Joint servo transmission system electromechanical coupling vibration analysis method considering friction

Abstract

The invention relates to a joint servo transmission system electromechanical coupling vibration analysis method considering friction, and belongs to the field of gear nonlinear vibration analysis. The method comprises the following steps: in order to improve the modeling precision of an industrial robot joint servo transmission system, providing a friction-introduced electromechanical coupling dynamic model for industrial robot joint servo transmission and researching vibration response characteristics; stribeck friction is adopted to construct a friction model of a low-speed shaft of the joint servo transmission system of the industrial robot, and the joint servo transmission system is simplified into a system composed of a motor, a speed reducer and a load; secondly, establishing a joint servo transmission electromechanical coupling dynamic simulation model introducing friction based on friction nonlinearity and a coupling relation between a low-speed shaft and the friction, and verifying the correctness of the dynamic model through simulation analysis; finally, the influence of friction nonlinearity on the vibration performance of the joint servo transmission system is analyzed, and the vibration characteristic of friction on the joint servo transmission system of the industrial robot under electromechanical coupling is obtained.

Description

Technical Field

[0001] The present invention relates to a method for analyzing the electromechanical coupling vibration of a joint servo drive system considering friction, and belongs to the field of gear nonlinear vibration analysis. Background Art

[0002] Nonlinear friction is a complex, nonlinear, and uncertain natural phenomenon. For the joint servo drive system of an industrial robot, the friction link becomes an obstacle to improving the system performance, causing the transmission system response to exhibit crawling, oscillation, or steady-state error. Due to the sometimes strong nonlinear characteristics of friction, the system is severely affected by friction during startup, stop, and speed reversal. In order to eliminate or reduce the influence of friction and further improve the performance of the transmission system, vibration analysis of the joint servo drive system containing nonlinear factors such as friction is carried out to provide a basis for the design and vibration control of the joint drive system. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for analyzing the electromechanical coupling vibration of a joint servo drive system considering friction, explore the influence law of the friction coefficient on the electromechanical coupling vibration characteristics of the joint servo drive system, thereby providing theoretical support for the vibration reduction and noise reduction of the joint servo drive system, and providing a reference for improving the transmission accuracy, service life, and reliability of the joint servo drive system.

[0004] In the present invention, the frictional torque refers to the torque generated by friction, which is usually related to factors such as the joint rotation speed and the friction coefficient.

[0005] In the present invention, friction nonlinearity refers to the characteristic that the frictional force changes nonlinearly with the joint rotation speed, and is described by the Stribeck friction model, which includes a combination of static friction, Coulomb friction, and viscous friction.

[0006] The present invention is achieved by the following technical means:

[0007] Step1: Introduce the joint current information to establish a vibration model of an industrial robot based on the joint current, and its expression is as follows:

[0008]

[0009] Step2: Simplify the joint servo drive system into an electromechanical coupling model of a "motor - reducer - load" system, and establish a mathematical model of the electromechanical coupling vibration of this system, and its expression is as follows:

[0010]

[0011] Step 3. Introduce the friction non-linearity factor into the electromechanical coupling model of the joint servo drive system. According to Newton's second law, the dynamic equation of the low-speed shaft can be written as

[0012] Substitute the dynamic equation of the low-speed shaft into the electromechanical coupling vibration mathematical model in Step 2 to obtain

[0013]

[0014] Step 4. Calculate the frictional torque using the joint current, introduce Equation Simplify and substitute it into the model in Step 1 to obtain If the joint motor rotates at a constant speed, then It can be obtained that iα = C1q + T f , considering the damping of the joint system as part of the friction, then T f = iα.

