Timing belts, gears, and ratios

[samualt]

I guess this is a silly question, but someone has to ask it.

I see allot of machines that use timing belt, gears, etc... to change the ratio of turns from the motor to X/Y movement.
1. Is this really needed? If I was using a Rack-and-Pinion type movement, couldn't I just hook the motor up straight to the rack (with one gear) without changing ratios, and tell the software to go slower or faster?
2. Is there some kind of formula for figuring what kind of ratio you might want?

I'm just trying to figure out why some machines get so complicated with such things. Thanks for any info........Sam

[sdwilson]

depending on the size of the gear will depend on the gear ratio

[balsaman]

Here is the formula:

Figure out how fast you want to go.

Figure out the rpm of the motor.

Figure out what gear ratio it takes to make your machine go it's max speed close to the motors max rmp.

Make sure your motors have enough torque to achieve this.

So, if your motors go 1000 rpm, and you want to go 100" per minute, you need a 10 tpi screw if you go 1:1 ratio (no belt). If your motors are 2000 rpm, you need a 2:1 ratio, or 4:1 if you use a 5 tpi screw.

If you have a rack and pinion, and the circumference of the gear is 3" (~1" diameter), then your motor would need to turn 33 rpm to go 100" per minute. Not very effecient use of your 1000 rpm motor, as it can't develop the hp at that low a speed.

Eric

[samualt]

Balsaman:
OK, so I have these motors that are 2000 rpm. If I want 100" minute then I need a 20:1 reduction on a rack-n-pinion. That is if the rack-n-pinion is 1:1 itself.

It sure would be keen to design it so that I could change the reduction ratio easily. I guess that's too hard to do.

[High Seas]

I've been looking at the gear change ideas too a bit - bet thats why the gear and belt drives keep poping up--eh? Could easily work an adapting mount accomodating the different size gears.

Just currious - as I haven't sourced any of those parts yet - where have you guys found a good supply of belts and cogs?
Jim

[thielert]

You need to consider the diameter of the pinion. A 1” diameter pinion will travel 3.14 inches per rotation. So if you want 100IPM you have to have an output of ~32 RPM. If your motors output 2000RPM you need to gear them down with a 62.5:1. This is not an easy task. Take note that your tourque is multiplied by your reduction ration. So, for example if you have 50 oz/in servos then you now have 3125 oz/in of torque. 3125 will easily move a 150Lbs gantry on a 1” pinion. 50 oz/in will NOT move that gantry.

Additional points to note:
Servos reach their rated torque as they approach their max RPM.
Steppers have their rated torque while not moving. Their torque quickly dissipates with speed.

[buscht]

If I understand thielert's point correctly, the reason we need a gear reduction for servo motor's is to maintain the servo's speed near the high end while simultaneously getting more torque at the desired feed speed. As the machine designer, we must create a tradeoff between top end speed, cutting speed, torque, gantry mass, motor size and cost, etc.

So with stepper motor's we have just the opposite problem, we want to keep the motor RPM's as low as possible to maintain better torque.

For example, I am looking at purchasing the FET3/Cruiser package from Stepperworld.com. They state that the stepper motors are 150 oz/in and are rated for 120 rpm. If I use a .333" pitch lead screw, then my max inches per minute travel would seem to be 40 inches per minute.

I would simply mount the stepper motor directly to the lead screw and bypass all the gears and timing belts like Samualt suggests.

What confuses me is that when I look at a lead screw table, such as on the Kerk lead screw website. They show a tremendous amount of pitches available.

http://www.kerkmotion.com/masterleadlist.html

For example, they have a 1" lead on a 1/2" diameter screw and they show the efficiency of the screw to be 85%, while the .333" pitch only has an effieciency of 73%.

It seems to me that I would want to use the 1" pitch and get rapids of 120" per minute, while my cutting speeds would be 20" per minute and I would keep the RPM of the stepper low and get good torque.

What am I missing?

[bb99]

You also have to take into account what resolution you want from the machine. For example, a 200 step motor attached to a 10 TPI will give you a potential resolution of 2000 steps per inch or .0005 of an inch per step. However, in reality, you won’t get that type of resolution. But you do need to keep it in mind. The fewer TPI, the more course your resolution will be.

--bb99

[arvidb]

Originally posted by thielert Additional points to note: Servos reach their rated torque as they approach their max RPM. Steppers have their rated torque while not moving. Their torque quickly dissipates with speed.

This is not entirely correct: servos reach their rated power as they approach their rated speed. Their torque is constant, until you go faster than the rated speed.

While steppers, as you say, quickly loose torque with speed. This can be counter-acted somewhat by using a PWM stepper drive (like the Gecko), but steppers will never have the speed or smoothness of a servo.

// Arvid

[samualt]

Is it possible to use a Worm Gear ???

A Worm Gear has a regular gear and a worm (The worm is a spiral looking tube which rests on the regular gear). They seem to have great reduction capability!

\/\/\/\/\/\/\/\/\/\
/\/\/\/\/\/\/\/\/\/
/\/\/\/\/\
----O--->
\/\/\/\/\/


However, although the motor can turn the worm both backwards and forwards, the regular gear can not turn the worm at all! This means you could not move the gantry by hand if the motors were hooked up.
(It makes since....If you have a bolt in one hand and a nut in the other you can easily turn the bolt in the nut and get movement. But if you were to just pull back on the nut the whole thing would just freeze. That motion is at the wrong angle.)

So, do most CNC machines let you move the gantry free-hand even with the motors hooked up?

[arvidb]

Originally posted by buscht For example, they have a 1" lead on a 1/2" diameter screw and they show the efficiency of the screw to be 85%, while the .333" pitch only has an effieciency of 73%. It seems to me that I would want to use the 1" pitch and get rapids of 120" per minute, while my cutting speeds would be 20" per minute and I would keep the RPM of the stepper low and get good torque. What am I missing?

You have to chose between speed and force. A 10 mm/turn ballscrew would give you twice the speed and half the cutting force and acceleration compared to a 5 mm/turn screw.

Actually, I'm not sure what this means for a stepper. The 10 mm/turn screw is faster but weaker, but since the stepper would not have to turn as fast as with the 5 mm/turn screw, it would have more torque, and thus the "weakness" of the screw would not matter as much.

Actually, i guess the best you could do with a stepper is find out at what RPM it develops the most power [watts], and select a screw lead that gives you the cutting speed and force you want/need at that RPM.
Or do it the other way around: find out what speed and force you'll need, calculate the power you need (Power [W] = Force [N] * Speed [m/s]), and then find a stepper that can deal with that with a reasonable screw lead.
Remember to include the efficiency of the screw in your calculation; a 50% efficient screw will require twice the motor power compared to a 100% efficient one. (But then, nothing is 100% efficient )

// Arvid

[balsaman]

Most machines can not be moved by hand. Most use lead screws with nuts, so, like a worm, it can only be move by turning the leadscrew.

Worm gear (gearbox) is a great option for getting the 60:1 ratio you need for rack and pinion drives. Watch out for backlash in this type of setup tho...It's hard to get out.

Eric