Parametric Self-Excitation of a Belt Into Transverse Vibration

Rhodes, J. Elmer

doi:10.1115/1.3408658

Cited by 19 publications

(6 citation statements)

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“…The test stand was suitably designed for the purpose of introducing disturbances in the form of camshaft pulley rotational vibrations or eccentricities, which can directly [11] or parametrically [3] give rise to resonance phenomena. Table 5 summarizes some results for the second and third layouts.…”

Section: Comparison Between Model Behaviour and Experimental Resultsmentioning

confidence: 99%

“…The exibility of belts allows them to absorb shock loads, but on the other hand the related compliance plays an important role with respect to large amplitude vibrations and noise problems [2][3][4][5], which represent a key concern, especially for applications in the automotive industry. Unfortunately, the analysis of belt noise is a rather dif cult task, and its correlation with belt mechanical vibrations is an even more complicated problem: in fact, the running noise generated in a power transmission belt can appear in a wide variety of types and may be caused by several generating mechanisms, as shown by Kubo et al [6] and commented upon in more detail below.…”

Section: Literature Surveymentioning

confidence: 99%

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Multi-body modelling of timing belt dynamics

Callegari

Cannella

Ferri³

2003

Proceedings of the Institution of Mechanical Engineers, Part K:

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Although timing belt drives have recently been increasingly used in mechanical design, their behaviour is still considered to a large extent to be unpredictable, especially under varying operative conditions. The acoustic emission of the transmissions, above all, has been thoroughly investigated in past years, but noise still represents an unresolved problem for many applications and a concern for belt designers; therefore, the availability of good predictive models would be very useful for both design and application phases. The present work describes a multi-body numerical model that has been developed for the characterization of the dynamic behaviour of timing belt transmissions, with the nal goal of assessing the acoustic radiation of a given design. Modelling and simulation have been performed by means of commercial software packages, but more additional programming was required to obtain dynamic models capable of simulating the complex behaviour of toothed belt transmissions. Several experimental tests have been performed to identify the many parameters that in uence system dynamics and to validate the resulting computer aided engineering (CAE) model.

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Section: Comparison Between Model Behaviour and Experimental Resultsmentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

Multi-body modelling of timing belt dynamics

Callegari

Cannella

Ferri³

2003

Proceedings of the Institution of Mechanical Engineers, Part K:

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“…First, it was shown, in a previous study [8], that there is a strong relation between the vibration of the belt spans at meshing frequency and the total acoustic power at the same frequency, in the case of a simple two-pulley belt drive. The second reason is that the test stand was suitably designed for the purpose of introducing disturbances, in the form of camshaft pulley rotational vibrations or eccentricities, which can directly or parametrically [9,20] give rise to resonance phenomena.…”

Section: Boundary Element Modelmentioning

confidence: 99%

A new approach to the measurement of transverse vibration and acoustic radiation of automotive belts using laser Doppler vibrometry and acoustic intensity techniques

Sante

Rossi

2001

Meas. Sci. Technol.

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This work aims at utilizing state-of-the-art and powerful measurement techniques to develop a tool for estimating the acoustic radiation of synchronous belts during the design stage. One of the main objects of this work is that of reducing the large number of tests currently employed. Effective measurement technologies, such as laser and acoustic intensity measurement techniques, are employed to support the entire development of the predicting tool, from the analysis of the noise and vibration phenomena to the validation of the numerical models. The proposed method can also be applied successfully to the analysis of noise generating mechanisms, especially belt vibration responses.In a previous work, it has been shown that the noise radiated at meshing frequency by a belt drive, simply composed of two pulleys and driven by an electric motor, can be estimated using vibration measurements, taken by a scanning laser Doppler vibrometer, as inputs for a boundary element model. The same approach is here extended to a more complex test bench, with an internal combustion engine cylinder head giving additional excitation. The test bench has been designed and realized in order to reduce the noise radiation due to interfering sources (electric motor, cooling system etc) and to make it possible to measure the noise contribution from the belt drive only.Reference noise measurements have been performed by acoustic intensity techniques. The sound power values obtained from these measurements have been compared to those obtained from the boundary element model. The techniques employed in this work have been shown to be able to analyse resonance and meshing phenomena on a real belt drive geometry, as had not been done before, based on the literature survey reported.

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“…Most nonlinear models used consider the transversal vibration of the belt only, without considering the effect of coupling between the transversal and longitudinal vibrations. Rhodes (1970) considered the case of transverse vibration parametric self-excitation of the belt span when a belt runs over the pulley. However, the modes of transverse vibration in this work are the same as those of a vibrating string.…”

Section: Introductionmentioning

confidence: 99%

Coupled longitudinal and transverse vibration of automotive belts under longitudinal excitations using analog equation method

Scurtu¹,

Clark²,

2011

Journal of Vibration and Control

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There are many studies on vibrations of moving belts originated from automotive belt drives. These studies, however, mainly consider the nonlinear effect of the transversal vibration of the belt under transversal excitation without considering the coupling effect between the transversal and longitudinal vibrations under longitudinal excitation. In this paper, a nonlinear model is built for a standing tensioned belt periodically excited longitudinally at one end with a known amplitude and frequency and with the other end clamped, which allows for coupling between the periodic longitudinal excitation and transversal vibration. The nonlinear system is solved using the Analog Equation Method. The two coupled nonlinear hyperbolic differential equations of the system are reduced to two uncoupled linear equations pertaining to the longitudinal and transverse deformation of a substitute beam with unit longitudinal and bending stiffness, respectively. The reduced equations are under a fictitious time-dependent load distribution with the same boundary and initial conditions. The fictitious forces are established numerically from the integral expression of the oscillation solution with the requirement that the equations of motion be satisfied at discreet time intervals. It is found that the transversal vibration appears as a stable and predictable beating phenomenon due to an internal resonance from the periodic energy transfer between the longitudinal excitation and the transversal vibration, which manifests itself as a standing wave.

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Parametric Self-Excitation of a Belt Into Transverse Vibration

Cited by 19 publications

References 0 publications

Multi-body modelling of timing belt dynamics

Multi-body modelling of timing belt dynamics

A new approach to the measurement of transverse vibration and acoustic radiation of automotive belts using laser Doppler vibrometry and acoustic intensity techniques

Coupled longitudinal and transverse vibration of automotive belts under longitudinal excitations using analog equation method

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