[0015] Step 5. By programming the motion state of robot joint 2, collect the joint current signal during the motion of robot joint 2; after filtering the collected current and substituting it into Equation T f = iα in Step 4, solve through the model to obtain the frictional torque corresponding to each speed. Establish a system parameter identification model through the non-linear least squares method, and use the L-M (Levenberg-Marquardt) method to iteratively solve the model to establish the non-linear Stribeck friction model of the joint servo drive. Its expression is as follows

[0016]

[0017] There are 4 parameters (F s , F c , v s , B) to be identified in the Stribeck friction model, and the identification result will directly affect the friction compensation accuracy. Therefore, introduce the goodness of fit R 2 to evaluate the fitting degree of the model. The value range of R 2 is [0, 1]. The closer the value of R 2 is to 1, the better the fitting degree to the observed values. The goodness of fit calculation formula is as follows

[0018]

[0019] Among them, in the formula: R 2 is the goodness of fit; SSR is the regression sum of squares; SST is the total sum of squares of deviations; is the model prediction value; is the mean value of the actual data; y i is the actual data.

[0020] Let the parameter to be estimated be χ = (F s , F c , v s , B), the number of samples is N, and the deviation between the model prediction value and the actual value Therefore, the least - squares expression is:

[0021]

[0022] Step6. Build a vibration simulation model of the joint servo drive system to analyze the electromechanical coupling vibration process of the joint servo drive system with introduced friction nonlinear factors, and obtain the vibration characteristics of the friction on the joint servo drive system of the industrial robot under electromechanical coupling.

[0023] The purpose of the present invention is to provide an electromechanical coupling vibration analysis method for a joint servo drive system considering friction in view of the influence of friction on the electromechanical coupling vibration characteristics of the joint servo drive system. The feature lies in starting from the electromechanical coupling torsional vibration model of the joint servo drive system, researching and analyzing the influence law of friction nonlinearity on the electromechanical coupling vibration characteristics of the joint servo drive system. The invention includes three parts. In the first part, mainly establish the electromechanical coupling torsional vibration model of the joint servo drive system; in the second part, mainly derive the electromechanical coupling torsional vibration model of the joint servo drive system with friction; in the third part, establish a vibration response model of the industrial robot based on the joint current, establish a system parameter identification model through the nonlinear least - squares method, use the L - M (Levenberg - Marquardt) method to iteratively solve the model, and establish a nonlinear Stribeck friction model of the joint servo drive. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is the flow chart of the electromechanical coupling vibration characteristic analysis method for the joint servo drive system considering friction of the present invention;

[0025] Figure 2 is the dynamic model of the joint servo drive system of the present invention;

[0026] Figure 3 is the Stribeck curve graph of the joint system of the present invention;

[0027] Figure 4 is the friction - speed curve graph of the present invention;

[0028] Figure 5 is the curve graph of the low - speed shaft friction on the electromechanical coupling vibration characteristics of the system of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0029] The flow chart of an electromechanical coupling vibration analysis method for a joint servo drive system considering friction in an embodiment of the present invention is as shown in Figure 1As shown below, the steps of the present invention will be described in detail with reference to the flowchart. The specific implementation steps are as follows:

[0030] Step1. Simplify the joint servo drive system into an electromechanical coupling model of a "motor - reducer - load" system;

[0031] As a further solution of the present invention, in Step1:

[0032] In this example, the joint servo drive system of joint 2 of the Qianjiang OJR6 - 1 type six - degree - of - freedom serial industrial robot is taken as the research object, and its specific parameters are shown in Table 1. The electromechanical coupling dynamic model of the joint servo drive system considering the friction of the low - speed shaft is as Figure 2 shown. The construction of this model is relatively complex. First, a low - speed shaft friction model is established with speed as the input, and then the frictional force output by it is input into the defined dynamic model of the low - speed shaft.

[0033] Table 1 Main parameters of the servo drive system of joint 2

[0034]

[0035] Step2. Introduce the joint current information to establish a vibration model of the industrial robot based on the joint current, and its expression is as follows:

[0036]

[0037] Step3. Simplify the joint servo drive system into an electromechanical coupling model of a "motor - reducer - load" system, and establish an electromechanical coupling vibration mathematical model of this system, and its expression is as follows:

[0038]

[0039] Step4. Introduce the friction non - linear factor into the electromechanical coupling model of the joint servo drive system, and obtain the dynamic equation of the low - speed shaft from Newton's second law. The equation is as follows:

[0040]

