{"id":2592,"date":"2017-06-20T10:50:48","date_gmt":"2017-06-20T08:50:48","guid":{"rendered":"http:\/\/gap47.astrosurf.com\/?page_id=2592"},"modified":"2019-12-19T16:36:41","modified_gmt":"2019-12-19T14:36:41","slug":"how-to-use-polishing-machines","status":"publish","type":"page","link":"https:\/\/gap47.astrosurf.com\/index.php\/how-to-use-polishing-machines\/","title":{"rendered":"How to use polishing machines"},"content":{"rendered":"

Grinding action of a polishing lap :<\/strong><\/span><\/em><\/span><\/p>\n

Many different factors come into action when a polishing lap is used to wear away glass. So much so that it is illusory to put this action into an equation. Yet, in order to understand better how optical surfaces are brought to the correct shape we can identify and study different phenomena that take place when \u00ab\u00a0wearing away\u00a0\u00bb glass.<\/span><\/p>\n

The Preston law : <\/strong><\/span><\/p>\n

That law establishes that the wearing effect is proportional to :<\/span><\/p>\n

\u2022 the pressure of the lap on the glass (and vice-versa)<\/span>
\n \u2022 the speed of the lap in relation to the glass<\/span>
\n \u2022 the time spent<\/span><\/p>\n

With a given lap, the pressure, the speed and the time spent are factors that influence the length of the polishing action, but they don’t influence the shape obtained.<\/span><\/p>\n

One last factor to consider is the friction coefficient. Its value mainly depends on the nature and the quality of the material the lap is made of (pitch, Polyurethane, Teflon…). It also depends on the polishing liquid (more or less aggressive substance, proportion of water…).<\/span><\/p>\n

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Translation and rotation movements : <\/strong><\/span><\/p>\n

Colonel Charles D\u00e9v\u00e9 contributed a lot to turn the practice of shaping optical surfaces into a theory. We must cite his book \u00a0\u00bb Le travail des verres d’optique de pr\u00e9cision\u00a0\u00bb, of which we’ll only recall some fundamental principles. Two types of movements must be identified :<\/span><\/p>\n

Translation movement : The element considered slides sideways following a trajectory that may be straight (linear) or circular (we then speak of circular translation), or even randomized. This type of movement brings about an action of \u00ab\u00a0even wear\u00a0\u00bb as every spot of the lap leads to the same amount of wear in a given time. This situation is found when we place a lap on the glass disk of a mirror as it rests on the rotating plate of a machine. If the lap doesn’t exceed the size of the mirror and if it is moved sideways by a pin which lets it free to rotate, it will follow the same rotating movement as the mirror (at the same speed). There won’t be any differential rotation movement between the mirror and the lap. The main differential movement will come from the action of the pin, following a trajectory determined by the stroke chosen. That movement will be a translation movement. In that precise case we’ll call the movement a circular translation and every spot of the lap will bring about a similar wear to the mirror.<\/span><\/p>\n\n\n\n\n
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Linear translation : The lap remains parallel to itself as it moves along a line or a curve<\/span><\/em><\/span><\/td>\nCircular translation : The lap spins at the same speed as the mirror. The only differential movement is a translation.<\/span><\/em><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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Rotation movement<\/strong> : In such a case, the element is in rotation if we consider a direction of reference. We are then in a situation of \u00ab\u00a0uneven wear\u00a0\u00bb. The wear action by a given spot of the lap is in proportion to its distance to the \u00ab\u00a0instantaneous center of rotation\u00a0\u00bb (see the definition given in C. D\u00e9v\u00e9’s book). Thus, every spot of the lap doesn’t bring about the same amount of wear at a given time. This is the situation we find when the lap is prevented from spinning freely around the pin. We get a differential rotation of the lap with reference to the mirror. The situation is the same when the lap, although left free to rotate by the pin, exceeds the side of the mirror. The surface of the lap in this overhanging situation doesn’t have a balanced rubbing action of the two opposite halves (which was the case when the lap did not exceed the limits of the disk). Because of this the lap begins to have a slow rotating movement with reference to the mirror.<\/span><\/p>\n\n\n\n\n
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When the lap comes into an overhanging situation there appears a differential movement between the mirror and the lap<\/span><\/em><\/span><\/td>\nThe lap is blocked and can’t rotate : there appears a differential movement between the two disks<\/span><\/em><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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During polishing and figuring of telescope mirrors the translation movement is generally chosen, because of its overall effect, preferably to the rotation movement, with its non-linear wearing off effect, which is hard to control to obtain a regular shape, free of zonal defects. To that effect the polishing laps will be left free to rotate around the driving pin (thanks to a ball-and-socket joint, for instance). But, as it is impossible to avoid overhanging positions (which are necessary when polishing and figuring) there will be a differential rotation of the lap. Such consequences can largely be limited thanks to the choice of the rotating speed of the revolving plate. That speed will be considerably inferior to the back-and-forth movement created by the eccentric : this way the translation movement becomes more important than the rotation movement and the final effect can be compared to that of an \u00ab\u00a0even wear\u00a0\u00bb configuration.<\/span><\/p>\n

