Isaac Hong

Gears are mission critical machine elements used for primary and accessory power transmission in many industrial, automotive and aerospace mechanical systems. In normal operation gear teeth experience torque dependent cyclic loading which can initiate and propagate fatigue cracks. One of the most prevalent manifestations of this fatigue action are fractures through the tooth root resulting in tooth separation, commonly called tooth bending fatigue. Probably the most cited and applied methodology for designing gears to resist these fractures is the ISO 6336 “Calculation of Load Carrying Capacity of Spur and Helical Gears” which provides analytical equations and tabulated reference data to estimate design safety factors against bending fatigue. Method A of the ISO standard considers experimental evaluations of fatigue resistance while Method B relies on tabulated reference data. It is important that gear designers understand potential differences in the resulting fatigue strength and location of failure on the tooth root (critical location) between different design methods to ensure designs are safe from fracture. However, there is little information available in English and with tabulated data that gives a comparison on the accuracy (critical location and fatigue life) between experimental methods and analytical results. Even less information is available in terms of failure due to cyclic loads exceeding the yield strength (Low Cycle Fatigue), even if such type of loading should be carefully analyzed in case of applications involving severe loading, such as aerospace applications, or to account for unexpected load peaks. This work explores bending fatigue failure in gears under cyclic plastic loading. A gear Single Tooth Bending (STB) fatigue methodology is used to perform Low Cycle Fatigue (< 10,000 cycles) tests to complement existing High Cycle Fatigue STB data on case-carburized gear specimens made from AISI 8620 (20NiCrMo2-2). The critical locations and the fatigue strengths are compared between the experimental methodology and the analytical results of ISO 6336 Method B, providing insight about the accuracy of ISO 6336 when cyclic plasticity is involved.

Planetary gear sets are considered the optimal arrangement for power transmission needs in many automotive and aerospace applications. However, the design criteria for durability can become more complex as compared to parallel axis arrangements due to the addition of more gearing components and the prevalence of using different materials and heat treatment for the ring component as compared to the sun and planet components. While there has been development in experimental methodologies to characterize fatigue strengths of gears there is little guidance in best practices for how to apply the experimental characterizations particularly within the context of a complex, multi-material system such as planetary gear arrangements. In this study, a general kinematics formulation is applied to determine loading frequencies of gear teeth in various planetary geartrains. These kinematic relationships are combined with Stress-Life (S-N) relationships considering mean stress and material effects along with linear and nonlinear cumulative damage formulations to describe fatigue damage on each planetary component. This fatigue damage is then leveraged to develop a generalized formulation to balance the relative allowable maximum tooth root stresses amongst the gear components of a planetary geartrain such that each gear in the system has the same bending fatigue life expectancy.

Modern developments in high strength polymers and thermoplastics have driven interest in the gearing industry as feasible material choices for lightweight E‑Mobility (wheelchairs, scooters, bicycles), accessory drives such as engine balancers and actuators, and other lower power density power transmission needs. Polymer gears offer some very desirable engineering and economic benefits over metals gears such as being lightweight (leading to cost savings in transportation of materials and product) and having higher internal damping, leading to reduced noise. However, the material properties of polymers are more complex (viscoelastic and temperature sensitive) and diverse (amorphous to semi-crystalline to fiber-reinforced). In addition, the lower elastic modulus can lead to higher deformations in both the tooth and gear body complicating the gear loaded tooth contact analysis. As such, there is a significant gap in the open literature on gear load-carrying capacity with different polymers. In addition, to maximize contact durability and improve efficiency (lower heat generation) these gear sets are lubricated using oils as is commonly done with metal gears but many of the already few studies on polymer gears have been done under grease, dry lubricants or no lubricant. In this study a back-to-back test methodology is utilized for experimentally evaluating the load carrying capacity and failure mode of oil lubricated gears made from Torlon® Polyamide-Imide (PAI) Grade 4203. The experiments are performed under multiple temperatures and a range of applied torques. An analysis of the temperature and torque dependent load carrying capacity is performed to benchmark the material and performance. Fractography is performed and analyzed to identify the critical failure modes.

Tooth bending fatigue failure is a primary design concern for gear designers in power transmission applications. Fracture of a gear tooth in operation results in overload conditions to adjacent teeth, which cascades into potential failure. Total loss of power transmission usually occurs within seconds of the primary failure. While standard constant stress amplitude fatigue evaluations are common to experimentally determine probabilistic stress–life (PSN) relationships, they do not directly measure the fatigue lives under complex, non-constant amplitude loading scenarios applied to gears in most applications. Various cumulative damage models exist to estimate fatigue life under duty cycle loading, but their accuracy is both material and stress state dependent. Most models are validated under only uniaxial stress states and for limited materials. There is a void of experimental data that would enable the evaluation of the accuracy of cumulative damage models for gear tooth bending fatigue in typical cases of carburized gear steels. This research study conducts a standard fatigue evaluation along with two sets of dual stress amplitude single tooth bending fatigue tests to empirically determine the effects of multi-stage loading. Various cumulative damage fatigue models are then employed to estimate the fatigue lives of the dual stress amplitude specimens, and the accuracy of each model is assessed.

