STATIC AND DYNAMIC ANALYSIS OF FUNCTIONALLY GRADED GEARS

Abstract

Gears are toothed mechanical components widely used to transmit power or motion in various industrial applications ranging from heavy machinery to precision instruments. One of the primary objectives of contemporary transmission research is the development of lightweight gears. Reduction in weight of the gear not only reduces the overall weight of the system but also significantly reduces the inertia forces. Material removal from low-stress areas has been traditionally used for gear weight reduction, but it results in compromised strength and performance. The use of polymer & metal composite materials for gear manufacturing and the development of bi-metal (Aluminum-Steel) and hybrid gears (metallic hub and teeth with composite web) have also been explored to obtain the best compromise between the strength and weight of gears. Whereas polymer gears are confined to low-power transmission applications, bi-metal and hybrid gears have limitations of high-stress concentration and delamination in the joint interfaces. Functionally graded materials (FGMs) are known to have better mechanical and tribological properties. FGMs are used in almost all engineering applications because of the ability to combine contrasting material properties. The use of FGMs in gears can help overcome the limitations of bi-metal and hybrid gears. FGMs have a compositional gradient, and material properties have a gradual spatial change. Delamination and stress concentration problems are thus avoided. FGMs contain the unalloyed form of each material, and the properties of both the constituent materials can be fully utilized without any compromise. Using FGM, the hardness of ceramic can be mated with the ductility of metal without compromising any of the two. This makes FGMs a promising gear material that can help meet performance requirements with reduced weight. With advancements in manufacturing processes, functionally graded gears (FGGs) are potential replacements for steel gears in applications where weight is a critical factor. Moderate strength and low-density material can be used on the inner (hub) side and high strength, wearresistant material on the outer (teeth) side, with properties varying radially outwards. The use of metal-ceramic FGGs can reduce weight and enhance the performance of gears, but still, it is a less explored research area. In this study, static and dynamic analyses of functionally graded gears (FGGs) have been performed to study the effect of gradation on their performance compared to steel gears. Static and vibration analyses of functionally graded gears (FGGs) have been performed using the FE-based numerical method to study the effect of gradation on root stress, tooth stiffness, and natural frequencies of FG gears. Dynamic response analysis is then performed using a 6-DOF dynamic model of a single-stage spur gear system. The system's steady-state response is analyzed in the time and frequency domain. For comparative assessment, the effect of gradation on peak-to-peak displacement, root mean square (RMS) velocity, and dynamic factor of FGGs has been studied with steel gears as reference. Aluminum-steel bi-metal gears are also analyzed for comparison. Finally, the effect of tooth spall of three severity levels on the dynamic response of FGGs is studied in both the time and frequency domains. The effect of spall severity on the statistical indicators like peak-to-peak amplitude, RMS, kurtosis, and crest factor is studied for FG and steel gears. Mesh stiffness used in the dynamic model has been evaluated explicitly using a finite-element-based numerical method employing contact analysis. To model FG gears, the gear body is divided into uniform thickness homogeneous subdomains conforming to the gear tooth profile. Material properties are assumed to vary in the radial direction according to power-law gradation, with metal at the innermost and ceramic at the outermost surface. The results show that for FGGs, root stress increases and the weight of the gear reduces with an increase in gradient index. It has been observed that the maximum difference in the fundamental frequencies of FGGs and steel gears is 12% compared to 25% for bi-metal gears. The FGGs show a 10% to 50% reduction in mesh stiffness with a 30% to 60% reduction in weight compared to steel gears of exact specifications. Compared to this, bi-metal gears show a 25% to 55% reduction in mesh stiffness and a 35% to 115% increase in the static transmission error with the same weight reduction. Also, FGGs show a 4% to 12% reduction in dynamic factor and a 9% to 17% reduction in peak-to-peak displacement amplitude than steel gears over the selected values of GI. Bi-metal gears also show comparable results. For different pinion speeds, all statistical indicators exhibited different susceptibility to spall. Statistical indicators are more sensitive to spall for FGGs at certain speeds, while more sensitive for steel gears at others. FGGs and steel gears have the same sensitivity for some indicator and speed combinations. With an increase in severity of the tooth spall, a significant increase in the magnitudes of the periodic impulse vibrations is observed in the time domain. Similarly, amplitudes of the sidebands increase with an increase in spall severity in the frequency domain. With an increase in GI, maximum amplitude sidebands shift to higher frequencies, and the amplitude decreases. The amplitude of higher-order sidebands depletes gradually. The results indicate that FGGs are a potential alternative of steel gears, which significantly reduce the weight without compromising the performance.