Harmonic reducer optimization method based on lumped parameter model

Abstract

The application discloses a harmonic reducer optimization method based on a lumped parameter model. The method comprises the following steps: simplifying a harmonic reducer transmission system to obtain a simplified model; analyzing equivalent interaction forces between elements in the simplified model; establishing an overall lumped parameter model; deriving and solving a dynamics differential equation to obtain a vibration response signal of the harmonic reducer transmission system; and analyzing frequency characteristics of the signal to help improve manufacturing of the harmonic reducer, monitor an operation state of the harmonic reducer and diagnose faults. The modeling method of the multi-degree-of-freedom coupled lumped parameter model of the harmonic reducer can well simulate vibration response frequency characteristics when an actual physical model is running, explains reasons for forming vibration response frequency distribution in the transmission process of the harmonic reducer, and solves the engineering problem that there is a lack of effective mechanism models to study multi-component coupled vibration response characteristics of the harmonic reducer.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery fault diagnosis and signal processing, specifically to a method for optimizing harmonic reducers based on lumped parameter models. Background Technology

[0002] Harmonic reducers, as a type of gear transmission system, are characterized by their small size, large transmission ratio, smooth transmission, and small transmission error, and are therefore widely used in aerospace, industrial robotics, and other fields. Although harmonic reducers were invented as early as the mid-20th century and have been studied in many aspects, such as motion error, torsional stiffness, and robotic applications, research on harmonic reducers, especially their vibration mechanisms, is still far from complete compared to traditional gear transmission systems.

[0003] In the prior art, Yang Congbin et al. proposed a nonlinear dynamic modeling method for harmonic reducer transmission systems. However, in the dynamic modeling process, only the interaction between the components of the harmonic reducer in the torsional direction was considered, without considering the interaction in the radial direction. At the same time, it is impossible to analyze and interpret the vibration response in the radial degree of freedom during the transmission process of the harmonic reducer. Since the vibration in the torsional direction and the radial direction of the harmonic reducer transmission system will be coupled under certain working conditions, the characteristic frequency analysis must consider all degrees of freedom at the same time. Therefore, this method cannot effectively explain the characteristic frequencies that appear in the vibration response of the harmonic reducer transmission system under general working conditions (Yang Congbin, Zhang Xueyang, Zhang Caixia, et al. A nonlinear dynamic modeling method for harmonic reducer transmission systems [P]. Beijing: CN113722846A, 2021-11-30.).

[0004] Studies on the dynamics of harmonic reducers have not fully considered the interactions between various components during the transmission process of harmonic reducers, and have been unable to effectively explain the characteristic frequencies that appear in the vibration response under normal operating conditions of harmonic reducers. Furthermore, a lumped parameter dynamic model with multiple degrees of freedom in all directions for the entire harmonic reducer has not been established. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing an optimization method for harmonic reducers based on a lumped parameter model. The dynamic differential equations of the harmonic reducer in nine degrees of freedom in the translational and torsional directions are established. Through mechanistic and simulation analysis, the frequency distribution law of the vibration response of the harmonic reducer is revealed, solving the engineering problem of lacking an effective mechanistic model to study the coupled vibration response characteristics of multiple components in a harmonic reducer.

[0006] The objective of this invention is achieved by at least one of the following technical solutions.

[0007] The optimization method for harmonic reducers based on lumped parameter models includes the following steps:

[0008] S1. The harmonic reducer transmission system is simplified to obtain a simplified model;

[0009] S2. Analyze the equivalent interaction forces between the components in the simplified model;

[0010] S3. Establish an overall lumped parameter model;

[0011] S4. Derive and solve the dynamic differential equations to obtain the vibration response signal of the harmonic reducer transmission system. Analyze the frequency characteristics of the signal to help improve the manufacturing of the harmonic reducer, monitor the operating status of the harmonic reducer, and diagnose faults.

[0012] Furthermore, in step S1, the harmonic reducer transmission system mainly consists of six components: cam, thin-walled bearing inner ring, roller, thin-walled bearing outer ring, flexible wheel, and rigid wheel;

[0013] The power of the harmonic reducer transmission system is input by the cam. The inner ring of the thin-walled bearing is tightly fitted with the cam, and the force is transmitted to the outer ring of the thin-walled bearing through the roller. The outer ring of the thin-walled bearing and the flexible wheel are in surface contact. Under the action of the roller, they undergo elastic deformation together, so that the teeth of the flexible wheel and the teeth of the rigid wheel mesh with each other to transmit the power to the load.

