Feasibility Question:How sensitive are the rollers to unbalance instabilities and vibrations?

Key Results:

Max Operating Speed

Estimated Effective Spring Constant

Estimated Natural Frequency

Result for Max Frequency Ratio

93.75 rad/s 521.5e6 N/m 2003 rad/s 0.05

Conclusions:

The max frequency ratio for the DS264 is much less than 1. Therefore, assuming a rotating unbalance system model, for essentially all operating conditions the output excitation will be reduced from input excitation due to unbalanced mass.

To gain more quantitative information about output excitation and force transmissibility, information about the damping parameter of the system must be measured or estimated.

We also need to measure and gain more data about how the roller is mounted and the dimensions of the mounting structures to get a better idea of how accurate this model is.

Assuming the spring constant can be estimated as a simply supported circular cross section beam, the expression for natural frequency of the roller is calculated and shown below. This allows us to see the relationship between parameters that we could potentially change and its impact on the natural frequency. We want the natural frequency to remain high relative to the operating frequencies to maintain reduction of response.

Where L is the length of the mounting rod, R is the radius of the mounting rod, M is the total mass of the roller and mounting rod, E is the modulus of elasticity of the mounting rod.