How Choosing Precisely the Secondary Length of an Electromagnetic Catapult Could Prevent Vibrations

Dealing with electromagnetic catapults, using a simplified numerical approach discretizing the secondary into small parallelepipeds, we demonstrate that short secondary linear induction motors usually produce superimposed periodic force modulations (large ripple). The paper begins with analyzing force modulations in the simple case of an aluminum sheet moving at constant speed inside a stationary sinusoidal magnetic field. The second part extends the analysis to the motor case when both the magnetic field and the sheet are moving at different speeds with an algorithm controlling accelerations through the motor slip. The third part presents an application of the calculation method simulating vibrations of a suspended mass elastically linked to a launching aircraft. The paper concludes that the linear motor thrust is modulated at a variable frequency which depends upon the motor control strategy. The frequency of this modulation is the ratio of the speed difference, between the field velocity minus the motor velocity, divided by the motor pole pitch. The thrust modulation could induce strong vibrations on heavy parts, such as fuel tanks, suspended onto aircraft wings, when meeting their resonance frequency. It is demonstrated how this modulation is avoided completely when the secondary motor length is an exact multiple of the stator pole pitch