Method for calculating joint motion parameters of hypoid mechanical arm by using nonlinear hybrid friction model

Abstract

The invention discloses a method for calculating joint motion parameters of a hypoid mechanical arm by using a nonlinear mixed friction model, and relates to the field of joint mechanics calculation of robotics. Although a traditional calculation model can describe the relation between the friction force and the relative movement speed or the positive pressure of the contact surface to a certain degree, the nonlinear characteristic of the friction force is ignored, large errors exist in movement parameters, and the current design requirement for a high-precision mechanical arm for rapid development of the industrial automation technology cannot be met. In order to improve the calculation precision of the joint motion parameters of the mechanical arm, the invention provides a method for calculating the joint motion parameters of the hypoid mechanical arm by using a nonlinear mixed friction model, the friction model is based on a Gauss friction model and is combined with a coulomb friction model, a viscous friction model and a Stribeck friction model, and the joint motion parameters of the hypoid mechanical arm are calculated. And a more accurate pre-calculation means is provided for subsequent structural design of the mechanical arm, manufacturing of a rod piece and a machine body and track control of an end effector.

Description

Technical Field

[0001] The present invention involves multiple interdisciplinary fields such as robotics, tribology and dynamic modeling, and is particularly aimed at the accurate calculation of joint parameters of high-precision and high-load-capacity industrial robotic arms. With the rapid development of industrial automation technology, robotic arms have been widely used in many fields such as manufacturing and logistics. The friction characteristics of robotic arm joints are key factors affecting their motion accuracy, dynamic performance and service life. The development of a nonlinear mixed friction model that can accurately calculate the joint parameters of robotic arms is of great significance for improving the overall performance of robotic arms. Background Art

[0002] Traditional robot joint friction models are mainly based on simple linear relationships, such as the Coulomb friction model and the viscous friction model. These models can describe the relationship between friction and relative motion speed or contact surface positive pressure to a certain extent, but ignore the nonlinear characteristics of friction, such as the change of friction coefficient, the conversion between static friction and dynamic friction, etc. Therefore, traditional models often have large errors when calculating robot joint parameters and cannot meet the design requirements of high-precision robot arms. In recent years, with the deepening of tribology research, people have gradually realized the nonlinear characteristics of friction and developed a series of more complex friction models, such as the Stribeck friction model and the Gaussian friction model. The Stribeck friction model can describe the complex relationship between friction and relative sliding speed, including static friction, dynamic friction and the transition stage between them. The Gaussian friction model is based on statistical principles and can more accurately describe the influence of joint friction on the driving force of the mechanism. However, these models still have some problems in practical applications, such as difficulty in determining parameters and high computational complexity.

[0003] Therefore, in order to overcome the limitations of traditional friction models and improve the calculation accuracy of robot arm joint parameters, the present invention proposes a method for calculating the robot arm joint motion parameters using a nonlinear mixed friction model. This method can more comprehensively describe the friction characteristics of the robot arm joints and provide a more accurate pre-calculation means for the design, manufacture and control of the robot arm. Summary of the invention

[0004] This algorithm proposes a method to calculate the motion parameters of the robot joint using a nonlinear mixed friction model, and establishes a nonlinear mixed friction model at the robot joint. The nonlinear mixed friction model is based on the Gaussian friction model, combined with the Coulomb friction model, the viscous friction model and the Stribeck friction model, which can more accurately describe the friction characteristics of the robot joint and more accurately calculate the relevant parameters of the robot joint motion.

[0005] 1. Limit the range of motion angles and speeds of each joint, and determine the range of friction parameters of each joint based on the contact material and lubrication conditions of the joints to ensure that the calculation range is consistent with the actual range of motion of the robot arm and avoid over-calculation.

[0006] 2. Use the "Delete" function in SolidWorks 3D software to remove parts that do not affect the calculation results to obtain a simpler and more intuitive 3D model. The removed parts are the motor, support structure, and shock-absorbing structure. The "Measure" function in SolidWorks 3D software can obtain the basic parameters of each connecting rod, including the rod mass, the center of mass position of the connecting rod, the moment of inertia of the connecting rod, and the value of the inertia tensor of the connecting rod.

