Study On Machining Mechanism Of Trajectory Envelope Grinding Method For Aspheric Surface

With the development of microelectronics, optoelectronics, solar photovoltaic technology and continuous integration of optics and electronics and increasingly fierce competition in the domestic market, advanced manufacturing technology of aspheric optical components is increasingly becoming an important manifestation of a country’s manufacturing strength. It is the constant pursuit of the goal to improve the aspheric machining accuracy, efficiency and reduce the aspheric machining costs. Arc trajectory envelope grinding method (AEGM) is not high on the equipment precision requirement, and greatly reduces the grinding wheel wear, which can realize ultra-precision machining of aspheric optical element. However, there are some problems in grinding with AEGM, such as uneven grinding wheel wear, surface roughness of uneven, which limits its application. Development of aspheric arc trajectory envelope grinding method can rapidly improve our aspheric level of ultra-precision machining, which are in line with our development needs. Aimed at the existing problems in the process of arc trajectory envelope grinding, this paper makes in-depth research on the mechanism of AEGM, the main contents are as follows:According to aspheric grinding principle with AEGM, structure of the arc revolving surface wheel has been analyzed and the law of grinding point sequentially mobile has been studied in grinding, which can improve effective utilization of abrasive grains. And some factors affecting arc trajectory envelope grinding have been studied, such as grinding methods of axisymmetric aspheric surface and non-axisymmetric, maximum diameter of the wheel, width of the wheel, the wheel end arc radius and others.Firstly, the motion model of grinding point has been established in grinding aspheric surface with AEGM in this paper,. Then the concept of the angular velocity of grinding points around the arc center of the wheel end has been put forward by relationship between arc wheel grinding point and the processing curve position, and the angular velocity of grinding point has been obtained in grinding with AEGM. On this basis, the linear velocity equation of grinding point is deduced, and some factors, which affect the linear velocity, have been studied, such as the radius of the arc of the wheel end, the aspherical conic shape parameters, etc. Secondly, mathematical model of axis-symmetrical aspheric surface grinding volume within unit time has been established by velocity calculation formula of grinding point in grinding aspheric surface, and axisymmetric aspheric constant removal grinding has been realized through the sub-feed control wheel feed rate. Experiments show that constant removal grinding can basically achieve uniform wear of the wheel. Finally, the ratio (λ) of the area of the wheel in grinding and aspheric removal within a unit time has been proposed, which will affect uniform wear of the wheel. Theoretical analysis shows that the value of λ has nothing to do with the feeding speed of the wheel,but is associated with the arc radius of the wheel end, aspheric quadratic curve vertex radius of curvature, aspherical shape parameters of the quadratic curve, and a grinding coordinates, etc. The results are in accordance with the theoretic analysis.Based on the Mathematical model of shape error in dressing arc revolving surface wheel, some influencing factors are analyzed in dressing the wheel, such as wheel setting error, radius of the wheel and arc radius of the wheel end. At the same time, by means of establishing mathematical model of tool setting errors in grinding axisymmetric aspheric surface, meridional cross curve equation of axisymmetric aspheric surface is deduced when tool setting errors exist. And influence of tool setting error in different directions on shape accuracy of axisymmetric aspheric surface is analyzed. The results show that tool setting errors affect the generatrix shape and position of axisymmetric aspheric surface.Based on analyzing the contact are length between arc revolving surface wheel and aspheric surface, the rule of grinding force in grinding aspheric surface with AEGM is studied. Experiments show that the grinding force is small in grinding with AEGM, wheel types and performance and other factors have a greater impact on the grinding force.Through surface forming analysis in grinding aspheric surface with AEGM, residual height mathematical model of aspheric surface is established, and the influence of aspherical radius of curvature, radius of the wheel ends and wheel feed rate on residual height is analyzed. The results show that grinding surface roughness can be adjusted by changing the feeding speed of the wheel and grinding walking control interval, which is an effective means to improve uniform roughness of aspheric in grinding. According to study on machining mechanism of trajectory envelope grinding method for aspheric surface, a new technology is proposed in grinding aspheric surface with AEGM which compromises roughness and surface precision surface. That is coarse grinding with the constant removal grinding firstly and fine grinding with constant scallop-height grinding and constant value of λ in grinding axisymmetric aspheric surface. For non-axisymmetric aspheric surface, constant scallop-height grinding and constant value of A are adopted in grinding.