1. 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
FB 361
Prepared by:
Abhishek Attal & Abhishek Sharma
Final Year Dual Degree Student
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
NL312, FB369

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

3. An example, this …

4. 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

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

6. 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

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

8. 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.

9. 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

10. Dynamic Balancing
Statically balanced?
Dynamically balanced? NO
YES

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

12. Dynamic Balancing A B

13. Dynamic Balancing A B

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

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