Calculating critical shaft speeds in SOLIDWORKS Simulation

It is essential to understand the critical speed of rotating machinery to ensure safe and reliable operation of the equipment. Critical shaft speed is the speed at which a shaft becomes resonant. At this speed, vibration can cause the machinery to function incorrectly and cause issues such as loosening of parts, poor vibration characteristics and even bearing and foundation damage. Unexpected downtime because of a mechanical issue can cost a company thousands of dollars in lost productivity.

Critical speed occurs when some part of a rotating machine begins to resonate in response to a frequency produced during operation. When that happens, the motion of the resonating part will be amplified, which can result in severe damage. Knowing the critical speed is therefore vital for both designers and operators of the equipment.

Fortunately, SOLIDWORKS Simulation makes the process of calculating critical shaft speed easy. All we need to do is setup a “Frequency study” and calculate the first natural frequency of vibration. The first natural frequency corresponds to the critical speed of our rotating machinery.

To demonstrate the techniques required, I will analyze a 2-part assembly consisting of a shaft and a fan mixer. The shaft is supported at its free end by two self-aligning bearings. Note that we do not need to include the actual bearings in our assembly. Instead, we make use of bearing fixtures. Our only task is to create split faces on the shaft where it is supported by the bearings.

To begin the process, create a new Simulation study. Choose “Frequency” as the study type and give it a name like “Critical speed.”

Make sure you have materials assigned to your fan and shaft. Material assignments that were made in the CAD model will automatically transfer to the Simulation Study. Any parts that did not have a material assignment in CAD when the Simulation study was created, will need to be manually assigned in the Simulation study.

To add the bearing fixtures right click on the “Fixtures” folder and choose the “Bearing Fixture” option.

Choose the upper split face. If your bearing is self-aligning (like a spherical bearing), make sure the “Allow self-alignment” option is checked.

Repeat this process to add the second bearing fixture.

The bearing fixtures will prevent translational rigid body modes. We still need to restrain the model from rotating around its axis. My shaft has a keyway above the top bearing where it is attached to a motor and torque is applied. Therefore, I will apply an “On Flat Faces” fixture, which will prevent the rotational rigid body mode. This can be found in the ‘Advanced Fixtures’ property manager. Make sure to toggle the option “Normal to face.”

By default, SOLIDWORKS Simulation will calculate the first 5 natural frequencies. You can calculate additional or fewer frequencies by changing this option in the study properties. Right click on the study name at the top of the Simulation Study tree and click “Properties.”

Although we are only interested in the first natural frequency for a critical shaft speed calculation, calculating additional frequencies does not really slow down the analysis, so I recommend leaving the default of 5 frequencies.

We are now ready to mesh and run the study. The results of a frequency study are the natural frequencies of vibration and the mode shapes. Since we are not looking at stress results in a natural frequency study, the quality of the mesh is not as critical as in a linear static study where we need a refined mesh to obtain accurate stress results. We generally obtain acceptable frequency results with the default mesh settings.

After the run completes, we can post-process the results. In any frequency study we get two results of interest. The first result is the natural frequencies of vibration. Right click on the results folder and choose the option “List Resonant frequencies.”

A table is displayed listing the first 5 natural frequencies.

The first natural frequency is my critical shaft speed in Hertz. I can convert from Hertz to RPM by simply multiplying by 60. In this case, the critical shaft speed is 33.595 Hz which is 2016 RPM.

The second result of interest in a frequency study is the mode shapes. Mode shapes depict the shape that the assembly will take if it vibrates at the selected natural frequency. It’s always instructive to animate your mode shapes to see how the assembly vibrates. Note that the magnitude of the mode shape deformation is meaningless in a frequency study. Only the shape is of meaning. In this case the first mode shape is a global bending of the shaft, because of the heavy fan at the end.

Calculating critical shaft speeds is essential for the safe and reliable operation of rotating machinery. Fortunately, setting up frequency studies in SOLIDWORKS Simulation is easy. Now go design some innovative rotating machinery with the help of SOLIDWORKS Simulation.

Alon Finkelstein
Simulation Product Specialist
Computer Aided Technology