[0014] Furthermore, in step S1, the harmonic reducer transmission system is simplified as follows:

[0015] Treating the inner ring of a thin-walled bearing as part of a cam, and simplifying the two into a single rigid body, is called an equivalent cam.

[0016] If we consider the outer ring of a thin-walled bearing as part of a flexure, and simplify the two into a single rigid body, we call it an equivalent flexure.

[0017] Furthermore, in the simplified model, power is input from the equivalent cam and transmitted to the equivalent flexible wheel via rollers. After the equivalent flexible wheel undergoes elastic deformation, its teeth mesh with the teeth of the rigid wheel to transmit power to the load.

[0018] Furthermore, in step S2, the meshing interaction force between the rigid wheel and the equivalent flexible wheel can be expressed as:

[0019] F fc (t)=f(T(t))

[0020] Where t is time, F fc(t) is the equivalent interaction force between the rigid wheel and the equivalent flexible wheel, T(t) is the function of the external load torque on the harmonic reducer changing with time, and f is the functional mapping relationship between the external load torque and the equivalent interaction force of the harmonic reducer.

[0021] This formula reflects the equivalent interaction force F between the rigid wheel and the equivalent flexible wheel. fc The periodicity of (t) will be consistent with the periodicity of the external load torque T(t) on the harmonic reducer, that is, the two have the same frequency characteristics.

[0022] Furthermore, the external load torque T(t) on the harmonic reducer includes its form, both constant load and variable load:

[0023] T(t) = T0

[0024] T(t) = T0 sin(2πf) c t)

[0025] Where t is time, f c It is the output frequency of the harmonic reducer, and T0 is the constant load;

[0026] F fc (t) is a function of time-varying equivalent force at the end of the long shaft of all forces acting on the meshing teeth of the harmonic gear during harmonic reduction transmission. Its components in each direction can be expressed as:

[0027]

[0028]

[0029]

[0030] in, Let β be the coordinate of the i-th gear tooth in the follower coordinate system OX'Y'. i Let f be the angle between the force acting on the i-th gear tooth and the axis of the following coordinate system OX'. i Let be the equivalent concentrated force on the i-th meshing tooth.

[0031] Furthermore, in step S2, the interaction force between the equivalent flexible wheel and the equivalent cam can be expressed as:

[0032]

[0033]

[0034]

[0035] Where m is the number of rollers, t is time, and F wfx(t) is a function of time-varying projection of the equivalent interaction force between the equivalent flexure and the equivalent cam along the x-axis, F. wfy (t) is a function of time representing the projection of the equivalent interaction force between the equivalent flexure and the equivalent cam onto the y-axis. M wf (t) is a function of time to represent the interaction torque generated by the equivalent interaction force between the equivalent flexure and the equivalent cam. ri F(t) is a function of the radial force at the i-th roller as a function of time. μi (t) is a function of the tangential force at the i-th roller as a function of time. It is a function of the angle between the radial force at the i-th roller and the x-axis direction as a function of time.

[0036] Furthermore, compared to the equivalent flexible wheel, the deformation of the roller can be ignored. In this case, the radial force on the roller can be considered as the force causing the deformation of the equivalent flexible wheel; therefore, the radial and tangential forces on the roller can be expressed as:

[0037] F ri (t)=max(Δρ i (t),0)k f

[0038] F μi (t)=F ri (t)μ

[0039] Where t is time, k f The deformation stiffness, Δρ, is determined by factors such as the material and shape of the equivalent flexible wheel itself. i (t) is a function of the deformation of the equivalent flexure at each roller position as a function of time, μ is the rolling friction coefficient between the roller and the equivalent flexure, and it is assumed to be pure rolling in the assumptions; the reason for taking max(Δρ,0) is that when Δρ is less than 0, it means that the roller and the equivalent flexure have lost contact, so the force on it is 0.

