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Dynamics Of Machine

NME:603

Presented byMD GULFARAZ ALAMAssistant professorJETGI Barabanki

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Force analysisUnit I

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Introduction When the inertia forces are considered in the analysis of

the mechanism, the analysis is known as dynamic force analysis. Now applying D’Alembert principle one may reduce a dynamic system into an equivalent static system and use the techniques used in static force analysis to study the system.

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D’Alembert principle The principle of virtual work states that the sum of the

incremental virtual works done by all external forces Fi acting in conjunction with virtual displacements δsi of the point on which the associated force is acting is zero.

δW = ∑ Fi · δsi = 0.

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dynamics of rigid link in plane motionIn many situations, it is

necessary to determine the forces to be applied on a mechanism to keep it in equilibrium or to accelerate it. Both are part of the same general problem. However, we treat them separately here. First we look at how the force is specified.

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Dynamic force analysis of planar mechanisms In many situations we are

interested in determining the forces that will keep a given mechanism stationary at a position. When the mechanism is at a position with no velocity, and the forces on the mechanism do not cause any acceleration, the mechanism is said to be in equilibrium in that position. The problem of finding forces causing equilibrium can be stated formally as follows.

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Force analysis techniques1. Superposition:

a. Given a mechanism with known position, velocity, and acceleration conditions, derive Newtons equations for dynamic equilibrium. These equations are linear in the forces and therefore Superposition principles can be applied: Inertial and applied forces on each link can be considered individually and then superposed to determine their combined effect.

b. This approach is good for building intuition and solving by hand.c. This approach can be very long

2. Matrix Methoda. All inertial and applied forces are considered at once. The dynamic

equations become coupled in the unknown forces and are solved using linear algebra techniques.

b. Note: Why are forces linear?c. This approach is the best for computer application, therefore our method of

choice.

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Force analysis techniques3. Energy method (Virtual work):

1. Here, only forces that do work on the mechanism are considered. An equation of conservation of energy is written that results in 1 scalar equation with 1 unknown (for a 1 dof system)

2. This is the easiest method if only the input force is required.

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Force analysis using the matrix methodIn the matrix method, equations of dynamic equilibrium

are written for FBD’s of all the links in the mechanism w/ all internal and external forces included. This results in a coupling of the unknown forces. However, the equations are linear in these forces and may be solved using linear algebra techniques.

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piston force and crank effort.• The motion of a non-

offset piston connected to a crank through a connecting rod (as would be found in internal combustion engines), can be expressed through severalmathematical equations. This article shows how these motion equations are derived, and shows an example graph.

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Turning moment on crankshaft due to force on piston.The turning moment diagram (also known as crank effort

diagram) is the graphical representation of the turning moment or crank-effort for various positions of the crank. It is plotted on Cartesian co-ordinates, in which the turning moment is taken as the ordinate and crank angle as abscissa.

Turning moment on the crankshaft,

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Turning moment diagrams for single cylinder double acting steam engine

Fig; Turning moment diagram for a single cylinder, double acting steam engine.

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Four stroke IC engine and multi-cylinder enginesA turning moment

diagram for a four stroke cycle internal combustion engine is shown in Fig. 16.2. We know that in a four stroke cycle internal combustion engine, there is one working stroke after the crank has turned through two revolutions, i.e. 720° (or 4 π radians).

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The variations of energy above and below the mean resisting torque line are called fluctuations of energy. The areas Bb C, Cc D, Dd E, etc. represent fluctuations of energy.

The difference between the maximum and the minimum energies is known as maximum fluctuation of energy.

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A flywheel controls the speed variations caused by the fluctuation of the engine turning moment during each cycle of operation.

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Dimension of Flywheel Rim

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Flywheel in Punching Press

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Problem 1

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