[0041] Substitute the dynamic equation of the low - speed shaft into the electromechanical coupling vibration mathematical model in Step3 to obtain:

[0042]

[0043] Step5. Calculate the frictional torque using the joint current, introduce Equation Simplify and substitute it into the model in Step1 to obtain:

[0044]

[0045] If the joint motor rotates at a constant speed, then It can be obtained that:

[0046] iα = C1q + T f

[0047] Regarding the damping of the joint system as part of the friction, it can be obtained that:

[0048] T f = iα

[0049] Step6. By programming the motion state of robot joint 2, use a current transformer to collect the joint current signal during the motion of robot joint 2; after filtering the collected current, substitute it into the formula T f = iα in Step4, and obtain the friction torque corresponding to each speed through model solution. Establish a system parameter identification model by the nonlinear least squares method, and use the L-M (Levenberg-Marquardt) method to iteratively solve the model to establish a nonlinear Stribeck friction model for joint servo drive. Its expression is as follows:

[0050] Its model is as Figure 2 shown.

[0051] Step7. There are 4 parameters (F s , F c , v s , B) to be identified in the Stribeck friction model, and the identification result will directly affect the friction compensation accuracy. Therefore, the goodness of fit R 2 is introduced to evaluate the fitting degree of the model. The value range of R 2 is [0, 1]. The closer the value of R 2 is to 1, the better the fitting degree to the observed values. The goodness of fit calculation formula is as follows:

[0052]

[0053] Let the parameter to be estimated be χ = (F s , F c , v s , B), the number of sampling is N, and the deviation between the model prediction value and the actual value Therefore, the least squares expression is:

[0054]

[0055] Here, the L-M method is used to estimate the parameter χ. It combines the advantages of the gradient method and the Newton method, greatly reducing the chance of the error function falling into a local minimum. However, the selection of the initial solution is also the key for the L-M algorithm to quickly fit the correct curve and avoid iteration falling into a local optimum. According to the characteristics of the Stribeck friction model, the initial solutions of each parameter can be obtained from the actual data points, where the maximum static friction force F s Take the torque corresponding to the minimum speed in the data points, and the Coulomb friction force F c Take the minimum torque in the data points, and the Stribeck speed v s Take the speed corresponding to the minimum torque in the data points, and the viscous friction coefficient B is taken as the slope of the straight line passing through the last two groups of data points. Take the initial solution χ0 as (6.4, 6.17, 0.35, 0.19). The parameters identified by the L-M method are shown in Table 2:

[0056] Table 2 Stribeck model parameters

[0057]

[0058] After substituting the identification results into the Stribeck model, the identification results are as Figure 4 shown.

[0059] Step 7: Substitute the identified parameters into the established vibration simulation model. The initial rotational speed is 1000 r / min, and the friction torques are set to 0.5 times, 1 time, and 2 times respectively. The curve of the electromechanical coupling vibration characteristics of the low-speed shaft friction on the joint servo drive system is as Figure 5 shown. From Figure 5 it can be seen that in the initial stage, there are obvious fluctuations in the motor rotational speed, which then gradually decay to stability. For the same rotational speed with different frictions, when the friction force gradually increases, the load rotational speed and torque amplitude will increase accordingly, and the adjustment time of the output rotational speed gradually becomes smaller. For the output torque, as the friction force gradually increases, the adjustment time of the torque gradually decreases. However, due to the existence of the friction force in the joint servo drive system, after stabilization, the load requires the motor to provide force to overcome the friction, and as the friction force increases, the required motor driving force will also become larger and larger.

[0060] Through the above example analysis, it is summarized that: The present invention can be applied to the analysis of the electromechanical coupling vibration characteristics of the joint servo drive system, and the influence law of the friction coefficient on the electromechanical coupling vibration characteristics of the joint servo drive system can be obtained. The present invention not only provides theoretical support for the vibration reduction and noise reduction of the joint servo drive system, but also provides a reference for improving the transmission accuracy, service life and reliability of the joint servo drive system.

