Balancing of rotating masses

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The balancing of rotating bodies is important to avoid vibration. In heavy industrial machines such as gas turbines and electric generators, vibration can cause catastrophic failure, as well as noise and discomfort. In the case of a narrow wheel, balancing simply involves moving the center of gravity to the centre of rotation. For a system to be in complete balance both force and couple polygons should be close in order to prevent the effect of centrifugal force. It is important to design the machine parts wisely so that the unbalance is reduced up to the minimum possible level or eliminated completely.

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Static balance

Static balance occurs when the centre of gravity of an object is on the axis of rotation. [1] The object can therefore remain stationary, with the axis horizontal, without the application of any braking force. It has no tendency to rotate due to the force of gravity. This is seen in bike wheels where the reflective plate is placed opposite the valve to distribute the centre of mass to the centre of the wheel. Other examples are grindstones, discs or car wheels. Verifying static balance requires the freedom for the object to rotate with as little friction as possible.

This may be provided with sharp, hardened knife edges, adjusted to be both horizontal and parallel. Alternatively, a pair of free-running ball bearing races is substituted for each knife edge, which relaxed the horizontal and parallel requirement. The object is either axially symmetrical like a wheel or must be provided with an axle. It is slowly spun, and when it comes to rest, it will stop at a random position if statically balanced. If not, an adhesive or clip on weight is securely attached to achieve balance.

Dynamic balance

Rotating shaft unbalanced by two identical attached weights, which causes a counterclockwise centrifugal couple Cd that must be resisted by a clockwise couple Fl = Cd exerted by the bearings. The figure is drawn from the viewpoint of a frame rotating with the shaft, hence the centrifugal forces. Unbalanced rotating shaft SVG1.1.svg
Rotating shaft unbalanced by two identical attached weights, which causes a counterclockwise centrifugal couple Cd that must be resisted by a clockwise couple Fℓ = Cd exerted by the bearings. The figure is drawn from the viewpoint of a frame rotating with the shaft, hence the centrifugal forces.

A rotating system of mass is in dynamic balance when the rotation does not produce any resultant centrifugal force or couple. The system rotates without requiring the application of any external force or couple, other than that required to support its weight. If a system is initially unbalanced, to avoid the stress upon the bearings caused by the centrifugal couple, counterbalancing weights must be added.

This is seen when a bicycle wheel gets a buckled rim. The wheel will not rotate to a preferred position but because some rim mass is offset there is a wobbling couple leading to a dynamic vibration. If the spokes on this wheel cannot be adjusted to center the rim, an alternative method is used to provide dynamic balance. [2]

To correct dynamic imbalance, there are three requirements: 1) a means of spinning the object 2) a frame to allow the object to vibrate perpendicular to its rotation axis 3) A means to detect the imbalance, by sensing its vibrating displacement, vibration velocity or (ideally) its instantaneous acceleration.

If the object is disk-like, weights may be attached near the rim to reduce the sensed vibration. This is called one-plane dynamic balancing. If the object is cylinder or rod-like, it may be preferable to execute two-plane balancing, which holds one end's spin axis steady, while the other end's vibration is reduced. Then the near end is freed to vibrate, while the far end spin axis is fixed, and vibration is again reduced. In precision work, this two plane measurement may be iterated.

Dynamic balancing was formerly the province of expensive equipment, but users with just occasional need to quench running vibrations may use the built in accelerometers of a smart phone and a spectrum analysis application. See ref 3 for example. A less tedious means of achieving dynamic balance requires just four measurements. 1) initial imbalance reading 2) an imbalance reading with a test mass attached on a reference point 3) The test mass moved to 120 degrees ahead and the imbalance again noted. 4) The test mass finally moved to 120 degrees behind the reference point. These four readings are sufficient to define the size and position of a final mass to achieve good balance. Ref 4

For production balancing, the phase of dynamic vibration is observed with its amplitude. This allows one-shot dynamic balance to be achieved with a single spin, by adding a mass of internally calculated size in a calculated position. This is the method commonly used to dynamically balance automobile wheels with tire installed by means of clip-on lead (or currently zinc) 'wheel weights'.

Unbalanced systems

When an unbalanced system is rotating, periodic linear and/or torsional forces are generated which are perpendicular to the axis of rotation. The periodic nature of these forces is commonly experienced as vibration. These off-axis vibration forces may exceed the design limits of individual machine elements, reducing the service life of these parts. For instance, a bearing may be subjected to perpendicular torsion forces that would not occur in a nominally balanced system, or the instantaneous linear forces may exceed the limits of the bearing. Such excessive forces will cause failure in bearings in short time periods. Shafts with unbalanced masses can be bent by the forces and experience fatigue failure.

Under conditions where rotating speed is very high even though the mass is low, as in gas turbines or jet engines, or under conditions where rotating speed is low but the mass is high, as in ship propellers, balance of the rotating system should be highly considered, because it may generate large vibrations and cause failure of the whole system.

Related Research Articles

Isaac Newton's rotating bucket argument was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the "properties, causes, and effects" of "true motion and rest" that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to what?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.

<span class="mw-page-title-main">Coriolis force</span> Force on objects moving within a reference frame that rotates with respect to an inertial frame

In physics, the Coriolis force is an inertial force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

<span class="mw-page-title-main">Precession</span> Periodic change in the direction of a rotation axis

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment.

