Machining Technology for non-axisymmetric Optical Surfaces and its Systematic Evaluation

Piezoelectric fast tool servo mechanism, with its existing nonlinear response and hysteresis, restricts greatly the precision when applied to machining of non-axisymmetric optical surface. In this paper, a feed-forward control method is applied to compensate the displacement of the fast tool servo. According to the workpiece surface feature and the tool path, the mathematical model of the minimum setting angle is established to avoid the interference between the tool and the surface to be machined. A new kind of control method-real time calculating control with table look-up is developed. This control method can shorten the calculating time and improve the precision of the machining surface at the same time. It puts forward qualitative and quantitative methods from the whole and partial aspects to evaluate the machined surfaces,and some demonstrative evaluations of the machined surfaces are also given. Keywords-feedforward control; non-axisymmetric optical surface; fast tool servo Most of optical instruments use mirrors and lens of spherical and plane. The two kinds of surfaces are easy to be processed, so they are widely used. However, mirrors and lens of spherical and plane have spherical aberration, coma-aberration, astigmatic aberration, field curvature and aberration. These aberrations have a great effect on the accuracy of the optical systems. In the past, many methods of reducing the aberrations have been raised. But these methods have certain limitations. And each method can only reduce certain type of aberrations. In order to reduce or eliminate the aberrations more effectively, the method of wavefront correctors to correct the aberrations was raised. The most typical and effective wavefront correctors is the non-axisymmetric optical surface mirror processed by Zernike aberration function. This method can correct many kinds of aberrations at the same time. So the accuracy of the optical system is greatly improved. When the method is used in large telescope optical system, the cost of the telescope can be greatly reduced. The application of wavefront correctors opens up a new way to further improve the precision of optical system and reduce manufacturing cost[1][2]. The points on the non-axisymmetric optical surface are asymmetrical to its geometric axis. Its axial dimension Z is not only the function of radial dimension x, but also the function of angle θ, i.e.: ) , ( θ x f Z = The processing schematic of nonsymmetric optical surfaces is given in Fig. 1. The cutting tools can move forth and back flexibly in axial direction with the changes of radial dimensions and angles, while the spindle gyrates and the tool transversely feeds. In an instant, according to the angle signals and the cutting tool’s transverse displacement signals, the computer can calculate the axial coordinates of the points on surface based on certain mathematical model. Through D/A transformation, amplifying circuit and the tool stretching controlled by the drive power source, we can make the cutting tool have a microdisplacement in its axial direction to make non-axisymmetric optical surfaces. Figure 1. The processing schematic of non-axisymmetric optical surfaces From the processing principle of non-axisymmetric optical surfaces we can learn that the axial positional error of the cutting tool can affect the machining precision of the workpiece surfaces directly. However, the main reason of the axial positional error is that the nonlinearity and hysteresis phenomenon in piezoelectric ceramic of the high-speed servo tool. For the single-pass(step-up trip or step-down trip)nonlinearity, we can solve for mathematical models of step-up curve and step-down curve respectively by Journal of Control Engineering and Technology (JCET) JCET Vol.1 No.1 July 2011 PP.47-52 www.vkingpub.com ○C American V-King Scientific Publish 48 experimental method, and then use the mathematical model to control the servo tool. But this method cannot eliminate the influence on the tool positional precision by hysteresis phenomenon. In the machining process, the cutting tool has different ranges for each stretch trip (or step-up trip, step-down trip). So the step-up curve and the step-down curve are also different, which makes it difficult to predict the response to the input voltage by tool position. This problem will affect the applications of piezoelectric ceramic seriously. At present, many scholars engage in this aspect research, and they have presented various error compensation control methods (such as average curve method, self-learning control method, closed-loop control method and so on), but these methods do not work very well[3]. This study adopts feed forward control method to compensate the cutting tool position. I. SERVO TOOLREST POSITION COMPENSATION The machining principle of non-axisymmetric optic mirror surfaces shows that the tool’s axial position error influence the machining precision of work-piece surfaces directly; and the main reasons of the tool’s position error are from the non-linearity and hysteresis of piezoelectric. At present, many scholars in the world are engaged in the research of servo toolrest position compensation, and have put forward various methods of error compensation control. Self-learning Control Among many self-learning control methods, P-Integral learning control is the most simple method without learning its model of controlled object. The equation of P-Integral controller is: