Ball screw reduction ratio

Hi,
How can I calculate the reduction ration of a ball screw?
For example, let's say I have a DC motor spinning at 3000RPM, with a maximum
of 2000oz-in torque. If I couple the motor to a ballscrew that is 200mm (8") long and has 6mm (0.236") screw lead, it's intuitive that if 3000RPM is mantained, then the screw will travel throughout its extension in 0.66 seconds.
Let me just double check my math... 3000RPM = 50 revolutions per second. The ball screw needs close to 33 revolutions (200mm/6mm per rev.) to travel the 200mm, therefore 33/50 = 0.66s. Therefore 3000RPM is roughly equivalent to 303mm/s.
What about torque?
Cheers
Padu
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Padu wrote:

This seems *awefully* fast for a ballscrew mechanism. These are generally made for precision, not speed, though speed is a relative thing.
Sources of ballscrew components like SKF provide engineering white papers with design calculations. Sounds like you're doing something for a steering mechanism. You may also want to look into rack-and-pinion (easier mechanically), hydraulic, and pneumatic. For the latter two you can provide positional feedback using a pot or encoder, and a PWM valve. These might be more durable, and you'd definitely get the speeds and torque you're looking for. The positional accuracy will depend on your control system, and the quality/type of proportional controlled valves you use.
-- Gordon
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"Gordon McComb"

I'm monitoring Ebay hoping to get a cheap ball screw set. I have the DC motor with the caracteristics I mentioned before, and now I have to translate it to linear motion. This is not for the steering, but for actuating the breaking mechanism. On my ATV, breaking is mechanical (steel cable and lever, as opposed to hydraulic), so it needs considerable force to get actuated. I will probably add a reduction lever or even a gearhead to the motor to achieve greater reduction. I probably don't need a very precise positional accuracy, a linear pot or a bunch of switches will do.
I thought about replacing the whole breaking system by a hydraulic one, but I think I'd be spending too much time on the mechanics, which I'm not very experienced with.
Cheers
Padu
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Padu wrote:

Since you're not looking for accuracy or smoothness in motion, a simpler leadscrew may work better, and would probably last longer. It works on the same basic principle as a ballscrew, but doesn't rely on the reciprocating ball bearings. These aren't all that expensive new; Reid Tool and others sell these in standard lengths, with various pitches and diameters to suit your needs. You'll also need some bearings and blocks to set the shaft into. These are actually more expensive than a 12" lead and matching nut!
My concern would be the "hammer effect" you'd get powering that motor to 3000 rpm for the under one second you need for full travel.
Are you sure a 200-300 rpm 12 volt gearmotor, attached to a long enough lever, wouldn't be enough to actuate the brakes? They're spring return already, I'd imagine. You can test the torque needs with a fish scale. Try it along different lengths of a 6-12 inch lever.
-- Gordon
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"Gordon McComb"

I've thought about lead screw, but I didn't like their efficiency. Since the solution goes on a mobile platform, I was thinking about the energy savings. Now you expose a new variable that I hadn't thought before (longevity). I'll have to rethink it, but since it will be used for breaking, I believe the duty cycle is very forgiving.

Yes, if no gear reduction is in place, I will have to carefully design the acceleration curve in order to avoid jerking. The thing is that we are out of [official] budget, and a new gearhead for this motor costs over $600 bucks. I'm monitoring ebay for something compatible with my motor, but so far no luck.

I have a 12V 190RPM laying around, but I need to perform a few tests to check its torque (ebay stuff, no datasheet). If I had the linear motion device (either a ball screw or a lead screw), then I could go one step further and test how it performs actuating the brakes.
Another thing that I haven't decided yet is if I will actuate brakes (front and rear) individually or have only one actuator for both. The first has a technical advantage for off-road riding, but increases the complexity of the system in all aspects (hardware, electronics and software)
Cheers
Padu

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Padu, have you checked our fabulous http://www.industrialliquidators.com/locations.html here in San Diego?

the
savings.
I'll
(front
the
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"Wayne Lundberg"