<span class="mw-page-title-main">Gyroscope</span> Device for measuring or maintaining orientation and angular velocity

A gyroscope is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.

<span class="mw-page-title-main">Centrifugal governor</span> Mechanism for automatically controlling the speed of an engine

A centrifugal governor is a specific type of governor with a feedback system that controls the speed of an engine by regulating the flow of fuel or working fluid, so as to maintain a near-constant speed. It uses the principle of proportional control.

<span class="mw-page-title-main">Artificial gravity</span> Use of circular rotational force to mimic gravity

Artificial gravity is the creation of an inertial force that mimics the effects of a gravitational force, usually by rotation. Artificial gravity, or rotational gravity, is thus the appearance of a centrifugal force in a rotating frame of reference, as opposed to the force experienced in linear acceleration, which by the equivalence principle is indistinguishable from gravity. In a more general sense, "artificial gravity" may also refer to the effect of linear acceleration, e.g. by means of a rocket engine.

<span class="mw-page-title-main">Balance shaft</span> Weights used to balance otherwise unbalanced engine movement

Balance shafts are used in piston engines to reduce vibration by cancelling out unbalanced dynamic forces. The counter balance shafts have eccentric weights and rotate in opposite direction to each other, which generates a net vertical force.

<span class="mw-page-title-main">Rolling</span> Type of motion which combines translation and rotation with respect to a surface

Rolling is a type of motion that combines rotation and translation of that object with respect to a surface, such that, if ideal conditions exist, the two are in contact with each other without sliding.

Engine balance refers to how the inertial forces produced by moving parts in an internal combustion engine or steam engine are neutralised with counterweights and balance shafts, to prevent unpleasant and potentially damaging vibration. The strongest inertial forces occur at crankshaft speed and balance is mandatory, while forces at twice crankshaft speed can become significant in some cases.

The Eötvös effect is the change in measured Earth's gravity caused by the change in centrifugal acceleration resulting from eastbound or westbound velocity. When moving eastbound, the object's angular velocity is increased, and thus the centrifugal force also increases, causing a perceived reduction in gravitational force.

<span class="mw-page-title-main">Gyro monorail</span> Single rail land vehicle

The gyro monorail, gyroscopic monorail, gyro-stabilized monorail, or gyrocar are terms for a single rail land vehicle that uses the gyroscopic action of a spinning wheel to overcome the inherent instability of balancing on top of a single rail.

In rail terminology, hammer blow or dynamic augment is a vertical force which alternately adds to and subtracts from the locomotive's weight on a wheel. It is transferred to the track by the driving wheels of many steam locomotives. It is an out-of-balance force on the wheel. It is the result of a compromise when a locomotive's wheels are unbalanced to off-set horizontal reciprocating masses, such as connecting rods and pistons, to improve the ride. The hammer blow may cause damage to the locomotive and track if the wheel/rail force is high enough.

<span class="mw-page-title-main">Balancing machine</span>

A balancing machine is a measuring tool used for balancing rotating machine parts such as rotors for electric motors, fans, turbines, disc brakes, disc drives, propellers and pumps. The machine usually consists of two rigid pedestals, with suspension and bearings on top supporting a mounting platform. The unit under test is bolted to the platform and is rotated either with a belt-, air-, or end-drive. As the part is rotated, the vibration in the suspension is detected with sensors and that information is used to determine the amount of unbalance in the part. Along with phase information, the machine can determine how much and where to add or remove weights to balance the part.

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed.

Rotordynamics is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotor dynamics is concerned with one or more mechanical structures (rotors) supported by bearings and influenced by internal phenomena that rotate around a single axis. The supporting structure is called a stator. As the speed of rotation increases the amplitude of vibration often passes through a maximum that is called a critical speed. This amplitude is commonly excited by imbalance of the rotating structure; everyday examples include engine balance and tire balance. If the amplitude of vibration at these critical speeds is excessive, then catastrophic failure occurs. In addition to this, turbomachinery often develop instabilities which are related to the internal makeup of turbomachinery, and which must be corrected. This is the chief concern of engineers who design large rotors.

<span class="mw-page-title-main">Tire balance</span>

Tire balance, also called tire unbalance or tire imbalance, describes the distribution of mass within an automobile tire or the entire wheel on which it is mounted.

<span class="mw-page-title-main">Centrifugal force</span> Type of inertial force

In Newtonian mechanics, the centrifugal force is an inertial force that appears to act on all objects when viewed in a rotating frame of reference. It is directed radially away from the axis of rotation. The magnitude of centrifugal force F on an object of mass m at the distance r from the axis of rotation of a frame of reference rotating with angular velocity ω is:

Rotating unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass, or rotor, is said to be out of balance when its center of mass is out of alignment with the center of rotation. Unbalance causes a moment which gives the rotor a wobbling movement characteristic of vibration of rotating structures.

A circle-throw vibrating machine is a screening machine employed in processes involving particle separation. In particle processes screening refers to separation of larger from smaller particles in a given feed, using only the materials' physical properties. Circle throw machines have simple structure with high screening efficiency and volume. However it has limitations on the types of feed that can be processed smoothly. Some characteristics of circle-throw machines, such as frequency, vibration amplitude and angle of incline deck also affect output.

References

  1. Gaetano Lanza (2009). Dynamics of Machinery (Reprint of 1911 ed.). BiblioBazaar. p. 112. ISBN   978-1-103-19721-7.
  2. Owen, David. "How to Balance a Bicycle Wheel".