Rotor Balancing

TYPES OF ROTORS

Depending on the position of the main mass of the rotor (M), it can be between-bearing, if a substantial part of the mass is located between the bearings (Fig. 1, a); overhung (cantilever), if it is located beyond one of the end bearings (Fig. 1, b); double overhung (double cantilever) with a substantial part of the mass located beyond both end bearings (Fig. 1, c). Mixed variants of the main mass location are also possible (Fig. 1, d). In Fig.1, m denotes the distributed mass of the rest of the rotor; A, B - bearings; l - distance between bearings; 1 and 2 - correction planes;  a_i - distances from the correction planes to the bearings.

A rotor in which the relative arrangement of masses changes during rotation, and which has at least one flexible or elastically mounted element, is called a rotor with variable geometry.

If, for a rotor balanced at a rotational speed lower than the first critical speed in two arbitrary correction planes, the values of the residual unbalances do not exceed the permissible limits at rotational speeds up to the maximum operational speed, such a rotor is called rigid. The first critical speed of a rigid rotor is much higher than its operational rotational speed.

Accordingly, a flexible rotor is one for which, after balancing at a rotational speed lower than the first critical speed in two arbitrary correction planes, the values of the residual unbalances may exceed the permissible limits at other rotational speeds up to the maximum operational speed.

Based on materials from the book: 

Gusarov A.A. Rotor Balancing of Machines. M.: Nauka, 2004

BASIC METHODS OF UNBALANCE CORRECTION

Unbalance correction is performed by adding/removing mass or by shifting the rotor axis (mass centering). The chosen correction method must guarantee that there is free space for adding/removing material sufficient to eliminate the maximum possible unbalance for this product. The ideal correction method implies finding the smallest initial unbalance. However, this is often difficult to achieve.

Conventional unbalance reduction methods allow achieving an unbalance reduction ratio of 10/1 in one run with careful machine setup.

Correction by adding mass, especially on fully automatic machines, can achieve a ratio of 20/1 in one run. If a sufficient unbalance level is not achieved in one run, the next run is performed, and so on.

CORRECTION BY ADDING MASS

• Adding a two-component epoxy compound. The disadvantage of this method is that it is difficult to position the compound so that its center of gravity is exactly in the right place.
• Adding standard weights. This method is fast, but its application is limited by the fact that the mass increment of the weights is quite large, so sufficient accuracy cannot be achieved.
• Adding weight by welding, i.e., applying molten metal to the rotor surface in the right place. Measures must be taken to prevent thermal deformation and damage to the rotor.

REMOVING MASS

• Drilling. Material is removed from the rotor by drilling to a certain depth. This is the most effective method of unbalance correction.
• Milling. Material is removed by milling to a certain depth and length. Used when it is necessary to remove fairly large masses.
• Grinding. Material is removed by a grinding wheel. This method is used quite rarely.

UNITS OF UNBALANCE

Unbalance is measured in gram-millimeters. It is the mass multiplied by the distance of that mass from the axis of rotation, or otherwise the radius of that mass. An unbalance of 100 g·mm, for example, means that one side of the rotor has an equivalent excess mass of 10 grams at a distance of 10 millimeters, or 20 grams at a distance of 5 millimeters. The following figure shows a rotor (side view) with an unbalance of 100 g·mm.

The same mass creates different unbalances depending on its distance from the axis of rotation. When determining unbalance, the mass is simply multiplied by its distance to the axis of rotation, or by the radius of that mass. Although the same mass creates the same unbalance at any rotational speed, the permissible residual unbalance is different for different rotating bodies.

As a rule, the higher the rotational speed of the rotor, the smaller the residual unbalance is allowed, and vice versa. In the absence of unbalance, the centrifugal force that creates vibration will no longer arise. Some residual unbalance always remains, and one has to accept this, just like a tolerance field in machining.

WHY IS BALANCING NECESSARY?

An unbalanced rotor creates vibration that is transmitted to its bearings. A well-balanced rotor means:

• Improved quality of the final product.
• Reduced vibration and noise.
• Minimum stress in the assembly or mechanism structure.
• Minimum power loss in the unit or assembly.
• Extended machine service life.