[0007] 3. The robot arm is modeled in the software, mainly using the Robotic toolkit in Matlab software. The toolkit needs to be installed and debugged repeatedly to ensure that the toolkit can adapt to the current computer software operating environment and run correctly. Execute the build command to obtain the animation file of the robot arm's movement process, and play it step by step to check whether there is discontinuity and excessive jitter during the movement of each joint of the robot arm.

[0008] 4. Perform kinematic calculations. The main purpose of this calculation is to verify that the set working conditions are achievable. Kinematic calculations include two steps: forward kinematic calculations and inverse kinematic calculations. The calculation steps are as follows: Figure 1 As shown. In the calculation process, the forward kinematics study is to calculate the position and posture of the tool coordinate system relative to the fixed coordinate system. After the joint angle is given, the general expression of the matrix transformation relationship between the two adjacent joint coordinate systems is obtained. The link transformation matrix is ​​multiplied to obtain a transformation matrix of the coordinate system {N} relative to the coordinate system {0}, which is a function of the joint variables. By obtaining the values ​​collected by the sensor at the joint position, the position and posture of the robot end link in the Cartesian coordinate system can be represented by the matrix. The inverse kinematics study is to find the joint angle so that the tool coordinate system is located in a specific position and posture of the fixed coordinate system. For a robot with 6 revolute joints, the coordinate systems of the last three joints intersect at the same point, and the Pieper solution is usually used for analysis.

[0009] 5. To calculate the friction torque, the process requires first determining the forces and torques on the joints. There are two types of mechanical arm joints in industrial robot systems: rotary joints and translational joints. The former's various combinations can cover a wider range of working areas and are more widely used because of their simple structure and smoother movement. The rotational joint will generate constraints F in three directions. x 、F y 、F z , the constraint moments T in three directions x 、Ty and T z After determining, the calculation model of the nonlinear mixed friction model is constructed, which includes the three types of friction as follows:

[0010] (1) Coulomb friction. Assume that the joint is only affected by the Coulomb friction torque after overcoming the maximum static friction torque. The Coulomb friction torque T generated by the joint constraint force and constraint torque is fc and the maximum static friction torque T fs It can be expressed as

[0011] T fc =μ cc N1R n +μ cc (N2+N3)R p

[0012] T fs =μ sc N1R n +μ sc (N2+N3)R p

[0013] μ cc and μ sc are the Coulomb friction coefficient and the static friction coefficient, R n is the friction arm, R p is the pin radius. The equivalent pressure N1 generated by the axial constraint is |F z |,|F z | indicates F z Take the absolute value; equivalent pressure under lateral constraint Normal pressure due to restraint moment R b To bend the reaction arm.

[0014] (2) Viscous friction model. The viscous friction model is a nonlinear function. Within the angular velocity range, after overcoming the Coulomb friction torque, as the speed increases, a viscous friction resistance torque will appear between the objects in relative motion, and it is linearly proportional to the speed. After static-dynamic conversion, the change in friction torque in the low-speed zone is proportional to the joint angular velocity. is linearly proportional, and its mathematical model is T v represents the viscous friction torque, B represents the viscous friction factor, Represents the joint angular velocity.

[0015] (3) Stribeck friction. The Stribeck effect is reflected in the transition stage between low speed and high speed. When the robot joint overcomes the static friction, the friction force is discontinuous at the moment when the joint changes from static friction to sliding friction. In the low-speed area, the joint friction torque decreases with the increase of angular velocity; in the transition stage, the Stribeck friction force becomes dominant. In the low-speed area, the Stribeck friction torque value is used instead of the viscous friction torque value. The formula of the Stribeck friction model is:

[0016]

[0017] T s is the Stribeck friction torque, θ sc is an empirical constant related to the nonlinearity of the Stribeck curve. The Stribeck curve is determined in the laboratory by performing a unidirectional friction test of a pin against a rotating disk under immersion lubrication conditions and creating a converging gap model based on the pin end contact shape.

[0018] Thus, the calculation model of the nonlinear mixed friction model is obtained. The nonlinear joint mixed friction model can better reflect the friction phenomenon in actual operation, especially the nonlinear behavior generated when the speed changes greatly. The expression of the friction torque of the joint in the case of rotational motion is:

[0019]

[0020] Where, T out is the external torque, |T out | represents the absolute value of the external torque; sgn(T out ) is a symbolic function. The specific calculation principle is as follows: out When the value is greater than 0, sgn(T out ) output is 1, when T out When the value is less than 0, sgn(T out ) output is -1, T out When the value is equal to 0, sgn(T out ) output is 0. The model can be used to accurately calculate the kinematic and dynamic parameters of the robot under different working conditions, such as speed, acceleration, torque, etc., to provide basic data support for subsequent optimization design.

