We start with the WHY
“Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” everyone says this was said by Archimedes, but the importance of who said it is less important than understanding it.
I will start with an example, in video 1 you can see a Nema 17 Stepper motor with a 100:1 ratio gearhead lifting a turret mill. This NEMA 17 with a gearhead replaced a Nema 23 without one. The NEMA 23 could not lift the load at all.
So you can see power, torque and speed are all different and quantifiable things. Let’s break down the equations of this one. We will not be using freedom unit except RPM:
Power (kW) = Torque (N.m) x Speed (RPM) / 9.5488
You see the horrible 9.5488 factor that is because of RPM. Why do we use this? Well, because people understand this intuitively far better than radians per second. Check out online calculators like:
So if we reduce the speed and keep the power the same you can see we have more torque. Torque being the actionable force in a rotating system.
Back to levers:
In Fig 1 we have a lever mechanism, if we change the ratios of the load arm and the effort arm, we change the amount of force required to lift the load. using the equation:
Torque= Force X perpendicular distance from
If we want to balance the beam about the Fulcrum we have so the
Moments on the left = Moments on the right
OutputLoad * LoadArmDistance = Effort * EffortArmDistance
Back to the gearbox
This is the basis of what we are up to inside the gearbox. Basically using levers to gain mechanical advantage at the expense of speed or the other way around.
What is a GearRatio:
In the true basic essence, if we remove frictional losses (which you can’t do in practice and this is really important) we have
Number of input shaft rotations: Number of Output shaft rotations
So now we have a look at some simple calculation examples:
If we have a 1Nm output at 100 RPM from a motor, and a 10:1 ratio gear reduction.
1*10 = 10 Nm output torque at 100/10 = 10 RPM.
So if you are looking for torque and you don’t need/want speed you can get away with a much smaller motor than one would think. There is an added advantage of keeping the power consumption down and being able to use the peak torque delivery of a motor right in that sweet spot for the motor as the torque curves are a lesson in themselves we won’t get into that, leave a comment if you want me to do something on that. Not to mention inertia matching….
Now to talk efficiency and maximum output torque.
No gearbox or gearhead is 100% efficient. The best get up there to the 90% but most are around 60%. So you have to factor that into the calculations when working out how powerful a gearbox you need. Most good manufacturers will have a guide on how they work out their effciencies for their gearboxes, I always suggest that you read that. But basically:
Effective power = Expected output Power X Efficiency
Maximum Torque output is normally a hard limit, otherwise, you get output shafts rupturing and gears breaking off teeth. Shown in fig 2 and fig3 below.
Once a tooth comes off in there the damage cascades due to the pieces getting jammed into other things and destroying the very tightly meshed gears inside the gearhead.
How to choose a Gearbox
I will leave the inertia matching and just stick to the basics:
1. Work out how much torque and speed you need.
2. Use this to find which combination will best fit your application.
This is often a back and forth process. But the effort is worth it as buying 2 motors is more expensive and will cost you more in time than doing the calculations.
Step 1 Working out how much torque and speed you need:
This is complicated, but it comes down to Newtonian mechanics, put as much information into the calculations as you can. There are books and books on this, but it comes down to how you apply F=ma. Then looking at what the masses in your system are, adding in the frictions you can find and then working out how much force you will need to move that load.
Once you know the force you need, you have to decide where and how to apply that force, usually, this will be with a belt, leadscrew or ballscrew. These all carry their own analysis and you can find a great example of how to do this in Shifley’s Machine Design https://www.amazon.com/Shigleys-Mechanical-Engineering-Design-McGraw-Hill/dp/0073398209
Step 2: Use this to find which combination will best fit your application
You can do this by hand, or you can build an excel spreadsheet but a large number of manufacturers have added design tools to their websites. https://www.faulhaber.com/en/driveselection/fdst/
This kind of tool will give you an indication of how well suited their products are for your application. It also means you can move to another manufacturer very quickly after realising they have nothing that will work for you.
If this helped please let me know in the comments. Also, ask, if there are any questions. We also provide a service where we do all the calcs and come up with a solution just for you. So please don’t hesitate to get in touch.
If there is a topic you really want to see please leave a comment or send me an email on our contact page.