Unbalance of just one rotating part of a unit or assembly leads to vibration of the entire machine. The vibration caused by this can lead to excessive wear of bearing units, spindles, and mounting surfaces. Vibrations can lead to resonance and cause complete destruction of the mechanism. Operational performance deteriorates due to energy absorption by the support structure.

Excessive vibrations can be transmitted to adjacent machines and significantly harm their accuracy and proper functioning.

Unbalance and Centrifugal Force Centrifugal force acts on the entire mass of the rotating body and causes each particle of this body to strive radially away from the axis of rotation. If the mass of the rotating body is evenly distributed relative to its axis, then the part is balanced and rotates without vibration.

However, if an excess mass exists on one side of the rotor, the centrifugal force acting on this heavy side exceeds the centrifugal force arising on the opposite side and pulls the entire rotor in the direction of the heavy side. The following figure shows a rotor (side view) with an excess mass on one side. Due to the centrifugal force created by the mass, the entire rotor tends to shift in the direction of the arrow.

The centrifugal force increases with the square of the rotational speed of the body having an uneven mass distribution, meaning unbalance will occur due to the excess centrifugal force caused by the rotation of the heavier side of the rotor. When the body is at rest, the excess mass does not cause centrifugal force and, consequently, vibration, but the unbalance still exists, and therefore unbalance is a quantity independent of the rotational speed and remains the same in a stationary body and during rotation (in the absence of deformation during rotation).

The centrifugal force, however, depends on the rotational speed. The higher the speed, the greater the centrifugal force caused by the unbalance and the stronger the vibration. The centrifugal force increases quadratically; when the rotational speed doubles, the centrifugal force increases four times, etc. This is why the higher the rotational speed, the more important balancing becomes.

CAUSES OF UNBALANCE

An excess of mass on one side of the rotor in the figure is unbalance or a "heavy spot". Unbalance can also arise from a lack of mass (holes, cavities, pits) and these places are called "light spots".

Unbalance can be caused by the following:

• Manufacturing defects, including machining and assembly defects.
• Changes in material structure (porosity, foreign inclusions).
• Asymmetric part design.
• Asymmetry arising during operation as a result of the movement of any parts.

A symmetrical design and correct assembly can often minimize problems related to balancing. A large unbalance requires significant correction. The need for balancing should be considered at the rotor design stage.

TYPES OF UNBALANCE

Next, four different types of unbalance, as defined by the International Organization for Standardization, will be presented. An illustration will be provided for each of the four mutually exclusive cases.

STATIC UNBALANCE

Static unbalance occurs when the principal axis of inertia is displaced parallel to the axis of rotation.

This type of unbalance typically occurs in thin parts such as various impellers and turbines. This type of unbalance can be corrected by placing an additional mass opposite the center of gravity in a plane perpendicular to the axis of rotation. Static unbalance can be detected by placing the rotor on two precisely horizontally aligned knife edges. The rotor will then turn until it reaches an equilibrium position where the "heavy spot" is at the very bottom.

The application of this method is very limited due to low accuracy. Static balancing is sufficient only for bodies rotating at low speeds up to 500 rpm.

COUPLE UNBALANCE

Unbalance in which the principal axis of inertia intersects the axis of rotation at the center of gravity.

This type of unbalance occurs when two unbalance sources are placed on opposite sides of the rotor and the angle between them is 180°. In this case, the static method of unbalance detection is completely inapplicable. Simply impart some angular velocity to a body with this type of unbalance, and the unbalance is easily detected and measured. This type of unbalance cannot be corrected by adding or removing mass in a single location. At least two such locations are required. In other words, couple unbalance needs another couple for its correction.

QUASI-STATIC UNBALANCE

This is unbalance in which the principal axis of inertia intersects the axis of rotation at a point other than the center of gravity.

This type of unbalance is a combination of static unbalance and couple unbalance, where the angular position of one component of the pair coincides with the angular position of the static unbalance. It is a special case of dynamic unbalance.

DYNAMIC UNBALANCE

This is unbalance in which the central principal axis of inertia is neither parallel to nor intersects the axis of rotation.

This is the most common type of unbalance, which can be corrected by mass correction in at least two planes perpendicular to the axis of rotation. Dynamic unbalance is a combination of static unbalance and couple unbalance, where the angular position of the static unbalance relative to the couple unbalance is neither 0° nor 180°.