Modeling method and device for harmonic reducer lumped parameter model and medium

Abstract

The invention discloses a modeling method and device for a harmonic reducer lumped parameter model and a medium. The method comprises the following steps: analyzing the interaction of the flexible gear and the thin-wall bearing outer ring to obtain an interaction model of the flexible gear and the thin-wall bearing outer ring; establishing a lumped parameter model of the whole harmonic reducer; analyzing the rotation rule of the thin-wall bearing outer ring and the influence of the rotation rule on the fault impact time interval; establishing a mathematical model excited when the thin-wall bearing has an impact fault, and taking the mathematical model as the input of a lumped parameter model; and establishing and solving a motion differential equation. The method can well simulate the characteristic frequency when the thin-wall bearing of the harmonic reducer breaks down, explains the forming reason of vibration response frequency distribution in the harmonic transmission process, and fills the research blank that the coupling vibration of multiple components of the harmonic reducer lacks an effective mechanism model.

Description

Technical Field

[0001] The present 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 concentrated parameter model of a harmonic reducer. Background Art

[0002] Harmonic reducers are widely used in aerospace, industrial robots, precision machining equipment, medical equipment and other fields due to their high precision and transmission efficiency, large transmission ratio and compact structure. Existing research has mainly focused on transmission accuracy, tooth shape optimization, flexible wheel deformation and stress distribution, stiffness, etc. Due to the complex structure of harmonic reducers and incomplete mechanism research, existing research on fault diagnosis has mainly focused on data-driven intelligent diagnosis.

[0003] Zhao Zida 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) used the finite element method to establish a dynamic model of thin-walled bearings, analyzed the stress distribution and motion characteristics, and studied the vibration response characteristics of thin-walled bearings during local faults. However, it was a separate study of thin-walled bearings and did not consider the impact of the harmonic reducer as a whole. 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 harmonic reducer as a whole and studied the frequency distribution law of vibration response under normal conditions. However, it regards the thin-walled bearing outer ring and flexible wheel with clearance fit and relative motion as a whole, and lacks common faults of harmonic reducers, which has certain limitations. Summary of the invention

[0004] In order to solve at least one of the problems existing in the prior art, the present invention provides a modeling method, device and medium for a harmonic reducer concentrated parameter model considering the impact type fault of a thin-walled bearing, providing mechanism support for the fault diagnosis of the harmonic reducer. By establishing a 12-degree-of-freedom harmonic reducer concentrated parameter model and a mathematical model of excitation when considering the impact type fault, the vibration response characteristics of the harmonic reducer when there is a local fault (impact fault) are revealed through mechanism and simulation analysis, filling the research gap of the lack of an effective mechanism model for the coupled vibration of multiple components of the harmonic reducer, and having certain engineering application value.

[0005] In order to achieve the purpose of the present invention, the present invention provides a modeling method of a lumped parameter model of a harmonic reducer considering an impact type fault of a thin-walled bearing, comprising the following steps:

[0006] The interaction between the flexspline and the outer ring of the thin-walled bearing is analyzed, and the interaction model between the flexspline and the outer ring of the thin-walled bearing is obtained;

[0007] Establish the overall lumped parameter model of the harmonic reducer;

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

[0009] A mathematical model of excitation when a thin-walled bearing has an impact fault is established as the input of the lumped parameter model.

[0010] Establish and solve the differential equation of motion 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 to obtain the interaction model between the flexspline and the outer ring of the thin-walled bearing includes:

[0012] Based on the variational principle of elastic dynamics, the elastic deformation w generated when the flexible wheel meshes with the rigid wheel in the working state is calculated. 1 (t,θ);

[0013] Based on the characteristics of harmonic transmission and the distortion characteristics of the flexspline, the elastic deformation w of the flexspline under the combined action of the wave generator and the rigid wheel is obtained by fitting. 2 (t,θ);

[0014] The deformation of the flexible wheel when the outer ring of the thin-walled bearing interacts with the flexible wheel is w(t,θ)=w 2 (t,θ)-w 1 (t,θ), the force exerted by the outer ring of the thin-walled bearing on the flexible wheel is obtained as:

[0015] q r (t,θ)=max(w(t,θ),0)·K

[0016] q t (t,θ)=μ·q r (t,θ)

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

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

[0019]

[0020] in, Represents the range of the force at one end of the major axis of the ellipse; ω n represents the input speed of the harmonic reducer; R represents the inner wall radius before the flexible wheel is deformed.

