'Force-position-speed' collaborative planning method and system considering the dynamic characteristics of flexible grinding and polishing system

Abstract

The present invention belongs to the technical field of grinding and polishing process planning, and in particular relates to a 'force-position-speed' collaborative planning method and system that takes into account the dynamic characteristics of a flexible grinding and polishing system of a robot. The method includes: establishing position splines and direction splines of the grinding and polishing path according to the grinding and polishing path. According to the specific scenario of grinding and polishing, a speed optimization model with the goal of optimizing the grinding and polishing efficiency is established, and the speed-arc length curve is represented by a B-spline; a constraint equation considering the robot kinematics and dynamics of the robot side in the flexible grinding and polishing system of the robot is established; the system response equation of the force-controlled actuator is analyzed, and the constraint equations of the grinding and polishing force, the grinding and polishing force derivative and the grinding and polishing speed are established according to the material removal model; according to the dynamic mixed constraint conditions, a segmented B-spline method of dynamically adjusting the control points is adopted to realize the process parameter planning of the grinding and polishing feed speed-grinding force. The present invention realizes constraint checking by using smaller arc length segments between control points as checkpoints, and finally realizes the generation of the optimal speed curve, and generates the optimized grinding and polishing speed-force through the material removal equation.

Description

Technical Field

[0001] The present invention belongs to, but is not limited to, the technical field of grinding and polishing process planning, and in particular relates to a 'force-position-speed' collaborative planning method and system considering the dynamic characteristics of a robot flexible grinding and polishing system. Background Art

[0002] At present, with the rapid development of science and technology, complex curved surface parts such as integral blisks and blades are increasingly widely used in aerospace, automobile, shipbuilding and other fields. The grinding and polishing of complex curved surface parts is the final process of part finishing, and its processing quality affects the final forming accuracy of grinding and polishing. With the gradual improvement of robot manufacturing accuracy, the grinding and polishing strategy of "robot + active force control actuator" has gradually become the main grinding and polishing method for complex curved surface parts. When performing complex curved surface parts grinding and polishing, the grinding and polishing force and grinding speed are usually coordinated based on the material removal model to ensure the material removal accuracy of the parts after grinding and polishing. Since the robot and the end effector are both servo drive elements, the dynamic characteristics of the robot and the end force control actuator will affect the feed rate and the accuracy of the grinding and polishing force during the grinding process. Most existing flexible grinding and polishing parameter planning methods use constant force grinding and polishing or constant speed variable force grinding and polishing, which fail to fully utilize the advantages of robot force control grinding and polishing. Therefore, when planning the grinding and polishing process parameters, it is necessary to consider the dynamic characteristics of the robot and the end force control actuator to achieve optimal planning of the grinding and polishing process parameters.

[0003] Through the above analysis, the problems and defects of the existing technology are as follows:

[0004] (1) When grinding and polishing complex curved surface parts, the existing constant force polishing or constant speed polishing method does not plan the contact force and grinding and polishing speed, which easily leads to uneven material removal and low processing efficiency.

[0005] (2) The existing variable force and variable speed grinding and polishing method does not consider the dynamic characteristics of the grinding and polishing system when planning process parameters, which easily leads to poor control accuracy of the planned grinding and polishing force and grinding and polishing speed in actual grinding and polishing. Summary of the Invention

[0006] In view of the problems existing in the prior art, the present invention provides a 'force-position-speed' collaborative planning method considering the dynamic characteristics of a robot flexible grinding and polishing system.

[0007] The present invention is implemented as follows: a 'force-position-speed' collaborative planning method considering the dynamic characteristics of a robot flexible grinding and polishing system, the method comprising:

[0008] S1, establishing the position spline and direction spline of the polishing path according to the polishing path.

[0009] S2, based on the specific scenario of grinding and polishing, establish a speed optimization model with the goal of optimizing grinding and polishing efficiency, and use B-spline to represent the speed-arc length curve;

[0010] S3, establish the constraint equations of the robot side considering the robot kinematics and dynamics in the robot flexible grinding and polishing system;

[0011] S4, analyze the system response equation of the force-controlled actuator, and establish the constraint equations of the grinding and polishing force, grinding and polishing force derivative and grinding and polishing speed according to the material removal model.

[0012] S5, according to the dynamic mixed constraint conditions, the segmented B-spline dynamic adjustment control point method is used to realize the process parameter planning of grinding feed speed-grinding force.

[0013] Furthermore, in step S1, the position spline and direction spline of the polishing path are established. Specifically, since the polishing path can be expressed as [P, Θ] by Euler angles in the workpiece coordinate system, the position spline P(ω) and direction spline Θ(η) of the polishing path can be established respectively by B-splines;

[0014] The material removal model equation used is:

[0015]

[0016] Where h is the material removal depth, k h is the material removal equation coefficient, v is the grinding feed rate, n is the spindle speed, F is the grinding force, c t with c w is the curvature of the tool and workpiece.

