THOERY OF MECHANISMS AND MACHINES Module-11 STATIC AND DYNAMIC BALANCING 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

Think about gears, cams, pulleys, turbines, aircraft-engines, … MOTIVATION Think about gears, cams, pulleys, turbines, aircraft-engines, … manoluv.deviantart.com www.bowhunting.net trade.indiamart.com www.pilotfriend.com en.wikipedia.org What would happen if these systems are not statically/dynamically balanced?

An example, this … https://www.youtube.com/watch?v=R2hO--TIjjA

Static Balancing Static Balance applies to things in motion Sum of all forces on the moving system should be ZERO Another name for Static Balance is SINGLE PLANE BALANCE The problem is essentially two-dimensional Examples: single gear or pulley on the shaft, a bicycle/ motorcycle wheel, a thin flywheel/ airplane propeller, individual turbine blade wheel (not the entire turbine) Commonality: All small in the axial direction compared to the radial direction and thus considered to be on a single plane

Static Balancing y x y x Unknown RHS does not depend on the angular velocity

Static Balancing y y x x Write x and y components separately … Retain signs to get the quadrant right… Infinitely many solutions… Choose the radius, find the mass or vice versa

Static Balancing y x y x The balance mass is confined to the single plane of the unbalanced masses

Dynamic Balancing Sometimes termed two plane balance Requires that sum of forces and moments must be ZERO Any rotating object/assembly relatively long in the axial direction (compared to the Radial direction) requires dynamic balancing Some examples requiring dynamic balancing are rollers, crank shafts, camshafts, axles, turbines, propeller shafts etc. To correct dynamic imbalance, adding/removing appropriate masses at appropriate locations should be done in two correction planes separated by a distance along the shaft.

Dynamic Balancing Sometimes termed two plane balance Requires that sum of forces and moments must be ZERO Always a good practice to first statically balance all individual components This would reduce the amount of dynamic imbalance that must be corrected in the final assembly, importantly, it will reduce the bending moment on the shaft, e.g., aircraft turbine consisting of a number of circular turbine wheels There can be some systems that are exceptions, e.g., electric motor --- one doesn’t have control on the windings

Dynamic Balancing Statically balanced? Dynamically balanced? NO YES

Dynamic Balancing Statically balanced? Dynamically balanced? NO YES How many correction planes did we have to use?

Dynamic Balancing A B

Dynamic Balancing A B

Dynamic Balancing All sine components y A y O x z B TWO equations: representing moments about the y axis and x axis

Dynamic Balancing Resolve and solve, first moment equations ... Resolve and solve, force equations ...