[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) is 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 flexspline calculated from the deformation of the flexspline w(t, θ) on the x-axis, y-axis and torsion direction.

[0026] Furthermore, when establishing the lumped parameter model of the harmonic reducer as a whole, the interaction between the camshaft and the rigid wheel is considered, and a lumped parameter model of the harmonic reducer as a whole is established with the equivalent cam-thin-walled bearing outer ring-flexible wheel-rigid wheel as the research object. The equivalent cam is a 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 wheel are clearance-fitted. The thin-walled bearing transfers the torque from the input shaft to the output shaft, which together makes the outer ring of the thin-walled bearing rotate significantly.

[0029] When analyzing local faults of thin-walled bearings, it is necessary to consider the frequency fluctuation caused by the rotation of the outer ring of the thin-walled bearing. The frequency of the outer ring is f o Substitute into the calculation, and the cage rotation frequency f r for:

[0030]

[0031] Where: d is the roller diameter, D is the median diameter of the thin-walled bearing, α is the roller contact angle, and f n is the input frequency of the harmonic reducer;

[0032] The characteristic frequency of the inner and outer ring faults of thin-walled bearings is:

[0033]

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

[0035] Furthermore, combined with the outer ring rotation law, an impact excitation model is established when there is an impact fault on the inner and outer rings of a thin-walled bearing:

[0036]

[0037] Among them, a in (t), a out (t), a c (t) represents the amplitude modulation of multiple frequencies with input rotation frequency, output rotation frequency, and the rotation frequency difference between the cage and the inner ring or the outer ring as the base frequency; t impi It indicates the time interval of fault impact affected by the fault type and the rotation of the outer ring of the thin-walled bearing. It represents the nth pulse excitation, and its occurrence time is the sum of the time intervals of the previous n pulses; t represents time.

[0038] Furthermore, the differential equation of motion is established, including:

[0039] The dynamic differential equation of the equivalent cam composed of the camshaft and the inner ring of the thin-walled bearing is established:

[0040]

[0041] Establish the dynamic differential equation of 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] Among them, m w 、m o、m f 、m c are the masses of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel respectively; I p , p=w, o, f, c, are the moments of inertia of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel respectively; x p , p = w, o, f, c, are the displacements of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the x-axis direction respectively; y p , p = w, o, f, c, are the displacements of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the y-axis direction respectively; θ p , p = w, o, f, c, which are the rotation amounts of the equivalent cam, thin-walled bearing outer ring, flexible wheel and rigid wheel in the torsion direction respectively; c pq , p=w,f,c, q=x,y,ξ, which are the damping of equivalent cam, flexspline and rigid wheel in x-axis, y-axis and torsional direction respectively; k pq , p=w,f,c, q=x,y,ξ, which are the stiffness of equivalent cam, flexspline and rigid wheel in x-axis, y-axis and torsional direction respectively; k wcq , q = x, y, respectively represent the connection stiffness between the equivalent cam and the rigid wheel in the horizontal and vertical directions, c wcq , q = x, y, respectively representing the damping between the equivalent cam and the rigid wheel in the horizontal and vertical directions; k woq , q = x, y, ξ, respectively represent the connection stiffness between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction; c woq , q = x, y, ξ, represents the damping between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsion direction; k foq , q = x, y, ξ, represents the connection stiffness between the flexspline and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional directions, c foq , q = x, y, ξ, represents the damping between the flexspline and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction; k fcq , q = x, y, ξ, represents the connection stiffness between the flexible wheel and the rigid wheel in the x-axis, y-axis and torsion direction, c fcq , q = x, y, ξ, represents the damping between the flexible wheel and the rigid wheel in the x-axis, y-axis and torsion direction; F impx 、F impy 、T impξ represents the projection of the impact excitation on the x-axis, y-axis and torsion direction; T in Indicates the input torque of the camshaft; T out Indicates the output torque transmitted by the rigid wheel; e f 、e c They represent the eccentricity of the flexible wheel and the rigid wheel respectively; e fop, p = x, y, ξ, represents the displacement excitation of the flexspline eccentricity in the x-axis, y-axis and torsion direction; e fcp , p = x, y, ξ, represents the displacement excitation of the rigid wheel eccentricity in the x-axis, y-axis and torsional direction.