[0017] Furthermore, in step S2, a speed optimization model is established with the goal of optimizing the polishing efficiency, and the specific form of the speed-arc length curve represented by the B-spline is:

[0018]

[0019] Where t is the total grinding and polishing time, s is the total arc length of the grinding and polishing path, S Σ is the total arc length of the polishing path, is the feed rate;

[0020] Since B-spline has the advantages of local support and strong local adjustment ability, the cubic B-spline curve Ψ(u) = (s, v) is used to express the relationship between the velocity curve and the arc length:

[0021]

[0022] Where u∈[0,1] is the spline parameter, B i,p (u) is the spline basis function, V i are the spline control points.

[0023] Furthermore, the step S3 of establishing the constraint equations of robot kinematics and dynamics on the robot side in the robot flexible polishing system specifically includes:

[0024] First, during the feed rate planning optimization process, the motion constraints on the robot side include path constraints and joint constraints. Path constraints refer to the feed rate constraints and acceleration constraints in the Cartesian space during the robot grinding process, and are expressed by the following constraint equation:

[0025]

[0026] Where V max and A max are the robot's terminal velocity and acceleration constraints;

[0027] Since the robot is directly driven by six joint axes, the robot joint constraints also need to be considered in the grinding feed rate planning. The robot joint constraints include joint motion constraints and dynamic constraints. The joint motion constraints come from the displacement, velocity, and acceleration of the robot joints. The constraint equations are as follows:

[0028]

[0029] in represents the robot joint value, joint velocity and acceleration; ik(s) represents the robot kinematic inverse function; Represents the robot joint motion constraint value; q′=dq / ds, q″=d 2 q / ds 2 Represents the first-order and second-order partial derivatives of the robot joint with respect to the arc length of the terminal motion;

[0030] The above are the kinematic constraints of the robot. The dynamic equation of the robot can be expressed as:

[0031]

[0032] where τ 6×1 represents the robot joint motion vector, M 6×6 is the robot inertia matrix, C 6×6 is the Coriolis force matrix, G 6×1 is the gravity component matrix, τ f6×1 represents the friction torque, τ load6×1 is the robot joint torque value caused by the external load;

[0033] Substituting equation (5) into equation (6), we can obtain the constraint conditions considering the robot's dynamic characteristics:

[0034]

[0035] where τ max is the robot dynamic torque constraint value.

[0036] Furthermore, the system response equation of the force-controlled actuator is analyzed in step S4, and the constraint equations of the polishing force, the polishing force derivative, and the polishing speed are established according to the material removal model, specifically including:

[0037] The force-controlled actuator can be simplified as a dual-mass spring-damper system, F m (t) is the motor output torque, F o (t) is the actual grinding contact force of the force-controlled actuator, m1 is the load mass on the motor side, m2 is the mass on the load side, c is the damping coefficient on the motor side, x1(t) is the output displacement on the motor side, x2(t) is the displacement on the load side, k1 is the spring stiffness, k e is the environmental stiffness; the equilibrium equation of the force-controlled actuator is expressed as:

[0038]

[0039] The above expression can be used to obtain the force transfer function of the force-controlled actuator through Laplace transform:

[0040]

[0041] Where s represents the Laplace variable. When using the end effector to grind high-rigidity parts, the system can be simplified to a second-order system:

[0042]

[0043] By introducing the PI controller, the closed-loop transfer function of the force control actuator is:

[0044]

[0045] The force control error transfer function can be expressed by the following equation:

[0046]

[0047] In the grinding and polishing process, since the actual force control actuator is a discrete system, the force control actuator will produce response errors when tracking the required force; the force control signal in each control cycle is regarded as a ramp signal The control error equation is as follows:

[0048]

[0049] According to the above force control error equation, when the robot is grinding, the derivative of the grinding force will affect the force control accuracy of the force control actuator, and the derivative of the grinding force will also affect the grinding feed speed. Therefore, the derivative of the grinding force needs to be considered when planning the grinding feed speed. The force constraint equation for grinding and polishing speed planning is established as follows:

[0050]

[0051] The relationship between the above formula and the grinding feed rate is established through the material removal model:

[0052]

[0053] in The above formula can be converted into:

[0054]

[0055] further, It can be calculated by the following formula:

[0056]

[0057] Therefore, the constraint equation of the dynamic characteristics of the force-controlled actuator considered in the grinding and polishing speed planning is:

[0058]

[0059] Furthermore, step S5 uses a segmented B-spline method to dynamically adjust control points based on dynamic hybrid constraints to achieve process parameter planning of grinding feed speed and grinding force. The specific steps are:

[0060] According to steps S1-S4, the optimization equation for the robot flexible polishing system is established with the goal of optimizing the polishing efficiency and considering the dynamic characteristics of the system:

[0061]

[0062] Another object of the present invention is to provide a 'force-position-speed' collaborative planning system that considers the dynamic characteristics of a flexible robotic grinding and polishing system and implements the 'force-position-speed' collaborative planning method that considers the dynamic characteristics of the flexible robotic grinding and polishing system. The system comprises:

[0063] Position spline and direction spline establishment module, which establishes the position spline and direction spline of the grinding and polishing path according to the grinding and polishing path;

[0064] The model building module is connected with the position spline and direction spline building modules. According to the specific grinding and polishing scenarios, a speed optimization model with the goal of optimizing grinding and polishing efficiency is established, and the speed-arc length curve is represented by B-spline.

[0065] The constraint equation establishment module establishes the constraint equations for the robot side of the robot flexible grinding and polishing system, considering the robot's kinematics and dynamics; analyzes the system response equations of the force-controlled actuator, and establishes the constraint equations for the grinding and polishing force, grinding and polishing force derivative, and grinding and polishing speed based on the material removal model;

[0066] The planning implementation module is connected with the constraint equation establishment module. According to the dynamic mixed constraint conditions, the segmented B-spline dynamic adjustment control point method is adopted to realize the process parameter planning of grinding feed speed-grinding force.

[0067] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the 'force-position-speed' collaborative planning method that considers the dynamic characteristics of the robot flexible grinding and polishing system.

[0068] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the steps of the 'force-position-speed' collaborative planning method considering the dynamic characteristics of the robot flexible grinding and polishing system.

[0069] Another object of the present invention is to provide an information data processing terminal, which is used to implement the 'force-position-speed' collaborative planning system that takes into account the dynamic characteristics of the robot flexible grinding and polishing system.

[0070] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0071] First, the present invention is a typical robot grinding and polishing process parameter planning problem. By considering the dynamic characteristics of the robot and the response characteristics of the force-controlled actuator in the robot flexible grinding and polishing system, a "force-position-speed" collaborative planning system of the robot flexible grinding and polishing process is realized.

[0072] Second, as auxiliary evidence for the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0073] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0074] The present invention proposes a 'force-position-speed' collaborative planning method for robotic grinding and polishing that takes into account the dynamic characteristics of the flexible grinding and polishing system. In actual commercial applications, it can be mainly used in the field of industrial automation to improve the accuracy of robotic force-controlled grinding and polishing, enhance the surface quality and contour accuracy of complex curved parts, reduce production costs, and improve production quality.

[0075] (2) The technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0076] In the industry applications of existing robots used in automated grinding and polishing, when industrial robots are used for force-controlled grinding and polishing, the dynamic characteristics of the robot during the grinding and polishing process are not taken into consideration, which will affect the grinding and polishing accuracy. The method proposed in the present invention that considers the dynamic characteristics of the grinding and polishing system can fill the technical gap in the industry caused by improper speed planning of robot force-controlled grinding and polishing, which has caused low force control accuracy and poor position accuracy.

[0077] (3) The technical solution of the present invention overcomes technical prejudice:

[0078] The planning of grinding force and grinding speed in traditional robotic grinding and polishing is usually single-objective optimization, such as optimizing the grinding force or grinding speed alone. It is difficult to achieve a better grinding and polishing process parameter combination by optimizing multiple objectives at the same time. The present invention overcomes the limitations of single-objective optimization through multi-objective optimization.

[0079] Third, the methods provided by the embodiments of the present invention solve multiple problems of the prior art in industrial applications and bring about significant technological progress. The following is a detailed explanation of these progress and problem solutions:

[0080] 1) Technical problem solving:

[0081] Coordinated planning of speed and force: Speed ​​and force planning are crucial in the grinding and polishing process. Traditional methods fail to consider the dynamic characteristics of the robotic grinding and polishing system when planning these two parameters, resulting in unstable processing quality. This invention achieves coordinated planning of speed and force by considering the robot's kinematic and dynamic constraints, as well as the dynamic characteristics of the force-controlled actuator.

[0082] Consideration of system dynamics: Previous approaches failed to fully consider the dynamics of the robot and force-controlled actuator, leading to operational issues. This invention incorporates these characteristics into the planning process through detailed dynamic modeling, improving system stability and performance.

[0083] 2) Technological progress:

[0084] - Improved processing efficiency and quality: By optimizing the velocity model, the present invention can improve grinding and polishing efficiency while maintaining processing quality. This is particularly important in large-scale production environments, as it can significantly reduce production time and costs.

[0085] - Improve system stability and reliability: By comprehensively considering the dynamic characteristics of the robot and force-controlled actuator, the present invention can reduce system vibration and errors, thereby improving overall stability and reliability.

[0086] -Achieve refined control: By establishing precise force constraint equations and material removal models, the present invention can achieve refined control of the grinding and polishing process, further improving machining accuracy and surface quality.

