Deutz-Fahr tractor gearbox failure (Deutz-Fahr)

ENGINEERING INTERPRETATION

Reverse Engineering of Gear Tooth Failure — Shaft Misalignment (0.1°)

The numerical results correspond to the gear pair described in the preceding table, considering an angular shaft misalignment of 0.1°, without additional assembly or positioning errors.

A reverse-engineering approach was adopted by investigating several misalignment angles and comparing the resulting contact pressure and subsurface equivalent von Mises stress distributions with the observed tooth damage.

Physical inspection revealed that approximately 14.5 mm of the 16.7 mm tooth face width had fractured, leaving only a 2.2 mm-wide segment intact. At a misalignment angle of 0.1°, the numerical analysis revealed pronounced edge loading, with the most severe contact pressures and subsurface stresses concentrated toward the damaged side of the tooth.

Importantly, the contact pressure distribution extends into regions beyond the fractured portion, but the corresponding von Mises stresses progressively decrease toward the opposite tooth edge. The presence of contact pressure does not necessarily imply failure across the entire loaded width, providing a plausible explanation for the survival of the remaining 2.2 mm-wide segment.

The calculated peak contact pressures and equivalent von Mises stresses are sensitive to numerical discretization, particularly near localized edge loading, and should not be interpreted as exact physical stress magnitudes. Their principal significance is to demonstrate how even a relatively small shaft misalignment (0.1°) can produce severe contact pressure and subsurface stress concentrations.

The observed correspondence between the numerical loading pattern and the physical damage geometry suggests that shaft misalignment may have been a significant contributing factor to the premature gear tooth failure. Although this correlation does not independently establish the root cause, it provides a technically grounded basis for further failure investigation. Although the calculated longitudinal contact region extends over approximately 15.5 mm, the stresses within an approximately 1 mm-wide portion may have remained below the relevant material failure threshold, allowing that portion of the tooth to remain intact.

ENGINEERING INTERPRETATION · IDEAL GEARING

Contact behavior under ideal shaft alignment

Even under ideal shaft alignment, the numerical results reveal an asymmetric distribution of contact pressure and subsurface equivalent von Mises stress. This asymmetry is associated with the geometry and spatial orientation of the contact region in helical gears. The inclined contact lines extend across the tooth face, and the local contact geometry and relative principal curvatures vary along the contact path.

For the analyzed gear pair, the right-hand end of the contact exhibits higher local pressure and a more pronounced subsurface stress concentration than the left-hand end. The longitudinal pressure profile shows an elevated peak near the right-hand boundary, while the subsurface calculation gives a maximum equivalent von Mises stress of approximately 1,300.0 MPa at x = 6.751 mm and z = 0.099 mm.

The contact region nevertheless extends over most of the analyzed face width, indicating that the load is distributed along a substantial portion of the tooth. The end peaks are sensitive to the numerical discretization and treatment of edge contact; their magnitudes should therefore be interpreted as model predictions rather than exact physical stresses.

These ideal-alignment results establish the reference contact state of the original, unmodified helical gear geometry. A quantitative comparison with shaft misalignment and with the combined shaft-misalignment and mounting-error condition will be presented after all three scenarios have been evaluated.

ENGINEERING INTERPRETATION · COMBINED MISALIGNMENT AND MOUNTING ERROR

Contact behavior under combined shaft misalignment and axial positioning error

The third numerical scenario considers the same helical gear pair and loading conditions as the preceding analyses, with an angular shaft misalignment of 0.1° and an additional 1 mm axial mounting error. The combined geometric deviations modify the contact conditions and produce a pronounced, non-uniform distribution of contact pressure along the tooth face.

The three-dimensional pressure field and longitudinal pressure profile reveal a localized concentration near one end of the contact region. The contact-area plot further illustrates the extent and shape of the loaded region, while the transverse pressure distribution characterizes the local variation across the contact strip.

The subsurface calculation predicts a maximum equivalent von Mises stress of 2,024.9 MPa, located at x = −8.641 mm and a depth of z = 0.075 mm. The enlarged contour plot highlights the highly localized stress concentration beneath the heavily loaded edge.

For the shaft-misalignment-only scenario, the corresponding reported maximum was 1,303.0 MPa. Under the combined condition, the calculated maximum is therefore approximately 55.4% higher. This is a comparison between the presented numerical scenarios, not an independently established prediction of fatigue life or failure probability.

The results indicate that axial mounting errors can substantially alter the local stress response when combined with shaft misalignment. As with the other cases, the predicted peak magnitudes depend on numerical discretization, contact-edge treatment, and model assumptions. Their main engineering value is to identify critical loading regions and motivate further assessment of assembly tolerances, tooth modifications, and the observed damage pattern.