# Shaky Breaky Part: Analyzing a U-Joint Driveshaft with SOLIDWORKS Motion

We all know how amazing the internal combustion engine is. From weed wackers to cars to bulldozers, it powers much of the equipment that makes our lives convenient. However, the engine wouldn’t be as useful without a way to transfer its motion. Without a way to get the engine’s power to the trimmer head of a weed wacker, the wheels of a car, and the tracks of a bulldozer, the engine is useless. So, the drivetrain (that doesn’t get nearly enough credit or moment in the limelight) is just as important as the engine.

Any mechanical engineer of heavy machinery will tell you how much care and consideration goes into the design of mechanisms and drivetrains. One of those considerations is how the system vibrates when power is driven through it. If the system is not properly designed, vibrations may cause premature wear, cracks, or an unpleasant experience for the operator. In this article, we will study how a universal joint (U-joint) driveshaft system vibrates as it is turned with SOLIDWORKS Motion!

Let’s study this simple U-joint system. The U-joints are shown in orange and are comprised of a pair of hinges held together by a cross shaft. The joint shown in blue is a prismatic joint, which means the units are allowed to slide in and out of each other, but if one rotates, the other rotates with it. The joint shown in green is a pin joint and will allow us to adjust the input and output angles to do some testing!

Let’s suppose that we build one of these in real life and, when driving it with a constant velocity electric motor, the system is shaking. Can we find out why that is? With SOLIDWORKS Motion we can!

Here is going to be the set up on our model:

There are no fasteners on the model at all. This helps reduce complexity and will, instead, be taken care of with mates. Now for the fun part! Between each member of the drivetrain (i.e. from U joint hinge to cross shaft to U joint hinge to prismatic joint etc.) we will specify solid body contact. This is what tells SOLIDWORKS that they should not pass though each other. And what kind of experiment would this be if we didn’t take any measurements? Let’s place a sensor on each of the areas of interest: the very beginning of the drive train, another on one of the prismatic joints, and one on the very end. These sensors will measure rotational velocity at each point. Last, but not least, we place a motor set to constant velocity on the beginning of the U-joints. It’s a good idea to set it at a slow velocity so we can really observe the effects (like 5 or 6 RPM is good).

Now, we should test a simple case to see if it matches our intuition, verifying that the set up is correct. The simplest case to do is one in which both the input shaft and output shaft angle is parallel to the ground (i.e. zero degrees). Let’s see how this works!

The results are as we expect: a constant velocity in the input results in a constant velocity in the prismatic joint (center) which also results in a constant velocity in the output, as if the whole system was a single component. Good! Now, let’s make it more interesting!

For this next simulation, lets change the angle mate on the input pin joint to incline at 30 degrees. For most purposes, it is not a practical configuration of a U-joint, but it will be interesting! So with all the other setting the exact same, let’s re-run the study!

This change shows that the constant velocity at the input transforms into an oscillating variation in speed as it crosses this U- joint bent at an angle. We can deduce from the first experiment that an angle of zero degrees on the U-joint results in no change in rotational velocity. Therefore, the result makes sense between the second and third graphs; they should be identical.

That’s cool and all, but how is this useful? If I put a constant rotational velocity on the input, I should get that in the output! What use is it if I’m going to shake the thing that’s connected to my output? Well, check this out: We will angle both ends at 30 degrees. This is the configuration that is found in most motor vehicles. The angle usually isn’t this extreme, but it’s the input and output shafts that are parallel.

Let’s see how this fares with the motion study. Same parameters, new angles.

The results are very exciting. It starts as a flat-line, constant velocity, changes into that sinusoidal rotational velocity, then magically changes back to a flat-line! Now, what could be going on here? We know that a U-joint at an angle will change the constant velocity to speed up and slow down. Let’s study that even further. The beauty of this configuration is that when the first joint is speeding up, the second joint is slowing down and vise versa. This actually cancels out the change in velocity! How fascinating!

The next question that some of you may be asking is if the parallelism of the input and output is the only condition that needs to be met for the changes in velocity to cancel out. We will find out in the next experiment!

For this one, we will phase (i.e. twist) one of the U-joints with respect to the other one, as shown in the diagram. Keep in mind that the input and output shafts are still parallel to each other at 30 degrees. That means the output should be a flat line, right? Well….

What a twist (pun not intended)! The result is that the output not only remains sinusoidal, but it also gains magnitude! This is because we have moved the phase of how the two motions combine. Instead of harmoniously canceling out, they now add up. When one joint speeds up, the other also speeds up. This makes a more aggressive fluctuation in speed that causes a vibration. This is why if you ever take the driveshaft out of a car, you must mark the phasing to remember the exact orientation it went in. Otherwise, you’re in for a bumpy ride once the car hits the road…

These results are important because even though the plots don’t directly measure vibration, they are enough to detect its presence and its overall magnitude. Since all the joints and the shaft have mass, changing its rotational velocity will cause inertial vibrations as indicated by the sinusoids. But one question remains. Are these results accurate, as in, does this phenomenon actually occur in real life? Well, let’s ask this guy because he will tell your part, your shaky breaky part!

Thank you for following along!

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