[0087] In summary, the technical solution of the present invention not only solves the problems of the existing technology, but also brings about significant technological progress, providing strong support for the industrial application of the robot flexible grinding and polishing system. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 A flow chart of a polishing speed-force process planning method provided in an embodiment of the present invention;

[0089] Figure 2 Schematic diagram of a force-controlled actuator and a force balance diagram provided for the implementation of the present invention;

[0090] Figure 3 A schematic diagram of recommended equipment provided in an embodiment of the present invention;

[0091] Figure 4 Schematic diagram of speed planning and speed error provided by the embodiment of the present invention and the comparison method;

[0092] Figure 5 Schematic diagram of planning force and force error provided by an embodiment of the present invention and a comparative method;

[0093] Figure 6 Schematic diagram of actual polishing depth removal error between the embodiment of the present invention and the comparative method. DETAILED DESCRIPTION

[0094] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0095] The embodiment of the present invention provides a 'force-position-speed' collaborative planning method considering the dynamic characteristics of a robot flexible grinding and polishing system, which specifically includes the following steps:

[0096] S1: Establish position spline and direction spline of polishing path

[0097] Based on the grinding and polishing path, the position and direction of the grinding and polishing path are expressed using Euler angles in the workpiece coordinate system. Position splines and direction splines are created using B-splines. These two splines ensure path smoothness and accuracy through the local support and adjustment capabilities of B-splines.

[0098] S2: Building a speed-optimized model

[0099] Based on the specific grinding and polishing scenarios, a speed optimization model is established to optimize grinding and polishing efficiency, and the speed-arc length curve is represented by a B-spline. Specifically, by optimizing the total time and total arc length of the grinding and polishing path, a cubic B-spline curve is used to represent the relationship between the speed curve and arc length, thereby optimizing the grinding and polishing feed rate.

[0100] S3: Establish the kinematic and dynamic constraint equations on the robot side

[0101] During feed rate planning, the robot's kinematic and dynamic constraints are considered and corresponding constraint equations are established. Kinematic constraints include path constraints and joint constraints, while dynamic constraints include the robot's joint displacement, velocity, acceleration, and dynamic equations. By comprehensively considering these constraints, the robot's stability and accuracy during the grinding and polishing process are ensured.

[0102] S4: Analyzing the system response equations of force-controlled actuators

[0103] The force-controlled actuator is simplified into a dual-mass spring-damper system. Its system response equation is analyzed, and constraint equations for the polishing force, its derivative, and the polishing velocity are established based on the material removal model. A PI controller is introduced to establish a force-controlled error transfer function, taking into account the dynamic characteristics of the force-controlled actuator to improve the accuracy of force control during the polishing process.

[0104] S5: Process parameter planning under kinetic mixing constraints

[0105] Based on dynamic hybrid constraints, a segmented B-spline method is used to dynamically adjust control points to achieve process parameter planning for grinding feed rate and grinding force. Through segmented B-spline adjustment, the feed rate and grinding force are optimized during the grinding process, thereby improving grinding efficiency and quality.

[0106] Industrial Application Example 1: High-precision mold polishing

[0107] In high-precision mold processing, the mold's surface quality directly affects the product's accuracy and service life. The present invention's "force-position-speed" collaborative planning method allows precise control of the polishing path, feed rate, and polishing force during the polishing process, thereby achieving high-quality polishing of the mold surface. The specific implementation steps include:

[0108] 1) Establish the mold grinding and polishing path: Based on the three-dimensional model of the mold, use B-spline to establish the position spline and direction spline of the grinding and polishing path.

[0109] 2) Optimize grinding and polishing speed: According to the mold material and grinding and polishing requirements, a speed optimization model is established, and the speed-arc length curve is expressed by cubic B-spline to optimize the grinding and polishing feed speed.

[0110] 3) Consider kinematic and dynamic constraints: During the grinding and polishing process, the kinematic and dynamic constraints of the robot are considered to ensure the stability and accuracy of the grinding and polishing process.

[0111] 4) Optimize grinding and polishing force control: By analyzing the system response of the force-controlled actuator, the constraint equation of the grinding and polishing force is established to ensure accurate control of the grinding and polishing force.

[0112] 5) Parameter planning: Based on the dynamic hybrid constraints, the control points are dynamically adjusted using segmented B-splines to optimize the grinding feed speed and grinding force.

[0113] Through this method, the polishing quality of the mold surface is significantly improved, achieving high-precision and high-quality processing effects.

[0114] Industrial Application Example 2: Aircraft Engine Blade Repair

[0115] Aircraft engine blades can become worn and damaged over time and require repair. The present invention's 'force-position-speed' collaborative planning method allows precise control of the polishing path, feed rate, and polishing force during blade repair, resulting in high-quality repair of the blade surface. The specific implementation steps include:

[0116] 1) Establish blade polishing path: Based on the 3D scanning data of the blade, use B-spline to establish the position spline and direction spline of the polishing path.