[0021] Combined with the actual situation of joint movement, this function is plotted and analyzed in detail. The function graph is as follows: Figure 2As shown. When the joint is about to start rotating, the friction force is dominated by the maximum static friction force, and the movement is hindered until the external force overcomes the maximum static friction force and relative sliding occurs. At this time, the friction force is no longer dominated by the maximum static friction force, but gradually decreases to a smaller value. This is because the lubrication state between the two surfaces has changed. First, due to the viscosity of the lubricant, it cannot completely fill the gap, and in the transition stage with lower speed, the lubricant can only provide some lubrication at the boundary and is in a boundary lubrication state, accompanied by the Stribeck phenomenon. Then, as the speed increases, the lubricant is better filled between the two contact surfaces and is in a partial fluid lubrication state. At this time, the friction force is dominated by viscous friction.

[0022] 6. Calculate the joint torque according to dynamics. The construction of the dynamic equation of the robot arm usually adopts the Newton-Euler method or the Lagrange method. The former divides the robot arm into multiple rigid bodies or links and considers the force and torque relationship between each rigid body. It is more suitable for rigidly connected robot arm systems, so its generalized form is selected to calculate the driving torque. The Newton-Euler recursive dynamics algorithm has two steps in the solution process. The velocity and acceleration of each link are recursively calculated from the robot base to the end of the joint; then the interaction force and torque between the links and the driving torque of the joint are recursively calculated from the end link of the robot to the base. The specific process and parameters used are as follows: Figure 3 As shown in the figure, the joint torque values ​​under the consideration of friction are compared. The graph is drawn with time as the horizontal axis and the joint torque value as the vertical axis. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flowchart of an embodiment of a method for calculating kinematics of a robot arm according to the present invention;

[0024] Figure 2 It is the function graph of the nonlinear mixed friction model proposed by the present invention;

[0025] Figure 3 A flowchart of an embodiment of a method for calculating mechanical arm dynamics according to the present invention;

[0026] Figure 4 A schematic diagram of a system for calculating a certain type of mechanical arm on sale in the market used in the calculation example of the present invention;

[0027] Figure 5 is the joint speed value of a certain robot arm on the market used in the calculation example of the present invention;

[0028] Figure 6 This is the joint torque result of a certain robot arm on the market used in the calculation example of the present invention. DETAILED DESCRIPTION

[0029] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention unless otherwise specifically stated.

[0030] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0031] A method for calculating joint motion parameters of a hyperbolic manipulator using a nonlinear mixed friction model, comprising:

[0032] (1) By limiting the range of motion angles and speeds of each joint in the working condition, the range of friction parameters of each joint is determined according to the material and lubrication conditions of the joint. The friction parameters include the viscous friction factor B, the Stribeck curve parameter θ sc , Coulomb friction torque T fc , Maximum static friction torque value T fs ;

[0033] (2) Using SolidWorks 3D software, disassemble the rod structure, use the "delete" or "hide" function to remove the components that do not participate in the calculation from the calculation list, and obtain a simplified shell 3D model. Use the software's built-in calculation function to obtain the basic parameters of each connecting rod and draw a parametric system diagram; the basic parameters of the connecting rod include the connecting rod mass, the connecting rod center of mass position, the connecting rod moment of inertia, and the connecting rod inertia tensor value. The basic parameters are all expressed in matrix form, and the number of rows is the number of movable joints of the robot arm;

[0034] (3) After installing the Robotic toolkit in Matlab software, the animation file of the robot arm motion process is gradually output through repeated debugging of the input running program;

[0035] (4) By constructing and executing the kinematic solution code, the motion parameters of each joint when the friction effect is ignored are obtained as the judgment conditions of the nonlinear mixed friction model; the motion parameters of each joint include the joint motion speed, the coordinate points of the end effector motion trajectory, and the joint driving torque.