[0040] Furthermore, step S3 includes the following steps:

[0041] S3.1 Based on the interaction force form between the rigid wheel and the equivalent flexible wheel, the relationship between the equivalent stiffness and the equivalent interaction force between the rigid wheel and the equivalent flexible wheel can be considered as follows:

[0042] F fcx 1 (t)=k fc (t)δ fc cos(α fc )

[0043] F fcy 1(t)=k fc (t)δ fc sin(α fc )

[0044] M fc (t)=k fc (t)δ fc r fc

[0045] Where t is time, F fcx 1 (t) is F fc (t) along x in the moving coordinate system 1 The projection along the axis is a function of time, F fcy 1 (t) is F fc (t) along y in the moving coordinate system 1 The projection along the axis is a function of time, M fc (t) is F fc The interaction torque generated under the action of (t) is a function of time, k fc (t) is a function of the equivalent stiffness between the rigid wheel and the equivalent flexible wheel as a function of time, δ fc It is the relative motion and displacement between the rigid wheel and the equivalent flexible wheel, α fc It is k fc In the moving coordinate system, with x 1 The angle between the axes, r fc It is the equivalent interaction radius between the rigid wheel and the equivalent flexible wheel;

[0046] S3.2. Based on the interaction force form between the equivalent flexible wheel and the equivalent cam, the relationship between the equivalent stiffness and the equivalent interaction force between the equivalent flexible wheel and the equivalent cam can be considered as follows:

[0047]

[0048]

[0049]

[0050] Where t is time, k wfx (t) is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the x-axis direction as a function of time, k wfy (t) is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the y-axis direction as a function of time, k wft (t) is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the torsional direction as a function of time. It is the average deformation of the equivalent flexible wheel, r wfIt is the equivalent interaction radius between the equivalent flexible wheel and the equivalent cam;

[0051] S3.3. Combining the equivalent lumped parameter model of the interaction between components in steps S3.1 and S3.2, establish the overall lumped parameter model of the harmonic drive.

[0052] Furthermore, step S4 includes the following steps:

[0053] S4.1 Establish the dynamic differential equation of the equivalent cam:

[0054]

[0055] S4.2 Establish the dynamic differential equation of the equivalent flexible wheel:

[0056]

[0057] S4.3 Establish the dynamic differential equation of the rigid wheel:

[0058]

[0059] Where t is time, m w ,m f ,m c These are the masses of the equivalent cam, the equivalent flexure, and the rigid wheel, respectively. w ,I f ,I c These are the moments of inertia of the equivalent cam, the equivalent flexure, and the rigid wheel, respectively, x w ,x f ,x c These represent the displacements of the equivalent cam, equivalent flexure, and rigid wheel along the x-axis, and y-axis, respectively. w ,y f ,y c These are the displacements of the equivalent cam, equivalent flexible wheel, and rigid wheel in the y-axis direction, respectively, θ. w ,θ f ,θ c These represent the rotational amounts of the equivalent cam, equivalent flexure, and rigid wheel in the torsional direction, respectively, c. wp ,c fp ,c cp (p = x, y, t) represent the damping of the equivalent cam, equivalent flexible wheel, and rigid wheel along the x-axis, y-axis, and torsional directions, respectively, and k wp ,k fp ,k cp (p=x,y,t) represent the stiffness of the equivalent cam, equivalent flexible wheel, and rigid wheel in the x-axis, y-axis, and torsional directions, respectively, and d fc1 ,d fc2 These are the relative displacements of the equivalent flexible wheel and the rigid wheel at both ends of the major axis along the equivalent stiffness direction, ω.n It is the input speed, T in (t) is a function of the input torque as a function of time, T out (t) is a function of the output torque as a function of time;

[0060] S4.4. Based on the actual working conditions, substitute the parameters and use the Runge-Kutta method to solve the dynamic differential equations to obtain the vibration response signal of the system. Analyze the frequency characteristics of the signal to help improve the manufacturing of the harmonic reducer, monitor the operating status of the harmonic reducer, and diagnose faults.

[0061] Compared with the prior art, the present invention has the following advantages and effects:

[0062] (1) The modeling method of the multi-degree-of-freedom coupled lumped parameter model of the harmonic reducer of the present invention fully considers the interaction force between each component of the harmonic reducer transmission, and provides a qualitative and quantitative calculation method for using a stiffness damping system to replace the interaction force. It is the first complete lumped parameter model of harmonic transmission.