[0117] 2) Optimize the grinding and polishing speed: Based on the blade material and grinding and polishing requirements, a speed optimization model is established, and the speed-arc length curve is expressed as a cubic B-spline to optimize the grinding and polishing feed speed.

[0118] 3) Consider kinematic and dynamic constraints: During the grinding and polishing process, the kinematic and dynamic constraints of the robot are considered to ensure the stability and accuracy of the grinding and polishing process.

[0119] 4) Optimize grinding and polishing force control: By analyzing the system response of the force-controlled actuator, the constraint equation of the grinding and polishing force is established to ensure accurate control of the grinding and polishing force.

[0120] 5) Parameter planning: Based on the dynamic hybrid constraints, the control points are dynamically adjusted using segmented B-splines to optimize the grinding feed speed and grinding force.

[0121] Through this method, the repair quality of the blade surface is significantly improved, restoring its original performance and service life, ensuring the safe operation of the aircraft engine.

[0122] like Figure 1 As shown, an embodiment of the present invention provides a 'force-position-speed' collaborative planning method considering the dynamic characteristics of a robot flexible grinding and polishing system, the method comprising:

[0123] S1, establishing the position spline and direction spline of the polishing path according to the polishing path.

[0124] S2, based on the specific scenario of grinding and polishing, establish a speed optimization model with the goal of optimizing grinding and polishing efficiency, and use B-spline to represent the speed-arc length curve;

[0125] S3, establish the constraint equations of the robot side considering the robot kinematics and dynamics in the robot flexible grinding and polishing system;

[0126] S4, analyze the system response equation of the force-controlled actuator, and establish the constraint equations of the grinding and polishing force, grinding and polishing force derivative and grinding and polishing speed according to the material removal model.

[0127] S5, according to the dynamic mixed constraint conditions, the segmented B-spline dynamic adjustment control point method is used to realize the process parameter planning of grinding feed speed-grinding force.

[0128] In step S1, the position spline and direction spline of the polishing path are established. Specifically, since the polishing path can be expressed as [P, Θ] by Euler angles in the workpiece coordinate system, the position spline P(ω) and direction spline Θ(η) of the polishing path can be established respectively by B-splines;

[0129] The material removal model equation used is:

[0130]

[0131] Where h is the material removal depth, k h is the material removal equation coefficient, v is the grinding feed rate, n is the spindle speed, F is the grinding force, c t with c w is the curvature of the tool and workpiece.

[0132] Furthermore, in step S2, a speed optimization model is established with the goal of optimizing the polishing efficiency, and the specific form of the speed-arc length curve represented by the B-spline is:

[0133]

[0134] Where t is the total grinding and polishing time, s is the total arc length of the grinding and polishing path, S Σ is the total arc length of the polishing path, is the feed rate;

[0135] Since B-spline has the advantages of local support and strong local adjustment ability, the cubic B-spline curve Ψ(u) = (s, v) is used to express the relationship between the velocity curve and the arc length:

[0136]

[0137] Where u∈[0,1] is the spline parameter, B i,p (u) is the spline basis function, V i are the spline control points.

[0138] Furthermore, the step S3 of establishing the constraint equations of robot kinematics and dynamics on the robot side in the robot flexible polishing system specifically includes:

[0139] First, during the feed rate planning optimization process, the motion constraints on the robot side include path constraints and joint constraints. Path constraints refer to the feed rate constraints and acceleration constraints in the Cartesian space during the robot grinding process, and are expressed by the following constraint equation:

[0140]

[0141] Where V max and A max are the robot's terminal velocity and acceleration constraints;

[0142] Since the robot is directly driven by six joint axes, the robot joint constraints also need to be considered in the grinding feed rate planning. The robot joint constraints include joint motion constraints and dynamic constraints. The joint motion constraints come from the displacement, velocity, and acceleration of the robot joints. The constraint equations are as follows:

[0143]

[0144] in represents the robot joint value, joint velocity and acceleration; ik(s) represents the robot kinematic inverse function; Represents the robot joint motion constraint value; q′=dq / ds, q″=d 2 q / ds 2 Represents the first-order and second-order partial derivatives of the robot joint with respect to the arc length of the terminal motion;

[0145] The above are the kinematic constraints of the robot. The dynamic equation of the robot can be expressed as:

[0146]

[0147] where τ 6×1 represents the robot joint motion vector, M 6×6 is the robot inertia matrix, C 6×6 is the Coriolis force matrix, G 6×1 is the gravity component matrix, τ f6×1 represents the friction torque, τ load6×1 is the robot joint torque value caused by the external load;

[0148] Substituting equation (5) into equation (6), we can obtain the constraint conditions considering the robot's dynamic characteristics:

[0149]

[0150] where τ max is the robot dynamic torque constraint value.

