The classical Preston equation considers that the material removal is linearly related to time, velocity, and pressure. However, in the wheel polishing technology, it is found through experiments that there is a nonlinear relationship between the rotational speed of the polishing wheel and the amount of material removed. In order to accurately control the material removal in the polishing wheel variable speed machining strategy, it is necessary to modify the classical Preston equation. In this paper, the control variable method is used to carry out the sampling experiment: the time and pressure are set as fixed values, and the polishing wheel speed is set as a variable and the value is between 0-4rps. Then the data points were analyzed and a least squares fit was used to obtain a non-linear function between the rotational speed of the polishing wheel and the amount of material removed. Finally, the classical Preston equation is modified to obtain the removal equation suitable for the variable speed machining strategy.
In this paper, industrial robot is used as motion carrier and self-developed flexible wheel tool is used as polishing tool to realize low-cost, high-efficiency, and high-precision optical processing. Firstly, the mapping formula between the workpiece coordinates and the road point coordinates is deduced, and the position and posture data required for robot programming are obtained. Secondly, a new type of wheel polishing tool is designed, which controls the polishing pressure through a pneumatic floating structure to ensure the stability of the removal function. Finally, an off-axis paraboloid of φ345mm was processed using this technology. After three times of processing for 10 hours, the surface error converged from PV-2.111λ, RMS-0.249λ to PV-0.119λ, RMS-0.01λ. PV and RMS converged by 94% and 96%, respectively. This proves that the technology has the advantages of high efficiency and high precision, and is expected to be widely used in the field of precision optical processing.
Computer-controlled optical surface forming technology (CCOS) can greatly improve the processing accuracy and processing efficiency of optical mirrors. The most critical problem is the solution of dwell time, which will directly affect the final convergence of the surface shape. it is found through analysis that the solution of the dwell time is a deconvolution process, which is the same as the mathematical model of the Lucy–Richardson algorithm in image restoration technology, so the algorithm can be applied to Solution of dwell time; At the same time, in order to eliminate the high-frequency shape errors caused by discontinuities at the edges of the face shapes, the original shapes need to be extended to achieve smooth connections. The two-dimensional Gercherg bandwidth-limited continuation algorithm can achieve this requirement. The simulation results show that the root mean square value (rms) and peak-valley value (pv) converge from the initial 0.2534λ, 1.494λ (λ=632.8nm) to 0.0158λ and 0.393λ, which proves the effectiveness of the algorithm. Compared with the Lucy-Richardson algorithm, other traditional solving methods have simpler calculation process, higher calculation efficiency, and higher convergence rate.
In this paper, a new type of wheel polishing tool is designed. Through the bevel gear structure, only one motor is used to realize the revolution and rotation of the polishing wheel, which makes the structure simple, small inertia, and stable operation. Traditional polishing wheels have a three-layer structure: internal rigid hub, middle flexible rubber, and external polishing pad. It is found through experiments that the hardness of rubber has a greater influence on the tool influence function (TIF). Therefore, by optimizing the hardness of the rubber, we obtained a TIF very close to the Gaussian shape, which is conducive to the rapid convergence of the surface error. Finally, the effects of polishing wheel speed, polishing pressure and polishing time on the TIF, as well as the stability of the TIF, are studied through experiments. Experiments show that: (1) There is no linear relationship between the removal efficiency of the polishing wheel, the polishing wheel speed, and the polishing pressure, but as the parameter increases, the increase in the removal efficiency slows down; (2) There is a good linear relationship between the removal amount of the polishing wheel and time; (3) The TIF is very stable, and the stability of the TIF reaches 98%.
An ABB IRB6640 industrial robot is used as a processing platform for optical polishing. The relationships of coordinate systems are defined, the algorithm of coordinate transformation, Euler angles and quaternion are provided. M-like removal function and Gaussian-like removal function are used to simulation process an off-axis aspheric surface. The surface error after polishing by M-like removal function is 1.5 to 2.5 times bigger than Gaussian-like removal function. This proves that M-like removal function also has good convergence speed. Then, the pentagram polishing head is used to polish a Φ600mm off-axis paraboloid surface. After 15 cycles, about 120 hours processing, PV converges from 5.8μm to 0.836μm, RMS converges from 1.2μm to 0.054μm, PV and RMS respectively converge 85% and 95%. The experiment shows M-like removal function has good convergence speed.
As one of the most challenging problems in Computer Controlled Optical Surfacing (CCOS), the edge effect greatly affects the polishing accuracy and efficiency. CCOS rely on stable tool influence function (TIF), however, at the edge of the mirror surface,with the grinding head out of the mirror ,the contact area and pressure distribution changes, which resulting in a non-linear change of TIF, and leads to tilting or sagging at the edge of the mirror. In order reduce the adverse effects and improve the polishing accuracy and efficiency. In this paper, we used the finite element simulation to analyze the pressure distribution at the mirror edge and combined with the improved traditional method to establish a new model. The new method fully considered the non-uniformity of pressure distribution. After modeling the TIFs in different locations, the description and prediction of the edge effects are realized, which has a positive significance on the control and suppression of edge effects
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