Influences of planetary gear parameters on the dynamic characteristics – a review

Planetary gear trains (PGTs) are widely used in the field of mechanical transmission. PGTs significantly differ from fixed-axis gear trains and exhibit unique dynamic behavior. Dynamic characteristics of PGTs are popular research topic, particularly when attempting to solve the problem of vibration noise. Moreover, the effects of the planetary gear parameters on the dynamic characteristics are paramount important. And significant researches have been conducted in this field. However, few reviews regarding these studies have been published. In this paper, the effects of certain parameters, which include mesh phase difference, geometric errors (tooth profile error, eccentricity error and misalignment), tooth profile modification, mesh stiffness, and etc., on the dynamic characteristics of PGTs are summarized. Several conclusions obtained can be used for the PGTs design and dynamic characteristics analysis. Finally, the potential research trends are pointed out

Novel design and geometry for mechanical gearing

This thesis presents quasi-static Finite Element Methods for the analysis of the stress state occurring in a pair of loaded spur gears and aims to further research the effect of tooth profile modifications on the mechanical performance of a mating gear pair. The investigation is then extended to epicyclic transmissions as they are considered the most viable solution when the transmission of high torque level within a compact volume is required. Since, for the current study, only low speed conditions are considered, dynamic loads do not play a crucial role. Vibrations and the resulting noise might be considered negligible and consequently the design process is dictated entirely by the stress state occurring on the mating components. Gear load carrying capacity is limited by maximum contact and bending stress and their correlated failure modes. Consequently, the occurring stress state is the main criteria to characterise the load carrying capacity of a gear system. Contact and bending stresses are evaluated for multiple positions over a mesh cycle of a contacting tooth pair in order to consider the stress fluctuation as consequence of the alternation of single and double pairs of teeth in contact. The influence of gear geometrical proportions on mechanical properties of gears in mesh is studied thoroughly by means of the definition of a domain of feasible combination of geometrical parameters in order to deconstruct the well-established gear design process based on rating standards and base the defined gear geometry on operational and manufacturing constraints only. From this parametric study, suitable suggestions for enhancing the load carrying capacity of the tooth flank are made by showing that the use of non-standard geometric parameters can improve the performance of gears. As this study also aims to improve the performances of epicyclic gearings specifically for low speed-high torque operating conditions, the optimum parameters found in the preliminary parametric analysis were applied to this category of systems. The design procedure based on the area of existence of gear geometry was extended to this case which required the determination of the domain of feasible combination for gears in internal mesh with the addition of constraints addressed to epicyclic configurations. Three epicyclic systems with same boundary design conditions but different combination of geometrical parameters have been modelled and analysed by means of quasi-static FEA. The results have shown that the improvements found for the case of two mating spur gears are also valid for the case of higher order systems in which multiple contacts are simultaneously occurring. Based on these results, suitable suggestions are made for the design of gears working in epicyclic systems for an enhanced torque capacity and a volume reduction for applications characterized by low speed and high loads conditions. An alternative solution to geared systems that guarantees compactness and high torque transmission capabilities has also been investigated; it consists of a cycloidal transmission system. The parametric equations for the cycloidal profile have been determined and an executive design, then manufactured, has been produced. The preliminary quasi-static Finite Element analysis has predicted the load sharing and stress distribution among multiple components confirming the mechanical advantage of this category of transmission systems