[0151] like Figure 2 As shown, the system response equation of the force-controlled actuator is analyzed in step S4, and the constraint equations of the polishing force, the polishing force derivative, and the polishing speed are established according to the material removal model, specifically including:

[0152] The force-controlled actuator can be simplified as a dual-mass spring-damper system, F m (t) is the motor output torque, F o (t) is the actual grinding contact force of the force-controlled actuator, m1 is the load mass on the motor side, m2 is the mass on the load side, c is the damping coefficient on the motor side, x1(t) is the output displacement on the motor side, x2(t) is the displacement on the load side, k1 is the spring stiffness, k e is the environmental stiffness; the equilibrium equation of the force-controlled actuator is expressed as:

[0153]

[0154] The above expression can be used to obtain the force transfer function of the force-controlled actuator through Laplace transform:

[0155]

[0156] Where s represents the Laplace variable. When using the end effector to grind high-rigidity parts, the system can be simplified to a second-order system:

[0157]

[0158] By introducing the PI controller, the closed-loop transfer function of the force control actuator is:

[0159]

[0160] The force control error transfer function can be expressed by the following equation:

[0161]

[0162] In the grinding and polishing process, since the actual force control actuator is a discrete system, the force control actuator will produce response errors when tracking the required force; the force control signal in each control cycle is regarded as a ramp signal The control error equation is as follows:

[0163]

[0164] According to the above force control error equation, when the robot is grinding, the derivative of the grinding force will affect the force control accuracy of the force control actuator, and the derivative of the grinding force will also affect the grinding feed speed. Therefore, the derivative of the grinding force needs to be considered when planning the grinding feed speed. The force constraint equation for grinding and polishing speed planning is established as follows:

[0165]

[0166] The relationship between the above formula and the grinding feed rate is established through the material removal model:

[0167]

[0168] in The above formula can be converted into:

[0169]

[0170] further, It can be calculated by the following formula:

[0171]

[0172] Therefore, the constraint equation of the dynamic characteristics of the force-controlled actuator considered in the grinding and polishing speed planning is:

[0173]

[0174] Furthermore, step S5 uses a segmented B-spline method to dynamically adjust control points based on dynamic hybrid constraints to achieve process parameter planning of grinding feed speed and grinding force. The specific steps are:

[0175] According to steps S1-S4, the optimization equation for the robot flexible polishing system is established with the goal of optimizing the polishing efficiency and considering the dynamic characteristics of the system:

[0176]

[0177] like Figure 3 , which is a schematic diagram of recommended equipment used in an embodiment of the present invention;

[0178] like Figure 4 , Figure 5 As shown in the figure, compared with the planning method that does not consider the dynamic constraints of the robot, the speed error and force control error of the method proposed by the present invention are reduced, indicating that the planning algorithm proposed by the present invention can achieve higher force control accuracy and speed accuracy. Figure 6The figure shows the comparison of the depth errors of the grinding and polishing material removal. It can be concluded that the method proposed in the present invention benefits from the improvement of force control accuracy and speed accuracy, and can achieve higher grinding and polishing material removal accuracy when applied to actual grinding and polishing.

[0179] 1. Specific application fields or related products of the present invention.

[0180] An embodiment of the present invention provides a 'force-position-speed' collaborative planning system considering the dynamic characteristics of a robot flexible grinding and polishing system, which implements the 'force-position-speed' collaborative planning method considering the dynamic characteristics of the robot flexible grinding and polishing system. The system includes:

[0181] Position spline and direction spline establishment module, which establishes the position spline and direction spline of the grinding and polishing path according to the grinding and polishing path;

[0182] The model building module is connected with the position spline and direction spline building modules. According to the specific grinding and polishing scenarios, a speed optimization model with the goal of optimizing grinding and polishing efficiency is established, and the speed-arc length curve is represented by B-spline.

[0183] The constraint equation establishment module establishes the constraint equations for the robot side of the robot flexible grinding and polishing system, considering the robot's kinematics and dynamics; analyzes the system response equations of the force-controlled actuator, and establishes the constraint equations for the grinding and polishing force, grinding and polishing force derivative, and grinding and polishing speed based on the material removal model;

[0184] The planning implementation module is connected with the constraint equation establishment module. According to the dynamic mixed constraint conditions, the segmented B-spline dynamic adjustment control point method is adopted to realize the process parameter planning of grinding feed speed-grinding force.

[0185] An embodiment of the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the 'force-position-speed' collaborative planning method that considers the dynamic characteristics of the robot flexible grinding and polishing system.

[0186] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the 'force-position-speed' collaborative planning method considering the dynamic characteristics of the robot flexible grinding and polishing system.

