1. ## Rack & Pinion versus Lead/ball Screw

Hi all,

Firstly I apologize if this has been posted before, but I am looking for a comparison between R&P and LS on the basis of linearly produced force. I find it difficult to get the right answers since most posts refer to these system being used in CNC machines for positioning.

I am working on a project that requires a linear force of 800N. Travel distance of 130mm, desired speed 30mm/s. When using the following equations for each device, I get the torque required for such an output.

R&P:
T=F.r
F=800N
r=0.004
T = 3.2N.m

Ball screw:
F=800N
L=8
T=1.13N.M

I used a diameter of 8mm and a lead of 8 to ensure the same travel distance per revolution. From this is it safe to say that a ball screw would be the best solution since it requires less torque from the motor? Does the mass moment of inertia of the screw equate to a considerable increase in torque required, that should be accounted for?

This is only a rough estimate to decide which of the two would work best for the application.

Thank you.

2. You're asking which is best without giving your criteria, other than motor torque required. Surely there are other considerations. Maybe life, cost, physical envelope, availability of components, design complexity, duty cycle, heat generated? Either option works for me.

3. Originally Posted by jboggs
You're asking which is best without giving your criteria, other than motor torque required. Surely there are other considerations. Maybe life, cost, physical envelope, availability of components, design complexity, duty cycle, heat generated? Either option works for me.

All those aspects are being taken into account. The purpose of the question is to compare the two regarding the torque. My decision will not be based on this alone.

4. The input torque to output force ratio is simply a matter of mathematics in both cases.
The requirement of the same travel distance per revolution seems arbitrary to me. Imposing it just pre-defines the result of your "comparison" without adding any real value to the analysis that I can see. Why do you care?

The mass moment of inertia of the screw only affects motor torque in acceleration or deceleration. Stationary or constant speed torque will not be affected by that.

5. Originally Posted by jboggs
The input torque to output force ratio is simply a matter of mathematics in both cases.
The requirement of the same travel distance per revolution seems arbitrary to me. Imposing it just pre-defines the result of your "comparison" without adding any real value to the analysis that I can see. Why do you care?

The mass moment of inertia of the screw only affects motor torque in acceleration or deceleration. Stationary or constant speed torque will not be affected by that.
The purpose of the question is to verify the mathematics? I referred to the speed of the system as a basis to compare the torque. There is no requirement to produce the same travel distance per revolution. If a pinion diameter of 15mm was chosen and a lead of 2mm how could you possibly compare the torque requirements of the separate mechanisms?

I apologize for my incompetence, but I fail to see how speed is irrelevant when determining a torque requirement?

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