Fatigue is sometimes used synonymously with age-related failure or equipment wear-out. There is a component of time, in relation to the cycles of vibration, but this can be matter of seconds in some cases. Fatigue failures are typically characterized as either low-cycle (<1,000 cycles) or high-cycle (>1,000 cycles).3 Theoretically, if a drivetrain is operating at 1,800 RPM and the speed coincides with a natural frequency that is synchronous with speed, short cycle fatigue failure could occur within 30 seconds, provided the stresses induced are above the material endurance limit.


Failures due to periodic impact loading can resemble those due to torsional oscillations. The impact represents one or several cycles of vibration which typically occur during start-up, shut-down, speed changes, or are a result of the mechanics of the process. Again, the magnitude of the stresses and frequency in which they occur will determine the fatigue life.


Understanding torsional dynamics


As with any form of vibration, the oscillatory movement of an object is governed by the universal laws of motion and is usually described in terms of a mass-damper- spring system. Analogous with mass in linear vibration, inertia describes a rotating mass in a torsional reference frame. In a drivetrain, examples of inertia include the motor rotors, gearing, flywheels, compressor rotors, pump impellers, etc. which are connected to each other with torsional springs such as couplings and shaft sections. A simple torsional system is shown in Figure 4, and could be used as a simple representation of a motor- driven fan. The undamped natural frequency of this system is defined in Equation 1. For larger drivetrains with additional inertias, the calculations for natural frequencies become more complex.


Figure 4: Simple 2-Inertia System showing external torque applied and resultant forces transmitted. Equation 1: Undamped Natural Frequency of 2-inertia system in Figure 4


When drivetrains are designed, it is typical that the torsional natural frequencies are calculated and compared with known excitation sources to ensure that resonant conditions do not exist under normal operating conditions throughout the intended speed range. A Campbell Diagram, as shown in Figure 5, is commonly used to determine where natural frequencies intersect with excitation sources.


Horizontal dotted lines represent the system natural frequency. When these intersect with potential forcing frequencies (1X RPM, 2X RPM, shown in the angled lines), there is a potential that you will have a resonant condition. This is of most concern when these intersections occur within the operational speed range.


68 | ISSUE 109 | SEP 2024 | THE REPORT


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