Polishing is the last step in parts processing, with very little material removal. Polishing methods include electrochemical polishing, magnetorheological polishing, plasma polishing, ultrasonic grinding and polishing, and mechanical polishing. Mechanical polishing is the most efficient and has the best controllability. This paper proposes an automatic polishing machine tool system design based on parallel robot technology, develops a prototype, and conducts polishing experiments.
This paper proposes an automated polishing machine tool system design based on parallel robot technology. It systematically studies the mechanism synthesis, workspace analysis, kinematic and dynamic performance calculation and analysis of a novel free-form surface polishing machine tool. An automated polishing machine tool based on parallel robots is designed and developed, and polishing experiments and performance evaluations are conducted. The research content mainly includes the following aspects: starting from the requirements of complex free-form surface polishing tasks, an automated polishing machine tool system scheme capable of achieving constant force polishing of free-form surfaces is proposed; a reasonable kinematic branch layout avoids the problem of concentrated force on a single kinematic branch; based on kinematic analysis, a parallel mechanism inverse dynamics model is established by combining Kane's equations and vector methods; finally, a prototype of the parallel automated polishing machine tool is developed, and constant force polishing experiments are conducted on free-form surface parts, achieving a polishing roughness of level 11.
Parallel Polishing Machine Tool System Design
For free-form surface parts, the polishing process requires the actuator to have at least three translational and two rotational degrees of freedom. Currently, most automated polishing equipment is based on a series mechanism design. While series mechanisms offer greater flexibility and a larger working space, the open-loop nature of these mechanisms leads to cumulative loads and errors. This means that the more degrees of freedom there are, the more severe the error accumulation on the end-effector platform becomes, necessitating an increase in the size and mass of the series mechanism to ensure sufficient rigidity and maintain the accuracy of the end-effector platform. The large inertia and weak rigidity of open-loop series mechanisms result in poor dynamic characteristics for free-form surface polishing based on them.
To overcome the load and error accumulation characteristics of free-form surface polishing systems based on traditional serial mechanisms, an overall scheme for an automatic polishing system based on a parallel mechanism is proposed. The parallel polishing machine tool includes a novel parallel mechanism with a large rotation angle of type 3R2 motion, a CNC rotary table, and a linear polishing moving platform with force feedback mounted on the moving platform, realizing the decoupled polishing task of free-form surfaces of large parts.
The mechanical body of the parallel polishing machine mainly consists of a five-degree-of-freedom parallel mechanism, a rotary CNC worktable, and a linear motion platform with force feedback. Figure 1 shows the internal structure of the parallel polishing machine. Figure 2 shows the structure of the moving platform, where a force sensor and a linear motor are installed between the parallel moving platform and the polishing spindle. The force sensor and linear motor are used to control the polishing force during the polishing process to ensure the polishing accuracy of the free-form surface.
(1) Five-DOF Parallel Mechanism: The five-DOF parallel mechanism is a pure parallel mechanism with three translational and two rotational degrees of freedom. The five branches of the parallel mechanism are all driven by hollow motors driving lead screws. This advanced driving method can greatly increase the driving length of the branches, thereby increasing the motion space of the parallel robot. The universal joint kinematic pair connecting the branches to the motion platform adopts the horn-shaped kinematic pair type. The horn-shaped universal joint can rotate over a wide range. The special joint design greatly improves the range of motion of the rotational degree of freedom of the motion platform of the parallel mechanism.
(2) The new parallel mechanism of the rotary CNC worktable has a large range of motion for its three spatial translational degrees of freedom and one pitch and rotational degree of freedom, but a smaller range of motion for its other left and right tilting degree of freedom. To expand the machining range of this parallel mechanism, a CNC rotary table for clamping parts is redundantly added to the stationary platform. The new parallel robot, in conjunction with the CNC rotary table, can perform five-sided machining of the workpiece. The CNC rotary table not only expands the machining space of the parts, but also enables the parallel robot to plan erratic paths.
(3) The linear motion platform of the parallel mechanism of the force feedback linear motion platform consists of a linear drive motor, a polishing spindle, and a force sensor connecting the linear motor mover and the polishing spindle. For polishing tasks, the control of polishing force is crucial throughout the polishing process. In this scheme, the linear motion platform uses the force sensor to feed back polishing force information during the polishing process to the control system. Combined with a high-resolution and high-dynamic linear motor, the position of the polishing spindle is adjusted according to the real-time force feedback information to achieve constant polishing force control during the polishing process.
(4) The parallel polishing machine control system consists of a German PowerAutomation real-time CNC control system that controls seven servo drive motors, an FPGA-based absolute joint measurement system, and a force sensor acquisition system.
The system comprises several components, including a CNC system that offers open PLC functionality, allowing users to perform 10-level logic programming for the CNC system. It also provides a CompileCycle interface, enabling users to write motion trajectory control algorithms in C/C++. A joint angle measurement system provides redundant feedback information for system control, while a force sensor acquisition system provides feedback data for polishing force control.
Freeform surface polishing parallel mechanism
The parallel polishing mechanism consists of a pure parallel mechanism composed of a 4URHU-1URHR motion chain and a redundant linear motion platform. Figure 3 is a schematic diagram of the new parallel polishing machine tool. The pure parallel part of the machine tool consists of a moving platform, a machine bed, and five motion chains. To control the polishing force during the polishing process, a linear servo motor is introduced into the parallel polishing machine tool. The linear servo motor drives the electric spindle, which is equipped with the polishing tool, to adjust the polishing force. In addition, a CNC rotary table is installed on the machine bed.
