# Torque for Rack and Pinion

SevenToFive
I need some help calculating a rough approximation for the amount of torque needed to lift a 3600lb platen. We are planning on using a motor and worm gearbox to drive 4 pinions to lift the platen. I'm looking to move this platen 48 inches in 6 seconds. The pinion is 4" diameter.

Am I correct in T=F*pitch/2*pi, where T is torque(in-lbs), F is the force(3600lbs), Pitch diameter would be 4 inches,
T=3600lbs*4/2*pi giving me approximately 22619in-lbs of torque needed to lift the 3600lb load.

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Gold Member
Not my field, but here goes just to get the thread started.
Pitch diameter would be 4 inches,
T=3600lbs*4/2*pi giving me approximately 22619in-lbs of torque needed to lift the 3600lb load.
You need to treat the pinion as a lever. The 4in. pitch diameter places the force at 2in. from the rotational center. That shows you need 7200in-lbs just to keep it moving.

The other part of the problem is you need to accelerate that 3600lbs from a stand-still to a speed of around 8ft per second in 3sec. (Assuming it spends as much time getting up to speed as it does slowing to a stop.)

I'l let the mechanical experts take it from here.

Edit: The distance traveled per pinion revolution would be π⋅D, wher D is the pinion pitch diameter; about 12.57 inches with a 4in pitch dia.

Cheers,
Tom

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Mentor
I need some help calculating a rough approximation for the amount of torque needed to lift a 3600lb platen. We are planning on using a motor and worm gearbox to drive 4 pinions to lift the platen. I'm looking to move this platen 48 inches in 6 seconds. The pinion is 4" diameter.
What is the platen used for -- what is this device?

What is your mechanical design background? Is there a reason you've chosen a Rack and Pinion mechanism to drive this platen? What is motivating the small size (4") of the Pinion gear? Have you considered other mechanisms to provide this lifting force? (linear screws, hydraulics, etc.)?

Mentor
Spur gears and racks do not work well in this type of application. The gears need lubrication, which creates a mess. Alignment is critical. There are significant forces pushing the gear and rack apart. If you stay with gears and racks, you will need to calculate the strength of the gear teeth. The procedure is in any undergrad machine design textbook.

A better system is to support the platen with synchronous belts. Alignment is less critical, and there is no lubrication mess. A simple schematic of such a system is shown in Figure 1A of US Patent 6,641,358. The largest and fastest version of that separator has carriages that weigh 900 lbs, and make vertical moves at accelerations of 500 in/sec^2. The belts are Gates Poly Chain: https://www.gates.com/us/en/power-transmission/synchronous-belts/poly-chain-synchronous-belts/c/120

Another system that works well is screws at the four corners, with all of the screws driven by a single chain or synchronous belt. The screws can be large acme thread screws, or ball screws. The separator carriages shown in US Patent 7,364,398 were originally driven by, and supported by, ball screws. They operated very well and lasted a long time, but were messy because the paper dust environment required a lot of oil to the ball nuts, which leaked out and made a mess.

Don't forget guarding so that nobody can get, or even reach, underneath the platen. That is required by OSHA in the US, and the Machinery Directive in the EU. Guarding is both a legal and a safety requirement. Do not cut corners on guarding.

berkeman
Gold Member
Another lifting approach is use a wire rope (cable) or a continuous chain at each corner, with a pulley/sprocket at the top of the corner columns. The motive force is still applied at the bottom with either a drum to wind the wire rope or a sprocket to drive the chain.

The advantage of this approach is its cost effectiveness and greater parts availability.

For stability, I also recommend diagonally cross-bracing the corner posts. Or at least a frame around the top (and bottom if possible) with strong gussets.

Cheers,
Tom

FAlonso
Another lifting approach is use a wire rope (cable) or a continuous chain at each corner, with a pulley/sprocket at the top of the corner columns. The motive force is still applied at the bottom with either a drum to wind the wire rope or a sprocket to drive the chain.

The advantage of this approach is its cost effectiveness and greater parts availability.

For stability, I also recommend diagonally cross-bracing the corner posts. Or at least a frame around the top (and bottom if possible) with strong gussets.

Cheers,
Tom

I totally agree. A winch system (rope/pulley) would be much more flexible and cheaper. Gearing would come with strict requirement on tolerances. Rack and pinion are not exactly known for load bearing capacities compared to other systems.

berkeman