# Imbalance

Static and dynamic imbalance

One speaks of an imbalance in the case of a rotating body whose axis of rotation does not correspond to one of its main axes of inertia . Imbalances lead to vibrations and increased wear , which is why they are balanced by counterweights . Typical examples of this are motor vehicle wheels, the cause of which is usually the tires, or the unbalance effects at high spin speeds of washing machines that were not correctly set up using cross spirit levels .

On the other hand, imbalances are often intentionally used for technical purposes.

A distinction is made between static and dynamic imbalance. Usually both forms occur at the same time.

## Static imbalance

Vibration behavior of unbalances

A static imbalance occurs when the axis of rotation does not pass through the center of gravity of the rotating body. It is a special case of dynamic imbalance. A characteristic of a static imbalance is that the plane in which the imbalance lies coincides with the radial plane of the center of gravity and thus generates circular mechanical vibrations at right angles to the axis of rotation when it is rotated. The imbalance is

${\ displaystyle U = ur}$

with unbalanced mass u and distance r from the axis of rotation. For balancing, a different mass can be used depending on the selected radius. The balance quality (also quality Q) is

${\ displaystyle G = \ omega U / m}$

with total mass m and angular frequency ω .

An imbalance is often specified in units of mm • g , and a balance quality in mm / s .

Example : If only one reflector is attached to a bicycle wheel, the side with the reflector always turns downwards. The wheel vibrates when driving fast.

## Dynamic imbalance

Dynamic imbalances (also moment imbalances) arise when the axis of rotation does not coincide with one of the stable main axes of inertia of the component, but is tilted in the center of gravity with respect to the main axes of inertia.

Dynamic imbalances only occur during operation. They express themselves in a bending moment, the so-called unbalance moment on the axis of rotation. At the ends of the axis they cause circular vibrations shifted by 180 degrees. The center of gravity of the rotating body remains at rest, while the axis wobbles due to the opposing circular movements.

The dynamic imbalance is caused, for example, in unprofessional balancing by two offset imbalances: and in the center distance . As a result, a force acts in each case and these cause a torque perpendicular to the axis of rotation of the rotation, which rotates with this axis of rotation. ${\ displaystyle U_ {1} = ru}$${\ displaystyle U_ {2} = - ru}$${\ displaystyle l}$${\ displaystyle F = F_ {1} = U_ {1} \ omega ^ {2} = - F_ {2} = - U_ {2} \ omega ^ {2}}$${\ displaystyle M = F_ {1} l / 2-F_ {2} l / 2 = lF}$

The moment of deviation in SI units m²kg results from

${\ displaystyle D = ulr = Ul}$

Example : two opposing reflectors attached to a bicycle wheel on different sides

One takes this form of unbalance z. B. with car wheels often true as "flutter". They are therefore dynamically balanced, which can mean that both sides (inside and outside) of the rim carry counterweights.

## Use of unbalance effects

Imbalances are not only a negative effect, they are also consciously used in technology in many areas. So z. B. container and silo walls cleaned with vibrators , materials compacted and driven by vibratory vibratory motors that convey or sort bulk goods. In mills are Plansichter added imbalances in vibration. Massage devices and the vibration alarms of cell phones also work with an imbalance set in rotation by a small motor. The unbalance bore is used to guide drills through stony to loamy sediment and thus to examine deeper layers of the earth. The pile (sheet piling, steel girders) is driven into the ground with a vibratory hammer. In the vibrating plate (construction machine), too , the compaction effect is based on imbalance forces.

## Critical speed

The critical speed is the speed at which the forces of the rotating imbalance cause a machine part or the entire machine to vibrate in resonance. The resonating system is a spring-mass system; there is z. B. from the rotor and shaft of an electric motor / turbine or from the entire motor and its foundation or its suspension.

Excitation by vibrations at the same frequency as the critical speed poses a risk to high-speed machines (turbines, centrifuges, etc.). The effects of such an excitation are achieved through good balancing, damping suspension, or particularly rapid passage through the critical speed when starting up decreased. The critical speed itself can also be changed by changing the stiffness . A reduction in stiffness takes place, for. B. by resilient suspension, which also reduces the critical speed.

In the case of vibratory conveyors and vibrators , on the other hand, the resonance frequency of the vibratory system is intentionally set in the range of the critical speed or vice versa.