Theory of Machines : Kinematics and Dynamics Analysis of single slider Crank Mechanism

1. INTRODUCTION

• As mentioned in the first chapter, analysis of mechanisms is the study of motions and forces concerning their different parts.
• The velocity analysis is the prerequisite for acceleration analysis which further leads to force analysis of various links of a mechanism.
• If the components of a machine accelerate, inertia forces are produced due to their masses. However, if the magnitudes of these forces are small compared to the externally applied loads, they can be neglected while analysing the mechanism. Such an analysis is known as static-force analysis.
• For example, in lifting cranes, the bucker load and the static weight loads may be quite high relative to any dynamic loads due to accelerating masses, and thus static-force analysis is justified.
• When the inertia effect due to the mass of the components is also considered, it is called dynamic-force analysis which will be dealt in this chapter.
• Dynamic forces are associated with accelerating masses. As all machines have some accelerating parts, dynamic forces are always present when the machines operate.
• For example, in case of rotors which rotate at speeds more than 80,000 rpm, even the slightest eccentricity of the centre of mass from the axis of rotation produces very high dynamic forces. This may lead to vibrations, wear, noise or even machine failure.

KINEMATIC ANALYSIS OF SINGLE-SLIDER CRANK MECHANISM

• Figure shows a slider-crank mechanism in which the crank OA rotates in the clockwise direction. ℓ and r are the lengths of the connecting rod and the crank respectively.
• In kinematic analysis, inertia of connecting rod is not considered in this analysis

DYNAMIC-ANALYSIS OF SINGLE-SLIDER CRANK MECHANISM

• An engine is acted upon by various forces such as weight of reciprocating masses and connecting rod, gas forces, forces due to friction and inertia due to acceleration and retardation of engine elements, the last being dynamic in nature.
• In this section, the analysis is made of the forces neglecting the effect of the weight and the inertia effect of the connecting rod.

Effective driving force to drive the piston (Total Piston effort, F)

• The piston effort is termed as the net or effective force applied on the piston.
• In reciprocating engines, the reciprocating masses accelerate during the first half of the stroke and the inertia force tends to resist the same. Thus, the net force on the piston is decreased.
• During the latter half of the stroke, the reciprocating masses decelerate and the inertia force opposes this deceleration or acts in the direction of the applied gas pressure and thus, increases the effective force on the piston.
• In a vertical engine, the weight of the reciprocating masses assists the piston during the out-stroke (down stroke), thus, increasing the piston efforts by an amount equal to the weight of the piston. During the in-stroke (up stroke), the piston effort is decreased by the same amount.

Then equating the horizontal components of forces,

Force/thrust along connecting Rod (F_c)

Let F_C = Force in the connecting rod (Fig)

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