[0187] An embodiment of the present invention provides an information data processing terminal, which is used to implement the 'force-position-speed' collaborative planning system that considers the dynamic characteristics of the robot flexible grinding and polishing system.

[0188] 2. Relevant evidence of the technical effects obtained by the embodiments of the present invention.

[0189] The experimental verification was carried out on an actual blade grinding and polishing robot. The dynamic characteristics of the robot flexible grinding and polishing system were not considered as a control test. The grinding and polishing material removal depth was set to 20μm. After four grinding passes, the single grinding and polishing depth was 5μm. The electric spindle speed was set to 18000rpm, and the model coefficient was k h =1.2299×10 -6 , the grinding tool has a particle size of 800 mesh and a radius of 4 mm. The constraint condition on the force side is set as F max =4N, The robot's Cartesian motion constraints are set as v max =5mm / s, a max =10mm / s 2 .

[0190] The actual speed during grinding and polishing is as follows: Figure 4 As shown in Figure 2, the results show that the proposed method reduces the maximum feed rate error in the grinding and polishing process from 0.5435 mm / s to 0.4327 mm / s, which is a 20.39% reduction compared with the comparison method. The actual grinding and polishing force results are shown in Figure 2. Figure 5 As shown in the figure, the maximum absolute force control error during the grinding and polishing process decreased from 0.6357N to 0.4740N, a reduction of 25.44%. The standard deviation of the grinding and polishing force control error decreased from 0.1072N to 0.0759N, a reduction of 29.20%. These results demonstrate that by considering the dynamic characteristics of the robot flexible grinding and polishing system during the grinding and polishing process parameter planning, the force control accuracy during the grinding and polishing process is improved, the force fluctuation is reduced, and the force control effect is more stable.

[0191] like Figure 6 As shown in the figure, the grinding profiles before and after grinding and polishing were measured using a three-dimensional coordinate measuring machine. The maximum material removal error of the proposed method was calculated to be 8.89 μm (2.22 μm / pass), which is basically consistent with the maximum profile error of the comparative method of 9.15 μm (2.29 μm / pass). However, the average profile error of the proposed method was 2.83 μm (0.71 μm / pass), while that of the comparative method was 3.76 μm (0.94 μm / pass), a 24.73% reduction in average error compared to the comparative method. These results indicate that the proposed method improves the dynamic stability of the grinding feed rate and force control by considering the mixed dynamic constraints of the grinding and polishing system, thereby improving the consistency of the grinding and polishing surface quality.