Effect of planetary gearboxes on the dynamics of rotating systems

The coupled dynamic behaviour of planetary geared rotor systems is much less well understood compared to the classical geared rotor systems. For a better understanding, this research project investigates the coupled dynamic behaviour of planetary geared rotor systems and how the planetary gearbox parameters affect their global dynamics. In the numerical study, a six degrees of freedom hybrid dynamic model of a planetary geared rotor system is created in the recently developed “GEAROT” rotor dynamics software by considering gyroscopic effects. Based on the modal analysis results of the hybrid dynamic model, the vibration modes are classified as coupled torsional-axial, lateral and gearbox for the helical gear configuration, and torsional, axial, lateral and gearbox for the spur one. Modal energy analysis is used to quantify the coupling level between the shafts and planetary gearbox, which highlights the effect of a planetary gearbox on the dynamic behaviour of a rotating system. An extensive planetary gearbox parameter study including gear contact, gearbox mass and support, and planet gear parameters is conducted using the hybrid dynamic model to investigate the parameter effects on the modal behaviour of planetary geared rotors. The sensitivity of planetary geared rotor vibration modes to the gearbox parameters is determined by computing the frequency shifts and comparing the mode shapes between the two extreme cases. In the experimental study, free-free impact hammer tests are carried out on a planetary geared rotor assembly to validate the numerical modal analyses results in “GEAROT”. On the basis of both experimental and numerical modal analysis of planetary geared rotors, the lateral vibration modes are identified as “in phase” and “out of phase”. Briefly, the numerically identified lateral modal behaviour of planetary geared rotor systems is successfully validated with the experimental modal analysis results.Open Acces

Modeling and dynamic analysis of spiral bevel gear coupled system of intermediate and tail gearboxes in a helicopter.

The coupled dynamic model of the intermediate and tail gearboxes’ spiral bevel gear-oblique tail shaft-laminated membrane coupling was established by employing the hybrid modeling method of finite element and lumped mass. Among them, the dynamic equation of the shaft was constructed by Timoshenko beam; spiral bevel gears were derived theoretically by the lumped-mass method, where the effects of time-varying meshing stiffness, transmission error, external imbalance excitation and the like were considered simultaneously; laminated membrane coupling was simplified to a lumped parameter model, in which the stiffness was obtained by the finite element simulation and experiment. On this basis, the laminated membrane coupling and effects of several important parameters, including the unbalance value, tail rotor excitation, oblique tail shaft’s length and transmission error amplitude, on the system’s dynamic characteristics were discussed. The results showed that the influences of laminated membrane coupling and transmission error amplitude on the coupled system’s vibration response were prominent, which should be taken into consideration in the dynamic model. Due to the bending-torsional coupled effect, the lateral vibration caused by gear eccentricity would enlarge the oblique tail shaft’s torsional vibration; similarly, the tail rotor’s torsional excitation also varies the lateral vibration of the oblique tail shaft. The coupled effect between the eccentricity of gear pairs mainly hit the torsional vibration. Also, as the oblique tail shaft’s length increased, the torsional vibration of the oblique tail shaft tended to diminish while the axis orbit became larger. The research provides theoretical support for the design of the helicopter tail transmission system

Results of NASA/Army transmission research

Since 1970 the NASA Lewis Research Center and the U.S. Army Aviation Systems Command have shared an interest in advancing the technology for helicopter propulsion systems. In particular, that portion of the program that applies to the drive train and its various mechanical components are outlined. The major goals of the program were (and continue to be) to increase the life, reliability, and maintainability, reduce the weight, noise, and vibration, and maintain the relatively high mechanical efficiency of the gear train. Major historical milestones are reviewed, significant advances in technology for bearings, gears, and transmissions are discussed, and the outlook for the future is presented. The reference list is comprehensive

Comportamiento dinámico de transmisiones de engranajes multietapa. Análisis del desfase en el engrane