In this study, an experimental methodology is presented for measuring power losses of rolling element bearings under combined radial and axial loading conditions. The set-up developed for this purpose consists of a pair of test bearings and another pair of center bearings whose function is to transmit the radial load to the test bearings. The center bearings are isolated from any axial load that is carried by the test bearings. The proposed methodology relies on a family of separate measurements (i) to remove center bearing losses from the losses of the tests bearings, and (ii) to separate load-independent (spin) and load-dependent (mechanical) components of power losses of the test bearings. The set-up includes a precise lubricant delivery system that controls flow rate and temperature of oil supplied to each test and center bearing individually. As the bulk temperatures of bearings tested impact the measured power losses significantly, a heat management system is implemented to maintain the bearing bulk temperatures at the same value as the set levels of the oil inlet temperature. The methodology is demonstrated on two deep-groove ball bearings of different sizes, considering wide ranges of axial and radial forces, rotational speed, oil flow rate, and oil inlet temperature (oil viscosity). The influence of bearing bulk temperatures on power loss measurements is demonstrated as well as the repeatability of the proposed methodology. Furthermore, spin and mechanical loss measurements are compared to a widely used calculation method to assess its accuracy.

This study presents a unique experimental methodology that synchronously measures various quasi-static responses of a simple four-planet planetary gear set, namely, planet load sharing, overall transmission error (OTE), and floating sun gear orbits. Strain gauges mounted directly on the planet pins were used to monitor the load shared among the planets, which is a crucial design criterion for durability and performance. High-precision optical encoders were used to measure the OTE of the gear set to explore its diagnostic value in identifying system errors. Radial motions of the floating sun gear, which are critical to the self-centering and load sharing behavior of the gear set, were monitored using magnetic proximity probes. The influence of various design parameters and operating conditions such as planet mesh phasing, carrier pin position errors, gear tooth modifications, and input torque on the system’s response will be investigated by performing an extensive set of experiments in a repeatable and accurate manner. Finally, these experimental results will be recreated theoretically using the static planetary load distribution model of Hu et al. (2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 53302) to not only validate the model but also comprehend the measured behavior.

In this study, an experimental methodology is presented to separate various components of the power loss of a gearbox. The methodology relies on two separate measurements. One is designed to measure total power loss of a gearbox housing a single spur gear pair under both loaded and unloaded conditions such that load-independent (spin) and load-dependent (mechanical) components can be separated. With the assumption that gear pair and rolling element bearings constitute the bulk of the gearbox power loss, a second measurement system designed to quantify rolling element bearing losses is proposed. With this setup, spin and mechanical power losses of rolling element bearings used in the gearbox experiments are measured. Combining the sets of gearbox and bearing data, power loss components attributable to the gear pair and rolling element bearings are quantified as a function of speed and torque. The results indicate that all gear and bearing related components are significant and a methodology such as the one proposed in this study is warranted.

High-cycle gear tooth bending fatigue lives of spur gears under fully reversed and fully released loading conditions are compared in this experimental study. The experimental methodology described in an earlier publication, (Hong et al. 2020, “A Rotating Gear Test Methodology for Evaluation of High-Cycle Tooth Bending Fatigue Lives Under Fully Reversed and Fully Released Loading Conditions,” Int. J. Fatigue, 133, p. 105432. 10.1016/j.ijfatigue.2019.105432), is employed to perform two sets of rotating, gear tooth bending fatigue tests. Statistical analyses are performed to regress stress versus life (S–N) curves under both loading conditions. These curves indicate that a gear under fully reversed loads has a shorter bending life at the same maximum tooth root stress as a gear under fully released loads. Various planetary gear set kinematic conditions with different stationary members are considered to determine the equivalent number of tooth loading cycles per revolution of the sun gear. They are combined with established S–N curves under both loading conditions to determine the ratios of allowable maximum tooth root stresses amongst the gear components of a P-planet gear set such that each gear in the set has the same bending fatigue life. A “stress-balanced” gear set designed to these stress ratios is expected to have the same bending fatigue life for its sun, ring, and planet gears, ensuring that the planetary gear set life is the longest.