# Case Study Of Rotor And Touchdown Bearing Models

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Rotor and touchdown bearing models
Fig. 1 features the case study of the high-speed rotor. The photo was taken after manufacturing of the electric motor part, when the rotor was carried to the laboratory for an experimental modal analysis. During normal operation, the rotor is supported by AMBs. In the dropdown event, the rotor is in contact with touchdown bearings at both ends of the rotor.

Fig. 1. Rotor under investigation.

In this work, the finite element model of the rotor employs Timoshenko beam elements. The contact forces between the rotor and the inner race, and the contact forces between the balls and the inner race are defined by a Hertzian contact model. A simplified spring-damper and mass model is utilized to model the bearing
Model of the contact
The radial contact force "F" _"r" between the rotor and touchdown bearing is modeled by modified Hertzian contact theory [4]:

"F" _"r" "=" {■("K" "δ" ^"10/9" ("1+" ("3/2" )"α" "δ" ̇ )" ;" "e" _"r" ">" "c" _"r" " and " "F" _"r" ">0" @" 0 ;" "e" _"r" "≤" "c" _"r" " and " "F" _"r" "≤0 " )┤ (15)

where "K" is the contact stiffness between the rotor and inner race, and "α" is a contact parameter that for steel ranges between 0.08 and 0.2 [22]. Numerical values for the stiffness and damping of the contact between the rotor and inner race are given in Table 1. In Equation (15), "δ" is the penetration of the rotor in the inner race and can be obtained as follows:

"δ=" "e" _"r" -"c" _"r" (16)

where "c" _"r" is the radius of the air gap between the rotor and touchdown bearing. Radial displacement of the rotor is "e" _"r" , which can be expressed as follows [4]:

"e" _"r" "=" √("e" _"x,r" ^"2" "+" "e" _"y,r" ^"2" ) (17)

where "e" _"x,r" and "e" _"y,r" are the radial displacement between the rotor and inner race in the "x" and "y" -directions. The model also includes the friction force "F" _"μ" between the rotor and inner race, which can be