Abstract
Using the first axiom of statics for equilibrium of a two forces system applied to points of a solid body, it was verified, that the pressure in the zone of contact of a tool with a lens during its abrasive processing by the grinding-free method is unevenly distributed. With this in mind, the nature of the distribution of the pressure profile has been presented graphically, showing the equilibrium condition when the tool is rotated around the center of the spherical surface of the lens relative to its axis of symmetry and the clamping force of the unions that are grinded has been recorded. On that base an expression is proposed for determining the current pressure at an arbitrarily chosen point on the surface of the lens. An expression for determining the continuously changing contact area of the instrument and the lens during its processing by grinding-free method is obtained. The calculation of current pressure at different points of the diametrical cross-section of the contact zone of the lapping surfaces of the tool, performing oscillatory motion, and the lens is performed. As a result, the uneven distribution of pressure in the area under study was revealed, with the minimum value of this indicator taking place in the zone of contact of the tool edge with the lens, and the maximum in the zone of contact of the lens edge with the tool. The observed non-uniformity increases with an increase in the angle of deviation of the tool from the axis of symmetry of the lens. Theoretical and experimental studies of the influence of the tool diameter on the polishing process of the lens under conditions of free grinding, which prevents the occurrence of local error in the marginal zone of the latter due to the pressure drop between the grinding surfaces during the instrument movement, are carried out. At the same time it was found that in order to avoid a “blockage of the edge”, it is necessary to use a tool with diameter of at least 0.8 of the diameter of the lens (in case it is the lower link). The obtained results allow assigning the optimal diameter of the tool depending on the size of the processed lens without preliminary laborious experiments and can be used in optical and optoelectronic instrument making.
Highlights
Using the first axiom of statics for equilibrium of a two forces system applied to points of a solid body, it was verified, that the pressure in the zone of contact of a tool with a lens during its abrasive processing by the grinding-free method is unevenly distributed
Graphically, showing the equilibrium condition when the tool is rotated around the center of the spherical surface of the lens relative to its axis of symmetry and the clamping force of the unions that are grinded has been recorded
On that base an expression is proposed for determining the current pressure at an arbitrarily chosen point on the surface of the lens
Summary
Используя первую аксиому статики для равновесия системы двух сил, приложенных к точкам твердого тела, обосновано, что давление в зоне контакта инструмента с линзой в процессе ее абразивной обработки по методу свободного притирания распределено неравномерно. С учетом этого графически представлен характер распределения эпюры давления, отображающий условие равновесия при повороте инструмента вокруг центра сферической поверхности линзы относительно ее оси симметрии, и записано усилие прижима притирающихся звеньев, на основе которого предложено выражение для определения текущего давления в произвольно выбранной точке на поверхности линзы. Получено выражение для определения непрерывно изменяющейся площади контакта инструмента и линзы в процессе ее обработки по методу свободного притирания. Проведены теоретические и экспериментальные исследования влияния диаметра инструмента на процесс полирования линзы в условиях свободного притирания, при котором исключается появление локальной погрешности в краевой зоне последней, обусловленное перепадом эпюры давления между притирающимися поверхностями в процессе переносного движения инструмента.
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