An analytical method to predict efficiency of aircraft gearboxes

A spur gear efficiency prediction method previously developed by the authors was extended to include power loss of planetary gearsets. A friction coefficient model was developed for MIL-L-7808 oil based on disc machine data. This combined with the recent capability of predicting losses in spur gears of nonstandard proportions allows the calculation of power loss for complete aircraft gearboxes that utilize spur gears. The method was applied to the T56/501 turboprop gearbox and compared with measured test data. Bearing losses were calculated with large scale computer programs. Breakdowns of the gearbox losses point out areas for possible improvement

A computer solution for the dynamic load, lubricant film thickness and surface temperatures in spiral bevel gears

A complete analysis of spiral bevel gear sets is presented. The gear profile is described by the movements of the cutting tools. The contact patterns of the rigid body gears are investigated. The tooth dynamic force is studied by combining the effects of variable teeth meshing stiffness, speed, damping, and bearing stiffness. The lubrication performance is also accomplished by including the effects of the lubricant viscosity, ambient temperature, and gear speed. A set of numerical results is also presented

Elastohydrodynamic lubrication and surface fatigue modelling of spur gears over the meshing cycle

This thesis presents a modern method to evaluate spur gears based on the transient elastohydrodynamic lubrication (EHL) emulation of the full meshing cycle, evaluating elastic stresses in the gear flanks, collecting the stress history and applying stress and strain-life methods to calculate fatigue parameters and cumulative fatigue damage, i.e. predicting the fatigue life taking measured surface roughness into account. The EHL model is formulated as the coupled system of the hydrodynamic Reynolds equation and the elastic deflection equation. These are solved simultaneously including the transient effect by incorporating the squeeze film term of the Reynolds equation with a Crank-Nicolson discretization of time. The finite difference discretisation of the elastic deflection equation utilises the differential form first formulated at Cardiff to allow coupling of the equations. The Reynolds equation can be discretised either by a finite difference or by a finite element method. The coupled system is solved simultaneously either by a narrow bandwidth Gaussian elimination or a Gauss-Seidel iterative method. The elastic stresses due to the superimposed discrete values of the EHL pressure and shear stress at the EHL mesh nodes are evaluated by carrying out the necessary convolution of the stresses by a Fast Fourier Transform method. The weighting functions required have been calculated analytically. The stresses are obtained on the EHL solution mesh and are interpolated to meshes fixed in the pinion and the gear flanks. They are then sorted and stored efficiently to enable fatigue life prediction algorithms to be applied. A detailed description of the EHL and the stress evaluation models are provided as well as a brief description of some fatigue life theories and calculations. The results of the complete analysis are provided for test gears obtained from the NASA Glenn laboratory fatigue tests and the Newcastle University Design Unit micro-pitting investigation. The analyses were carried out for real operating conditions from gear testing under extreme conditions. The surface roughness profiles used were real measured profiles taken from the test gears after initial running-in. The simulations reported are therefore as realistic as can be achieved and represent the true mixed lubrication conditions occurring in heavily loaded gears. The research also shows the importance of precise alignment of the roughness profiles in these conditions

Elastohydrodynamic lubrication and surface fatigue modelling of spur gears over the meshing cycle