[0192] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0193] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A 'force-position-speed' collaborative planning method considering the dynamic characteristics of a robot flexible grinding and polishing system, characterized in that: The method includes: S1, establishing the position spline and direction spline of the polishing path according to the polishing path; S2, based on the specific scenario of grinding and polishing, establish a speed optimization model with the goal of optimizing grinding and polishing efficiency, and use B-spline to represent the speed-arc length curve; S3, establish the constraint equations of the robot side considering the robot kinematics and dynamics in the robot flexible grinding and polishing system; S4, analyzing the system response equation of the force-controlled actuator and establishing the constraint equations of the grinding and polishing force, the grinding and polishing force derivative and the grinding and polishing speed according to the material removal model; S5, based on the dynamic hybrid constraint conditions, the method of dynamically adjusting the control points using segmented B-spline is used to achieve the process parameter planning of grinding and polishing feed speed-grinding and polishing force; In step S1, the position spline and direction spline of the polishing path are established. Specifically, since the polishing path is represented by the Euler angle [P, Θ] in the workpiece coordinate system, the position spline P(ω) and direction spline Θ(η) of the polishing path are respectively established by B-splines; The material removal model equation used is: Where h is the material removal depth, k h is the material removal equation coefficient, v is the grinding feed rate, n is the spindle speed, F is the grinding force, c t with c w is the curvature of the tool and workpiece; In step S2, a speed optimization model is established with the goal of optimizing the polishing efficiency. The specific form of the speed-arc length curve represented by the B-spline is: Where t is the total grinding and polishing time, l is the current arc length position of the grinding and polishing path, and L ∑ is the total arc length of the polishing path, is the feed rate; Since B-spline has the advantages of local support and strong local adjustment ability, the cubic B-spline curve ψ(u) = (l, v) is used to express the relationship between the velocity curve and the arc length: Where u∈[0,1] is the spline parameter, B i,p (u) is the spline basis function, V i are the spline control points; The step S3 of establishing the constraint equations of robot kinematics and dynamics on the robot side of the robot flexible grinding and polishing system specifically includes: First, during the feed rate planning optimization process, the robot's motion constraints include path constraints and joint constraints. Path constraints refer to the feed rate constraints and acceleration constraints in Cartesian space during the robot grinding process, and are expressed as the following constraint equations: Where V max and A max are the robot's terminal velocity and acceleration constraints; Since the robot is directly driven by six joint axes, the robot joint constraints also need to be considered in the grinding feed rate planning. The robot joint constraints include joint motion constraints and dynamic constraints. The joint motion constraints come from the displacement, velocity, and acceleration of the robot joints. The constraint equations are as follows: in represents the robot joint value, joint velocity and acceleration; ik(l) represents the robot kinematic inverse function; Represents the robot joint motion constraint value; q'=dq / dl, q"=d 2 q / dl 2 Represents the first-order and second-order partial derivatives of the robot joint with respect to the arc length of the terminal motion; Equations (4) and (5) are the kinematic constraints of the robot, and the dynamic equation of the robot is expressed as: Where τ represents the robot joint motion vector, M is the robot inertia matrix, C is the Coriolis force matrix, G is the gravity component matrix, τ f represents the friction torque, τ load is the robot joint torque value caused by the external load; Substituting equation (5) into equation (6), we get the constraint condition considering the robot's dynamic characteristics: where τ max is the robot dynamic torque constraint value; The analysis of the system response equation of the force-controlled actuator in step S4 and the establishment of the constraint equations of the grinding and polishing force, the grinding and polishing force derivative, and the grinding and polishing speed according to the material removal model specifically include: The force control actuator is simplified into a dual-mass spring-damper system, F m (t) is the motor output torque, F o (t) is the actual grinding and polishing contact force of the force-controlled actuator, m1 is the mass on the motor side, m2 is the mass of the grinding tool head of the force-controlled actuator, c is the damping coefficient on the motor side, x1(t) is the output displacement on the motor side, x2(t) is the displacement on the load side, k1 is the spring stiffness, k e is the environmental stiffness; the equilibrium equation of the force-controlled actuator is expressed as: Formula (8) is used to obtain the force transfer function of the force-controlled actuator through Laplace transform: Where s represents the Laplace variable; when using the end effector to grind high-rigidity parts, the system is simplified to a second-order system: By introducing the PI controller, the closed-loop transfer function of the force control actuator is: The force control error transfer function is expressed by the following equation: In the grinding and polishing process, since the actual force control actuator is a discrete system, the force control actuator will produce response errors when tracking the required force; the force control signal in each control cycle is regarded as a ramp signal The force control error equation is as follows: According to the above force control error equation, when the robot is grinding, the derivative of the grinding force will affect the force control accuracy of the force control actuator, and the derivative of the grinding force will also affect the grinding feed speed. Therefore, the derivative of the grinding force needs to be considered when planning the grinding feed speed. The force constraint equation for grinding and polishing speed planning is established as follows: The relationship between the above formula and the grinding feed rate is established through the material removal model: in The above formula is converted to: further, Calculated by the following formula: Therefore, the constraint equation of the dynamic characteristics of the force-controlled actuator considered in the grinding and polishing speed planning is: The step S5 implements the process parameter planning of grinding and polishing feed speed-grinding and polishing force by adopting the segmented B-spline dynamic adjustment control point method according to the dynamic hybrid constraint condition; the specific steps are: According to steps S1-S4, the optimization equation for the robot flexible polishing system is established with the goal of optimizing the polishing efficiency and considering the dynamic characteristics of the system:

2. A 'force-position-speed' collaborative planning system considering the dynamic characteristics of a robotic flexible grinding and polishing system, which implements the 'force-position-speed' collaborative planning method considering the dynamic characteristics of a robotic flexible grinding and polishing system as described in claim 1, characterized in that: The system includes: Position spline and direction spline establishment module, which establishes the position spline and direction spline of the grinding and polishing path according to the grinding and polishing path; The model building module is connected with the position spline and direction spline building modules. According to the specific grinding and polishing scenarios, a speed optimization model with the goal of optimizing grinding and polishing efficiency is established, and the speed-arc length curve is represented by B-spline. The constraint equation establishment module establishes the constraint equations for the robot side of the robot flexible grinding and polishing system, considering the robot's kinematics and dynamics; analyzes the system response equations of the force-controlled actuator, and establishes the constraint equations for the grinding and polishing force, grinding and polishing force derivative, and grinding and polishing speed based on the material removal model; The planning implementation module is connected with the constraint equation establishment module. According to the dynamic mixed constraint conditions, the segmented B-spline dynamic adjustment control point method is adopted to realize the process parameter planning of grinding feed speed-grinding force.

3. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the 'force-position-speed' collaborative planning method considering the dynamic characteristics of the robot flexible grinding and polishing system as claimed in claim 1.

4. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the 'force-position-speed' collaborative planning method considering the dynamic characteristics of the robot flexible grinding and polishing system as claimed in claim 1.

5. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the 'force-position-speed' collaborative planning system that takes into account the dynamic characteristics of the robot flexible grinding and polishing system as claimed in claim 2.

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