# Calculating acceleration constant for linear actuator

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1. Aug 3, 2015

### Apothus

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?

2. Aug 4, 2015

### Nidum

Methods of designing linear actuators and their systems are well established and well documented .

Do some research on :

Control theory and motion control systems .
Design of CNC machine tool slideway drives and robotics .

There are many websites dealing with control and drive systems - both professional level and relating to DIY builds of CNC and robotic devices. Some of the latter might be more useful to you initially .

Just to start you off :

A simple system just trying to match motor torque to load demand all the time will never be stable unless you are very very lucky .

Start in a different place :

Establish the range of accelerations , steady state velocities and loads needed for your application . Refer these quantities back into rotational values at the motor shaft . Loads includes inertial loads , frictional loads and any load coming back from something you are driving against - eg cutting loads on a machine tool .

Establish the type of position control to be used - open loop or closed loop . Basically with positional feed back or without .

Many variants possible . Two simplest are stepper motors driven open loop and servo motors driven closed loop .

Choose motor type and characteristic to suit application . Manufacturers data is usually very comprehensive and includes detailed application notes .

Get back to me if you have specific questions .

3. Aug 4, 2015

### Apothus

A lot of this work is based on existing actuators we have at work. They are a bit of a mix but we are shifting everything towards BLDC motors with a closed loop control system. The idea behind this work is to actually design our actuators and control systems with a higher level of design than we currently uses. In this way we want to be able to look at a motion profile we want to use and know ahead of time that our actuator should be able to achieve it.

I had not thought of looking at CNC machines, that makes a lot of sense, thank you. Not to mention coming from the other angle as well, although it would help us refine the models of our older actuators.

4. Aug 12, 2015

### Apothus

I have made some progress on these calculations. My expectation is to calculate the inertia of the load and with the rated torque of the motor determine my acceleration

T=Iα

Load inertia comes from a ball screw Is driving a carriage Ic with a mass mc and driving a constant downwards force. Not knowing how to incorporate the force I have converted it into a mass mL

Is= mscrew*rscrew/2 = 19.5*0.02/2 = 3.896⋅10-3 Kg⋅m2
Ic= (mc+mL)(P/)2*10-6 = 30(10/6.28)*10-6=7.6⋅10-5 Kg⋅m2

This is based on information from here http://www.intechchennai.com/appServoMotor.php

With the 15:1 reduction gearbox I expect a reflected inertia on the motor = ratio2Iload+IG/box = (0.0666)2(3.896⋅10-3+7.6⋅10-5) + 6.7*10-5 = 8.465 * 10-5

Therefore with T=Iα substituting the rated torque of my motor and the reflected inertia i have an angular acceleration of 60601 rad⋅s-2
extrapolating this back out as a linear acceleration for my payload = ϖ/(2π)*ratio*pitch = 6.4ms-2

However this does not seem to be right. Using the Copper Hill VisualSizer pro software, I am seeing an acceleration of 300mms-2 for the same load, inertia and gerbox setup. This makes me thing something in my angular velocity equation is missing something or failing to take something in as a factor. Can anyone help me clean up these calculations?