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Number of passages :<\/strong><\/span><\/p>\n

Just as it is for pressure and speed, it is obvious that the wear effect of any given zone of a mirror is all the more important as the polishing lap passes over it more often.<\/span><\/p>\n\n\n\n
\"\"<\/td>\nIf you only look at the lap, it doesn’t bring an even wear in the different zones of its surface as it is moved sideways, because of its round shape. We are going to show this in the following picture :When the polishing lap is moved sideways by a distance called d <\/strong>, we can compare the amount of wear brought about by two different zones of equal width of the lap (called l <\/strong>). One is situated at the centre of the lap, the other one on the outskirts of it. It is evident that the length covered by the central zone (and therefore the surface covered) is more important than that covered by the outwards zone. Thus, as the lap is moved over the surface of the mirror, the glass surface swept over by the central zone of the lap (painted yellow) will be more important than the surface swept over by the outside zone (in green). In consequence, the wear effect will be more important at the centre of the lap. A model representation of the efficiency of the different zones of the lap, represented as a cross section, would result in a Gaussian graph.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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If we now consider the lap’s movement over the mirror, it becomes evident that all the spots of it are not equally swept over. The polishing courses, whether by hand or by machine, are all, more or less, back and forth movements across the centre. Consequently the lap will sweep over the centre more often than over the outskirts. This phenomenon is magnified by the fact that the central zones are comparatively smaller in surface than the zones at the outskirts. To be more convincing, let us consider the global surface of a mirror as a juxtaposition of rings of equal width. For any given sweep of the lap, an outwards ring will be proportionately less affected than a central zone, and consequently less rapidly worn away.<\/span><\/p>\n\n\n\n\n
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The blue curve represents the path followed by the centre of the lap during work <\/span><\/em><\/span><\/td>\nA graph showing how many times the centre of the lap sweeps over any spot of the mirror according to its distance to the centre <\/span><\/em><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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Other factors that have an influence over the shape created :<\/strong><\/span><\/em><\/span><\/p>\n

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Importance of pressing  :<\/strong><\/span><\/p>\n

It is fundamental to start any work session with a careful pressing of the pitch lap, whether hand-polishing or machine-polishing. To that effect, one usually brings the lap to the proper temperature (in warm water or by using an heat lamp), then one must press it over the mirror with a layer of polishing paste in between, plus a good amount of weight on top. When starting a long polishing session it is not essential to press the lap with great accuracy as during work the pitch will naturally get warmer and the lap will soon adapt to the shape of the mirror and quickly eliminate the faults it might have created because of its irregular shape at the beginning. Yet, during the figuring sessions, it becomes impossible to compensate for a faulty pressing as the sessions become much shorter. One must be especially careful when pressing the lap otherwise it will be impossible to master the evolution of the shape. There exists a test to know whether a subdiameter lap is not well-pressed : if you place it over the mirror in an offset position (no overhang !) and you start the rotating plate (the eccentric being at rest) the polishing lap must rotate at the same speed as the mirror if the pressing of the lap is satisfactory. Otherwise you will get a difference of speed or an irregular movement of the lap. It is possible to make this phenomenon more evident if you place pen marks both on the mirror and the lap.<\/span><\/p>\n

When left unused for a long time, a lap will lose its shape : the pitch squares will melt down and become convex. This is even more important if the lap is stored in a warm room (mainly in summer). In that case it is advisable to keep it in a refrigerator (which also reduces the evaporation of solvents). It is necessary to press the lap for a long time if its squares have seriously lost their shape, but if you conduct frequent polishing sessions the shape of the lap will remain rather stable : it is then only necessary to cold-press it for a few minutes before each session.<\/span><\/p>\n

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Quality of the pitch  :<\/strong><\/span><\/p>\n

The physical qualities of the pitch used play a fundamental part in a lap’s capacity to produce a quality job that is adapted to the characteristics of the optical object to polish or to figure. Its plasticity depends on different factors :<\/span><\/p>\n