The Research Of Measure And Control Technique To Process High-order Aspherical

The processing of aspheric surface optical element is recognized as the difficult problem at home and abroad currently. In order to gain an aspherical curved surface with ultraprecision and continuous smoothness, it needs accurate path curve, tools with reasonable moving ways and effective control system to solve the ripple error.The problem of the traditional institutions forming technology is of low accuracy. Processing high-order aspherical with tangent rotary method not only has the significant advantages in ensuring high accuracy and high surface quality of the request, but also has the advantages of high processing efficiency and low cost. So this processing technology is a innovative technology. Compared all aspheric surface processing technology at present, processing high-order aspherical with tangent rotary method will become more effective technology in aspheric surface processing areas. The CNC of numerical control processing areas usually only has the interpolation function of the line, arc and helical, and exists the contradiction and between fitting precision and generating data. The processing technology is that curves are discrete into short line. It destroys the first derivative continuity of the components profile curve and affects the smooth of components surface. Using a large number of small line segments to approach the profile curve of components leads the components processing speed to be difficult to meet the required feeding speed. The theory of rotation tangent method processing high-order aspherical optical element is according to predetermined curve tangent to control. In other words, we use the first derivative of the curve to control. So we need the speed control; In order to ensure that the smooth finish of optical elements surface, in speed control process, we must ensure consistency of symbol of the acceleration. It means that the curve’s second derivative has the same symbol without inflection point. The servo control system in current market can not complete the task above. So the numerical control system that uses the theory of speed interpolation algorithm as the core provides an opportunity to master the advanced manufacturing core technology.This thesis analyses the theory of the processing high-order aspherical with tangent rotary method and lucubrates the control law of the processing high-order aspherical, and it summarizes a control mode of the3-axis linkage electronic CAM.It uses three times spline interpolation PVT control mode, but this PVT control mode uses fixed error compensation table.So the Hidden Markov model theory is introduced to realize ahead forecast compensation in this system. In the following several aspects has obtained the certain innovation achievement.1. The establishment of speed interpolation CNC servo system modelBy analysing the theory that using rotary tangent method to process high-order aspherical optical element and the characteristics of the corresponding numerical control machine tool’s motion locus we refine the main factors.Turning tangent method is the first derivative of the curve in mathematics, and it is the speed control mode in the control system; because the velocity is controlled by the acceleration, so in order to ensure the surface of optical parts more smooth, velocity and acceleration must have the same sign in the regulation of the project. Consider the numerical control processing’s requirements as the constraint conditions to establish the mathematical model that we see the grinding wheel center’s mobile distance in the X axis, Y axis and the swing Angle of the Z axis as the control model of the three axes linkage with rate interpolation.2. Forward-looking new methods--Speed interpolation algorithmSpeed interpolation algorithm is based on the use of spline interpolation PVT speed control mode. Because the object study of HMM consists of two state sequences, so the forward projections introduces the Hidden Markov Model (HMM) in the control process. One state sequence is named observation symbol which can be measured directly, another state sequence is named the hidden state which is not visible. However, there is an inevitable link between observation symbols and hidden state, and the probabilistic model determines the changes of them. Speed interpolation algorithm is designed to control the speed which can increase or decrease in a monotonic of one processing cycle. Speed interpolation algorithm is based on the actual position which is measured by the grating, and the relation of speed and position accords with the HMM theory. It can forecast and compensate the speed error by Hidden Markov Model (HMM), because position error and velocity error will be linked through a probability distribution.3. The numerical control software and computer simulation software Prepare are programmed based on hidden Markov model control methodIt proves that the control method based on hidden Markov model is an effective method to control both position and velocity and it is also the development trend of speed servo control technology.