This thesis presents a modern method to evaluate spur gears based on the transient elastohydrodynamic lubrication (EHL) emulation of the full meshing cycle, evaluating elastic stresses in the gear flanks, collecting the stress history and applying stress and strain-life methods to calculate fatigue parameters and cumulative fatigue damage, i.e. predicting the fatigue life taking measured surface roughness into account. The EHL model is formulated as the coupled system of the hydrodynamic Reynolds equation and the elastic deflection equation. These are solved simultaneously including the transient effect by incorporating the squeeze film term of the Reynolds equation with a Crank-Nicolson discretization of time. The finite difference discretisation of the elastic deflection equation utilises the differential form first formulated at Cardiff to allow coupling of the equations. The Reynolds equation can be discretised either by a finite difference or by a finite element method. The coupled system is solved simultaneously either by a narrow bandwidth Gaussian elimination or a Gauss-Seidel iterative method. The elastic stresses due to the superimposed discrete values of the EHL pressure and shear stress at the EHL mesh nodes are evaluated by carrying out the necessary convolution of the stresses by a Fast Fourier Transform method. The weighting functions required have been calculated analytically. The stresses are obtained on the EHL solution mesh and are interpolated to meshes fixed in the pinion and the gear flanks. They are then sorted and stored efficiently to enable fatigue life prediction algorithms to be applied. A detailed description of the EHL and the stress evaluation models are provided as well as a brief description of some fatigue life theories and calculations. The results of the complete analysis are provided for test gears obtained from the NASA Glenn laboratory fatigue tests and the Newcastle University Design Unit micro-pitting investigation. The analyses were carried out for real operating conditions from gear testing under extreme conditions. The surface roughness profiles used were real measured profiles taken from the test gears after initial running-in. The simulations reported are therefore as realistic as can be achieved and represent the true mixed lubrication conditions occurring in heavily loaded gears. The research also shows the importance of precise alignment of the roughness profiles in these conditions

Transmission Efficiency Measurements and Correlations with Physical Characteristics of the Lubricant

Data from helicopter transmission efficiency tests were compared to physical properties of the eleven lubricants used in those tests. The tests were conducted with the OH-58 helicopter main rotor transmission. Efficiencies ranged from 98.3 to 98.8 percent. The data was examined for correlation of physical properties with efficiency. There was a reasonable correlation of efficiency with absolute viscosity if the viscosity was first corrected for temperature and pressure in the lubricated contact. Between lubricants, efficiency did not correlate well with viscosity at atmospheric pressure. Between lubricants, efficiency did not correlate well with calculated lubricant film forming capacity. Bench type sliding friction and wear measurements could not be correlated to transmission efficiency and component wear

The Influence of Roughness on Gear Surface Fatigue

Gear working surfaces are subjected to repeated rolling and sliding contacts, and often designs require loads sufficient to cause eventual fatigue of the surface. This research provides experimental data and analytical tools to further the understanding of the causal relationship of gear surface roughness to surface fatigue. The research included evaluations and developments of statistical tools for gear fatigue data, experimental evaluation of the surface fatigue lives of superfinished gears with a near-mirror quality, and evaluations of the experiments by analytical methods and surface inspections. Alternative statistical methods were evaluated using Monte Carlo studies leading to a final recommendation to describe gear fatigue data using a Weibull distribution, maximum likelihood estimates of shape and scale parameters, and a presumed zero-valued location parameter. A new method was developed for comparing two datasets by extending the current methods of likelihood-ratio based statistics. The surface fatigue lives of superfinished gears were evaluated by carefully controlled experiments, and it is shown conclusively that superfinishing of gears can provide for significantly greater lives relative to ground gears. The measured life improvement was approximately a factor of five. To assist with application of this finding to products, the experimental condition was evaluated. The fatigue life results were expressed in terms of specific film thickness and shown to be consistent with bearing data. Elastohydrodynamic and stress analyses were completed to relate the stress condition to fatigue. Smooth-surface models do not adequately explain the improved fatigue lives. Based on analyses using a rough surface model, it is concluded that the improved fatigue lives of superfinished gears is due to a reduced rate of near-surface micropitting fatigue processes, not due to any reduced rate of spalling (sub-surface) fatigue processes. To complete the evaluations, surface inspection were completed. The surface topographies of the ground gears changed substantially due to running, but the topographies of the superfinished gears were essentially unchanged with running

