Generation and Stress Analysis in New Version of Novikov Helical Gear Combining Double Circular Arc and Crowned Involute Profiles

New version of Novikov helical gear combining double circular arc profile with crowned involute profile has been proposed in this paper. Generation of this gear is carried out using the required equations for these two profiles which are programmed using SOLIDWORK. To compare the resulting contact and bending stresses, three models of gear pairs are generated and investigated using finite element software package (ANSYS). The profiles of these models are as following: double circular arc for first model, crowned involute for second model, while the third model formed by combining double circular arc with involute crowned profiles. The results of stress analysis show that the generated stresses are lower in the proposed (combined) gear especially when the contact in the circular arc side. Keywords: Generation of gears, versions of Novikov Gears, circular arc gear, crowned involute gear, stress analysis in gears

Computerized Design and Generation of Low-Noise Gears with Localized Bearing Contact

The results of research projects directed at the reduction of noise caused by misalignment of the following gear drives: double-circular arc helical gears, modified involute helical gears, face-milled spiral bevel gears, and face-milled formate cut hypoid gears are presented. Misalignment in these types of gear drives causes periodic, almost linear discontinuous functions of transmission errors. The period of such functions is the cycle of meshing when one pair of teeth is changed for the next. Due to the discontinuity of such functions of transmission errors high vibration and noise are inevitable. A predesigned parabolic function of transmission errors that is able to absorb linear discontinuous functions of transmission errors and change the resulting function of transmission errors into a continuous one is proposed. The proposed idea was successfully tested using spiral bevel gears and the noise was reduced a substantial amount in comparison with the existing design. The idea of a predesigned parabolic function is applied for the reduction of noise of helical and hypoid gears. The effectiveness of the proposed approach has been investigated by developed TCA (tooth contact analysis) programs. The bearing contact for the mentioned gears is localized. Conditions that avoid edge contact for the gear drives have been determined. Manufacturing of helical gears with new topology by hobs and grinding worms has been investigated

Modified geometry of spur gear drives for compensation of shaft deflections

One of the main problems when standard spur gears are in mesh is the appearance of edge contact on the gear tooth surfaces caused by misalignments. Those misalignments are caused partially by deflections of gear supporting shafts. As a result of an edge contact, a non-favorable condition of the bearing contact occurs, yielding high level of contact stresses. An intensive research and many practical solutions have been directed to modify the gear tooth surfaces in order to avoid edge contact. An innovative procedure is proposed here for: (1) determination of errors of alignment caused by shaft deflections, (2) compensation of predicted shaft deflections during generation of spur gears, and (3), obtaining a favorable function of transmission errors for the design load. A finite element model of a spur gear drive that comprises pinion and gear supporting shafts is used for the determination of errors of alignment along a cycle of meshing. Compensation of misalignments caused by shaft deflections in gear generation is then accomplished by modification of pinion tooth surfaces whereas the gear tooth surfaces are kept unmodified. Additional modifications of pinion tooth surfaces may be required for obtaining a favorable function of transmission errors. The effect of several misalignment compensations in the reduction of contact stresses has been investigated. Postprocessing of load intensity functions and loaded transmission errors is included. The developed approach is illustrated with numerical examples.The authors express their deep gratitude to the Spanish Ministry of Economy and Competitiveness (MINECO) for the financial support of research projects Refs. DPI2010-20388-C02-01 (financed jointly by FEDER), DPI2013- 47702-C2-1, and DPI2013-47702-C2-2

Topology of modified helical gears

The topology of several types of modified surfaces of helical gears is proposed. The modified surfaces allow absorption of a linear or almost linear function of transmission errors. These errors are caused by gear misalignment and an improvement of the contact of gear tooth surfaces. Principles and corresponding programs for computer aided simulation of meshing and contact of gears have been developed. The results of this investigation are illustrated with numerical examples

Design of Gear Drives With High Gear Ratio

A three part paper to describe the results of several gear drive types with a high gear ratio is presented. A single stage planetary gear train with double helical gears is described with methods to reduce transmission errors and improve load distribution by regulating backlash during assembly. A new arrangement for face gear is also described. This new mechanism can perform rotations between axes that are collinear and intersected. Finally the design and simulation of an isostatic planetary gear train is presented. Conditions that can lead to noise and vibration of the planetary gear drive are described

Topology of modified helical gears and Tooth Contact Analysis (TCA) program

The contents of this report covers: (1) development of optimal geometries for crowned helical gears; (2) a method for their generation; (3) tooth contact analysis (TCA) computer programs for the analysis of meshing and bearing contact of the crowned helical gears; and (4) modelling and simulation of gear shaft deflection. The developed method for synthesis was used to determine the optimal geometry for a crowned helical pinion surface and was directed to localize the bearing contact and guarantee favorable shape and a low level of transmission errors. Two new methods for generation of the crowned helical pinion surface are proposed. One is based on the application of a tool with a surface of revolution that slightly deviates from a regular cone surface. The tool can be used as a grinding wheel or as a shaver. The other is based on a crowning pinion tooth surface with predesigned transmission errors. The pinion tooth surface can be generated by a computer-controlled automatic grinding machine. The TCA program simulates the meshing and bearing contact of the misaligned gears. The transmission errors are also determined. The gear shaft deformation was modelled and investigated. It was found that the deflection of gear shafts has the same effect as gear misalignment

Az arkhimédészi spirál fogirányvonalú hengeres fogaskerekek burkolásának a burkolt felületsereg elosztását jellemző aspektusáról

A görbe vonalú hengeres fogaskerekek előállításának célja a terhelhetőség növelése. Bizonyított tény, hogy a konvex-konkáv kapcsolódó fogfelület-párosítás a terhelhetőség jelentős növelését eredményezi. A közleményben szereplő fogaskerék lefejtés-kinematikájának sajátos aspektusai a kétparaméteres burkolás modelljével nem írhatók le, ezért bevezettük a pulzáló fogasléc modelljét. A kapcsolódási egyenlet megoldása nem elegendő, ugyanis ki kell zárni az elő-, illetve az utólenyesés jelenségét. Ez a relatív mozgás vágóélszintre lehozott kinematikájának részletes elemzésével valósul meg. A valós generáló felületek eloszlása annyira egyenetlen, hogy a burkolás tanulmányozása nehézkessé válik. Jelen közleményben az előbb jelzett hátrány kiküszöbölésére kidolgozott alternatív módszer matematikai modelljét mutatjuk be. A módszer sajátossága abban áll, hogy a burkolt kerék tengelyére merőleges síkokban keletkező görbeseregek relatív elhelyezkedését vizsgáljuk

Gearing

Gearing technology in its modern form has a history of only 100 years. However, the earliest form of gearing can probably be traced back to fourth century B.C. Greece. Current gear practice and recent advances in the technology are drawn together. The history of gearing is reviewed briefly in the Introduction. Subsequent sections describe types of gearing and their geometry, processing, and manufacture. Both conventional and more recent methods of determining gear stress and deflections are considered. The subjects of life prediction and lubrication are additions to the literature. New and more complete methods of power loss predictions as well as an optimum design of spur gear meshes are described. Conventional and new types of power transmission systems are presented

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

Acta Universitatis Sapientiae - Electrical and Mechanical Engineering

Series Electrical and Mechanical Engineering publishes original papers and surveys in various fields of Electrical and Mechanical Engineering