# Design of a Flywheel FLYWHEEL

## Transcription

Design of a Flywheel FLYWHEEL

ME 209: Machine Design I 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. FLYWHEEL Design of a Flywheel Asanga Ratnaweera Department of Mechanical Engineering Faculty of Engineering University of Peradeniya Manual press 2/14/2006 IC Engines: The basic operation In internal combustion engines, the energy is developed during the power (expansion) stroke and the engine runs for the whole cycle on the energy supplied during that stroke. ACR/ME209/2006 Power press ACR/ME209/2006 IC Engines: The basic operation Power is produced only during the power stroke Intake 2/14/2006 Combustion engines 2/14/2006 Compression Power Exhaust ACR/ME209/2006 1 IC Engines: The basic operation IC Engines: Turning Moment Pressure and temperature rapidly increases during the combustion and hence the piston is pushed down. Therefore, there is a significant fluctuation of energy during once engine cycle The torque at the crank shaft or the turning moment is largely dependent on; The in-cylinder gas pressure The inertia force of the reciprocating parts As explained above the gas pressure fluctuates over a complete cycle The acceleration and deceleration of the piston assembly also changes during the motion over a cycle Therefore the Turning Moment also fluctuates over an engine cycle IVO - intake valve opens, IVC – intake valve closes EVO – exhaust valve opens, EVC – exhaust valve closes 2/14/2006 ACR/ME209/2006 IC Engines: Turning Moment The Fluctuation Turning Moment can be controlled to some extent by increasing number of cylinders (Multi-cylinder engines) 2/14/2006 ACR/ME209/2006 IC Engines: Turning Moment There are two common configurations used in multi-cylinder engines Inline Engine 2/14/2006 ACR/ME209/2006 2/14/2006 V Engine ACR/ME209/2006 2 IC Engines: Turning Moment Practically it is not possible to build engines with cylinders beyond a certain number. (depends on the capacity) Therefore, a complete smoothness can not be achieved by only increasing the number of cylinders A flywheel is usually coupled to the crank shaft to limit the fluctuation of turning moment and hence the fluctuation of speed. 2/14/2006 ACR/ME209/2006 Design of a Flywheel This design exercise deals with the design of a flywheel to bring the fluctuation of the engine speed to a required limit. 2/14/2006 Design of a Flywheel: Procedure Selection of the engine Data tables will be provided and select the problem based on the serial number Calculation of Turning Moment Design of a Flywheel: Procedure Calculation of torque due to inertia forces TDC the indicator diagram of the engine will be provided where M is the mass of the reciprocating parts α Obtain the turning moment and hence find the mean torque Calculation of the Moment of Inertia of the Flywheel to limit the speed fluctuation to given value Design of the flywheel with the required Moment of Inertia 2/14/2006 .. The total Inertia force Q = M x x calculation of torque due to inertia forces calculation of torque due to pressure forces ACR/ME209/2006 ACR/ME209/2006 l=nr x = l + r − [r cos θ − l cos α ] x = (n + 1)r − [r cos θ − nr cos α ] nr sin α = r sin θ θ r 2/14/2006 cos α = (n 2 − sin 2 θ )1/ 2 n ACR/ME209/2006 3 Design of a Flywheel: Procedure Calculation of torque due to inertia forces Design of a Flywheel: Mass x = (n + 1)r − r cos θ − r (n 2 − sin 2 θ )1/ 2 Mass of the reciprocating parts are largely due to Mass of the piston Contribution from the connecting rod .. cos 2θ ⎤ ⎡ x = ω 2 × r ⎢cos θ + n ⎥⎦ ⎣ .. Q=M x M is the mass of reciprocating parts 2/14/2006 ACR/ME209/2006 2/14/2006 ACR/ME209/2006 Design of a Flywheel: Mass Calculation of the contribution from the connecting rod Design of a Flywheel: Mass Find the equivalent mass system m1 B A B A l2 l l Therefore the total mass M = piston mass + m2 2/14/2006 ACR/ME209/2006 2/14/2006 m 2 x l2 = m 1 x l1 Therefore; l1 l2 l1 m2 G G If the mass of the connecting rod = m m = m1 + m2 m2 = l1 m (l1 + l2 ) Usually for internal combustion engines; l2 = 3 x l1 Mass of the con. Rod = 10g/mm ACR/ME209/2006 4 Design of a Flywheel: Procedure Calculation of torque due to pressure force Design of a Flywheel: Procedure P = S cos α l=nr T = Ph The indicator diagram of an engine can experimentally be obtained by measuring the in-cylinder gas pressure and plotting the variation of pressure against the volume over one cycle θ r h 2/14/2006 ACR/ME209/2006 2/14/2006 Design of a Flywheel: Procedure Calculation of resultant torque P T = ( P − Q)h Q T = Ph − Qh S α Use the Indicator diagram The pressure force at given crank angle can be obtained using the indicator diagram T = Sh cos α S α Calculation of pressure force (P) P Design of a Flywheel: Procedure θ r Draw the given indicator diagram on the drawing sheet Calculate the scale factors for pressure axis and displacement axis l=nr ACR/ME209/2006 Consider the given maximum pressure and the stroke of the engine Draw the configuration diagram to obtain h at each crank position Tabulate the pressure and the value of h at each crank position. Tabulate the gas torque, inertia torque and the total torque at each crank position. Draw the Turning Moment diagram and the mean torque line Calculate the maximum fluctuation of energy h 2/14/2006 ACR/ME209/2006 2/14/2006 ACR/ME209/2006 5 Design of a Flywheel: Fluctuation of Energy Design of a Flywheel: Fluctuation of Energy Use the Planimeter to calculate the area hence the energy fluctuation Then calculate the moment of inertia of the flywheel ∆E = 2/14/2006 ACR/ME209/2006 2/14/2006 Design of a Flywheel: Planimeter The two basic types of flywheels Disc type Rim type Area = Planimeter constant x number of revolutions Note : Planimeter constant = 10. ACR/ME209/2006 ACR/ME209/2006 Design of a Flywheel 2/14/2006 1 1 2 2 × Iω1 − × Iω2 2 2 2/14/2006 ACR/ME209/2006 6 Design of a Flywheel: Key and Keyway Design of a Flywheel The major components Arms Keys are used to transmit torque from a component to the shaft. Hub Shaft Rim Key and Keyways 2/14/2006 ACR/ME209/2006 2/14/2006 Design of a Flywheel: Key and Keyway Design of a Flywheel: Key and Keyway Types for Keyways ACR/ME209/2006 Types for Keys Rectangular keys 2/14/2006 ACR/ME209/2006 2/14/2006 ACR/ME209/2006 7 Design of a Flywheel: Key and Keyway Failure modes A key has two failure mechanisms: Design of a Flywheel: Shaft It can sheared off It can be crushed due to the compressive bearing forces. The diameter of the shaft should be large enough to prevent from failure due to the torque on it. T τ = J r r = distance from the centre D = diameter of the shaft τ = shear stress on the shaft at radius r T = torque on the shaft J = Polar second moment of area J= 2/14/2006 ACR/ME209/2006 2/14/2006 32 ACR/ME209/2006 Design of a Flywheel Design of a Flywheel: Rim and arms πD 4 If the speed of rotation is ω; Centrifugal force on the element dF = dm × ω 2 × R 2 F = 2 ρAR ω 2 2 σ = The End F A Arms can be designed as specified in Mechanical Engineering Handbooks or any acceptable standards 2/14/2006 ACR/ME209/2006 2/14/2006 ACR/ME209/2006 8