Simplified analytical model of a six-degree-of-freedom large-gap magnetic suspension system

Original publisher: Hampton, Va. : National Aeronautics and Space Administration, Langley Research Center ; [Springfield, Va. : National Technical Information Service, distributor, 1997]. OCLC Number: (OCoLC)41172577 Excerpt: ... 0 000 0 000 0 0 " vMz / I_ 0 0 000 0 000 0 0 0 vM_ / Iy 0 000 0 0 vMz / Iz 000 0 0 0 000 0 100 0 0 0 0 0 000 0 010 0 0 0 0 0 000 0 001 0 0 0 0 ( 40 ) W 2 = 0 000 0 0 0 000 vMz / m ¢ 0 0 000 0 0 0 000 0 vM_ / m, 0 000 0 0 0 0 vM_ / m_ 000 0 100 0 000 0 0 0 0 0 010 0 000 0 0 0 0 0 001 0 000 0 0 0 0 Next, expanding CBresults in o,-rf_ / tgI 1 d-rf_ / tgI 2... aT_ / cTl m " ovry / a-I 1 o3Ty / o-tl 2... ( 41 ) o_ / 3I l... B = W 1 Evaluating the first term in equation ( 41 ) at X o results in ( 42 ) o-ff_ / _l [ x =-vM_d-tBy / d-I1 Since the fields and gradients are linear functions of coil currents, the components of By produced by coil n of an m-coil system can be written as ( 43 ) By, = ky, ( I_ / I_ ) where I_ is the maximum coil current, k_ is a constant that represents the magnitude of Brn produced by I_, and In is the coil current. To simplify, define 13