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

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

[0050] A computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements a modeling method for the aforementioned harmonic reducer concentrated parameter model.

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

[0052] (1) The present invention takes into account the relative rotation and interaction characteristics and matching state of the thin-walled bearing outer ring and the flexible spline, and establishes an interaction model between the thin-walled bearing outer ring and the flexible spline by calculating the deformation and force of the flexible spline, thereby obtaining a more complete harmonic transmission concentrated parameter model.

[0053] (2) The present invention establishes a mathematical model of the impact sequence that takes into account 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 concentrated parameter model of the harmonic reducer that takes into account impact-type faults.

[0054] (3) The present invention reveals the vibration response characteristics of the harmonic reducer when a local fault exists through mechanism and simulation analysis, filling the research gap of the lack of an effective mechanism model for the coupled vibration of multiple components of the harmonic reducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of a modeling method of a lumped parameter model of a harmonic reducer taking into account impact-type faults of thin-walled bearings provided by an embodiment of the present invention.

[0056] Figure 2 Schematic diagram of the experimental platform constructed in the embodiment of the present invention.

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

[0058] Figure 4It is a schematic diagram of the rotation frequency variation curve of the outer ring of a thin-walled bearing under different working conditions measured in an embodiment of the present invention.

[0059] Figure 5 It is a simulated signal spectrum diagram solved by using the proposed method in an embodiment of the present invention.

[0060] Figure 6 It is a demodulation spectrum of a simulated signal solved by using the proposed method in an embodiment of the present invention.

[0061] Figure 7 4 is a spectrum diagram of a signal measured in an experiment of an embodiment of the present invention.

[0062] Figure 8 3 is a demodulation spectrum diagram of a signal measured in an experiment of an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] See also Figure 1 The present invention provides a modeling method for a lumped parameter model of a harmonic reducer considering an impact-type failure of a thin-walled bearing, comprising the following steps:

[0065] S1. Analyze the interaction between the flexspline and the outer ring of the thin-walled bearing, and obtain the interaction model between the flexspline 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 w generated when the selected flexible wheel with fixed bottom (such as top hat type flexible wheel) meshes with the rigid wheel in the working state. 1 (t,θ);

[0068] S12. Based on the characteristics of harmonic transmission and the distortion characteristics of the flexible wheel, the elastic deformation w of the flexible wheel under the combined action of the wave generator and the rigid wheel is fitted. 2 (t,θ);

[0069] S13, the deformation of the flexible wheel when the outer ring of the thin-walled bearing interacts with the flexible wheel is w(t,θ)=w 2 (t,θ)-w 1 (t,θ), and then the force exerted by the outer ring of the thin-walled bearing on the flexible wheel is obtained:

[0070] q r (t,θ)=max(w(t,θ),0)·K

[0071] q t (t,θ)=μ·q r (t,θ)

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

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

[0074]

[0075] The equivalent stiffness is calculated as:

[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, Indicates the range of the force at one end of the major axis of the ellipse; k fox (t), k foy (t), k foξ (t) are the equivalent stiffness in the horizontal, vertical and torsional directions, δ i (t), i = x, y, ξ, is the projection of the average deformation of the flexspline calculated from the deformation of the flexspline w(t, θ) on the x-axis, y-axis and torsion direction; R represents the inner wall radius before the flexspline is deformed; ω n Indicates the input speed of the harmonic reducer.

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

[0081] On the basis of step S1, combined with 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 with the equivalent cam (the whole composed 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 shown in Figure 3 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 clearance-matched, and the thin-walled bearing, as a core transmission component, must transfer the torque from the input shaft to the output shaft, which together causes the outer ring to rotate significantly;

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

[0086] In some embodiments of the present invention, the harmonic drive test bench is constructed as follows: Figure 2 As shown, the servo motor is connected to the harmonic reducer through a coupling, and a load is set at the output end of the harmonic reducer. An endoscope is set to collect images, and the resolution and frame rate of the endoscope collected images are 1920×1080 and 30fps respectively. An acceleration sensor is used to collect vibration acceleration, and the sampling frequency of vibration acceleration data is 25600Hz.

