Balancing of a High Speed Rotor in Aerodynamic Bearings


For applications in laser display technology, a polygonal line scanning device based on aerodynamic hemispherical bearings is being developed in our laboratory. The rotor of the device requires precise balancing for reliable performance at rotational speeds >60 000 rpm. We estimate the necessary balancing quality from basic considerations and describe, how balancing is being performed. Sufficiently precise balancing for operation at target speed is shown to be achieved within the rigid rotor approximation. Stability is satisfactory according to preliminary results, obtained with a dummy system. To further extend life time, tests have been carried out with compensating polygon related unbalances on the part itself. The results fully confirm our expectations. This shows, that the design concept is sound and that the intended optical quality will be realised with the final system. INTRODUCTION For future high definition television (HDTV) or for simulations of virtual environments, a high performance laser display technology (LDT) is being developed /1/. A major component of the new technology is a line scanning device for the deflection of the laser beam with a writing speed of >30 000 lines/sec. Miniaturised devices as i.e. micro mirror arrays have been proposed and investigated. However, they are still in a status of basic research. Currently, devices based on a multiple facet polygonal mirror rotating at high speed, seem to be more feasible. A prototype of such a polygonal scanner is currently being developed in our laboratory /2, 3/. Fig. 1 gives a schematic crossectional view of the device. The design is based on a pair of aerodynamic hemispherical bearings supporting a rotable shaft, and attached to it, a polygonal mirror and a drive magnet. With a brushless DC motor a rotational speed of >60,000 rpm is obtained. The gaps of the air bearings have to be adjusted and maintained at a width of a few μm. To prevent thermal drift, low thermal expansion glass-ceramic is used as a major constituent in the construction. Figure 1: Schema of the Polygonal Scanner While load carrying capacity of the air bearings is inherently limited, centrifugal forces are considerable at such speed. Therefore a precise balancing of the rotor is mandatory for the performance of the device. AERODYNAMIC SPHERICAL BEARINGS To achieve self-acting of the bearing, the hemispherical surface of the rotating shaft is added with a microstructure in the form of spiral grooves. Fig. 2 shows details of the pumping structure. The groove angle relative to the meridian has been calculated to about 75 Degrees and the groove depth to roughly twice the bearing gap for maximum load capacity /4/. The latter is known to decrease quickly with increasing gap on a μm scale, when air is used as a lubricant. In the present design, grooves of several μm depth are used. To provide high bearing stiffness for advanced rotor speeds and good optical stability, mechanical accuracy of the bearing shape to the sub-μm range and adjustment of the gap to μm precision are required. Figure 2: Microstructured Shaft Surface Assembly of the device is greatly simplified by the hemispherical bearing principle, since no directional adjustment is required. There is an increased balancing requirement, however, as load carrying capacity is maximal in the axial direction, but -for geometrical reasonsreduced by a factor of about 2 in the radial direction. ROTOR The rotor is composed of a glass-ceramic shaft, which holds the polygonal mirror, a permanent magnetic ring as driving element and threaded Aluminum rings on both ends of the shaft for balancing. Details of the construction can be inferred from Fig. 3. The total weight of the rotor amounts to less than 100 grams with nearly half of the mass contained in the polygon. Joining of the various parts is done by a combination of adhesives, adapted to the specific materials and selected for high stiffness as well as minimal shrinkage. From the figure one can see that the joint of the polygon to the shaft is quite critical. BALANCING REQUIREMENTS For optical reasons, dynamic wobble or tilt of the polygon due to rotor unbalance is limited to ± 2 arc seconds. For a rigid rotor of length 60 mm, this amounts to a radial displacement of the shaft in the bearing of less than ± 0.3 μm. Once the stiffness of the air bearing is specified, this defines the tolerable bearing load due to unbalance. From dimensional comparison with previous designs /2/, the radial stiffness of the air bearing at full speed can be estimated to > 2 N/μm. Figure 3: Rotor with Polygon, Magnet and Compensation Rings Assuming only 1 N/μm for safety reasons, the upper values for the radial displacement correspond to a bearing force of F = 0.3 N or an unbalance of U = 8⋅10 3 gram mm at rotational frequencies of 1000 Hz (60,000 rpm). For speeds of 85,000 rpm, which are planned in the future, these values have essentially to be halved. This is due to a quadratic increase of centrifugal forces with increasing speed, in contrast to, at best, a linear increase in load carrying capacity. BALANCING INSTRUMENTATION AND METHOD Balancing measurements are performed at low speeds with a commercial „soft bearing“ machine, supplemented by additional measurement electronics. The rotor is mounted in its bearings in a rigid housing, which is positioned horizontally on two pedestals. Radial vibrations of the housing induced by unbalance forces are sensitively detected by moving coils and evaluated according to the influence coefficient method /5/ in the overcritical regime. At higher speeds (up to 3000 Hz) and with optional orientation of the rotational axis, another measurement system based on piezo acceleration transducers can also be used. With this instrumentation we are able to resolve unbalances down to lower than 10 gram mm, as compared to about 8⋅10 gram mm, considered necessary from the discussion above. Calibration of the equipment and gross balancing are performed by adjusting fine screws to the Aluminum rings that can be seen in Fig. 3 on both ends of the


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