[0063] (2) The modeling method of the multi-degree-of-freedom coupled lumped parameter model of the harmonic reducer of the present invention can well show the frequency distribution law of the vibration response of the harmonic reducer, and lay a theoretical foundation for the fault diagnosis research of the harmonic reducer. Attached Figure Description

[0064] Figure 1 This is a flowchart of the harmonic reducer optimization method based on a lumped parameter model according to the present invention;

[0065] Figure 2 This is a diagram of the lumped parameter model of harmonic drive established in this invention;

[0066] Figure 3 This is a structural diagram of the harmonic reducer experimental platform used in this invention;

[0067] Figure 4 This is the simulated signal spectrum obtained by using the proposed method in Embodiment 1 of the present invention;

[0068] Figure 5 This is the spectrum of the signal measured in the experiment of Embodiment 1 of the method of the present invention;

[0069] Figure 6 This is the simulated signal spectrum obtained by using the proposed method in Embodiment 2 of the present invention;

[0070] Figure 7 This is the spectrum of the signal measured in the experiment of Embodiment 2 of the method of the present invention;

[0071] Figure 8This is the simulated signal spectrum obtained by using the proposed method in Embodiment 3 of the present invention;

[0072] Figure 9 This is the spectrum of the signal measured in the experiment of Embodiment 3 of the present invention. Detailed Implementation

[0073] 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.

[0074] Example 1: Simulation and Experiment Comparison of Harmonic Reducer with Input Speed ​​of 3000 r / min

[0075] The experimental setup structure is as follows: Figure 3 As shown, the parameters of the experimental setup are listed in Table 1. The sampling frequency of the sensor is f. s =51200Hz, load is T=80cos(2πf) c t)N·m.

[0076] Table 1. Operating Parameters for Example 1

[0077]

[0078] Using the modeling method proposed in this invention, the vibration response of the harmonic reducer during the transmission process under this working condition is simulated, and the correctness of the proposed method is verified by experimental results.

[0079] In this embodiment,

[0080] Optimization methods for harmonic reducers based on lumped parameter models, such as Figure 1 As shown, it includes the following steps:

[0081] S1. The harmonic reducer transmission system is simplified to obtain a simplified model;

[0082] The harmonic reducer transmission system mainly consists of six components: cam, thin-walled bearing inner ring, roller, thin-walled bearing outer ring, flexible wheel, and rigid wheel;

[0083] The power of the harmonic reducer transmission system is input by the cam. The inner ring of the thin-walled bearing is tightly fitted with the cam, and the force is transmitted to the outer ring of the thin-walled bearing through the roller. The outer ring of the thin-walled bearing and the flexible wheel are in surface contact. Under the action of the roller, they undergo elastic deformation together, so that the teeth of the flexible wheel and the teeth of the rigid wheel mesh with each other to transmit the power to the load.

[0084] The harmonic reducer transmission system is simplified as follows:

[0085] Treating the inner ring of a thin-walled bearing as part of a cam, and simplifying the two into a single rigid body, is called an equivalent cam.

[0086] If we consider the outer ring of a thin-walled bearing as part of a flexure, and simplify the two into a single rigid body, we call it an equivalent flexure.

[0087] Furthermore, in the simplified model, power is input from the equivalent cam and transmitted to the equivalent flexible wheel via rollers. After the equivalent flexible wheel undergoes elastic deformation, its teeth mesh with the teeth of the rigid wheel to transmit power to the load.

[0088] S2. Analyze the equivalent interaction forces between the components in the simplified model;

[0089] The meshing interaction force between the rigid wheel and the equivalent flexible wheel can be expressed as:

[0090] F fc (t)=f(T(t))

[0091] Where t is time, F fc (t) is the equivalent interaction force between the rigid wheel and the equivalent flexible wheel, T(t) is the function of the external load torque on the harmonic reducer changing with time, and f is the functional mapping relationship between the external load torque and the equivalent interaction force of the harmonic reducer.

[0092] This formula reflects the equivalent interaction force F between the rigid wheel and the equivalent flexible wheel. fc The periodicity of (t) will be consistent with the periodicity of the external load torque T(t) on the harmonic reducer, that is, the two have the same frequency characteristics.

[0093] The external load torque T(t) on the harmonic reducer includes its form, both constant load and variable load:

[0094] T(t) = T0

[0095] T(t) = T0 sin(2πf) c t)

[0096] Where t is time, f c It is the output frequency of the harmonic reducer, and T0 is the constant load;

[0097] F fc (t) is a function of time-varying equivalent force at the end of the long shaft of all forces acting on the meshing teeth of the harmonic gear during harmonic reduction transmission. Its components in each direction can be expressed as:

[0098]

[0099]

[0100]

[0101] in, Let β be the coordinate of the i-th gear tooth in the follower coordinate system OX'Y'. i Let f be the angle between the force acting on the i-th gear tooth and the axis of the following coordinate system OX'. i Let be the equivalent concentrated force on the i-th meshing tooth.