[0036] (5) By constructing and executing the calculation model of the nonlinear mixed friction model and running it, the motion parameters of each joint when the influence of friction on the running results is considered, and by constructing and executing the dynamic solution code, the torque value of each joint when the influence of friction is ignored is obtained; the model includes four judgment intervals. When the speed falls in different intervals, the code will run different calculation formulas. The overall expression of the model is: Among them, the robot arm joint speed External torque Tout , viscous friction factor B, Coulomb friction torque T fc , maximum static friction torque T fs , an empirical constant θ related to the nonlinearity of the Stribeck curve sc The calculated output parameter is the friction torque of the joint of the robot arm

[0037] (6) In the same time period, the joint torque values ​​with and without friction are compared, and a comparison chart is drawn by controlling the variables to show the change trend.

[0038] It is obtained by using the built-in calculation command of Matlab. When solving the dynamics forward, the input of the corresponding command is the trajectory point and the output is the joint torque.

[0039] The joint driving torque It is a matrix. The number of matrix rows is the number of movable joints of the robot arm or the number of joints studied. The number of matrix columns is the data set capacity related to the calculation step size. Within a certain working time, if the calculation step size is smaller, the number of matrix columns is larger. If the calculation step size is larger, the number of matrix columns is smaller.

[0040] The various joint motion parameters when considering the influence of friction on the operation results include the joint motion speed under the influence of friction, the end effector motion trajectory coordinate points under the influence of friction, the joint friction torque

[0041] The joint friction torque It is a matrix. The number of matrix rows is the number of movable joints of the robot arm or the number of joints studied. The number of matrix columns is the data set capacity related to the calculation step size. Within a certain working time, if the calculation step size is smaller, the number of matrix columns is larger. If the calculation step size is larger, the number of matrix columns is smaller.

[0042] 1. Take a robot arm currently available on the market as an example to develop a specific implementation method of the present invention. The robot arm has six rotating joints and is commonly used in welding scenarios. The motion conditions of the robot arm in the factory are complex and changeable. It is necessary to fully guarantee the reliability and safety of the robot arm structure and constrain and limit the joint operation speed and angle range. The motion range of the first three joints of the robot arm is (-170°, 170°), (-160°, 90°), (-90°, 175°), and the angle operation range of the last three joints is plus or minus 180°.

[0043] The parameters of the robot arm connecting rod are as follows.

[0044]

[0045]

[0046] The first three joints of the robot arm use rotary vector reducers, and the last three joints use hypoid gear reducers. The models of the hypoid joints are HY1-4, HY1-5, and HY1-6 respectively.

[0047] The viscous friction coefficient of the first three joints is 2.0Nms / rad, the empirical constant related to the nonlinearity of the Stribeck curve is 0.05, the Coulomb friction torque is 10N·m, and the maximum static friction torque is 20N·m; the viscous friction coefficient of the last three joints is 0.5Nms / rad, the empirical constant related to the nonlinearity of the Stribeck curve is 0.03, the Coulomb friction torque is 1.25N·m, and the maximum static friction torque is 3.6N·m.

[0048] 2. Use SolidWorks to disassemble the motor, reducer, and support structure in the 3D model of the robotic arm, and evaluate and measure the six rods to obtain the basic parameters of each connecting rod, as shown in the following table.

[0049]

[0050] Determine and draw the system construction results of the robot arm as follows Figure 4 As shown, the kinematics of the robot arm is calculated based on this.

[0051] 3. Take a working condition of the robot arm that lasts for 2 seconds as an example, set the upper arm and the lower arm to extend to a horizontal posture, and the joints at both ends of the lower arm and the elbow rotate. Because their rotation axes intersect vertically, external torque is generated on the components. Execute the build command to output the animation of the robot arm operation, and check step by step to ensure that the joints operate smoothly under this working condition.

[0052] 4. Perform kinematic calculations on the robot arm. The main purpose of kinematic calculations is to ensure that the set working conditions are achievable. The output joint motion speed is the basic judgment condition for the subsequent calculation of joint friction torque. Draw the motion of each joint as shown in Figure 5 As shown in the figure, the image verifies that the joint operates smoothly under this working condition. Among them, joint 1 does not move, so the curve is a straight line, and the speed of joint 2 is the same as that of joints 3, 4, 5, and 6, but in the opposite direction, so the increase and decrease trends of the curve are opposite, but the absolute value remains the same.

[0053] 5. Calculate the torque values ​​of each joint without considering the influence of friction factors according to the dynamic method, where the value of inertia moment is obtained by extrapolation method and the value of driving moment is obtained by internalization method. Thus, the first set of output data is obtained.

