thin-walled bearing of the harmonic reducer when a fault occurs is obtained. A mathematical model of the excitation when a thin-walled bearing has an impact-type fault is established as the input to the lumped parameter model; Establish and solve the differential equations of motion to obtain the vibration response signal; The analysis of the interaction between the flexible gear and the outer ring of the thin-walled bearing yields an interaction model, including: Based on the variational principle of elastic dynamics, the elastic deformation of the flexible wheel when meshing with the rigid wheel under working conditions is calculated. ; Based on the characteristics of harmonic drive and the distortion properties of the flexible wheel, the elastic deformation of the flexible wheel under the combined action of the wave generator and the rigid wheel is obtained by fitting. ; The deformation of the flexure when the outer ring of the thin-walled bearing interacts with it is obtained as follows: The force exerted by the outer ring of the thin-walled bearing on the flexure is obtained as follows: in, , These represent the radial and tangential forces exerted by the outer ring of the thin-walled bearing on the flexure, respectively. , These represent the angular coordinates of time and different positions of the flex wheel, respectively. The static stiffness of the flexible wheel; This is the coefficient of dynamic friction between the outer ring of the thin-walled bearing and the flexure. Replace the interaction between the outer ring of the thin-walled bearing and the flexible wheel rotating with the wave generator, and the two ends of the long shaft, with the resultant forces in the horizontal, vertical, and torsional directions of the absolute coordinate system, respectively: in, , This indicates the range of the force acting at one end of the major axis of the ellipse. Indicates the input speed of the harmonic reducer; This represents the radius of the inner wall surface of the flexible wheel before deformation.

2. The modeling method for a lumped parameter model of a harmonic reducer according to claim 1, characterized in that, The equivalent stiffness is: , , The equivalent stiffnesses are respectively in the horizontal, vertical, and torsional directions; , , is the amount of deformation of the flexible wheel. The calculated average deformation of the flexure is in axis, Projection of the axis and the direction of torsion.

3. The modeling method for a lumped parameter model of a harmonic reducer according to claim 1, characterized in that, When establishing the overall lumped parameter model of the harmonic reducer, the interaction between the camshaft and the rigid wheel is considered. A lumped parameter model of the overall harmonic reducer is established with the equivalent cam-thin-walled bearing outer ring-flexible wheel-rigid wheel as the research object. The equivalent cam is the whole composed of the camshaft and the thin-walled bearing inner ring.

4. The modeling method for a lumped parameter model of a harmonic reducer according to claim 1, characterized in that, The analysis of the rotation law of the outer ring of the thin-walled bearing and the influence of the rotation law on the fault impact time interval includes: The outer ring of the thin-walled bearing and the flexible gear are in clearance fit. The thin-walled bearing transmits torque from the input shaft to the output shaft, which together causes the outer ring of the thin-walled bearing to rotate significantly. When analyzing local faults in thin-walled bearings, it is necessary to consider the frequency fluctuations caused by the rotation of the outer ring of the bearing, using the outer ring rotation frequency as... Substituting into the calculation, the cage frequency... for: In the formula: Where is the diameter of the roller. The mean diameter of the thin-walled bearing. For roller contact angle, The input frequency of the harmonic reducer; The characteristic frequencies of inner and outer ring failures in thin-walled bearings are: in, The number of rollers.

5. The modeling method for a lumped parameter model of a harmonic reducer according to claim 1, characterized in that, The mathematical model for the excitation of impact-type failures in the inner and outer rings of thin-walled bearings is as follows: in, , , These represent amplitude modulation using the input frequency, output frequency, and the difference between the cage frequency and the inner or outer ring frequency as the fundamental frequency, respectively; This indicates the excitation of the nth pulse; This indicates the fault impact time interval affected by the fault type and the rotation of the outer ring of the thin-walled bearing; Indicates time.

6. A modeling method for a lumped parameter model of a harmonic reducer according to any one of claims 1-5, characterized in that, Establish the differential equations of motion, including: Establish the dynamic differential equations of the equivalent cam formed by the camshaft and the inner ring of the thin-walled bearing: Establish the dynamic differential equation for the outer ring of the thin-walled bearing: Establish the dynamic differential equation of the flexible wheel: Establish the dynamic differential equation of the rigid wheel: in, , , , These are the masses of the equivalent cam, the outer ring of the thin-walled bearing, the flexure, and the rigid wheel, respectively. , These are the moments of inertia of the equivalent cam, the outer ring of the thin-walled bearing, the flexure, and the rigid wheel, respectively. , These are the equivalent cam, thin-walled bearing outer ring, flex wheel, and rigid wheel, respectively. Displacement in the axial direction; , These are the equivalent cam, thin-walled bearing outer ring, flex wheel, and rigid wheel, respectively. Displacement in the axial direction; , These represent the rotational amounts of the equivalent cam, the thin-walled bearing outer ring, the flexible wheel, and the rigid wheel in the torsional direction, respectively. , , The equivalent cams are respectively in axis, Damping in the axial and torsional directions; , , , respectively the flexible wheel in axis, Damping in the axial and torsional directions, , , The rigid wheel is respectively in axis, Damping in the axial and torsional directions; , , The equivalent cams are respectively in axis, Stiffness in the axial and torsional directions; , , , respectively the flexible wheel in axis, Stiffness in the axial and torsional directions; , , The rigid wheel is respectively in axis, Stiffness in the axial and torsional directions; , , representing the connection stiffness between the equivalent cam and the rigid wheel in the horizontal and vertical directions, respectively. , , representing the damping between the equivalent cam and the rigid wheel in the horizontal and vertical directions, respectively; , , respectively representing the equivalent cam and the outer ring of the thin-walled bearing in terms of... axis, Connection stiffness in the axial and torsional directions; , This indicates the distance between the equivalent cam and the outer ring of the thin-walled bearing. axis, Damping in the axial and torsional directions; , This indicates that there is space between the flexible wheel and the outer ring of the thin-walled bearing. axis, Connection stiffness in the axial and torsional directions, , This indicates that there is space between the flexible wheel and the outer ring of the thin-walled bearing. axis, Damping in the axial and torsional directions; , This indicates the interaction between the flexible and rigid gears. axis, Connection stiffness in the axial and torsional directions, , This indicates the interaction between the flexible and rigid gears. axis, Damping in the axial and torsional directions; , , Indicates impact incentives in axis, Projection along the axis and in the torsional direction; This indicates the input torque of the camshaft; This indicates the output torque transmitted by the rigid wheel; , These represent the eccentricity of the flexible wheel and the eccentricity of the rigid wheel, respectively. , This indicates that the flexible wheel is eccentric in axis, Displacement excitation in the axial and torsional directions; , This indicates that the rigid wheel is eccentric in axis, Displacement excitation in the axial and torsional directions.

7. The modeling method for a lumped parameter model of a harmonic reducer according to claim 6, characterized in that, The Runge-Kutta method is used to solve the differential equations of motion, and the vibration response signal of the system is obtained to realize simulation analysis.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the modeling method for the lumped parameter model of the harmonic reducer as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the modeling method for the lumped parameter model of the harmonic reducer as described in any one of claims 1 to 7.

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