18 Questions
What is the main problem caused by a wheel that is not balanced?
Vibration and damage
What is the purpose of balancing in rotating or reciprocating masses?
To eliminate unwanted inertia forces
What term is used to describe the uneven distribution of mass about a rotor's rotating centerline?
Unbalance
In primary balancing, how are unbalanced mass components resolved?
In one plane only
What is the requirement for static balance in a moving system?
Zero sum of all forces
What does secondary balancing in rotating objects primarily involve?
Correcting primary forces
What is another name for static balance?
Single-plane balance
In static balance, what type of problem is it essentially?
Two-dimensional problem
Which forces are of concern in static balance?
Inertia forces
How can external forces affect the balancing process in static balance?
External forces cannot be balanced by altering the system's internal geometry
What is secondary balancing focused on resolving?
Primary and secondary forces
When does an object require dynamic balancing for complete balance?
When it is relatively long in axial direction compared to radial direction
What is the main purpose of dynamic balance in a system?
To cancel out the unbalanced moment
What is required to correct dynamic imbalance in a system?
Creating counter forces through mass adjustment at proper angular locations
Which term refers to the imaginary force that brings a rigid body to equilibrium?
Inertia force
What is the purpose of adding or removing mass in single-plane balance?
To statically balance the system
What is the function of a counter couple in balancing a system?
To cancel out the unbalanced moment
What is the primary purpose of secondary balancing in a system?
To create counter forces in multiple planes
Study Notes
History of Balancing
- The concept of balancing originated with the invention of the wheel, which needed to be round and rotate evenly to avoid vibration and damage.
Balancing
- Balancing is the technique of correcting or eliminating unwanted inertia forces or moments in rotating or reciprocating masses by changing the location of the mass centers.
- Unbalance exists when vibratory force or motion is imparted to the bearings of a rotor due to centrifugal forces, resulting from uneven mass distribution about its rotating centerline.
Primary Balancing
- Primary balancing is the process of resolving primary forces caused by unbalanced mass components in a rotating object into one plane and balancing by adding a mass in that plane only.
- Static balance, also known as single-plane balance, requires that the sum of all forces on the moving system be zero (∑ 𝐅−𝐦𝐚=𝟎).
Static Balance
- Static balance applies to things in motion, and concerns the accelerations of masses in the system.
- Example: a bicycle or motorcycle tire and wheel, a thin flywheel, an airplane propeller.
Equations
- 2 2 2 − 𝑚1 𝑅1 𝜔 − 𝑚 2 𝑅 2 𝜔 − 𝑚𝑏 𝑅 𝑏 𝜔 =0
- 𝒎𝒃 𝑹𝒃=− 𝒎𝟏 𝑹𝟏 − 𝒎𝟐 𝑹 𝟐
Secondary Balancing
- Describes the process of resolving primary forces and secondary force couples caused by unbalanced mass components in a rotating object into two (or more) planes and balancing by adding mass increments in those planes.
Dynamic Balance
- Any rotating object or assembly that is relatively long in the axial direction compared to the radial direction requires dynamic balancing for complete balance.
- Dynamic balance requires two criteria to be met: the sum of forces must be zero (∑ 𝑭=𝟎) and the sum of moments must also be zero.
Sample Problem
- Four masses (200 kg, 300 kg, 240 kg, and 260 kg) with corresponding radii of rotation (0.2 m, 0.15 m, 0.25 m, and 0.3 m) and angles between successive masses (45°, 75°, and 135°) require finding the position and magnitude of the balance mass.
Unbalance
- Inertia force is an imaginary force that brings a rigid body into equilibrium position.
- Unbalance force or shaking force is the resultant of all forces acting on the body of the engine due to inertia forces only.
Test your understanding of center of gravity of two masses in steady condition and in motion, as well as methods of balancing rotors. Explore the history of balancing and the consequences of having an uneven wheel.
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