[0087] The harmonic reducer includes a camshaft, a thin-walled bearing, a flexible wheel and a rigid wheel. The flexible wheel is fixed and the rigid wheel is output. The number of teeth of the flexible wheel and the rigid wheel are 200 and 202 respectively, and the speed ratio is 101. The number of rollers of the thin-walled bearing is 21, the roller diameter is 4mm, the bearing middle diameter is 36.74mm, and the roller contact angle is 0°. The experimental conditions are shown in Table 1.

[0088] Table 1 Working condition parameters of the embodiment

[0089]

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

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

[0092]

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

[0094] The characteristic frequency of the inner and outer ring faults of thin-walled bearings is:

[0095]

[0096] Among them, z n is the number of rollers. It can be seen that the outer ring of the thin-walled bearing rotates in the same direction as the camshaft, which will cause the fault characteristic frequency to fluctuate within a specific range lower than the theoretical value. Correspondingly, 1 / f ni and 1 / f no That is, the fault impact time interval will also fluctuate.

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

[0098] This step specifically includes:

[0099] Combined with the outer ring rotation law observed in the experiment, an impact excitation model is established when there is an impact fault on the inner and outer rings of the thin-walled bearing:

[0100]

[0101] Among them, a in (t), a out (t), a c (t) represents the amplitude modulation of multiple frequencies with input rotation frequency, output rotation frequency, and the rotation frequency difference between the cage and the inner ring or the outer ring as the base frequency; t impi Indicates the fault impact time interval affected by the fault type and the rotation of the thin-walled bearing outer ring; Indicates the nth pulse excitation, the time of its occurrence is the sum of the time intervals of the previous n pulses.

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

[0103] This step specifically includes:

[0104] S51. Establish the dynamic differential equation of the equivalent cam composed of 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] Among them, m w 、m o 、m f 、m c are the masses of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel respectively; I p , p=w, o, f, c, are the moments of inertia of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel respectively; x p , p = w, o, f, c, are the displacements of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the x-axis direction respectively; y p , p = w, o, f, c, are the displacements of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the y-axis direction respectively; θ p , p = w, o, f, c, which are the rotation amounts of the equivalent cam, thin-walled bearing outer ring, flexible wheel and rigid wheel in the torsion direction respectively; c pq , p=w,f,c, q=x,y,ξ, which are the damping of equivalent cam, flexspline and rigid wheel in x-axis, y-axis and torsional direction respectively; k pq , p=w,f,c, q=x,y,ξ, which are the stiffness of equivalent cam, flexspline and rigid wheel in x-axis, y-axis and torsional direction respectively; k wcq , q = x, y, respectively represent the connection stiffness between the equivalent cam and the rigid wheel in the horizontal and vertical directions, c wcq , q = x, y, respectively representing the damping between the equivalent cam and the rigid wheel in the horizontal and vertical directions; k woq , q = x, y, ξ, respectively represent the connection stiffness between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction; c woq , q = x, y, ξ, represents the damping between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsion direction; k foq , q = x, y, ξ, represents the connection stiffness between the flexspline and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional directions, c foq , q = x, y, ξ, represents the damping between the flexspline and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction; k fcq , q = x, y, ξ, represents the connection stiffness between the flexible wheel and the rigid wheel in the x-axis, y-axis and torsion direction, c fcq, q = x, y, ξ, represents the damping between the flexible wheel and the rigid wheel in the x-axis, y-axis and torsion direction; F impx 、F impy 、T impξ represents the projection of the impact excitation on the x-axis, y-axis and torsion direction; T in Indicates the input torque of the camshaft; T out Indicates the output torque transmitted by the rigid wheel; e f 、e c They represent the eccentricity of the flexible wheel and the rigid wheel respectively; e fop , p = x, y, ξ, represents the displacement excitation of the flexspline eccentricity in the x-axis, y-axis and torsion direction; e fcp , p = x, y, ξ, represents the displacement excitation of the rigid wheel eccentricity in the x-axis, y-axis and torsional direction.

