Theoretical basis of balancing
General terms

Rotor - a body that, when rotated, is held by its bearing surfaces in supports.

Unbalance - the state of the rotor, characterized by a mass distribution that during the rotation causes variable loads on the rotor supports and its bending.

There are static, moment, dynamic and quasi-static unbalances.

Mass eccentricity

- position vector of the center of mass in question relative to the axis of rotor.

Unbalance

- a vector quantity equal to the unbalanced mass multiplied by its eccentricity.

Mass eccentricity

position vector of the center of the mass in question relative to the axis of the rotor.

Unbalance value

- numeric value, equal to the the unbalanced mass multiplied by its eccentricity module.

Unbalance angle

- angle determining the position of the unbalance vector in the coordinate system related to the axis of rotor.

Correction mass

- mass used to reduce rotor unbalance

Correction plane

- plane, perpendicular to the axis of rotor, in which the center of the correction mass is located.

- plane, perpendicular to the axis of rotor, in which the value and the angle of unbalance are set.

Unbalance measurement plane

- plane, perpendicular to the axis of the rotor, in which the value and the angle of unbalance are measured.

Initial unbalance

- unbalance in the plane, perpendicular to the axis of the rotor, before correcting its masses.

Residual unbalance

- unbalance in the plane under examination, perpendicular to the axis of the rotor, which remains in it after correcting its masses.

Acceptable unbalance

- the biggest acceptable residual unbalance in the plane, perpendicular to the axis of the rotor.

Specific unbalance

- ratio of the main unbalance vector modulus to the rotor mass. Specific unbalance determines eccentricity of center of mass of the rotor.

Acceptable specific unbalance

- the biggest appectable specific unbalance.

Minimum achievable residual specific unbalance

- the smallest value of the residual specific unbalance that can be achieved on the machine while balancing the control rotor by method determined in the instructions for this machine.

Balancing
Rotor balancing

- process of determining values and angles of unbalances of the rotor and reducing them by adjusting its masses.

Static balancing

- balancing, during which main vector of unbalances of the rotor is determined and reduced, characterizing its static unbalance.

Moment balancing

-balancing, which determines and reduces the main moment of unbalances of the rotor, characterizing its momentary unbalance.

Dynamic balancing

- balancing, during which the unbalances of the rotor are determined and reduced, characterizing its dynamic unbalance.

I-first correction plane, II-second correction plane.

Balancing machines
Balancing machine

- machine that determines the unbalances of the rotor to reduce them by adjusting the masses. It is a necessary technological equipment for dynamic balancing and static balancing in dynamic mode.

Static balancing machine

- balancing machine, which determines only the main vector of unbalances.

Dynamic balancing machine

- balancing machine, which determines unbalances on the rotor rotated by it.

Hard-bearing balancing machine

- a dynamic balancing machine whose rotational speed for balancing is lower than the lowest natural oscillation frequency of the system consisting of a rotor and a parasitic mass.

Resonance balancing machine

- a dynamic balancing machine whose rotational speed during balancing is equal to the natural oscillation frequency of the system consisting of a rotor and a parasitic mass.

Soft-bearing balancing machine

- a dynamic balancing machine whose rotational speed for balancing is higher than the highest natural oscillation frequency of the system consisting of a rotor and a parasitic mass.

Balancing mandrel

- a balanced shaft on which the product to be balanced is mounted.

Finding the necessary accuracy of balancing. Method of calculation
Balancing accuracy classes according to GOST ISO 22061­76
mm*rad/s or balancing accuracy classes according to ISO 1940
Rotor types
1 0,4 Spindles, grinding wheels and rotors of electric motors of precision grinding machines. Gyroscopes.
2 1,0 Drives of tape recorders and players. Drives of grinding machines. Rotors of small special purpose electric motors.
3 2,5 Gas and steam turbines, including the main turbines of merchant vessels. Turbogenerators with rigid rotors. Turbochargers. Drives of metalworking machines. Rotors of medium and large electric motors with special requirements. Rotors of small electric motors. Turbopumps
4 6,3 Parts of technological equipment. Main reducers of merchant vessel turbines. Drums of centrifuges. Fans. Rotors of aviation gas turbine engines in collection. Flywheels. Impellers of centrifugal pumps. Parts of machine tools and general-purpose machines. Rotors of conventional electric motors. Separate engine parts with special requirements.
5 16 Drive shafts (shafts of ship propellers, cardan shafts) with special requirements. Crusher parts. Parts of agricultural machinery. Separate parts of engines (gasoline or diesel) of cars, trucks and locomotives. Engine crankshaft assembly with six or more cylinders with special requirements.
6 40 Crankshaft assembly of high-speed diesel with six or more cylinders. Engines in assembly (petrol and diesel) for cars and trucks and locomotives.
7 100 Car wheels, wheel rims, tyres, drive shafts, brake drums of the car, wheel pairs.
Balancing accuracy classes system

2. Using the graph shown in Figure 1.4, knowing the maximum operational speed of the product, draw a vertical line up to the intersection with the upper boundary of the selected class and, on the ordinate axis, find the value of the specific unbalance et.

Fig.1.4. Dependence graph of specific unbalance on rotor speed and balance accuracy class

3.Determine main vector of acceptable unbalance of the rotor by formula:

Ds.a. = еt * mrotor - Ds.t. - Ds.o.,

where еt - tabular value of specific unbalance;

Ds.t. - value of the main vector of product's technological unbalances, resulting from assembly of the rotor, due to mounting of parts (pulleys, half-couplings, bearings, fans, etc.) that have their own unbalances, due to deviation of shape and arrangement of surfaces and seats, radial clearances etc;

Ds.o. - value of the main vector of a product's operational unbalances arising from uneven wear, relaxation, burning, cavitation of the rotor parts, and so on for the given technical resource or before the repair, which includes balancing.

As practice has shown, in most cases, if we choose the specific unbalance at the lower boundary of the accuracy class (with specific unbalance 2.5 times lower than specific imbalance, determined for the upper class boundary), the main vector of the acceptable unbalance can be calculated from the formula:

Ds.a = еt * mrotor.

4. Main vector of acceptable unbalance is recalculated into the acceptable unbalances of the correction planes (D1 and D2) by the ratio of distances from the center of mass of the rotor to these planes (a special case for the inter-bearing type of rotor).

Da1 = Ds.a. * (L2/(L1+L2));

Da2 = Ds.a. * (L1/(L1+L2));

Ds.a. = Da1 + Da2.