[0102] The interaction force between the equivalent flexure and the equivalent cam can be expressed as:

[0103]

[0104]

[0105]

[0106] Where m is the number of rollers, t is time, and F wfx (t) is a function of time-varying projection of the equivalent interaction force between the equivalent flexure and the equivalent cam along the x-axis, F. wfy (t) is a function of time representing the projection of the equivalent interaction force between the equivalent flexure and the equivalent cam onto the y-axis. M wf (t) is a function of time to represent the interaction torque generated by the equivalent interaction force between the equivalent flexure and the equivalent cam. ri F(t) is a function of the radial force at the i-th roller as a function of time. μi (t) is a function of the tangential force at the i-th roller as a function of time. It is a function of the angle between the radial force at the i-th roller and the x-axis direction as a function of time.

[0107] Compared to the equivalent flexible wheel, the deformation of the rollers can be ignored. Therefore, the radial force on the rollers can be considered as the force causing the deformation of the equivalent flexible wheel. Thus, the radial and tangential forces on the rollers can be expressed as:

[0108] F ri (t)=max(Δρ i (t),0)k f

[0109] F μi (t)=F ri (t)μ

[0110] Where t is time, k fThe deformation stiffness, Δρ, is determined by factors such as the material and shape of the equivalent flexible wheel itself. i (t) is a function of the deformation of the equivalent flexure at each roller position as a function of time, μ is the rolling friction coefficient between the roller and the equivalent flexure, and it is assumed to be pure rolling in the assumptions; the reason for taking max(Δρ,0) is that when Δρ is less than 0, it means that the roller and the equivalent flexure have lost contact, so the force on it is 0.

[0111] S3. Establish a lumped parameter model, including the following steps:

[0112] S3.1 Based on the interaction force form between the rigid wheel and the equivalent flexible wheel, the relationship between the equivalent stiffness and the equivalent interaction force between the rigid wheel and the equivalent flexible wheel can be considered as follows:

[0113] F fcx 1 (t)=k fc (t)δ fc cos(α fc )

[0114] F fcy 1 (t)=k fc (t)δ fc sin(α fc )

[0115] M fc (t)=k fc (t)δ fc r fc

[0116] Where t is time, F fcx 1 (t) is F fc (t) along x in the moving coordinate system 1 The projection along the axis is a function of time, F fcy 1 (t) is F fc (t) along y in the moving coordinate system 1 The projection along the axis is a function of time, M fc (t) is F fc The interaction torque generated under the action of (t) is a function of time, k fc (t) is a function of the equivalent stiffness between the rigid wheel and the equivalent flexible wheel as a function of time, δ fc It is the relative motion and displacement between the rigid wheel and the equivalent flexible wheel, α fc It is k fc In the moving coordinate system, with x 1 The angle between the axes, r fcIt is the equivalent interaction radius between the rigid wheel and the equivalent flexible wheel;

[0117] S3.2. Based on the interaction force form between the equivalent flexible wheel and the equivalent cam, the relationship between the equivalent stiffness and the equivalent interaction force between the equivalent flexible wheel and the equivalent cam can be considered as follows:

[0118]

[0119]

[0120]

[0121] Where t is time, k wfx (t) is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the x-axis direction as a function of time, k wfy (t) is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the y-axis direction as a function of time, k wft (t) is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the torsional direction as a function of time. It is the average deformation of the equivalent flexible wheel, r wf It is the equivalent interaction radius between the equivalent flexible wheel and the equivalent cam;

[0122] S3.3. Combining the equivalent lumped parameter model of the interaction between components in steps S3.1 and S3.2, establish the overall lumped parameter model of the harmonic drive. The results are as follows: Figure 2 As shown.