Claims

1. A method for analyzing the electromechanical coupling vibration of a joint servo drive system considering friction, characterized in that, The method comprises the following steps: Step 1: Introduce joint current information and establish an industrial robot vibration model based on joint current, and its expression is as follows: where q, represent the joint angle, angular velocity, and angular acceleration respectively; F is the joint input torque; M (q) is the robot inertia matrix; is the centrifugal and Coriolis force vector; G(q) is the gravity vector; T f is the frictional torque; Step 2: Simplify the joint servo drive system into an electromechanical coupling model of a "motor - reducer - load" system, and establish the electromechanical coupling vibration mathematical model of this system, and its expression is as follows: Among them, J E , J M , J L are the moment of inertia of the motor, the moment of inertia of the reducer, and the moment of inertia of the load respectively; C E , C M , C L are the viscous damping coefficient of the motor, the viscous damping coefficient of the reducer, and the viscous damping coefficient of the load respectively; T E , T W1 , T W2 , T L are the electromagnetic torque of the motor, the torque of coupling shaft 1, the torque of coupling shaft 2, and the load torque respectively; are the angular velocity of the permanent magnet synchronous servo motor, the angular velocity of the reducer, and the angular velocity of the end load respectively; C W1 , C W2 are the viscous damping coefficients of shafts 1 and 2 respectively; K W1 , K W2 are the stiffness coefficients of shafts 1 and 2 respectively; u is the reduction ratio; Step 3: Introduce friction nonlinear factors into the electromechanical coupling model of the joint servo drive system. According to Newton's second law, the dynamic equation of the low-speed shaft can be written as: Among them, is the angular acceleration of the low-speed shaft, T f is the frictional torque of the low-speed shaft, T W2 is the joint torsional torque, τ M is the output torque of the reducer; Substitute the dynamic equation of the low-speed shaft into the electromechanical coupling vibration mathematical model in Step 2 to obtain: Step 4: Calculate the frictional torque using the joint current, and introduce the formula After simplification and substitution into the model in Step 1, we get The joint motor rotates at a constant speed, so We can obtain iα = C1q + T f , considering the damping of the joint system as part of the friction, we can get T f = iα; where I j is the harmonic current amplitude; j is the harmonic order; θ j is the harmonic rotation angle, and α is the motor torque constant; Step 5: By programming the motion state of robot joint 2, collect the joint current signal during the motion of robot joint 2; after filtering the collected current, substitute it into formula T in Step 4 f = iα, and solve for the friction torque corresponding to each speed through model solution; establish a system parameter identification model by the nonlinear least squares method, and use the L-M (Levenberg-Marquardt) method to iteratively solve the model to establish a nonlinear Stribeck friction model for joint servo drive, and its expression is as follows: Among them, the variable ω is the joint rotation speed (r / s); F s is the joint static friction force (N); F c is the joint Coulomb friction force (N); B is the system viscous friction coefficient (Ns / m); v s is the Stribeck speed (m / s); Step 6: Build a vibration simulation model of the joint servo drive system to analyze the electromechanical coupling vibration process of the joint servo drive system with friction nonlinear factors introduced, and obtain the vibration characteristics of the friction on the joint servo drive system of the industrial robot under electromechanical coupling.

2. The method according to claim 1, characterized in that, The friction nonlinear factor is the Stribeck friction model. Among them, the four parameters of the model include the joint rotation speed, the joint static friction force, the Coulomb friction force, and the system viscous friction coefficient.

3. The method according to claim 1, wherein The dynamic equation of the low-speed shaft in Step 3 is expressed by Newton's second law. Among them, there is a relationship between the angular acceleration of the low-speed shaft, the friction torque, the joint torsion torque, and the output torque of the reducer.

4. The method according to claim 1, wherein The friction torque in Step 4 is calculated through the joint current, and is solved in combination with the harmonic current amplitude and the harmonic rotation angle, and then a friction model is established.

5. The method according to claim 1, wherein In Step 6, the model is iteratively solved by the nonlinear least squares method and the L-M (Levenberg-Marquardt) method to establish the nonlinear Stribeck friction model of the joint servo drive.

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