# Selecting a gear reduction: torque vs speed

I have just sized the DC motors I want to use (corresponding to my robot and its intended applications - my figures include a 50% uncertainty factor to account for friction in reducers and other losses). Now I need to actually choose the exact motors I want to buy from the manufacturer (I am targeting maxon motors as I am not an expert and want no problem). I have a few down to earth questions about linking the mechanical needs to the electrical characteristics, among them:

Question #4:

The motor I chose (maxon brushed DC: 310005 found here) has nominal speed = 7630rpm - nominal torque = 51.6mNm. My needs are max speed = 50.42rpm / max torque = 10620 mNm. This means a reduction factor of 151 for speed and 206 for torque. Should I choose a gear closer to 151 or 206?

## 3 Answers

If you choose 151 you'll get the speed but won't get the torque, if you choose 206 you'll get the torque but won't get the speed. You can either play with your needs to be able to use that motor or use another higher torque/speed motor.

You have to select the motor for the worst case. (Assuming you cannot change your specification) it just may turn out that you have excess of speed or an excess of torque. In your example you have selected a motor that only handles the best case. You need a larger motor. (or to reduce your specification or to reduce your safety factor.)

My preference would be to have available more torque than required by specification as you really should NEVER stall a motor.

I think the better practice might be to start with what you need to the transmission to do and work backwards to make your motor selection.

1. Start with your max torque requirement (10.6 Nm). What kind of "max" is this? Is it a momentary maximum that the system will routinely reach or is it an absolute maximum that may occur accidentally. Let's assume that it is the former and not the latter.

2. Design starting with the transmission (aka reducer, gearbox) rather than the motor. How "sloppy" can your gearing be? If you need very low backlash and/or low weight, then you will need something like a harmonic drive. If not, you might be able to use a lower precision solution like planetary gearing.

3. Given your output torque requirements, look through a guide like this. I've linked to a guide from Harmonic Drive, but there are lots of other manufacturers. If you look through the specs starting on p. 19 you will see a spec for "Limit for Repeated Peak Torque". Let's take this as your max torque spec. (If you meant a momentary peak torque that is not routinely hit, then look at "Limit for Momentary Torque").

4. You are looking for a transmission that can support 10.6 Nm repeated peak torque. The tables indicate that a size 14 gear (planetary or harmonic) could handle this with margin.

5. Next you need to decide on your speed requirement. Do you care how fast your element can slew? If you are not sure, then make a table of implied max output speeds for each gear model/available ratio given the max input speed listed in the specs. For example, looking at the CSF models, you could support output speeds of 85, 106.25, and 170 rpm with the CSF-14-100, -80, and -50, respectively. Step back and look at these and decide which of the candidates are acceptable and which are not.

6. At this point you might have a mix of harmonic drive and planetary drive candidates. If you are not particularly concerned with backlash and weight, then you probably will want to use a planetary drive for cost. Otherwise you will select a harmonic drive. (You could also make this choice up front, but maybe it is best to enumerate all the candidates up front).

7. You will also want to add a column for "nominal" output torque in each case. Here you could pull in the "Average Torque" specs. You could estimate average speed by multiplying the max speed by the ratio of average torque rating to momentary peak torque rating.

8. Divide the speeds, average torques, and momentary peak torques in your table by the gear ratio. At this point you will have a table listing the average and maximum speeds that your motor needs to support. You can go to your favorite motor suppliers catalog and select accordingly.

I've just illustrated this with a set of planetary and harmonic drives, but of course you could throw other types of transmissions into the mix. These two are the most common for robot arms.