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Angele developed the original lapping and polishing machines and described the manufacturing method (see Fig.1 and ref.6). The original lapping and polishing machines were built by Ed White at the Marshal Space Flight Center and transferred to Stanford University in 1970. The machines have tetrahedral symmetry: the axes of the laps coincide with the axes of a regular tetrahedron. All the first experimental rotors were manufactured using these machines. Later, a new polishing machine was designed and built at Stanford University (see ref.7 and Fig. 2). Both polishing machines were later modified and used in manufacturing the science mission rotors. To achieve the most uniform action, Angele selected the following six motions of the polishing laps (cycles):
| 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | |
| A (upper) lap | F | B | F | B | F | B | ||
| B (left) lap | B | F | B | F | F | B | ||
| C (back) lap | B | F | F | B | B | F | ||
| D (right) lap | F | B | B | F | B | F |
Table 1.
F=forward, B=backward
The motors of the original machine were equipped with analog speed controllers, augmented by digital controllers with tachometer feedback, to assure further uniformity, (ref.8) . The new Stanford machine is computer controlled. The rotation angle of each axis is controlled by means of servo motors and shaft position encoders (ref.9).
During the process, the sphere is supported by the laps. Due to the weight of the sphere (and given the symmetrical configuration) the pressure of the upper lap is smaller than the pressure of the lower laps, which support the weight of the sphere. As shown in Fig.3 the laps are annular calottes closely conforming to the sphere. During the process, the sphere slowly decreases in size and the shape of the laps adjusts accordingly. Therefore one can not arbitrarily switch spheres during the polishing process unless they are of the same size.
All this applies to both lapping and polishing machines, which have very similar general configuration. They differ however in many small details. In the following the emphasis will be on polishing, which is the most demanding process.
During the polishing process the sphere slowly rotates as a result of the combined action of all four laps (see note 10). The direction of the sphere rotation corresponds to the vector sum of the rotations transmitted from each of the four laps to the sphere (the lower three being equal and the upper one somewhat smaller due to the smaller pressure). The axis of rotation of the sphere points slightly downward between each pair of lower laps, depending on the cycle. Since the sphere rotates during polishing, it exerts net reaction torques upon the laps. As the laps are supprted by an elastic structure or a pivoted arm, these torques tend to induce larger pressure on the side of the lap where the sphere moves toward the lap. Therefore by using the lap mounts with a pivot close to the sphere, rather than a longer arm, we obtained an improvement of sphericity.
One of the most critical parameters determining the quality of the manufactured spheres was found to be the machine alignment. The construction of the original machine was such that the alignment was not easy and it tended to change, requiring periodic adjustment. Thus the new Stanford Machine was designed with the alignment problem in mind. A hole in the center of the base plate allows the insertion of a precision shaft bound to the vertical structure serving as the reference axis. Therefore the common intersection point of the vertical shaft with the lower laps shafts can be easily checked.
Another important parameter is the balance between the pressures exerted by the four laps on the sphere. The original machine uses specially made springs. The springs used for lower three laps are selected for a similar force at the working compression level and the forces are equalized by using adjustable back planes for the springs. For the new machine, only weights and pulleys were originally used. These were easy to equalize, but the central position of the sphere was unstable. After adding weak stabilizing springs the motion was quite stable and uniform.
As mentioned above, the new Stanford machine is controlled
by computer. It uses a commercial control system (see ref.9).
The control was such that the laps move in time through a periodic sequence
of angular positions. We suspected that this could lead to repeating polishing
patterns. We developed a model where the position of the instantaneous
axis of rotation of the sphere was followed in a coordinate system fixed
within the sphere (see Fig.7). Under some conditions
the model showed repetitive patterns, rather than a uniform random distribution.
We then introduced a slight random variation in the duration of the cycles
and used random permutations in the cycle sequence to avoid such repetition.
This improved the sphericity and lowered the reject rate.