THOERY OF MECHANISMS AND MACHINES Module-12 STATIC AND DYNAMIC BALANCING 4 BAR LINKAGES AND IC ENGINES Instructed by: Dr. Anupam Saxena Associate Professor Department of Mechanical Engineering Indian Institute of Technology Kanpur anupams@iitk.ac.in FB 361 Prepared by: Abhishek Attal & Abhishek Sharma Final Year Dual Degree Student Department of Mechanical Engineering Indian Institute of Technology Kanpur attalab@iitk.ac.in, abhishr@iitk.ac.in NL312, FB369

Balance of Multi-Cylinder Engines pA f x Q H V T Q pA N Crank rotates with constant speed

Balance of Multi-Cylinder Engines V pA H N Q H V T Net unbalanced force is the Horizontal force on the frame pA - H Q pA N This will be transferred to the Foundation via the crank...

Balance of Single Cylinder Engines x y q = t r l f m a + m 2 m co m cr m b + m s m 1

Balance of Single Cylinder Engines m a + m 2 l m b + m s m 1 r q = t f x x

Balance of Multi-Cylinder Engines What if we place another identical second system to drive the same crank shaft y We place the system smartly... m a + m 2 r l m b + m s m 1 + m 1 q m b s + x r x l m 2 + m a Two centripetal forces get balanced out Two reciprocatory inertial forces may or may not

Balance of Multi-Cylinder Engines What if we place another identical second system to drive the same crank shaft y We place the system smartly... m a + m 2 r l m b + m s m 1 + m 1 q m b s + x r x l m 2 + m a Two centripetal forces get balanced out Two reciprocatory inertial forces may or may not

Balance of Multi-Cylinder Engines What if we place TWO EXTRA PAIRS of the same system ? y Again, we place the systems smartly... r r l l q x r l r l x F R2 F R1 F R3 F R4 F R1 = F R2 = F R3 = F R4 = Do these forces balance out?

Balance of Multi-Cylinder Engines Another way of looking at the force balance... y Primary components r r q r r x Primary forces balance and so do their components

Balance of Multi-Cylinder Engines Another way of looking at the force balance... y Secondary components 2q x Secondary forces balance and so do their components F R1 = F R2 = F R3 = F R4 =

Balance of Multi-Cylinder Engines How about moments ? y All axes PARALLEL 1 All single cylinder systems IDENTICAL 2 r r l l Distances between axes the same q x r l r l x F R2 F R1 F R3 4 F R4 3 1 a 2 INLNE SYSTEM a 3 a 4

Balance of Multi-Cylinder Engines How about moments ? y All axes PARALLEL 1 All single cylinder systems IDENTICAL 2 r r l l Distances between axes the same q x r l r l x F R2 F R1 F R3 4 F R4 3 1 F R1 a 2 F R2 a INLNE SYSTEM 3 F R3 a 4 F R4

Balance of Multi-Cylinder Engines

Balance of Multi-Cylinder Engines

Balance of Multi-Cylinder Engines

Balance of Multi-Cylinder Engines Firing in TWO STROKE cycle y n: number of cylinders 1 2 r r l l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a 2 F R2 a 3 F R3 a 4 F R4

Balance of Multi-Cylinder Engines Firing in FOUR STROKE cycle y n: number of cylinders 1 2 r r l l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a 2 F R2 a 3 F R3 a 4 F R4

Balance of Multi-Cylinder Engines Consider moment about CENTERLINE... Consider 2 stroke cycle and firing order as 1-2-3-4... y 1 2 r r l Unbalanced and NON zero l q x r l r l x F R2 Pitching moment F R1 F R3 O 4 F R4 3 z 1 F R1 a 2 F R2 a 3 F R3 a 4 F R4

Balance of Multi-Cylinder Engines What stops us from reshuffling the cylinders? ... y 1 2 r r l l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a F R2 2 a 3 F R3 a F R4 4

Balance of Multi-Cylinder Engines What stops us from reshuffling the cylinders? ... Consider 2 stroke cycle... y 1 2 Unbalanced and NON zero r r l But lower than previous case? l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a F R4 4 a 3 F R3 a F R2 2