I am trying to size a servo motor and my basic physics and math is so rusted that I can't figure out how to go about it? The scenario is as follows: I need to lift an object in the vertical direction against gravity. The object has a mass of 30kg. It is lifted to a height of 1m. It takes 5 sec to lift the object. I want to select a servo motor which is capable of doing this task. I have two options for the mechanism, rack and pinion (R&P) or lead screw (LS). I want the lifting to be done in three sections
- Acceleration of 250 mm/s^2 for 1 sec. distance covered is 125mm
- Constant velocity of 250 mm/s for 3 sec. distance covered is 750mm.
- Deceleration of 250 mm/s^2 for 1 sec. distance covered is 125mm.
First thing is the power of the motor. From basic physics I know that
Weight (force) = mass x g = 30 x 10 = 300N Work = Force x Distance = 30 x 1 = 300Nm Power = Work/time = 300/5 = 60W
This is the base Power if I add in some friction and a safety factor I would say that 100W-120W should be enough. But I have serious doubts about this calculation.
- Is the power calculation same when I have a Rack and Pinion or a Lead Screw?
- The downwards force due to gravity in case of Lead screw is acting at an angle on the screw threads so should I be resolving that weight component?
- What happens to the equations in case of downward motion?
I was doing some online research and many factors came up in sizing of servos. For example the Inertia ratio, velocity profile, max torque, RMS torque .
I found a forum post which suggested calculating motor RPM based on linear distance and pitch of the lead screw .
Then calculating the motor torque using this relationship
Torque = 30 x Power / pi x RPM .
But this formula is not accounting for the required velocity and acceleration
- Also how can I find the inertia ratio for a vertical moving load? Do I need to calculate the inertia of my payload when the payload is moving in linear direction only?
I want to understand the basic principles to the sizing so I can size the motor for a belt or a rack and pinion or any other mechanism. Any help or guidance is appreciated.
Edit:  I was trying to follow this two part video tutorial https://www.youtube.com/watch?v=4MaGqSQfYOk&t=210s  https://www.physicsforums.com/threads/calculate-torque-power-needed-to-lift-a-4-kg-load.661367/#post-4211630  http://wentec.com/unipower/calculators/power_torque.asp
and some other sources https://www.orientalmotor.com/technology/motor-sizing-calculations.html https://www.motioncontroltips.com/tips-for-sizing-a-servo-motor/ https://www.motioncontroltips.com/faq-how-do-i-calculate-the-inertia-of-a-servo-driven-system/