Theory of Machines : Flywheels and Governors

• 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.

2. 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

                                                                           Fig.1: Schematic of single-slider crank mechanism

 2.1 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

 2.2 Velocity Analysis (V) of piston

 2.3 Acceleration Analysis (f) of piston

 2.4 Angular velocity of connecting rod

2.5 Angular Acceleration of connecting rod

   Let ∝_CR = angular acceleration of the connecting Rod

3. 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.

                                                                               Fig.2: Dynamics of single-slider crank mechanism

4. 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.

4.1 FLUCTUATION OF ENERGY

• 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.         

• 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 = N_max -N_min

• The difference between the maximum and minimum kinetic engines of the flywheel is known as the maximum fluctuation of energy.

4.2. REQUIREMENT OF FLYWHEEL IN POWER PRESSES

•   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.
• 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.

4.3 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

                                                                Fig.3: Rim type Flywheel                         Fig.4: Cross-section of flywheel

5. INTRODUCTION- GOVERNORS

• The function of a governor is to regulate the mean speed of an engine, when there are variations in the load e.g. when the load on an engine increases, its speed decreases, therefore it becomes necessary to increase the supply of working fluid and governor ensures to supply this excess fuel to the engine, hence maintaining the mean speed.
• The function of a governor is to maintain the speed of an engine within specified limits.

 5.1 TYPES OF GOVERNORS

5.1.1 WATT GOVERNOR (SIMPLE CONICAL GOVERNOR)

• The simplest form of a centrifugal governor is Watt governor. It is basically a conical pendulum with links attached to a sleeve of negligible mass.

                                                                                      Fig.5 Schematic and Dynamics of Watt Governor

5.1.2PORTER GOVERNOR

• The Porter governor is a modification of the Watt’s governor, with central dead load attached to the sleeve.

                                                                              Fig.6: Schematic and Dynamics of Porter Governor

5.1.3 PROELL GOVERNOR

A Porter governor is known as a Proell governor if the two balls are fixed on the upward extensions of the lower links which are in the form of bent links BAE and CDF as shown in Figure.

                                                                                  Fig.7: Schematic and Dynamics of Proell governor

5.1.4 HARTNELL GOVERNOR (SPRING CONTROLLED GOVERNORS)

• It is a spring-controlled governor in which balls are mounted on the bell crank lever and sleeve is loaded by spring force as shown in Fig.
• Initially, the spring is fitted in compression so that a force is applied to the sleeve.
• Two bell-crank levers, each carrying a mass at one end and a roller at the other, are pivoted to a pair of arms which rotate with the spindle. The rollers fit into a groove in the sleeve.

Fig.8: Schematic and Dynamic of Hartnell Governor

5.2 GOVERNOR TERMINOLOGY

5.2.1  Stability:

• A governor is said to be stable if with the increase in the speed, radius of rotation of balls increases.
• A stable governor brings the speed of the engine to the required value and there is not much hunting.      

5.2.2  Sensitiveness of a Governor:

• A governor is said to be sensitive when there is larger displacement of the sleeve due to a fractional change in speed.
• Sensitiveness of the governor shall be defined as the ratio of speed range to the mean speed.

5.2.3.  Isochronous Governor:

• A governor is said to be isochronous when the equilibrium speed is constant (i.e. range of speed is zero) for all radii of rotation of the balls within the working range, neglecting friction.

5.2.4. Hunting:

• An excessive fast to & fro motion of the sleeve between the stoppers is known as hunting. It is the worst situation & will introduce noise and vibration.
• Hunting takes place in oversensitive governor.
• Higher the sensitiveness of the governor, the problem of hunting becomes more acute.

5.3 Controlling force:

• When the balls of a governor rotate in their circular path, the centrifugal force on each ball tends to move it outwards which is resisted by an equal and opposite force acting radially inwards and is known as the controlling force (CF).

                                                                                                             Fig.9: Controlling force

Fig.10: Graphical representation of various spring-controlled governors

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