RESUMEN Las transmisiones de engranajes son sistemas complejos compuestos por numerosos elementos de geometría complicada. El correcto funcionamiento de una transmisión de engranajes, y más concretamente una transmisión planetaria, necesita de la sinergia de muchos factores y se ve afectado por muchos condicionantes que dificultan la identificación de los problemas. A pesar de su complejidad o quizá consecuencia de ella, las transmisiones de engranajes planetarios han adquirido un papel muy relevante en la industria en las últimas décadas. Nuevas aplicaciones y aplicaciones clásicas han surgido o evolucionado hasta el punto en que las transmisiones de engranajes epicicloidales tienen un papel determinante en su buen funcionamiento. Este desarrollo también ha llevado al planteamiento de nuevas hipótesis y a la aparición de nuevos problemas. En relación con la aparición de nuevos problemas y aplicaciones, esta Tesis trata de analizar en profundidad algunos de ellos, así como, estudiar otros posibles escenarios en busca de dar respuesta a algunos de los interrogantes que surgen tanto a fabricantes como a investigadores sobre el correcto funcionamiento de dichas transmisiones. Principalmente, esta Tesis se centra en el papel que juega la geometría en el comportamiento de las transmisiones planetarias. En lo que se refiere a la geometría, en esta Tesis el interés se centra en el impacto del espaciado angular y la fase de engrane, que son consecuencia directa de los criterios de diseño de la transmisión. En más detalle, esta Tesis analiza el impacto que tienen esos criterios en el reparto de carga en transmisiones planetarias. El reparto de carga se escoge como la magnitud que permite analizar el estado de la transmisión a lo largo de las simulaciones. Una vez que se ha establecido el impacto del espaciado y la fase en el comportamiento de la transmisión, se incluyen nuevos efectos. En este caso, se considera la importancia que tienen los inevitables errores de fabricación en las transmisiones planetarias. Estos errores afectan a la calidad, durabilidad y el comportamiento de las transmisiones planetarias, lo cual da una idea de la importancia que los errores tienen en este campo. En esta Tesis, los errores escogidos se limitan a errores en el espesor de los dientes, así como, errores de montaje de los planetas en el portaplanetas. Además, dadas las características de estos errores, su influencia varía dependiendo de las condiciones de trabajo, por esto, se amplía el estudio a diferentes niveles de carga y sentidos de aplicación de la carga. Después de esto, el interés se centra en el análisis de los procedimientos experimentales de medida y su validez. En esta parte de la Tesis se combinan los estudios anteriores con el uso de la medida de deformaciones en la raíz de los dientes del sol para el cálculo de reparto de carga en transmisiones planetarias. Los resultados demuestran que en configuraciones en fase solo se hace visible la influencia del espaciado de los planetas cuando los apoyos de las ruedas cuentan con flotabilidad. Además, la influencia de la flotabilidad en los apoyos demuestra tener un efecto diferente para transmisiones de 5 planetas que para transmisiones de 3 planetas. Además, el comportamiento de las transmisiones con fase secuencial prueba ser peor, en su reparto de carga, que el de la configuración en fase análoga. Esto, se hace más visible cuando se incluyen errores en las transmisiones simuladas. El desequilibrio creado por un error es mayor y el impacto que tiene en los valores máximos y mínimos de carga es mayor debido a la fase en el engrane. En cuanto a las medidas experimentales, los resultados prueban ser imprecisos en comparación con el reparto de carga real en la transmisión. Además, la inclusión de secuencia en la fase de engrane y errores afecta notablemente la precisión de las medidas de deformaciones como una herramienta de cálculo del reparto de carga en transmisiones planetarias. Finalmente, como conclusiones extraídas de los resultados comentados anteriormente, se demuestra como la secuencia en el engrane afecta notablemente al equilibrio en el reparto de carga en las transmisiones y genera desequilibrios debidos al desfase en el engrane. Esta fase de engrane también incrementa el impacto de los errores en el reparto de carga de la transmisión. Por otra parte, otro factor que incrementa el impacto de los errores es el aumento del número de planetas. El impacto de la rigidez se hace patente con otros cambios como la modificación del número de planetas en la transmisión y el tamaño de los ejes sobre los que se montan las ruedas. En cuanto a las medidas experimentales, prueban ser imprecisas en cualquier configuración diferente de una transmisión equiespaciada y en fase sin errores. Además, esta falta de precisión crece con el tamaño del error y se hace mayor para configuraciones secuenciales. Vistas las conclusiones que se extraen es posible plantear nuevas líneas para continuar con este trabajo. En primer lugar, el modelo se puede extender a un planteamiento tridimensional para tener en cuenta la influencia de esta tercera dimensión en los fenómenos estudiados mediante el análisis de transmisiones planetarias helicoidales. Al mismo tiempo, el número de planetas se puede incrementar por encima de 5, así, nuevos escenarios de estudio aparecen, principalmente en configuraciones con un número par de planetas superior a 5. No obstante, en el modelo plano con el número de planetas ya estudiado, las técnicas de medida experimental estudiadas se pueden extender a otros procedimientos que también se utilizan habitualmente