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How can I model the shaft for linear structural analysis?


I designed a shaft where one end is connected to a motor and other and is connected to a valve so motor can transmit power using the shaft to open and close the valve.  shaft is free to rotate but constraint to move xyz. One end we have Torque, other end is connected to the valve.   


When i add the loads, I add Torque to one end where motor connects, then  centrifugal acceleration to the whole body .  I am confused on where to put the constraints because it is a rotating part with free ends. I thought to pin the end where valve enters in, so it limits xyz movement but allows rotation. But do I have to pin both ends ? 

  When I animate with this configuration, I expect to see it rotating but instead free end moves up and down.