I am trying to model the maximum performance of a linear actuator assembly and create a flexible excel tool for calculating other systems in the future. The actuators are simple ball screws driven through a gearbox by a motor, typically BLDC so the torque is relatively constant over most of the range. We often run into a situation where people want to drive the actuator in a cyclical manner with a desired frequency and displacement, so the actuator rarely moves out of the acceleration region to a stable velocity. As such we need to calculate an acceleration constant that we can recalculate with different loads, screw pitches and gearbox ratios. So far I have been able to build an equation that looks at the total torque acting on the actuator that incorporates the inertia of the screw as well, (these can be up to two meters so not insignificant). However I am at a loss on how to compare that with the motors specifications and derive an acceleration for the assembly. Can someone point me in the right direction?