How to use torque measurements to determine acceptable stress levels


To make practical use of the measured torque, the value needs to be related to the mechanical stress which it induces in a drivetrain component. Torque can be damaging to equipment when it induces stresses in the load-transmitting material that exceed the endurance limit or yield limit. The endurance limit is the maximum stress that a material can be subjected to repeatedly without failing from fatigue. These values are typically much lower than the stress required to yield (permanent deformation) or fracture the material from a single applied load. Fatigue typically progresses in (3) stages: crack initiation, crack propagation, and final fracture. During the initial stages of fatigue crack propagation (Photograph 1a), no deformation of the material occurs so long as the stresses remain below the yield limit. This is the one of the primary reasons that torsional failures are difficult to detect. Later in the failure progression, or in cases of high amplitude loads, deformations (yielding) of a rotating shaft, flexible coupling, or gear teeth can typically be detected using traditional means of vibration analysis because they can cause the component to rotate


eccentrically, producing a mass imbalance (Photo 1b). It should be noted that material yielding can occur once a fatigue crack has grown and the component is no longer capable of transmitting the nominal load even if they are below the material yield limit. Also cracks and fractures which occur at a 45-degree angle on a shaft are typical in torque related failures.


One relatively simple method for determining acceptable stress levels from alternating loads is the Modified Goodman Diagram. This method plots the value of mean stress on the horizontal axis and the value of alternating stress on the vertical axis. A combination of mean and alternating stresses in the region below the ‘yield line’ and ‘modified Goodman line’ (shaded gray in the figure) indicates an infinite fatigue life. Stresses outside of this region indicate finite life. The values plotted in Figure 2 were calculated to understand the effect of alternating loads on the fatigue life for gear teeth, specifically bending fatigue in the tooth root. The mean stress was considered to be the stress from the nominal driving torque (based on nameplate power and speed). As torque measurements were not available, hypothetical values of alternating torque where then added, based on an increasing percentage of the nominal torque. The analysis showed that mean stresses of 4 to 5 times the nominal values combined with cyclic loads could create would create a finite life situation. While gear tooth stresses are relatively simple to calculate, other methods such as finite element analysis are better suited for more complex geometries.


Photographs 1a and b: Failed rotating component in the (a) early and (b) later stages of failure.


64 | ISSUE 109 | SEP 2024 | THE REPORT


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