Dennis P. Townsend

Dynamic loading of spur gears with linear or parabolic tooth profile modifications

A computer simulation was conducted to investigate the effects of both linear and parabolic tooth profile modification on the dynamic response of low-contact-ratio spur gears. The effect of the total amount of modification and the length of the modification zone were studied at various loads and speeds to find the optimal profile modification for minimal dynamic loading. Design charts consisting of normalized maximum dynamic load curves were generated for gear systems operated at various loads and with different tooth profile modification. An optimum profile modification can be determined from these design charts to minimize the dynamic loads of spur gear systems.

Effect of Contact Ratio on Spur Gear Dynamic Load With No Tooth Profile Modifications

Abstract : This paper presents a computer simulation showing how the gear contact ratio affects the dynamic load on a spur gear transmission. The contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size (diametral pitch), and the center distance. The analysis presented in this paper was performed by using the NASA gear dynamics code DANST. In the analysis the contact ratio was varied over the range 1.20 to 2.40 by changing the length of the tooth addendum. In order to simplify the analysis, other parameters related to contact ratio were held constant. The contact ratio was found to have a significant influence on gear dynamics. Over a wide range of operating speeds a contact ratio close to 2.0 minimized dynamic load. For low-contact-ratio gears (contact ratio less than 2.0), increasing the contact ratio reduced the gear dynamic load. For high-contact-ratio gears (contact ratio equal to or greater than 2.0), the selection of contact ratio should take into consideration the intended operating speeds. In general, high-contact-ratio gears minimized dynamic load better than low-contact-ratio gears.

Influence of Linear Profile Modification and Loading Conditions on the Dynamic Tooth Load and Stress of High Contact Ratio Gears

This paper presents a computer simulation for the dynamic response of high-contact-ratio spur gear transmissions.High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this paper examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. This paper shows that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High contact ratio gears were found to require less modification than standard low-contact-ratio gears.

Optimal Tooth Numbers for Compact Standard Spur Gear Sets

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

Experimental and Analytical Load-Life Relation for AISI 9310 Steel Spur Gears

Life tests were conducted at three different loads with three groups of 8.9 cm pitch diameter spur gears made of vacuum arc remelted VAR AISI 9310 steel. Life was found to vary inversely with load to the 4.3 and 5.1 power at the L10 sub and L50 sub life levels, respectively. The Weibull slope varied linearly with maximum Hertz contact stress, having an average value of 2.5. The test data when compared to AGMA standards showed a steeper slope for the load-life diagram.

Increased Surface Fatigue Lives of Spur Gears by Application of a Coating

ABSTRACT Hard coatings have potential for increasing gear surface fatigue lives. Experiments were conducted using gears both with and without a metal-containing, carbon-based coating. The gears were case-carburized AISI 9310 steel spur gears. Some gears were provided with the coating by magnetron sputtering. Lives were evaluated by accelerated life tests. For uncoated gears, all of fifteen tests resulted in fatigue failure before completing 275 million revolutions. For coated gears, eleven of the fourteen tests were suspended with no fatigue failure after 275 million revolutions. The improved life owing to the coating, approximately a six-fold increase, was a statistically significant result. Keywords: Gear, life, fatigue, pitting, coatings. INTRODUCTION The power density of a gearbox is an important consideration for many applications and is especially important for gearboxes used on aircraft. One factor that limits gearbox power density is the need to transmit power for the required number of cycles while avoiding gear surface fatigue failure (micropitting, pitting or spalling). Effective and economical methods for improving surface fatigue lives of gears are therefore highly desirable. Thin hard coatings have potential for improving gear performance. In fact, coatings are reported to have some successful applications [1-3] where product durability improvements have been achieved by the application of thin hard coatings to gears. Diamond-like carbon and related materials have the potential for a wide variety of applications that require wear protection and/or low-friction properties. Because of the widely recognized potential, the deposition methods and resulting properties of the films have been studied extensively [4-6]. Today’s deposition technology allows for the production of a great diversity of coatings, but the ability to tailor the tribological behavior of a coating for a particular application has been elusive. Aerospace gearing requirements are demanding, calling for high power density, long life, and excellent reliability. The low friction properties and high hardness of diamond-like and related coatings offer the possibility to improve the performance of aerospace gearing. Naik, et al [7] tested the adherence and toughness of two coatings using both disk-on-rod rolling-contact and gear tests, and they reported promising results. Alanou, et al [8] found that coatings could increase the scuffing load capacity of rolling and sliding disks used to simulate aerospace gearing contacts, but they also reported poor adherence for one particular substrate and coating combination. Joachim, Kurz and Glatthaar [3] reported promising results of evaluations of tungsten carbon carbide and amorphous boron carbide coatings using laboratory tests, but they also report mixed results when applying such coatings to commercial applications. The purpose of the present investigation was to compare the surface fatigue lives of coated and uncoated gears using accelerated life tests. The testing is considered as accelerated in that the contact stresses used for testing exceeds the stresses used for design of the target application (helicopter gearing). The metal-containing, carbon-based diamond-like (Me-DLC) coating selected for this study was designed specifically for the aerospace gearing applications. NASA/TM—2003-2124631