Figure 4 is a schematic diagram of the parallel polishing machine tool structure. The parallel machine tool consists of five kinematic chains. The central kinematic chain L1 has a kinematic pair distribution of URHR, which consists of a universal joint U, a motor mover rotary joint R, a screw joint H, and a rotary joint R connecting the moving platform. It is a five-degree-of-freedom kinematic chain, with three translational and two rotational degrees of freedom. The other four identical kinematic chains Li (i=2,3,4,5) have a kinematic pair distribution of URHU. They differ from the central kinematic chain L1 in that they are connected to the moving platform through the universal joint U, making them six-degree-of-freedom kinematic chains. According to the linear correlation theory of degrees of freedom in screw theory, the degrees of freedom of the moving platform of the parallel machine tool are consistent with the degrees of freedom of the central kinematic chain. That is, the degrees of freedom of the parallel mechanism are T3R2 (three translational, two rotational, none). A linear motion platform with force feedback is installed at the end of the parallel polishing mechanism to achieve decoupled control of the polishing force.
Motion model of a five-degree-of-freedom parallel mechanism
As shown in Figure 5, P represents the central branch L. The center point of the revolute joint R on the moving platform is given coordinates xp, yp, zp in the global coordinate system; θ represents the rotation angle of the central branch L1 screw about the axis in the e14 direction; φ represents the rotation angle of the moving platform about the e15 direction. The central branch of the purely parallel part of the polishing system has one less rotational degree of freedom than the other four branches. To unify the derivation of the kinematic and dynamic formulas for the central branch and the other four branches, a virtual revolute joint R is added to the central branch, and θ16 is set to 0. For the task space, xxp, yp, zp, θ, and φ are chosen as generalized variables of the parallel mechanism.
Let Bij represent the j-th rigid body in the i-th branch, where Bi1 represents the first rotating rigid body of the universal joint; Bi2 represents the stator of the hollow motor; Bi3 represents the rotor of the hollow motor; Bi4 represents the ball screw; and Bi5 represents the horn universal joint component. When i=1, Bi15 represents the moving platform. In describing the velocity and acceleration of the moving platform in the global coordinate system using generalized coordinates, the joint angle variables θ11θ12θ13θ14θ15 of the central branch are used as intermediate variables to simplify the relationship between the velocity and acceleration of the moving platform and the generalized variables. The following equation (1) can be obtained:
Based on the above geometric relationships, calculations were performed to establish the inverse kinematic model of the parallel mechanism. Velocity and acceleration analyses were conducted on each rigid body component of the mechanism. Based on the kinematic analysis, the efficient Kane equations were applied to establish the rigid body inverse dynamic model of the parallel polishing mechanism. The dynamic equations were transformed into control state equations, which were then applied to the motion trajectory tracking control of the parallel mechanism. Combining the advantages of efficient computational torque method, optimal control, and robust control, the established hybrid method based on computational torque method was applied to the inverse kinematic motion trajectory tracking control of the parallel mechanism, thereby achieving a high-speed, high-precision trajectory control algorithm for the parallel mechanism.
Force feedback control scheme for constant force polishing
To achieve constant polishing force control, a servo linear motor equipped with a high-resolution grating was installed on the moving platform of the parallel machine tool. A three-dimensional force sensor was also installed between the polishing tool and the linear motor's mover, as shown in Figure 6. Force feedback from the three-dimensional force sensor is used to adjust the position of the polishing tool using the linear motor, thereby achieving constant force polishing control. Since the overall mass of the mover and the fixed platform of the polishing tool is relatively large, a spring was added between the mover and the moving platform to balance the weight of the mover and its fixed platform, reducing the static drive current of the linear motor.
Figure 7 is a simplified model diagram of the moving platform of the parallel polishing machine tool, in which the moving platform is connected to the parallel moving platform by a spring. The angle between the parallel moving platform and the direction of gravity is α. Let the mass of the moving platform and the power platform be m. The total mass of the polishing tool and the holder is m. The stiffness of the spring is k, and the damping is c. The moving platform is subjected to spring force fk and damping force fc, respectively. During the polishing process, the polishing pressure and polishing torque on the polishing tool are ft and mt, respectively. The internal force on the sensor is Fs, which can be measured by the force sensor itself.
Parallel polishing machine polishing experiment
Polishing experiments were conducted on freeform surface parts using a parallel polishing machine. The discrete points and normal vectors of the freeform surface were saved as files and imported into a fractal path generation module developed in Matlab to generate Hilbert fractal trajectory curves. These curves were then imported into the parallel polishing machine simulation software to obtain the Hilbert fractal trajectory on the freeform surface. The simulation software automatically calculates the optimal freeform surface polishing trajectory with the best task flexibility based on the input data and automatically generates the following G-code data file.
Figure 8-a shows the surface roughness test results of a part that has only undergone impurity treatment with a polishing cloth but has not been polished by a parallel polishing machine. Its roughness Ra = 0.1735 μm, and the maximum profile height Rz = 0.3839 μm, which is a roughness grade of 9. Figure 8-b shows the surface roughness test results of a part that has been polished by a parallel polishing machine. Its roughness Rz = 0.0431 μm, and the maximum profile height Rz = 0.1194 μm, which is a roughness grade of 11. This demonstrates that after fractal trajectory polishing and constant force polishing by a parallel polishing machine, the surface roughness of the part polished with a polishing cloth can be improved from grade 9 to grade 11.
The results of the polishing experiments demonstrate that the automatic polishing system proposed in this paper utilizes a novel parallel polishing mechanism to realize the position execution device of the polishing moving platform. A constant force polishing platform with polishing force feedback is used to polish free-form parts. The high-rigidity parallel mechanism and the decoupled constant force polishing platform can achieve high-precision polishing of free-form surfaces.
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