[0113] S55. Combined with the established lumped parameter model, the Runge-Kutta method is used to solve the dynamic differential equations and obtain the vibration response signal of the system to 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 when the processor executes the computer program, a modeling method for a concentrated parameter model of a harmonic reducer taking into account impact-type failures of thin-walled bearings provided in the aforementioned embodiment is implemented.

[0115] In some embodiments of the present invention, a computer-readable storage medium is also provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for modeling a concentrated parameter model of a harmonic reducer taking into account impact-type failures of thin-walled bearings provided in the aforementioned embodiment is implemented.

[0116] In some embodiments of the present invention, the spectrum diagram of the simulated signal obtained by the present invention is as follows: Figure 5 As shown, the demodulated spectrum is Figure 6 As shown, the spectrum diagram and demodulation spectrum diagram of the corresponding experimental signal are as follows Figure 7 and Figure 8 Obviously, the degree of agreement at the characteristic frequency is high, and the accuracy of the method and related conclusions of the present invention is verified by comparing with the experimental signal, indicating that the present invention can provide a theoretical basis for the state monitoring and fault diagnosis of the harmonic reducer.

[0117] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and 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: The following steps are involved: The interaction between the flexspline and the outer ring of the thin-walled bearing is analyzed, and the interaction model between the flexspline and the outer ring of the thin-walled bearing is obtained; Establish the overall lumped parameter model of the harmonic reducer; The rotation law of the outer ring of the thin-walled bearing and its influence on the time interval of fault impact are analyzed, and the characteristic frequency of the harmonic reducer thin-walled bearing failure is obtained; A mathematical model of excitation when a thin-walled bearing has an impact fault is established as the input of the lumped parameter model. Establish and solve the differential equation of motion to obtain the vibration response signal.

2. The modeling method of a lumped parameter model of a harmonic reducer according to claim 1, characterized in that: The interaction between the flexspline and the outer ring of the thin-walled bearing is analyzed to obtain an interaction model between the flexspline and the outer ring of the thin-walled bearing, including: Based on the variational principle of elastic dynamics, the elastic deformation w1(t,θ) generated when the flexspline meshes with the rigid wheel in the working state is calculated; Based on the characteristics of harmonic transmission and the distortion characteristics of the flexspline, the elastic deformation w2(t,θ) of the flexspline under the combined action of the wave generator and the rigid wheel is obtained by fitting. The deformation of the flexible wheel when the outer ring of the thin-walled bearing interacts with the flexible wheel 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 flexible wheel is obtained as: q r (t,θ)=max(w(t,θ),0)·K q t (t,θ)=μ·q r (t,θ) Among them, q r (t,θ),q t (t,θ) respectively represent the radial and tangential forces of the outer ring of the thin-walled bearing on the flexspline; t and θ respectively represent the angular coordinates of the time and the different positions of the flexspline; K is the static stiffness of the flexspline; μ is the dynamic friction coefficient between the outer ring of the thin-walled bearing and the flexspline; Replace the interaction between the outer ring of the thin-walled bearing and the flexible wheel rotating with the wave generator at both ends of the long shaft with the resultant forces in the horizontal, vertical and torsional directions of the absolute coordinate system: in, Represents the range of the force at one end of the major axis of the ellipse; ω n represents the input speed of the harmonic reducer; R represents the inner wall radius before the flexible wheel is deformed.

3. The modeling method of a lumped parameter model of a harmonic reducer according to claim 2 is characterized in that: The equivalent stiffness is: k fox (t)=F x (t) / δ x (t) k foy (t)=F y (t) / δ y (t) k foξ (t)=M(t)·R / δ ξ (t) k fox (t), k foy (t), k foξ (t) is 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 flexspline calculated from the deformation of the flexspline w(t, θ) on the x-axis, y-axis and torsion direction.

