be found using the following expression, [Anon, 2]. a
(5.1) Where, Disp is the displacement of the instrum ent from the defining axis, at a dis tance dmm, from the carriage bearing and a is defined as the angular displacement of the carriage, with respect to the vertical carriage way axis, measured in arc seconds. For figures 5.4 and 5.5, Disp represents the displacement of carriage instrum entation away from the traverse axis and is represented by the variable Est-
A similar expression can also be used to calculate error in positional accuracy as sociated with pitch and yaw motion. In these cases Disp is replaced with L E p and
L E y for pitch and yaw motion respectively.
Yaw Error In Seconds
Carriage
Centre Line Of Carriage Point of Measurement
Top View
The effects of roll, pitch and yaw vary across different carriage way designs. How ever the cause is normally machining error during the manufacturing stage. When carriage ways are machined, it is extremely difficult to obtain precise long straight machining passes and care must be taken in the relationship of the tool to the work piece, [Barkman, 4]. Departured from straightness are typically due to a variation in the machine gears which control how the cutting head and the work piece move. The result is a surface th at is approximately straight, but has a variation about the flat surface. This variation is normally periodic in nature, but departures from periodic variation can be found and depends upon the manufacturing process. The frequency of variation depends upon initial cause, high frequency variation, or ” Roughness,” can be caused by machine tool scaring, or by machine vibration at the tim e of manufacture. Low frequency variation, or ” Waviness,” can be formed by pe riodic irregularities in the production machine gear systems. Figure 5.7 summarises
LE,
Measurement Point
Pitch Error In Seconds
Carriage
Carriage Way
Side View
W av in e ss sp a c in g
W a v in e ss
i
R o u g h n e s s
R o u g h n e s s s p a c i n g
Figure 5.7: Effects of Waviness and Roughness on Surface Form
the effect of a combination of waviness and roughness, [Dagnall, IS].
The variation of carriage way surface form can have a profound effect on a m ea surem ent systems ability to measure the position of a carriage, as it moves along a carriage way. If the frequency of either surface roughness, or waviness is too large, a similar effect to micro-rumble or static friction is encountered and the measureiiu'nt system begins to lose counts, resulting in a loss of positional accuracy. Thus, it is im po rtan t, where high accuracy positioning is required, to have a carriage way that has a low surface roughness and a waviness with a low frequency variation. The cor rection of roll, pitch and yaw motions, in conjunction with this project, is possible using the laser reference system, with small additional modifications, however this work is beyond the scope of this thesis.
5 2.4.2 T h e A ir B earing
Whenever either fixed or rolling element bearings are used in conjunction with a carriage way, there is always a degree of either static friction, or micro-rumble asso ciated with the carriage motion. However, there are a class of bearing which do not suffer from these problems, namely air bearings.
In an air bearing the two substrate materials th a t form the bearing, are separated by a thin layer of gas. No physical contact is made between the bearing m aterials when
&
1
Figure 5.8: Air Bearing Carriage Way After Assembly at OSL
in operation. One element, in the bearing, has a series of small pores distributed across i t ’s surface, which when this element is supplied with a compressed gas feed, allow a cushioning layer of gas to be formed between this element and the rest of the bearing substrate.
Since there is no physical contact between the bearing components, in subsequent motion of the bearing there is no micro-rumble, friction, or static friction. However, the construction of an air bearing is extremely sensitive to both the surface form and the surface quality of the bearing substrates. Errors in surface form can result in pitch yaw and roll errors, similar to fixed or rolling element bearings. The surface quality of air bearings is especially im portant. T he gap between the two bearing substrates is normally very small, to reduce the gas loss to a manageable level. If the surface of bearing substrates are irregular and have a high roughness, this can result in a distortion of the gas cushioning layer. Such distortions can have many effects, including perm itting contact between the two bearing substrates. However, this is a very serious case and normally it is found th a t surface irregularities in the bearing substrates will cause periodic irregularities in motion, such a bearing precession and vibration. If the bearing is correctly manufactured, these effects are at a minimum. In this project, there is a need for high precision positioning, as defining in C hapter 1, of the m easurem ent instrum entation above the surface under test. The use of an
(».«)
TOP VIEW
F R O N T VIEW
C 1 = 19084-00
Figure 5.9: Air Bearing Schematics from Dover Instrum ent Corporation
air bearing can facilitate the high precision needed far simpler than other types of carriage way, [Barkman, 4]. Also, there is not a large price difference between the purchase price of an air bearing carriage way and other mechanical carriage ways, for the traverse distance required in this project. Figure 5.9 shows a schematic of the air bearing used in this project supplied by Dover Instrum ent Corporation^. T he air bearing was supplied by Dover Instrument Corporation and consisted of a granite carriage way, 2120.9 m m long, with a cross section of 93.98mm by 75.31mni. T h e instrum ent carriage enclosed the granite carriage way and was supplied with a gas supply, oxygen free nitrogen, at a regulator pressure of 70PSI. Instrum entation m ounting holes were provided down each side of the carriage. Figure 5.8 shows a photograph of this air bearing, after assembly at OSL.
Supporting the granite air bearing, used in this project, in the correct m anner ^D over In stru m en t C orp oration , 200 Flanders R oad , P O B ox 200, W estb o ro u g h , M A . 10581.
is critical, since granite is extremely sensitive, both to point contact forces and torsional forces. Point contact forces are typically caused by either irregularities in the flatness mounting surfaces, or mounting surfaces th at are not parallel, causing load differences between the mounting points. From information obtained from Dover Instrum ent Corporation, the mounting surfaces should be parallel and flat to within a tolerance of 2.5^m. Torsional effects can also be caused by mounting surface irregularities, causing a variation in loading across the granite beam. This has the effect of twisting the beam and can result in severe damage.
Ideally, the granite air bearing should be supported at three points, located at the Airy points of the beam. These are the points of minimum deflection, and their use results in a minimum of stress being placed on the beam. However, the granite air bearing could be mounted at only two points, provided th at a substantially reduced instrum ent load was used. For initial testing of the granite beam this was acceptable. A two point mounting system is acceptable for experimentation purposes however, when large optical surfaces must be tested, it is more economic to move the test instrum ent to the optic. The reason for this is financial, since large Im plus optics cost far more to produce than a granite air bearing thus, if a granite air bearing is damaged during the movement to an optic it is far cheaper to replace the air bearing compared to the optic. This is especially true in the final stages of optical production, where it can involve many months of careful work in polishing and figuring to complete an optic.
The granite beam portion of the air bearing is extremely sensitive to external point contact forces and torques. Thus in order to move the air bearing, from a storage location to a test surface the beam itself cannot be moved without danger of damage. To avoid damage of the air bearing, work has been carried out, using computer modeling, on the design of a lifting and mounting frame.