[0123] S4. Derive and solve the dynamic differential equations to obtain the vibration response signal of the harmonic reducer transmission system. Analyze the frequency characteristics of the signal to help improve the manufacturing of the harmonic reducer. Monitor the operating status of the harmonic reducer and diagnose faults, including the following steps:

[0124] S4.1 Establish the dynamic differential equation of the equivalent cam:

[0125]

[0126] S4.2 Establish the dynamic differential equation of the equivalent flexible wheel:

[0127]

[0128] S4.3 Establish the dynamic differential equation of the rigid wheel:

[0129]

[0130] Where t is time, m w ,m f ,mc These are the masses of the equivalent cam, the equivalent flexure, and the rigid wheel, respectively. w ,I f ,I c These are the moments of inertia of the equivalent cam, the equivalent flexure, and the rigid wheel, respectively, x w ,x f ,x c These represent the displacements of the equivalent cam, equivalent flexure, and rigid wheel along the x-axis, and y-axis, respectively. w ,y f ,y c These are the displacements of the equivalent cam, equivalent flexible wheel, and rigid wheel in the y-axis direction, respectively, θ. w ,θ f ,θ c These represent the rotational amounts of the equivalent cam, equivalent flexure, and rigid wheel in the torsional direction, respectively, c. wp ,c fp ,c cp (p = x, y, t) represent the damping of the equivalent cam, equivalent flexible wheel, and rigid wheel along the x-axis, y-axis, and torsional directions, respectively, and k wp ,k fp ,k cp (p=x,y,t) represent the stiffness of the equivalent cam, equivalent flexible wheel, and rigid wheel in the x-axis, y-axis, and torsional directions, respectively, and d fc1 ,d fc2 These are the relative displacements of the equivalent flexible wheel and the rigid wheel at both ends of the major axis along the equivalent stiffness direction, ω. n It is the input speed, T in (t) is a function of the input torque as a function of time, T out (t) is a function of the output torque as a function of time;

[0131] S4.4. Based on the actual working conditions, substitute the parameters and use the Runge-Kutta method to solve the dynamic differential equations, obtaining the simulated signal spectrum as shown below. Figure 4 As shown in the figure, the signal spectrum obtained from the comparative experiment is as follows: Figure 5 As shown, the components of the characteristic frequency at even multiples of the input frequency are in high agreement, verifying the effectiveness of the proposed method.

[0132] In terms of improving the manufacturing of harmonic reducers, after calculating the vibration response characteristic frequency of the harmonic reducer, in the actual design and manufacturing process of the harmonic reducer, the natural frequency of the designed harmonic reducer should be kept away from overlapping with the calculated vibration response characteristic frequency components, so as to avoid resonance phenomenon and accelerate the damage of the harmonic reducer, so as to make the harmonic reducer have a longer service life.

[0133] The presence of frequency components at odd multiples of the input frequency component of the experimental signal indicates that the device suffers from eccentricity or misalignment due to processing or installation.

[0134] In terms of condition monitoring and fault diagnosis of harmonic reducers, the vibration response signal of the harmonic reducer during operation is monitored in real time and compared with the calculated simulation signal. When the frequency components in the operating signal do not match those in the calculated signal, it indicates that the operating status of the harmonic reducer has encountered problems or some faults. At this time, the equipment should be stopped for inspection and maintenance.

[0135] Example 2: Simulation and Experimental Comparison of Harmonic Reducer with Input Speed ​​of 3500 r / min

[0136] The experimental setup structure is as follows: Figure 3 As shown, the parameters of the experimental setup are listed in Table 2. The sampling frequency of the sensor is f. s =51200Hz, load is T=80cos(2πf) c t)N·m.

[0137] Table 2 Operating Parameters for Example 2

[0138]

[0139] Using the modeling method proposed in this invention, the vibration response of the harmonic reducer during the transmission process under this working condition is simulated, and the correctness of the proposed method is verified by experimental results.

[0140] The obtained simulated signal spectrum is as follows: Figure 6 As shown in the figure, the signal spectrum obtained from the comparative experiment is as follows: Figure 7 As shown, the characteristic frequencies of the simulated signal are in high agreement with the characteristic frequency components of the experimental signal, verifying the effectiveness of the proposed method.

[0141] Example 3: Simulation and Experiment Comparison of Harmonic Reducer Input Speed ​​of 4000 r / min

[0142] The experimental setup structure is as follows: Figure 3 As shown, the parameters of the experimental setup are listed in Table 3. The sampling frequency of the sensor is f. s =51200Hz, load is T=80cos(2πf) c t)N·m.