Lubricated contact analysis of a spur gear pair with dynamic loads

In the present research study, a comprehensive spur gear lubrication analysis has been carried out to understand the gear contact behaviour under lubrication conditions. The modelling works have been extended to consider the effects of thermal mechanical, non-Newtonian fluid, surface roughness, transient squeeze and dynamic load conditions. First, the elastohydrodynamic lubrication theory is studied and relevant numerical approaches are introduced. The reduced Reynolds equation technique is applied to deal with any potential "asperity contacts" or any other ultra-thin film situations. Those situations could be a result of the surface roughness or the dynamic load effect. This approach allows us to capture local information about pressure, traction, film thickness, etc., within the nominal contact zone. Influence of working conditions, i.e. load, rolling speed, as well as the sliding to roll ratio are discussed with those models (Newtonian or non-Newtonian fluids, isothermal or thermal conditions). The non-Newtonian fluid effect has been investigated with a Ree-Eyring fluid model and a power-law fluid model and the thermal effect is studied by solving energy equations of interacting solids and the film numerically with the sequential sweeping technique. The dynamic effect on contact performance is also studied. The dynamic load is calculated using a two degree-of-freedom lumped parameter system dynamic model in which the varying mesh stiffness is considered as the excitation. The dynamic model is solved using the Runge-Kutta method. The effects of the dynamic load effect on pressure distribution and film thickness in a whole mesh period are discussed. The normal contact stiffness of a spur gear pair is also predicted based on the deterministic tribology models. The main contributions from the present research could be summarized as follows: i. An elastohydrodynamic lubrication model for a spur gear pair is developed by taking into account the effects of transient squeeze, the non-Newtonian fluid, the rough surface and the thermal mechanical contacts which makes the proposed model one of the most advanced models currently evaluating gear lubrication performance. This model can also be applied to bearings, cams, or other gear types with some modifications. ii. The friction behaviour, which is not investigated as extensively as the film thickness in existing work, is studied. The effects of the working conditions (the load, the rolling speed, the slide/roll ratio), the non-Newtonian conditions, the rough surface conditions, as well as the thermal conditions on friction behaviour are discussed. The conclusions suggest controlling surface topography patterns and working conditions aiming at a reduced friction coefficient and a longer service life. iii. The dynamic effect on lubrication performance and effect of lubrication on normal contact stiffness of a spur gear pair are studied. The work provides a potential gateway for a more comprehensive evaluation of spur gear pair working performance using a tribology-dynamic coupled method which is the next area this author would like to explore

Analytical characterization of damping in gear teeth dynamics under hydrodynamic conditions

Using an analytical method, we characterize damping and stiffness in lightly loaded, lubricated gear pairs at different operating speeds and lubricant temperatures. This is accomplished by employing a trace method to approximate and model the hysteresis loop of the lubricant reaction, thus recording the energy transformation mechanism during the gear teeth oscillatory motion. The method can be expanded for use in a variety of problems where hydrodynamic vibro-impacts lead to energy dissipation

