THOERY OF MECHANISMS AND MACHINES Module-12 ENGINE DYNAMICS, BALANCING INLINE ENGINES FLYWHEELS, BELT-PULLEY DRIVES Instructed by: Dr. Anupam Saxena Associate Professor Department of Mechanical Engineering Indian Institute of Technology Kanpur FB 361 Prepared by: Abhishek Attal & Abhishek Sharma Final Year Dual Degree Student Department of Mechanical Engineering Indian Institute of Technology KanpurNL312, FB369 Engine Dynamics p a p 0 22 33 44 g suction compression power exhaust 4 Stroke Cycle Pressure inside a cylinder is NOT a CONSTANT varies with crank angle Engine Dynamics p 0 /2 3 /222 g 2 Stroke Cycle Pressure inside a cylinder is NOT a CONSTANT varies with crank angle Gas Torque pA Q Q H V T H V Consider torque transferred ONLY due to gas pressure N N x r l Ignore higher powers in Balance of Multi-Cylinder Engines If the load torque/cycle > supply torque/cycle, system halts. If the load torque/cycle < supply torque/cycle, system speed rises indefinitely. If the load torque/cycle = supply torque/cycle, system in steady state. even though the crankshaft has a steady speed of rotation, small fluctuations in speed within each cycle will exist minimization of which is achieved through a flywheel... Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses FORCE BALANCE Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses FORCE BALANCE Should be ZERO for all crank rotations Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses PITCHING MOMENT BALANCE Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses PITCHING MOMENT BALANCE Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses PITCHING MOMENT BALANCE Should be ZERO for all crank rotations Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses Considering both conditions Balance of Multi-Cylinder Engines x y x r l Generalization aa a F R1 F R F R F R4 4 All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses Primary forces, primary and secondary moments balanced... Secondary forces not balanced = = 0 Balance of Multi-Cylinder Engines r l Generalization All crank lengths All conrod lengths All reciprocating masses m Assume balance due to Rotating masses GOAL Find condition for Balance due to Reciprocating masses = = 0 https://en.wikipedia.org/wiki/Firing_order Primary forces, primary and secondary moments balanced... Secondary forces not balanced Balance of Multi-Cylinder Engines How would one design the firing sequence? https://en.wikipedia.org/wiki/Firing_order p 0 22 33 44 p 0 22 33 44 4 stroke 2 stroke Would the firing sequence affect system balance? Wrapping pairs https://en.wikipedia.org/wiki/Belt_(mechanical)#Power_transmission Belt: loop of flexible material that mechanically links two or more rotating shafts, often parallel.shafts looped over pulleyspulleys may have a twist between them the shafts need not be parallel Power transmission is achieved by specially designed belts and pulleys The belt pulley system runs smoothly, with little noise, strength is less compared to gears or chains T 1 and T 2 are tensions in the tight and slack side of the belt v is the belt velocity... is the coefficient of friction, and is the angle subtended by contact surface at the centre of the pulley Wrapping pairs https://en.wikipedia.org/wiki/Belt_(mechanical)#Power_transmission T + dT T dd N dT cos(d /2) 2T sin(d /2) dT cos(d /2) ~ dT = N = 2 T sin(d /2) ~ T d dT/T = d ln(T1/T2) = ( 2- 1) = https://en.wikipedia.org/wiki/Belt_(mechanical)#Power_transmission Different kinds: flat belt, rope drives, round belts, V-belts (best for power transmission) multi-grooved belts ribbed belts film belts, timing belts Wrapping pairs Wrapping pairs