a b s t r a c t   In this paper the dynamic behavior of a single stage spur gear reducer in transient regime is studied。 Dynamic response of the single stage spur gear reducer is investigated at different rotating velocities。

First, gear excitation is induced by the motor torque and load variation in addition to the fluctuation of meshing stiffness due to the variation of input rotational speed。 Then, the dynamic response is computed using the Newmark method。 After that, a parameter study is made on spur gear powered in the first place by an electric motor and in the second place by four strokes four cylinders diesel engine。 Dynamic responses come to confirm a significant influence of the transient regime on the dynamic behavior of a gear set, particularly in the case of engine acyclism condition。76205

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Contents

1。 Introduction 3089

2。 Model of a single stage spur gear transmission  3090

2。1。 Electric motor modeling   3091

2。2。 Combustion engine modeling  3092

3。 Numerical simulations3092

3。1。 Gear reducer powered by an electric motor 。  3093

3。2。 Gear reducer powered by a four strokes four cylinders inline diesel engine   。       3097 4。 Conclusions 3100 References 。 3101

1。 Introduction

Gear reducers are frequently used to provide speed and torque conversions from a rotating power source to connected mechanical devices。 There are internal and external sources of excitations for the gear set。 The internal one is induced by the time varying mesh stiffness。 Many authors [1,2] considered this fluctuation as the main source of excitation of the system and at the origin of the observed noise and vibrations。 Bartelmus [3,4] and Chaari et al。 [5–7] introduced this varying mesh stiffness in a dynamic model of a spur gear system in order to study its response in presence of defects。 Amplitude modulations were observed with added frequency components in response spectra。 Bartelmus [3,4] and Walha

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E-mail address:  mtkhabou@hotmail。com (M。T。 Khabou)。

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et al。 [8] studied the effect of backlash on the dynamic response of a two stage gearbox。 He concluded that tooth separation occurs at  the  transient regime with increase in  the vibration    level。

The external sources of excitation are mainly induced by the fluctuation of the input velocity and torque caused by the motor at its transient regime。 The load condition variation can also be considered a significant external source of excitation。 But, it seems that the effects of input rotational velocity on the linear dynamic behavior of gears were investigated only on few occasions。 Sika [9] and Sika and Velex [10] proposed a model to study in transient regime the backlash and backstrike effect and the influence of gear tooth geometry as well as shaft and gear-shaft-bearing casing positioning on the dynamic behavior of a gear system。 The starting of gear system powered by an electric motor was also investigated by Hugues [11]。

Hugues [11] studied the effect of time varying load conditions on the dynamic behavior of a two stage gearbox and planetary gearbox, he noticed that the presence of distributed faults induces an increase in the vibration levels when load increases。 Bartelmus and Zimroz [12–14] proposed a new approach to the condition monitoring of planetary gearboxes under time varying load conditions and stated that there are two dominant low-frequency causes that influence vibration signal modulation, i。e。 the varying load and the carrier  rotation。