gear ratio help

[Erick Davidson]

Greetings,
I am building a 60" x 120" plasma and I am trying to figure the correct pinion diameter for my rack, as well as the belt reduction to achieve the recommended 3:1. I understand how to figure the ratio through gears or belt reduction. My question is the ratio to the rack. If I achieve a 3:1 reduction with my timing belt, how do I include the reduction or overdrive of the final drive of the pinion? i mean, what is 1:1 with the rack? One revolution = x travel? I plan to use the 12pd rack Mcmaster carr sells as I want the 1/4" counterbore of the predrilled rack as I am thinking of running cam followers on the backside. Any help or suggestions would be appreciated. This is a fantastic site. Gave me the confidence to embark on this!
Cheers, Erick Davidson

[NC Cams]

Look up the definition of "gear pitch", specifically diametral pitch. Once you do that, the relationship between pitch and travel per rev of the gear should become self evident.

"Machine Design" by M.F. Spotts is a good source...

[Erick Davidson]

Thank you, I appreciate the help.
Cheers, Erick Davidson

[jcc3inc]

Sir,

I would start with 20 degree pressure angle rack as it runs more smoothly that 14 1/2 degree rack. In addition, you need only 18 teeth to avoid undercutting of the pinion teeth for 20 degree rack as opposed to 32 teeth min for 14 1/2 degree gearing. Second, choose 24 dp or 20 dp rack so that your pinion diameter will be reasonable.

You can purchase gear rack from Standard Steel Specialty Co., 260 Parkway East, Duncan, SC 29334, Phone 800-486-9500. They stock 20 DP rack in 1/2 x 1/2 x 6 foot lengths. The price is good. You can buy 20 degree pinions from Boston Gear, I think.

You don't need cam followers on the back of the rack. The weight of your machine and general design should eliminmate the need for this. Your motor/gearbox should be spring loaded into the rack, with the pivot point being approximately on the rack pitch line. The necessary spring loading force can be determined by multiplying the anticipated drive force by Tan 20 degrees; If you expect a max of 50# force due to drag + Acceleration, you need (50 x {Tan 20}) = 18# spring load of the pinion into the rack.

If you choose a 20T, 20 DP pinion, it will be 1" diameter at the pitch line, and you will travel 1 x Pi = 3.14159 inches per revolution. Using DC servos or steppers results in different gearing approaches.

If you'd like more info, jccinc-at-owc-dot-net

Regards,
Jack C.

[JerryFlyGuy]

Just some food for thought. Before you spec out the rack, you should look at the stepper's [ or servo's] your using and figure out the max torque they are going to put out, then multiply it by 3 [ your reduction ratio] this will give you a number to check your rated strength of the pinion gear. I'm finishing up a large format milling machine and ended up using 12DP as anything less than that was just going to bust the gear. 20DP sounds great until you look at it.. its TINY! I know that plasma's typically don't run into the same cutting forces as a mill or router, however.. Acceleration is your worst enemy, and rumor has it that some plasma's really move.. upwards of 1000IPM so.. make sure the pinion you pick is strong enough for your application.

Bostongear.com has some great info you can look up and check to see if your pinion will stand up to the torque load.

My 2 cents..

Jerry