[0143] Table 3. Operating Parameters for Example 3

[0144]

[0145]

[0146] Using the modeling method proposed in this invention, the vibration response of the harmonic reducer during the transmission process under this working condition is simulated, and the correctness of the proposed method is verified by experimental results.

[0147] The obtained simulated signal spectrum is as follows: Figure 8 As shown in the figure, the signal spectrum obtained from the comparative experiment is as follows: Figure 9 As shown, the characteristic frequencies of the simulated signal are in high agreement with the characteristic frequency components of the experimental signal, verifying the effectiveness of the proposed method.

[0148] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A harmonic reducer optimization method based on a lumped parameter model, characterized in that, Includes the following steps: S1. The harmonic reducer transmission system is simplified to obtain a simplified model; the harmonic reducer transmission system consists of six components: cam, thin-walled bearing inner ring, roller, thin-walled bearing outer ring, flexible wheel, and rigid wheel; The harmonic reducer transmission system is simplified as follows: Treating the inner ring of a thin-walled bearing as part of a cam, and simplifying the two into a single rigid body, is called an equivalent cam. Treating the outer ring of a thin-walled bearing as part of a flexible wheel, and simplifying the two into a single rigid body, is called an equivalent flexible wheel. S2. Analyze the equivalent interaction forces between the components in the simplified model; S3. Establish an overall lumped parameter model; S4. Derive and solve the dynamic differential equations to obtain the vibration response signal of the harmonic reducer transmission system. Analyze the frequency characteristics of the signal to help improve the manufacturing of the harmonic reducer, monitor its operating status, and diagnose faults. Specifically, this includes the following steps: S4.1 Establish the dynamic differential equation of the equivalent cam: S4.2 Establish the dynamic differential equation of the equivalent flexible wheel: S4.3 Establish the dynamic differential equation of the rigid wheel: in, It is time. These are the masses of the equivalent cam, the equivalent flexible wheel, and the rigid wheel, respectively. These are the moments of inertia of the equivalent cam, the equivalent flexible wheel, and the rigid wheel, respectively. These are the displacements of the equivalent cam, equivalent flexible wheel, and rigid wheel in the x-axis direction, respectively. These are equivalent cams, equivalent flexible wheels, and rigid wheels. Displacement in the axial direction, These are the rotational amounts of the equivalent cam, equivalent flexible wheel, and rigid wheel in the torsional direction, respectively. These are the equivalent cam, equivalent flexible wheel, and rigid wheel on the x-axis. Damping in the axial and torsional directions, , These are the equivalent cam, equivalent flexible wheel, and rigid wheel on the x-axis. Stiffness in the axial and torsional directions, These are the relative displacements of the equivalent flexible wheel and the rigid wheel at both ends of the major axis along the equivalent stiffness direction. It is the input speed. It is a function of the input torque as a function of time. It is a function of the output torque as a function of time; It is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the x-axis direction as a function of time. It is the equivalent flexible wheel and the equivalent cam in The equivalent stiffness in the axial direction is a function of time. It is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the torsional direction as a function of time. It is the equivalent interaction radius between the equivalent flexible wheel and the equivalent cam; It is a function of the equivalent stiffness between the rigid wheel and the equivalent flexible wheel as a function of time. yes In the moving coordinate system and The angle along the axial direction, It is the equivalent interaction radius between the rigid wheel and the equivalent flexible wheel; S4.

4. Based on the actual working conditions, substitute the parameters and use the Runge-Kutta method to solve the dynamic differential equations to obtain the vibration response signal of the system. Analyze the frequency characteristics of the signal to help improve the manufacturing of the harmonic reducer, monitor the operating status of the harmonic reducer, and diagnose faults.

2. The harmonic reducer optimization method based on a lumped parameter model according to claim 1, characterized in that: In step S1, The power of the harmonic reducer transmission system is input by the cam. The inner ring of the thin-walled bearing is tightly fitted with the cam, and the force is transmitted to the outer ring of the thin-walled bearing through the roller. The outer ring of the thin-walled bearing and the flexible wheel are in surface contact. Under the action of the roller, they undergo elastic deformation together, so that the teeth of the flexible wheel and the teeth of the rigid wheel mesh with each other to transmit the power to the load.

3. The harmonic reducer optimization method based on a lumped parameter model according to claim 1, characterized in that: In the simplified model, power is input from the equivalent cam and transmitted to the equivalent flexible wheel via rollers. After the equivalent flexible wheel undergoes elastic deformation, its teeth mesh with the teeth of the rigid wheel to transmit power to the load.

