![]() ![]() The bottom line is we didn’t have to do any math did we? AutomationDirect provides all the inertias we need in the data sheets and we used an on line calculator to do the units conversions. Here’s all of our inertia’s converted to the correct units. Put the units you have here, the units you want here and there’s the answer. Go out on the web and search for an inertia units converter. The only problem is all of these units are different and how in the world do you convert these units with inches squared to these units with seconds squared – that doesn’t seem right does it? Here’s the trick. ![]() For this demo we want ounce inch seconds squared so when we’re done we can just read the answer right off the motor curves which are in ounce inches of torque. This is really important: We need for all of our inertia values to be in the same units. We don’t have a gear box but if we did, we would put it’s here and divide the downstream inertias by the square of the gear ratio. If we had a gear box, same thing – just get the inertia from that datasheet. This slide can handle 110 pounds, so let’s divide that by the acceleration to get our mass number, multiply that by the handy inertia factor and we now have the inertia for this payload and the system inertia of the carriage and coupler. And since force is mass times acceleration, we just divide the payload weight by the acceleration – which is gravity in this case, 32.2 feet per second per second, or since we need inches in this example that would be 386.4 inches per second per second. Be careful here – is this the weight in pounds? No, it’s the mass. And if we go to the lead screw spec sheet – look at this! It’s already calculated the inertia of everything associated with the linear slide AND it gives us a factor we multiply the payload mass by to give us that inertia. You can add it in later once you have selected one to make sure it doesn’t affect anything. If you don’t know what motor you are using yet, just leave it blank. For the motor inertia, we just go to the spec sheet and see the inertia of the rotor is 0.56 oz.-inches squared. And while you CAN do all that math that if you want to, there is a MUCH easier way to do it. If you look in the SureStep user manual, Appendix C there’s a whole bunch of scary looking equations that show you how to calculate all of this stuff. In our example we don’t have a gear box so there is no inertia and the gear ratio is 1 to 1 so that gets rid of this term. The gearbox impacts the inertia of everything behind it by the square of the gear ratio. So we need to sum all of those inertia’s to get the total inertia. And all of those things have mass so they all have inertia – which means they are all going to work against us when we try to get things moving. Get what moving? Well, for a linear slide: The motor has to rotate, the gearbox has to rotate, the coupler has to rotate, the screw has to rotate, and the carriage has to move. And since we are rotating stuff here, we need torque to get it moving. ![]() So inertia is just a measure of how much an object doesn’t want to be moved. That force has to be large enough to overcome what? The inertia of the object. And because it has more mass it takes more force to get it moving. For example, which is harder to get moving – a clay brick or a Styrofoam brick? The clay brick of course. And it’s solely dependent on the mass of the object. What exactly is inertia? It’s just a measure of how much an object resists being moved. And acceleration torque is inertia times the change in speed over the change in time. Step 4: How much Torque do we need to move the carriage on the linear slide? The total torque we need to worry about is how much Torque it takes to keep things moving and how much torque it takes to accelerate the load. We’ll also take a look at how to use that information to so the same thing for other types of mechanisms. In this video we’ll learn how to calculate the torque required and then use that and the speed to select a motor. In part one we saw it was pretty easy to calculate the number of pulses needed, the step resolution and the motor speed. ![]()
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