Yes, the other day I made the mistake of going there with my wife, and needless to say, after 1 hour browsing the nice stuff they have, she was pretty upset. Unfortunately they don't have a good selection of gearheads (they have lots of stepper motors though), and the only ball screw I could find they didn't have the nut.
I'm still working on the steering mechanism of my rover, so I have plenty of time to lurk on ebay.
Cheers
Padu
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I have a ball screw, nut and some motors I'm not using. Stop by and take a look. Make an offer... money or talent later on in my new project. It's up on the rack and I'm too lazy to get to it now. But it's about 18 inches long, about 5/8 dia and the nut is circulating balls for high accuracy.

lots
didn't
of
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"Wayne Lundberg"

Thanks for the offer. Right now I'm monitoring a mini ball screw on ebay that would be perfect in both dimensions (price and length) for my project. Right now price is $1, but I foresee buying it for about $20-$30. If I don't win the auction I'll stop by. We should really get together sometime to chat over some beers about our projects, seems like there are lots of overlaps between them.
Cheers
Padu
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Sounds good to me!

a
project.
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Padu wrote:

Hi, I have not ridden ATC's, but old motorcycles used lever and cable front brakes and pedal and linkage rear brakes. The braking action on either the front or rear brake is going to be proportional to the force applied to the cable more then the position, although it's probably very non-linear. It is also not likely to be a constant relationship, as brake heating and wear will change it for you.
Almost certainly, you don't want to use the same actuator on the front and rear brakes. On motorcycles and I assume ATC's, the weight shifts forward very heavily in braking operation. The result of this is it's very easy to lock up he rear brake which can cause unpleasant results! If I had the choice of a single actuator driving both brakes or only driving the front brake, I would take the front brake only. ATC people may have a different opinion, but this is something to watch for.
Good Luck, Bob
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Let's see if I can remember any mechanics...
Force, rather than torque (as the output is linear rather than rotational). You need to know the diameter of the screw as well as the pitch (screw lead). That'll let you work out the angle of the threads to the axis of the screw, and convert the torque of the motor into a force at the edge of the screw. You already know the input force is normal (at right angles) to the axis of the screw. The reaction (as in Newton's 3rd law) of the screw to the input force is normal to the threads of the screw. The output force is along the axis of the screw. Now you can draw a diagram like this:
F _ |<-----/| | / | I / | / R | / | / V
I (down) is your input force. R (up and to the right) is the reaction, normal to the screw threads. F (left) is the output force, along the axis of the screw. (I hope the diagram makes sense, it's a bit tricky with ASCII).
Plug in I (calculated from your motor torque and the radius of the screw), the angle of R to I (from your screw diameter and pitch), and do a bit of trigonometry to work out F, your output force. This neglects friction of course, but I expect you can find a typical efficiency value for ball screws on the web somewhere, and multiply your answer for F by that.
Tim
--
Did I really still have that sig?

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You don't need to know the diameter/radius; that term cancels out. The truth is, diameter is not even very well defined in this situation.
tangential force = torque / radius
effective slope = pitch / circumference = pitch / (2*pi*radius)
axial force = tangential force / effective slope = (torque / radius) / (pitch / (2*pi*radius)) = torque / (pitch / 2*pi) = 2*pi*torque/pitch
At high force, ballscrews are quite efficient. If you hold them on end, ballnuts will spin and slide down a screw on their own. Try that with a leadscrew!
chris
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Hi Chris,
Let me see if I understood, so axial force in my case would be
2*pi*(1900oz-in)/(6mm) converting to SI: 2*pi*13Nm/0.006m081N !!
Considering efficiency of ball screw close to 80%, net force would be about 11000N? That would be enough to support 10 times my own weight. Is this correct?
Cheers
Padu
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That is correct. If you have trouble believing that, think of it this way:
A 1 meter radius circle has a circumference of 6.28 meters. The energy required to push 13N around that circle once is: 6.28m * 13N = 84J
This will cause a 0.006m linear motion with 14081N force: 0.006m * 14081N = 84J
Keep in mind that 14081N is the stall torque; it won't actually be able to push that hard while moving.
chris
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Well, that made me very happy. It means that I won't need to use the 1900oz-in motor to push the load. In fact, maybe even a strong stepper could do it, since the load is static. I'll do some experiments.
Cheers
Padu
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