4. The harmonic reducer optimization method based on a lumped parameter model according to claim 1, characterized in that, In step S2, the meshing interaction force between the rigid wheel and the equivalent flexible wheel is expressed as: in, It is time. It is the equivalent interaction force between the rigid wheel and the equivalent flexible wheel. It is a function of the external load torque on the harmonic reducer as a function of time. This represents the functional mapping relationship between the external load torque and the equivalent interaction force of the harmonic reducer. This formula reflects the equivalent interaction force between the rigid wheel and the equivalent flexible wheel. The periodicity will be related to the external load torque on the harmonic reducer. Their periodicity is consistent, meaning they have the same frequency characteristics.

5. The harmonic reducer optimization method based on a lumped parameter model according to claim 1, characterized in that, External load torque on the harmonic reducer It includes two forms: constant load and variable load. in, It is time. It is the output frequency of the harmonic reducer. For fixed load; It is a function of time-varying equivalent force at the end of the long shaft of all forces acting on the meshing teeth of the harmonic gear during harmonic reduction transmission, and its components in each direction are expressed as: in, For the first Each gear tooth in the following coordinate system coordinates For the first The forces acting on each gear tooth and the following coordinate system The included angle of the axis, For the first The equivalent concentrated force on each meshing tooth.

6. The harmonic reducer optimization method based on a lumped parameter model according to claim 1, characterized in that, In step S2, the interaction force between the equivalent flexure and the equivalent cam is expressed as: in, It is the number of rollers. It is time. It is a function of time-varying projection of the equivalent interaction force between the equivalent flexible wheel and the equivalent cam onto the x-axis. It is the equivalent interaction force between the equivalent flexible wheel and the equivalent cam. The projection along the axis is a function of time. It is a function of time-varying interaction torque generated by the equivalent interaction force between the equivalent flexible wheel and the equivalent cam. It is the first The radial force at each roller is a function of time. It is the first The tangential force at each roller is a function of time. It is the first The angle between the radial force at the roller and the x-axis direction is a function of time.

7. The harmonic reducer optimization method based on a lumped parameter model according to claim 6, characterized in that, Compared to the equivalent flexible wheel, the deformation of the rollers is negligible. In this case, the radial force on the rollers is considered the force causing the deformation of the equivalent flexible wheel; the radial and tangential forces on the rollers are expressed as: in, It is time. The deformation stiffness is determined by the material and shape of the equivalent flexible wheel itself. Let be a function of the deformation of the equivalent flexure at each roller location as a function of time. Let be the coefficient of rolling friction between the roller and the equivalent flexible wheel, which is assumed to be pure rolling in the assumptions.

8. The harmonic reducer optimization method based on a lumped parameter model according to claim 7, characterized in that, Step S3 includes the following steps: S3.1 Based on the interaction force form between the rigid wheel and the equivalent flexible wheel, consider the relationship between the equivalent stiffness and the equivalent interaction force between the rigid wheel and the equivalent flexible wheel as follows: in, It is time. yes Along in the moving coordinate system The projection along the axis is a function of time. yes Along in the moving coordinate system The projection along the axis is a function of time. yes The interaction torque generated under the action of is a function of time. It is a function of the equivalent stiffness between the rigid wheel and the equivalent flexible wheel as a function of time. It refers to the relative motion and displacement between the rigid wheel and the equivalent flexible wheel. yes In the moving coordinate system and The angle along the axial direction, It is the equivalent interaction radius between the rigid wheel and the equivalent flexible wheel; S3.

2. Based on the interaction force form between the equivalent flexible wheel and the equivalent cam, the relationship between the equivalent stiffness and the equivalent interaction force between the equivalent flexible wheel and the equivalent cam is as follows: in, It is time. It is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the x-axis direction as a function of time. It is the equivalent flexible wheel and the equivalent cam in The equivalent stiffness in the axial direction is a function of time. It is a function of the equivalent stiffness of the equivalent flexure and equivalent cam in the torsional direction as a function of time. It is the average deformation of the equivalent flexible wheel. It is the equivalent interaction radius between the equivalent flexible wheel and the equivalent cam; S3.

3. Combining the equivalent lumped parameter model of the interaction between components in steps S3.1 and S3.2, establish the overall lumped parameter model of the harmonic drive.

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