Modal Analysis of Multistage Gear Systems Coupled With Gearbox Vibrations

This paper presents an analytical procedure to simulate vibrations in gear transmission systems. This procedure couples the dynamics of the rotor-bearing gear system with the vibration in the gearbox structure. The modal synthesis method is used in solving the overall dynamics of the system, and a variable time-stepping integration scheme is used in evaluating the global transient vibration of the system. Locally each gear stage is modelled as a multimass rotor-bearing system using a discrete model. The modal characteristics are calculated using the matrix-transfer technique. The gearbox structure is represented by a finite element model, and modal parameters are solved by using NASTRAN. The rotor-gear stages are coupled through nonlinear compliance in the gear mesh while the gearbox structure is coupled through the bearing supports of the rotor system. Transient and steady state vibrations of the coupled system are examined in both time and frequency domains. A typical three-geared system is used as an example for demonstration of the developed procedure.

Vibration signature and modal analysis of multi-stage gear transmission

Abstract An analysis is presented for multi-stage multi-mesh gear transmission systems which predicts the overall system dynamics and transmissibility to the gear box or the enclosed structure. The modal synthesis approach of the analysis treats the uncoupled lateral/torsional modal characteristics of each stage or component independently. The vibration signature analysis evaluates the global dynamics coupling in the system. The method synthesizes the interaction of each modal component or stage with nonlinear gear mesh dynamics and modal support geometry characteristics. The analysis simulates transient and steady state vibration events due to torque variations, speed changes, rotor imbalances and gear box support motion excitations. A vibration signature analysis scheme examines the overall dynamic characteristics of the system, and the individual modal component responses. The gear box vibration analysis also examines the spectral characteristics of the support system.

Computer-Aided Design of High-Contact-Ratio Gears for Minimum Dynamic Load and Stress

This paper presents a numerical procedure for minimizing dynamic effects on high-contact-ratio gears by modification of the tooth profile. The paper examines and compares both linear and parabolic tooth profile modifications of high-contact-ratio gears under various loading conditions. The effects of the total amount of modification and the length of the modification zone were systematically studied at various loads and speeds to find the optimum profile design for minimizing the dynamic load and the tooth bending stress. Parabolic profile modification is preferred over linear profile modification for high-contact-ratio gears because of its lower sensitivity to manufacturing errors. For parabolic modification a greater amount of modification at the tooth tip and a longer modification zone are required. Design charts are presented for high-contact-ratio gears with various profile modifications operating under a range of loads. A procedure is illustrated for using the charts to find the optimum profile design.

Effect of Shot Peening on Surface Fatigue Life of Carburized and Hardened AISI 9310 Spur Gears

Surface fatigue tests were conducted on two groups of AISI 9310 spur gears. Both groups were manufactured with standard ground tooth surfaces, with the second group subjected to an additional shot peening process on the gear tooth flanks. The gear pitch diameter was 8.89 cm (3.5 in.). Test conditions were a gear temperature of 350 K (170 F), a maximum Hertz stress of 1.71 billion N/sq m (248,000 psi), and a speed of 10,000 rpm. The shot peened gears exhibited pitting fatigue lives 1.6 times the life of standard gears without shot peening. Residual stress measurements and analysis indicate that the longer fatigue life is the result of the higher compressive stress produced by the shot peening. The life for the shot peened gear was calculated to be 1.5 times that for the plain gear by using the measured residual stress difference for the standard and shot peened gears. The measured residual stress for the shot peened gears was much higher than that for the standard gears.