Minimizing motor cogging and vibration for the Thirty Meter Telescope

The Thirty Meter Telescope (TMT) needs to maintain precise positioning of the optical elements to deliver unprecedented image quality. Any vibration from observatory sources must therefore be minimized; model-based analysis leads to maximum allowable forces from any individual source typically of order a Newton or less in the most sensitive frequency band. Careful attention throughout the design process is needed to ensure that these challenging requirements are satisfied. We focus here in particular on cogging forces from the azimuth motor drive. Each motor yields periodic tangential and vertical forces of order 100's of Newtons, with higher harmonics of the waveform potentially exciting telescope structural resonances. There are 56 drive motors, and appropriate phasing between them can ideally cancel most of the net torque or net vertical force. However, the moment created between non-collocated forces still produces image motion even if the net force cancels, and further, small errors in forcer positioning result in imperfect cancellation. We provide a general methodology for estimating total cogging forces and then present an example of the expected TMT performance impact from motor cogging placed in context with the larger challenge of demanding vibration requirement.