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

5. The modeling method of 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 wheel are clearance-fitted. The thin-walled bearing transfers the torque from the input shaft to the output shaft, which together makes the outer ring of the thin-walled bearing rotate significantly. When analyzing local faults of thin-walled bearings, it is necessary to consider the frequency fluctuation caused by the rotation of the outer ring of the thin-walled bearing. The frequency of the outer ring is f o Substitute into the calculation, and the cage rotation frequency f r for: Where: d is the roller diameter, D is the median diameter of the thin-walled bearing, α is the roller contact angle, and f n is the input frequency of the harmonic reducer; The characteristic frequency of the inner and outer ring faults of thin-walled bearings is: Among them, z n is the number of rollers.

6. The modeling method of a lumped parameter model of a harmonic reducer according to claim 1, characterized in that: The mathematical model of excitation when there is an impact fault on the inner and outer rings of thin-walled bearings is: Among them, a in (t), a out (t), a c (t) respectively represent the amplitude modulation of multiple frequencies with input rotation frequency, output rotation frequency, and the rotation frequency difference between the cage and the inner ring or the outer ring as the base frequency; represents the nth pulse excitation; t impi It represents the fault impact time interval affected by the fault type and the rotation of the thin-walled bearing outer ring; t represents time.

7. A method for modeling a lumped parameter model of a harmonic reducer according to any one of claims 1 to 6, characterized in that: Set up the differential equations of motion, including: The dynamic differential equation of the equivalent cam composed of the camshaft and the inner ring of the thin-walled bearing is established: Establish the dynamic differential equation of 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: Among them, m w 、m o 、m f 、m c are the masses of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel respectively; I p , p=w, o, f, c, are the moments of inertia of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel respectively; x p , p = w, o, f, c, are the displacements of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the x-axis direction respectively; y p , p = w, o, f, c, are the displacements of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the y-axis direction respectively; θ p , p = w, o, f, c, which are the rotation amounts of the equivalent cam, thin-walled bearing outer ring, flexible wheel, and rigid wheel in the torsion direction respectively; c pq , p=w,f,c, q=x,y,ξ, which are the damping of equivalent cam, flexspline and rigid wheel in x-axis, y-axis and torsional direction respectively; k pq , p=w,f,c, q=x,y,ξ, which are the stiffness of equivalent cam, flexspline and rigid wheel in x-axis, y-axis and torsional direction respectively; k wcq , q = x, y, respectively represent the connection stiffness between the equivalent cam and the rigid wheel in the horizontal and vertical directions, c wcq , q = x, y, respectively representing the damping between the equivalent cam and the rigid wheel in the horizontal and vertical directions; k woq , q = x, y, ξ, respectively represent the connection stiffness between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction; c woq , q = x, y, ξ, represents the damping between the equivalent cam and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsion direction; k foq , q = x, y, ξ, represents the connection stiffness between the flexspline and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction, c foq , q = x, y, ξ, represents the damping between the flexspline and the outer ring of the thin-walled bearing in the x-axis, y-axis and torsional direction; k fcq , q = x, y, ξ, represents the connection stiffness between the flexible wheel and the rigid wheel in the x-axis, y-axis and torsion direction, c fcq , q = x, y, ξ, represents the damping between the flexible wheel and the rigid wheel in the x-axis, y-axis and torsion direction; F impx 、F impy 、T impξ represents the projection of the impact excitation on the x-axis, y-axis and torsion direction; T in Indicates the input torque of the camshaft; T out Indicates the output torque transmitted by the rigid wheel; e f 、e c They represent the eccentricity of the flexible wheel and the rigid wheel respectively; e fop , p = x, y, ξ, represents the displacement excitation of the flexspline eccentricity in the x-axis, y-axis and torsion direction; e fcp , p = x, y, ξ, represents the displacement excitation of the rigid wheel eccentricity in the x-axis, y-axis and torsional direction.

8. The modeling method of a lumped parameter model of a harmonic reducer considering impact type failure of a thin-walled bearing according to claim 7 is characterized in that: The Runge-Kutta method is used to solve the differential equation of motion and obtain the vibration response signal of the system to realize simulation analysis.

9. 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, the modeling method of the lumped parameter model of the harmonic reducer according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the modeling method of the lumped parameter model of the harmonic reducer according to any one of claims 1 to 8 is implemented.

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