# Could I have help on understanding stepper motor speed?

I'm confused about stepper motor speed. On their data sheet it doesn't really specify a maximum speed. I want to use a stepper motor with a 3:1 gear ratio. This is the motor that I am looking at:

So with the gear ratio, the torque will increase from 3Nm to 9Nm, and the speed will be reduced by 3 times.

However, what will the speed be? I appreciate any help on helping me understand.

• The horizontal axis is steps/second, pre gearing. Typical small steppers are 200 steps/rev, some 400 steps/rev . Check docs for this number... Torque also depends on voltage (determines dI/dt) and to a lesser degree on driver electronics type and configuration. There's a tradeoff vs EMI and some other stuff. Feb 18, 2022 at 13:44
• Oh, I thought the horizontal axis is RPM! Ok thank you, the step angle is 1.8 degrees, so it's 200steps/rev. So does that mean, if I want to use the 3Nm of torque, it will be around 100steps/second (from looking at the graph), therefore in 2 seconds the shaft will complete one revolution? Feb 18, 2022 at 14:28
• I was assuming the motor data describes torque pre-gearing. That's important, maybe not the case. But if so, use the 1Nm line at the motor, to get 3Nm at the gear output. In reality you lose some, so leave breathing room there). So for example "57A3" purple line has 1Nm at <900 step/s, which is <4.5 rev/s, which is <270 RPM . At higher speeds, having the 48V voltage that is suggested by the product description becomes important too. Stepper datasheets sometimes give multiple curves for the same motor run at various supply voltages. Feb 18, 2022 at 14:38
• Thank you for your reply, I think I am starting to understand! So I would like to get 3Nm torque from this motor itself, and 9Nm torque with using gears with gear ratio 3:1. Does that work? Feb 18, 2022 at 14:47
• depending on which way the gearing goes. I didn't read your linked docs in detail. check info carefully / good luck. Feb 18, 2022 at 14:51

If a gear is used on the shaft of the motor, then assuming:

• $$T_M$$ is the motor torque (also the gear input)
• $$n_M$$ is the rpm (also the gear input)
• $$T_g$$ is the gear output torque
• $$n_g$$ is the gear output rpm
• $$i$$ is the gear ratio (assume that $$i>1$$ means a reduction of rpm)

then the following equation hold: $$T_g = i\cdot T_M, \qquad n_g = \frac{n_M}{i}$$

## Torque (a bit more complex)

Torque of a stepper motor is a bit more complex. I.e. the relationship between torque and rpm is not linear, but in reality is more similar to the image below. So, with increasing rpm on the motor the Torque output is affected. So you might need to consult the datasheet of your motor manufacturer.

Additionally, other factors like the selected driver of the stepper motor can have an effect depending on the supplied voltage.

• Thank you!! So from the curve that has been provided for the motor that I am looking at (I added the curve to my question). If I need the whole 3Nm of torque, does that mean the speed will be around 75RPM. And if I use a gear ratio of 3:1, the speed will be around 25RPM. Is this correct? Feb 18, 2022 at 13:03
• Yes if the motor rpm is 75 then at the gear reducer you'd get 25 and triple the torque.
– NMech
Feb 18, 2022 at 15:16
• Thank you, however, I believe the graph is steps/sec according to another answer for this question. I thought it was RPM. So, at 2.8Nm it's around 100steps/revolution according to the graph. Therefore, with 3:1 gear ration it's is 33steps/second. Is this correct or is it different for steps/second? Feb 18, 2022 at 16:16
• Yes rpm and steps per sec are completely proportional
– NMech
Feb 18, 2022 at 17:19