Dynamic behaviour of a slider–crank mechanism associated with a smart flexible connecting rod is investigated。 Effect of various mechanisms’ parameters including crank length, flexibility of the connecting rod and the slider's mass on the dynamic behaviour is studied。 Two control schemes are proposed for elastodynamic vibration suppression of the flexible connecting rod and also obtaining a constant angular velocity for the crank。 The first scheme is based on feedback linearization approach and the second one is based on a sliding mode controller。 The input signals are applied by an electric motor located at the crank ground joint, and two layers of piezoelectric film bonded to the top and bottom surfaces of the connecting rod。 Both of the controllers successfully suppress the vibrations of the elastic linkage。79932

& 2016 Society of CAD/CAM Engineers。 Publishing Servies by Elsevier。 This is an open access article under the CC BY-NC-ND license 

Keywords: Slider–crank mechanism; Flexible connecting rod; Piezoelectric; Dynamic response, Nonlinear controller

1。Introduction

High operating speed, superior reliability and accurate performance are major characteristics of modern industrial machinery and commercial equipments。 A traditional rigid- body analysis, which presumes low operating speeds, becomes insufficient to describe the performance of such high speed systems。 A thorough understanding of the dynamic behaviour of the modern machines undergoing high-speed operations, which are based on multibody systems such as slider–crank mechan- isms, is necessary。 Several researchers have worked on devel- opment of suitable formulations with these mechanisms。 Neubauer et al。 examined the transverse deflection of an elastic connecting rod of a slider–crank mechanism by neglecting the longitudinal deformation, the Coriolois, relative tangential and relative normal components of the acceleration [1]。 Hsieh and Shaw studied the nonlinear resonance of a flexible connecting rod by considering both longitudinal and transverse deflection of

the rod [2]。 They investigated that the connecting rod behaves as a system with a softening type of nonlinearity, which is subjected to external and parametric excitations。 Chen and Chian studied effect of crank length on the dynamic behaviour of damped flexible connecting rod [3]。 Zheng et al。 and Muvengi et al。 have considered the effect of joint clearance and Reis et al added the effect of friction in dynamic analysis of the mechanism [4–6]。 Complexity of the dynamic model of flexible mechanisms and their high nonlinearities make these systems hard to control。 A few researchers have attempted to reduce or eliminate the vibrations of flexible mechanisms induced by one or more of the flexible links [7–9]。

Karkoub and Yigit designed a controller for a four-bar mechanism with a flexible coupler。 Their closed-loop system was able to trace a prescribed motion at the input link level。 The PD controller was able to move the mechanism to the desired position and absorb the elastodynamic vibrations [10]。 Karkoub has also developed a controller based on μ synthesis for suppressing the elastodynamic vibrations of a slider–crank

element dynamics model。 The results were implemented on an experimental test bed using a pair of piezoceramic sensors/

Using the mode summation technique, the deflection w is given by

actuators [12]。

Here, we focus on studying effect of various mechanisms’ parameters on the dynamic behaviour and rotation of the crank

considering  the  transverse  deflection  of  the  connecting rod。

Even with no external excitation, rotation of the crank excites the connecting rod and induces vibration。 We successfully suppressed the vibrations of the elastic linkage using two piezoelectric actuators and nonlinear controllers designed based on feedback linearization and sliding  mode。