A Study of Radial Runout For Circular Geometries
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A critical step in geometrical stacking for rotating machinery assembly requires mathematical representation of parts. Vector addition and Least-squares approximation were used to represent a part based on runout. Vector addition yielded a vector representing the net-effect of runout for a feature of a part. Least-squares yielded an approximate location of the physical center-point with respect to the ideal center-point. Representing a part mathematically would be a stepping stone to developing methods of geometrical stacking. Two sets of 8-point runout data was generated to represent the forward and aft of a part. The data and collection was to mimic manual measurement techniques where dial indicators are used. After converting the points to polar form, vector addition and least- squares was applied. Both yielded vectors with angular location where inferences could be made with regards to the physical meaning. For vector addition the resulting vector that represents the positions where runout had the greatest effect over the part. This could have been considered as a high point on the part. Least-squares was more easy to visualize as the vector represented the displaced of the physical center with respect to the ideal center of (0,0). It was noted that the angular locations of both methods were the same but this was due to the calculation methods used for least-square.