Thermal Distortion Effects on Cylindrical Gear Teeth Contact

El comportamiento térmico de engranajes es uno de los temas que menos atención ha recibido en el último siglo. Aunque el origen del calor generado es conocido, su estudio se ha limitado a la predicción de la temperatura estacionaria del lubricante ya que tiene una influencia directa en el fallo de los mismos. Sin embargo, la revisión de la literatura científica ha puesto en evidencia que los efectos de su expansión térmica apenas han sido analizados. Entretanto, la experiencia en turbo-máquinas indica que las distorsiones de geometría de origen térmico tienen un papel fundamental en la alteración de los patrones de contacto pudiendo incluso provocar la rotura del dentado si no se toman medidas. El objetivo principal de esta tesis es predecir, evaluar y corregir el comportamiento mecánico no uniforme de parejas de engranajes rectos y helicoidales debido a la distorsión de la geometría inducida térmicamente. Para este fin, el calor generado por fricción debe ser cuantificado y la distribución de temperatura estacionaria debe ser predicha. Así mismo, debe desarrollarse un modelo de deformación térmica capaz de integrarse en los algoritmos de cálculo de distribución de carga habituales. La comprensión del tipo y magnitud de la distorsión térmica, junto a sus efectos en la distribución de carga, permitirán corregir la geometría del dentado y compensar comportamientos no deseados. En los primeros capítulos de esta tesis se analiza el origen de la distorsión térmica y se revisa el estado del arte. Tras esto, se describen la geometría y cinemática de engranajes rectos y helicoidales y se desarrolla un modelo de distribución de carga analítico basado en el concepto de secciones delgadas. Posteriormente, se estudia el comportamiento del rozamiento en el engrane, se cuantifica el calor generado por el mismo y se predice la distribución de temperatura mediante el uso de redes térmicas. En cada uno de estos capítulos se desarrollan nuevos modelos que son validados con datos experimentales de la literatura científica. El modelo de distorsión térmica es introducido en el sexto capítulo, se desarrolla un estudio paramétrico y se analiza un caso práctico, desde la distorsión de la geometría hasta su comportamiento mecánico. Así mismo, se recogen recomendaciones de diseño para hacer frente a este fenómeno y se proponen directrices de modificación del dentado. Finalmente, se lleva a cabo un estudio experimental del error de transmisión termomecánico, se extraen conclusiones generales y se definen las líneas de trabajo a futuro. Los resultados presentados muestran que, contrariamente a la creencia común, la distorsión térmica en engranajes de acero sí afecta a la distribución de carga y el error de transmisión y, por lo tanto, debe ser considerado en el análisis de contacto.The thermal behaviour of geared transmissions has been one of the mechanical issues receiving the least amount of attention in the last century. Although the origins of heat generated in gearboxes is already understood, its analysis has been limited to the prediction of steady-state oil temperature, which has a direct influence in gear failure. However, scientific literature review has shown that the effects of thermal expansion have been hardly analysed. Meanwhile, field experience in turbo-machinery industry, proofs that thermally-induced geometry distortion does play a significant role on contact pattern shift leading to tooth breakage if no counter-measures are provided. The main objective of the present thesis is to predict, evaluate and correct uneven mechanical behaviour of spur and helical gears due to thermally-induced flank geometry distortion. For this purpose, heat generated in the gear mesh needs to be quantified and resulting steady-state temperature distribution must be predicted. Then, a model to determine thermal deformation of gear teeth must be developed and implemented on common load distribution calculation flowcharts. The understanding of the type and amount of thermal distortion, along with its effects on loaded behaviour, will allow to correct tooth geometry and compensate for undesired contact behaviour. In the first chapters of the present thesis, a brief description of the origins of thermal distortion is presented and current state of art is reviewed. Then, spur and helical gear teeth geometry and kinematics are described and an analytical load distribution model following the so called “thin-slice” approach is developed. Next, sliding friction behaviour in meshing gears is analysed, the amount of heat generated in the mesh is quantified and temperature distribution is predicted based on the thermal-network concept. New models are developed within each of these chapters and results are validated with experimental measurements from literature. The thermal distortion model is introduced in chapter six, a parameter analysis is carried out and a test case is fully analysed, from geometry distortion to full thermo-mechanical behaviour. At the end of this chapter, design recommendations to cope with thermally-induced deformations are gathered and tooth modification rules are proposed. Finally, an experimental study on thermallyinduced transmission error behaviour is carried out, conclusions are withdrawn and future work in the field is pointed out. Results show that, contrary to common belief, thermal distortion in steel gears does affect load distribution and transmission error and therefore it should be considered in gear tooth contact analysis.Engranajeen portaera termikoa arreta gutxien jaso duen arazo mekanikoetako bat izan da azken mendean. Sortutako beroaren jatorria dagoeneko ulertu arren, bere analisia olioaren tenperatura egonkorraren iragarpenera mugatu da, engranajeen hutsegitean eragin zuzena baitu. Alabaina, literatura zientifikoaren berrikuspenak erakutsi du dilatazio termikoaren ondorioak ia ez direla aztertu. Bitartean, turbo-makinen industriako esperientziak frogatu du termikoki eragindako geometriaren distortsioak zeregin garrantzitsua duela karga banaketaren aldaketan hortzen haustura eragiten duelarik neurririk hartzen ez bada. Doktorego tesi honen helburu nagusia termikoki eragindako engranaje zuzen eta helikoidalen geometriaren distortsioak sortutako portaera mekaniko irregularra aurreikustea, ebaluatzea eta zuzentzea da. Asmo horrekin, engranaje parean sortutako beroa kuantifikatu egin behar da eta tenperatura egonkorraren banaketa aurreikusi behar da aldez aurretik. Ondoren, hortzen deformazio termikoa zehazteko eredu bat garatu behar da karga banaketa kalkuluen ohiko fluxuan inplementatuz. Distortsio termiko mota eta zenbatekoa jakiteak, kargapean duen portaeraren ulermenarekin batera, hortzaren geometria zuzenketa ahalbidetuko du kontaktuaren portaera desegokia konpentsatuz. Tesiaren lehen ataletan distortsio termikoaren jatorria deskribatzen da eta gaur egungo egoera berrikusten da. Ondoren, engranaje zuzen eta helikoidalen geometria eta zinematika aztertzen dira eta karga banaketa kalkulatzeko eredu analitiko bat garatzen da "thin slice" izeneko metodoa erabiliz. Segidan, engranaje pareen irristaketa marruskaduraren portaera aztertzen da, kontaktuan sortutako beroa kuantifikatzen da eta gurpil parearen tenperatura-banaketa aurreikusten da sare termikoen kontzeptuan oinarrituta. Kapitulu bakoitzean eredu berriak garatzen dira eta emaitzak literatura zientifikoko datu esperimentalekin baliozkotzen dira. Distortsio termikoa aurreikusteko eredua seigarren kapituluan aurkezten da, parametro ezberdinen analisia egiten da eta adibide praktiko bat goitik behera aztertzen da, geometriaren distortsiotik abiatuta portaera termomekanikoa ikusi arte. Kapitulu honen amaieran, termikoki eragindako deformazioei aurre egiteko diseinu gomendioak biltzen dira eta hortzak zuzentzeko arauak proposatzen dira. Azkenean, transmisio errorearen portaera termomekanikoa esperimentalki aztertzen da, ondorioak laburbiltzen dira eta etorkizuneko ildoak azpimarratzen dira. Emaitzen arabera, eta ohiko ustearen aurka, altzairuzko engranajeen distortsio termikoak karga banaketan eta transmisio errorean eragina du eta, ondorioz, kontuan hartu behar da haien kontaktu analisian

