Residual Stress And Fatigue Performance

Gear transmission is widely applied in various mechanical equipment due to its advantages of accurate transmission ratio and high transmission efficiency. China has now become a major gear-producing country—with the output value of the gear industry exceeding 236 billion yuan in 2017, ranking first in the world, and a relatively complete industrial system has been formed. As the core component for power transmission and energy output, gear performance directly affects the operational efficiency and reliability of equipment. During transmission, gears bear extremely complex loads, making them prone to failure phenomena such as pitting, spalling, wear, scuffing, and bending fatigue fracture. In the past, gear strength design mainly considered tooth surface contact strength; however, with the development of engineering technology, gear transmission systems tend to be lightweight, and tooth root bending fatigue strength has gradually become a key factor.

During gear transmission, the maximum tensile stress on the gear tooth acts on the loaded side, while the maximum compressive stress acts on the opposite side. The zero-stress point is located below the intersection of the root circle and the tooth centerline, resulting in severe stress concentration at the tooth root on the loaded side. With the continuous operation of the gear, the dangerous section becomes a prone area for fatigue crack initiation—the first stage of gear tooth fracture.

The initiated cracks further propagate toward the zero-stress point, which moves downward along the tooth root as the cracks expand. This is the second stage—stable crack propagation (see Figure 1). The stable propagation stage can be generally divided into two sub-stages: in Stage I, the crack propagates along the direction of the 45° maximum shear stress with a shallow depth; in Stage II, due to different orientations and grain boundary obstruction, the propagation direction is gradually affected by normal stress and changes to a direction perpendicular to the normal stress.

When the remaining part of the tooth root can no longer bear the external load, instantaneous fracture occurs—the third stage: unstable crack propagation (fracture). The corresponding area on the fatigue fracture surface is relatively rough, often accompanied by folds formed by material tearing.

It is generally believed that the existence of tensile residual stress will increase the average stress level in the cyclic stress, thereby accelerating the fatigue crack growth rate and reducing gear reliability. In contrast, compressive residual stress is beneficial to extending the fatigue life of gears. During gear processing, the amplitude of residual stress generated in gear teeth can reach thousands of megapascals, which has a significant impact on the fatigue performance of gears. Therefore, residual stress is an indispensable factor in gear anti-fatigue manufacturing, and the accurate monitoring of the residual stress state at the tooth root holds important engineering significance.

Typical residual stress distribution curves of the tooth root surface after carburizing and quenching are generally shown in Figure 2. In actual gear production, the residual stress on the tooth root surface does not always present the ideal distribution as shown in Figure 2(a). In practical working conditions, due to the coupling effect of thermal stress and structural stress during quenching and cooling, surface plastic deformation causes the maximum compressive residual stress layer to shift to the subsurface, possibly presenting the distribution characteristic shown in Figure 2(b). Currently, in domestic gear production, decarburization and internal oxidation are unavoidable on the surface of gear teeth after carburizing and quenching. Especially, internal oxidation forms non-martensitic structures. At this time, the typical residual stress distribution of the hardened layer is shown in Figure 2(c)—that is, tensile residual stress is formed on the outermost surface of the gear tooth, and due to geometric structure factors, this tensile stress is often more severe at the tooth root.

The distribution characteristics of residual stress directly determine the fatigue performance of gears. However, it should be particularly noted that the heat treatment process of gears is a complex nonlinear process involving the interaction of temperature, structural transformation, and stress, accompanied by plastic deformation. Therefore, it is almost impossible to obtain residual stress using analytical methods. Thus, in practical engineering, determining residual stress is of great significance for evaluating gear service life and performance.

Currently, there are many methods for measuring residual stress, but the most commonly used and high-precision method in engineering is X-ray diffraction (XRD) technology. XRD technology enables non-destructive testing, and portable equipment can quickly complete on-site testing in production. At present, this technology has been internationally recognized, with domestic and foreign standards to ensure measurement accuracy, and the measurement equipment and supporting instruments are relatively sophisticated. The equipment shown in Figure 3 has been used in the gear industry at home and abroad to measure the residual stress at the gear root. Among them, the dangerous section of the tooth root is generally defined by the 30° tangent method, and the residual stress at this position is selected to represent the root residual stress. For the specific method of measuring residual stress by XRD, refer to the previous article "How to Determine Residual Stress by X-ray Diffraction Method?"