[0054] 6. Calculate the friction torque value of each joint in this working condition, and the calculation formula is the nonlinear mixed friction model mentioned in the invention content. The judgment condition of this model is the joint speed. Get the second set of output data, from Figure 6 It can be seen that compared with the traditional calculation method, the driving torque required by the robot arm is greater when friction is taken into account; the average increment of each joint is 23.48%. This clearly shows that the friction at the joint will have an unignorable impact on the design of the robot arm joint motor and reducer. The nonlinear mixed friction model discussed in this article is accurate and of great significance, and also provides more accurate data for subsequent lightweight design, robot arm trajectory control, life calculation and other research.

[0055] The nonlinear mixed friction model of the present invention can more accurately describe the friction characteristics of the robot arm joints, thereby more accurately calculating the relevant parameters of the robot arm movement. The model provides a more accurate calculation method for the design, manufacture and control of the robot arm, which helps to improve the movement accuracy and stability of the robot arm.

Claims

1. A method for calculating the joint motion parameters of a hyperbolic manipulator using a nonlinear mixed friction model, characterized in that: include: (1) By limiting the range of motion angles and speeds of each joint in the working condition, the range of friction parameters of each joint is determined according to the material and lubrication conditions of the joint. The friction parameters include the viscous friction factor B, the Stribeck curve parameter θ sc , Coulomb friction torque T fc , Maximum static friction torque value T fs ; (2) Using SolidWorks 3D software, disassemble the rod structure, use the "delete" or "hide" function to remove the components that are not involved in the calculation from the calculation list, obtain a simplified 3D shell model, use the built-in calculation function of the software to obtain the basic parameters of each connecting rod and draw a parametric system diagram; The basic parameters of the connecting rod include the mass of the connecting rod, the position of the center of mass of the connecting rod, the moment of inertia of the connecting rod, and the value of the inertia tensor of the connecting rod. The basic parameters are all expressed in the form of a matrix, and the number of rows is the number of movable joints of the robot arm. (3) After installing the Robotic toolkit in Matlab software, the animation file of the robot arm motion process is gradually output through repeated debugging of the input running program; (4) By constructing and executing the kinematic solution code, the motion parameters of each joint when the friction effect is ignored are obtained as the judgment conditions of the nonlinear mixed friction model; the motion parameters of each joint include the joint motion speed, the coordinate points of the end effector motion trajectory, and the joint driving torque T θ ; (5) By constructing and executing the calculation model of the nonlinear mixed friction model and running it, the motion parameters of each joint when the influence of friction on the running results is considered, and by constructing and executing the dynamic solution code, the torque value of each joint when the influence of friction is ignored is obtained; the model includes four judgment intervals. When the speed falls in different intervals, the code will run different calculation formulas. The overall expression of the model is: Among them, the robot arm joint speed External torque T out , viscous friction factor B, Coulomb friction torque T fc , maximum static friction torque T fs , an empirical constant θ related to the nonlinearity of the Stribeck curve sc The calculated output parameter is the friction torque of the joint of the robot arm (6) In the same time period, the joint torque values ​​with and without friction are compared, and a comparison chart is drawn by controlling the variables to show the change trend.

2. The method according to claim 1, characterized in that: It is obtained by using the built-in calculation command of Matlab. When solving the dynamics forward, the input of the corresponding command is the trajectory point and the output is the joint torque.

3. The method according to claim 1, characterized in that: The joint driving torque It is a matrix. The number of matrix rows is the number of movable joints of the robot arm or the number of joints studied. The number of matrix columns is the data set capacity related to the calculation step size. Within a certain working time, if the calculation step size is smaller, the number of matrix columns is larger. If the calculation step size is larger, the number of matrix columns is smaller.

4. The method according to claim 1, characterized in that: The various joint motion parameters when considering the influence of friction on the operation results include the joint motion speed under the influence of friction, the end effector motion trajectory coordinate points under the influence of friction, the joint friction torque 5. The method according to claim 1, characterized in that: The joint friction torque It is a matrix. The number of matrix rows is the number of movable joints of the robot arm or the number of joints studied. The number of matrix columns is the data set capacity related to the calculation step size. Within a certain working time, if the calculation step size is smaller, the number of matrix columns is larger. If the calculation step size is larger, the number of matrix columns is smaller.

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