AGMA 05FTM12-2005 pdf download.Modal Failure Analysis of a Gear and Drive Ring Assembly.
MODELLING
Two questions are always asked about modeling, what size and how many elements should be used? With MA more is not necessarily better. For lower frequencies, the fewest elements possible should be used. I have found that around the circumference, the number of elements should be multiplies of 2, 3, and 4 and perhaps 5. The internal spline has 93 teeth and four elements were used across each tooth, for a total of 372. In this model, 372 elements around the circumference will produce good modes, since it has multiplies of 2, 3, and 4. Brick and wedge elements were used, since tetrahedrons are usually stiffer in bending than the actual part causing the calculated natural frequencies to err on the high side of the actual natural frequencies. Since the gear hub is substantially stiffer than the drive ring, the gear teeth were modeled as a cylinder with an outside diameter equal to the pitch diameter.
Before the modal analysis can be performed, the component needs to be constrained. For this analysis, six equally spaced nodes were radially constrained in the bore and three equally spaced nodes were axially constrained on the face of the gear bore (drive ring side). These constraints do affect the stiffness, so they need to be applied with caution. For over constrained parts, the model will show higher natural frequencies than the actual part. For under constrained parts, the model will show lower natural frequencies than the actual part Use a sensitivity study to determine how to constrain the model, since the analysis runs fast.
Modal analysis was run on the original design drive ring and gear assembly. For small displacements, strain is linear with displacement. The relationship of stress to strain is linear as long as the strains being studied are linear and elastic [3]. This indicates that the displacement gradients are a good indication of the stress gradients. The crack will propagate along the stress gradient when the stress is at the fatigue strength. Since the fatigue strength is below the yield strength and in the elastic range of the stress strain curve, the strain will be linear and elastic. The pattern of the crack as shown in Figure 2 resembled the displacement gradients of the 1 ‘ mode as shown in Figure 6. When the mode is animated the drive ring wobbles about the gear, so it is given the descriptor “Wobble.”
Once the crack is initiated, the part will have a lower natural frequency and magnitude of the modal excitation may be reduced, but the stress concentration of a sharp edge crack increases. Each time the operating speed passes through the natural frequency, there may be enough excitation to propagate the crack. The beach marks in Figure 3 are indications of fluctuating stresses from vibration and the transmitted torque.
CAMPBELL DIAGRAMS
The Campbell Diagrams in Figures 7, 9, 10, 12 and 13 thru 15 shows the transmission input speed for the different critical modes, and the original and redesigned High Range Gear & Drive Ring Assembly. A point of concern is when a critical frequency (horizontal line) crosses the Gear Tooth Frequencies for each range (diagonal line).AGMA 05FTM12 pdf download.