Study Notes for Flywheel Notes | EduRev

Theory of Machines (TOM)

Mechanical Engineering : Study Notes for Flywheel Notes | EduRev

The document Study Notes for Flywheel Notes | EduRev is a part of the Mechanical Engineering Course Theory of Machines (TOM).
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Introduction

  • 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.

Kinematic Analysis of Single-Slider Crank Mechanism

  • Figure below 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
    Study Notes for Flywheel Notes | EduRev
     Schematic of single-slider crank mechanism
    ω = dθ/dt
    sinβ = 1/n sinθ
    Study Notes for Flywheel Notes | EduRev
  1. Displacement Analysis (x) of piston
    Let x = displacement of piston from inner-dead centre at the moment when the crank has turned through angle θ from the inner-dead centre
    Study Notes for Flywheel Notes | EduRev
  2. Velocity Analysis (V) of piston
    Study Notes for Flywheel Notes | EduRev
  3. Acceleration Analysis (f) of piston
    Study Notes for Flywheel Notes | EduRev ← Acceleration of Reciprocating mass
  4. Angular Velocity of Connecting rod
    Study Notes for Flywheel Notes | EduRev
  5. Angular Acceleration of Connecting rod
    Let ∝CR = angular acceleration of the connecting Rod
    Study Notes for Flywheel Notes | EduRev

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.
Study Notes for Flywheel Notes | EduRevFig.2: Dynamics of single-slider crank mechanism

Total Piston Effort (F)
Study Notes for Flywheel Notes | EduRev (mg is used for vertical engines)
Force/thrust along connecting Rod (Fc)
Let Fc = Force In the connecting rod (Fig. 2)
Then equating the horizontal components of forces,
Study Notes for Flywheel Notes | EduRev
Normal thrust to cylinder walls (Fn)
It Is the normal reaction on the cylinder walls.

Study Notes for Flywheel Notes | EduRev
Radial thrust on crank shaft Bearings (Fr
The component of FC along the crank (In the radial direction) produces a thrust on the crankshaft bearings.
Study Notes for Flywheel Notes | EduRev

Crank Effort (Ft)
Force Is exerted on the crankpln as a result of the force on the piston. Crank effort Is the net effort (force) applied at the crankpln perpendicular to the crank which gives the required turning moment on the crankshaft. It Is the force needed to drive crank.
Study Notes for Flywheel Notes | EduRev
Turning moment on crank-Shaft:
Study Notes for Flywheel Notes | EduRev

Flywheel

  • A flywheel acts as an energy reservoir, which stores energy during the period when the supply of energy is more than the requirement and releases energy during the period when the requirement is more than the supply.
  • In case a variable torque is supplied where demand is a constant torque or demand is variable torque whereas constant torque is supplied. In both these cases there is mismatch between the supply and demand. This results in speed variation.
  1. Fluctuation of Energy
    (i) The fluctuation of energy may be determined by the turning moment diagram for one complete cycle of operation. The variations of energy above and below the mean resisting torque line are called fluctuations of energy.
    (ii) The difference between the greatest speed and the least speed is known as the maximum fluctuation of speed and the ratio of the maximum fluctuation of speed to mean speed is define as the coefficient of fluctuation of speed.
    Maximum fluctuation of speed = Nmax -Nmin
    Coefficent of fluctuation of Speed, Cs = (Nmax -Nmin)/(Nmean)  
    (Nmean = mean speed of engine)
    (iii) The difference between the maximum and minimum kinetic engines of the flywheel is known as the maximum fluctuation of energy.
    ΔE = Iω2Cs
  2. Requirement of Flywheel in Power Presses
    (i) When the load on the crankshaft is constant or varies and the input torque varies continuously during a cycle, a flywheel is used to reduce the fluctuations of speed.
    (ii) A flywheel can perform the same purpose in a punching press or a riveting machine in which the torque available is constant but the load varies during the cycle.
  3. Designing of Flywheel Rim
    Below we are studying Rim (Ring shaped) type flywheel, which is practical not usable.
    Let, A → cross section area of the rim
    Study Notes for Flywheel Notes | EduRevFig.3: Rim type Flywheel
    Fig.4: Cross-section of flywheel
    For safe designing, σ ≤ σb (bearing strength)
    Study Notes for Flywheel Notes | EduRev
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