A model of spur gears supported by ball bearings

Viadero, F.; Rincón, Alfonso Fernández del; Sancibrián, Ramón; Fernández, Pablo García; De-Juan, Ana

doi:10.2495/cmem070701

Cited by 17 publications

(12 citation statements)

References 13 publications

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“…Regarding bearings, the model proposed in [4] was kept unmodified except for the capability of including waviness and localized defects, which will not be discussed in this work. Random relative sliding of the rolling elements with respect to the cage was also added bearing in mind the smoothing out of the spectral content due the ball pass frequency.…”

Section: Model Descriptionmentioning

confidence: 99%

“…That means that it could be used as an analysis tool more than a design tool. With the aim of extending its capabilities, the original formulation was analysed searching for the most expensive computational task, arriving at the conclusion that the solution of the non-linear system of equations present in the original formulation [4] was the critical one. Consequently, this task was avoided by the pre-calculation of the contacting stiffness for a certain load by means of a previous quasi-static analysis where the goodness of the original model can be exploited.…”

Section: Pre-calculation Of Meshing Stiffnessmentioning

confidence: 99%

“…Following the procedure described in [4], gear contacting forces are obtained based of the model proposed by Andersson and Vedmar [6], where tooth deformations are divided into two groups; one near the contact that is treated by an analytical non-linear formulation of Hertzian type, and another of elastic nature determined by means of a dedicated finite element model. This kind of formulation achieves an efficient treatment of gear teeth contacts, not requiring a highly refined mesh at the contact surfaces.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Pursuing this objective, a quasi-static model including those features was presented by the authors in a previous work [4]. The procedure for gear contact force calculation employs a hybrid approach dividing the elastic deflections in teeth into two different contributions: global deflections including bending, and Input Ω (constant) Output Torque shearing and local deflections in the vicinity of theoretical contact points.…”

Section: Introductionmentioning

confidence: 99%

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A dynamic model for the study of gear transmissions

Rincón¹,

Viadero²,

Sancibrián³

et al. 2009

WIT Transactions on Modelling and Simulation

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In this work a previous model developed by the authors for the quasi-static analysis of spur gear transmissions supported by ball bearings was modified extending its capabilities to dynamic analysis. The model combines a finite element and an analytical formulation achieving sufficient accuracy and computational efficiency to make dynamic analysis feasible. Non-linearity associated with the contact among teeth was included, taking into account the flexibility of gears, shafts and bearings. Furthermore, parametric excitations originating both from gear and bearing supports, as well as clearance, were also taken into account. An example of a simple transmission is presented providing several results obtained using the proposed model. Nevertheless, in spite of its usefulness, particularly in the case of variable torque loads, and its improved capabilities compared with other procedures, this approach still requires a high computational effort. As a consequence in those cases where the transmission operates under stationary conditions the formulation could be simplified by using a pre-calculated value for each the gear tooth stiffness as a function of the angular position. Once again, the original model is useful, taking advantage of its computational efficiency in the calculation of these stiffness coefficients throughout a meshing period. The improved model is applied to the same transmission and the consequences of a misleading calculation of the stiffness coefficients are shown. Then, it was used to study the vibratory behaviour under different levels of applied torque, showing the modifications suffered by the orbits, meshing contact forces and particularly the spectra obtained for bearing forces.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Pre-calculation Of Meshing Stiffnessmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A dynamic model for the study of gear transmissions

Rincón¹,

Viadero²,

Sancibrián³

et al. 2009

WIT Transactions on Modelling and Simulation

Self Cite

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show abstract

“…Subsequently, the procedure used for the meshing forces calculation was adapted in order to consider different types of tooth defects as cracks and pitting [4] as well as profile deviations [5]. Although these models are mainly focused on simulating the main features of gears, bearings have been also modelled, as they constitute a crucial part of mechanical transmissions [1]. This aspect, which includes a variable compliance model for bearings, has been included in the model for the assessment of the vibrations of gear transmissions due to transmitted torque [3].…”

Section: Introductionmentioning

confidence: 99%

Gear transmission dynamics: Effects of index and run out errors

et al. 2016

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Abstract. This work describes a non-linear dynamic model for the study of the vibration signals generated by gear transmissions. The developed model considers both the parametric excitations due to the variable compliance of bearings and gears, can handle changes in the transmitted torque and allows the integration of the dynamic equations quickly and accurately. This model has been developed previously by the authors to assess the profile deviations on the dynamic behavior of gear transmissions and its influence on the transmitted torque. It also includes the presence of gear defects as cracks and pitting during the calculation of meshing forces. In this paper, the model has been enhanced in order to include two common defects such as index errors and run out or eccentricity errors. Index errors occur as a result of a non-uniform angular distribution of the tooth profiles along the pitch circle. Run out appears due to the displacement of the geometric center of the gear with respect to the center of rotation of the shaft on which it is mounted. Although both errors are caused by different reasons, sometimes they have been confused because of their similitudes. The procedure for including both kinds of errors in the model is described and simulations under several transmitted torques are presented. The results are assessed and compared focusing the attention on certain transmission parameters and magnitudes as transmission error, load forces in the tooth flanks and demodulation techniques on the resulting vibratory signals.

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