Elastohydrodynamic Analysis of Spur Gears Using Load-Sharing Concept: Running-In and Steady-State

Gears are widely used in industry and hence their performance is of vital importance. Under the typical operating conditions of gears, the lubricant layer formed between the teeth of the pinion and the gear cannot completely separate the surfaces and contact of asperities of the pinion and gear occurs. This case is usually referred to as mixed lubrication problem. In this research the load-sharing concept has been employed to predict the performance of the pinion-gear system. The load-sharing concept is an efficient method to solve the mixed lubrication problem and is capable to predict the thickness of the lubricant film, contribution of the fluid film and asperities in carrying the load, friction coefficient, lubricant temperature, and wear with fairly good accuracy. During the initial stage of contact, a considerable number of plastic contact occurs between asperities resulting in permanent change of surface roughness profile. This period which is called running-in has a significant effect on the steady-state performance of the pinion-gear system. The developed model has the capability to predict the variation of surface roughness and contribution of fluid film as well as asperities in carrying the load during running-in. The steady-state wear of gears is predicted using the thermal desorption model. A test rig is designed and built which is capable to mimic the operating condition of any point on the involute profile of gear. Two motors are used to rotate the rollers to generate the same rolling and sliding speed as the corresponding point of the involute profile of pinion-gear system. A hydraulic system is used to exert the desired load on the rollers and keep them in contact under the applied load. The sensors that are mounted on this test rig monitor the speed of each shaft, applied load, surface temperature, and wear depth. The results of the experiments that are conducted on the fresh rollers as well as broken-in roller are shown to be in good agreement with the predicted running-in behavior and steady-state behavior, respectively