Manufacturing Trend 2010/10, Technical Diagnostics Section

"Instead of firefighting and major repairs"

It is not sufficient to identify the problems of machines using various diagnostic methods; action must also be taken to eliminate them, otherwise the continuity of production will hardly be sustainable.

Resolving numerous machine faults – even quite serious ones – may involve assembly, but two, namely the most common types of faults, can be relatively easily solved: dynamic balancing of rotating parts and – on machines with clutches – alignment of the shaft axis. Both interventions – which moreover require no additional material or tools – should be carried out as soon as possible: by eliminating the overload of bearings, their service life can be extended, and premature replacement will not be necessary.

Dynamic Balancing

In the world of rotating machinery, imbalance is the most common fault. It should be noted that imbalance is always present, it just may not reach the threshold to be considered a fault. There is no perfectly balanced rotating part, only one that meets our expectations and the requirements of relevant standards.

We speak of imbalance when the center of gravity of a rotating part does not coincide with its axis of rotation. Depending on how these axes relate to each other, the following types of imbalance are distinguished:

• in the case of static imbalance, the axis of rotation and the center of gravity are parallel
• we talk about couple, opposite, or torque imbalance when the axis of rotation and the center of gravity intersect at an angle
• in the case of dynamic imbalance, the axis of rotation and the center of gravity are deviated

Centrifugal Force

Due to the fact that the center of gravity (or centerline) and the axis of rotation (or rotational axis) do not coincide, centrifugal force occurs. This force burdens the support of the rotating part: the bearings and structural elements. The resulting centrifugal force naturally rotates around the axis of rotation with the same frequency as the axis itself. The centrifugal force resulting from imbalance

can be calculated based on the following equation: F = m × r × ω² where F is the centrifugal force, m is the unbalanced mass, r is the distance of the unbalanced mass from the center of rotation, and ω is the angular velocity (angular frequency). As implied by the equation, the centrifugal force is quadratically dependent on the rotational speed, so eliminating imbalance is particularly important for machines with higher speeds. The centrifugal force performs circular motion, so the force acting on a distinguished point of the bearings or the structure is not constant but shows sinusoidal pulsation: it reaches its maximum once and then its minimum within one revolution.

Equation: F(t) = m × r × ω² × sin(ω×t)

To counteract this force, bearings and the structure must exert an equal and opposite force to keep the rotating part in place. The resulting motion – the vibration measured on the bearing housings – also depends on the stiffness of the structure. Therefore, the vibration measured on the supports, bearing housings (hereinafter bearings) is – exclusively in the case of imbalance – proportional to the centrifugal force. Based on this realization, we can determine the extent of imbalance and perform balancing. This can be done on a balancing machine or on-site, using the machine's own bearings. In this article, we do not discuss balancing on a machine; on-site balancing can be done depending on the instrumentation either with the so-called three-point method or with the vector method based on amplitude-phase measurement.

Three-Point Method

This method is used to eliminate the imbalance of disc-shaped rotating parts and is the simplest way of balancing: it only requires a manual vibration meter. Satisfactory results can be achieved with five to six runs. The steps of balancing are as follows:

1) Start the machine and measure the radial vibration velocity of the bearing at the operational speed of the rotating part (v0). 2) Determine the required trial weight (P) and attach it to any location. 3) Start the machine and measure the vibration velocity (v1). 4) Move the trial weight 120º from the previous position and measure the bearing vibration (v2). 5) Move the trial weight another 120º and measure the vibration (v3). 6) Plot the measured values v1, v2, v3 on a 120º coordinate system in the same rotational direction as the numbering of the rotating part, with a suitably chosen scale. 7) Construct the center of the circle passing through the endpoints of the vectors (A). Connect the origin and point A to determine the direction of imbalance. Mark this direction on the rotating part. 8) Place the trial weight 180º opposite to the direction of imbalance, then perform vibration measurement (v4). 9) The magnitude of imbalance and the mass required for balancing can be calculated from the measured data using the following relationship:

For the success of the procedure, it is essential that the vibrations involved in the calculation originate mainly from imbalance. However, manual vibration meters are not suitable for determining this, as they measure the wideband level rather than the rotational frequency component of the vibration. Therefore, for balancing, a frequency analyzer should preferably be used. The main disadvantage of the procedure is that a large number of at least six starts are required together with the check to perform the balancing. This high number of starts is often not feasible due to the characteristics of the machine or it may take an extremely long time.

Vector (trial weight-based) method

The basis of the procedure is the vibration vector measured in the radial direction of the rotating part to be balanced, i.e., the rotational frequency vibration amplitude, and its phase. The phase angle describes the angular position of the unbalanced weight relative to a defined point (reference marking) on the rotating part. This angular position depends on the machine's elasticity and time constant (i.e., its mechanical system properties), as well as on the phase measurement parameters of the used measuring system (measurement principle, application of integration or double integration, signal processing delay, etc.). All these factors are constants for a given machine and measuring system, but can vary significantly between different machines and instruments. At the beginning of a new balancing, we cannot know where the additional mass causing the imbalance is located. Therefore, we are forced to create a change in the system with a mass placed at a known magnitude, known angular position, and radius, and thus determine the machine's reaction to imbalance and its sensitivity.

As an example, we present a single-plane balancing: the measured vibration vector (red) after intervention is the sum of the original R vibration vector (black) and the effect vector T of the trial mass (green). The original vector and the effect vector can determine the magnitude of the original imbalance, i.e., the required correction mass:

The angle enclosed by the original and effect vectors shows how many degrees the correction mass should be placed relative to the trial weight. In our example, the trial weight must be removed after the measurement (if you want to keep it, then the equation should consider the R+T vector instead of the R vector). For simplicity and ease of understanding, we have described the process of single-plane balancing. This method provides satisfactory results when balancing disc-shaped rotating parts. For more complex or "long" rotating parts, two-plane or multi-plane balancing is necessary.

 

The machine's reaction to imbalance and its sensitivity can be described, for example, using the so-called response matrix. For each balancing plane, this matrix contains the effect of the unbalanced weight on itself and on the other planes of the machine. In the case of two-plane balancing, the response matrix may look like this:

a11= 0.0948653 mm/s b11= 169.8548317° a21= 0.0624921 mm/s b21= 190.5289268° a22= 0.1141621 mm/s b22= 346.5672016° a12= 0.991200 mm/s b12= 282.560746°

Interpretation of the response matrix

For simplicity, let's assume that our machine is in a balanced state. If we mount 1 unit of weight at 1 unit of radius, at 0-degree angular position on the first balancing plane, then the vibration at the measuring point corresponding to plane 1, with a frequency of rotation, increases by magnitude a11 in the direction of phase angle b11, and at the measuring point corresponding to plane 2, it increases by magnitude a21 in the direction of phase angle b21 (due to the cross-coupling). If we then move the above weight from plane 1 to plane 2, the vibration at the measuring point corresponding to plane 1 increases by magnitude a12 in the direction of phase angle b12 (due to the cross-coupling), and at the measuring point corresponding to plane 2, it increases by magnitude a22 in the direction of phase angle b22. This practically represents the sensitivity to machine imbalance, based on which, for a subsequent balancing of the same machine (assuming sensors and rotation reference are mounted in the same position and angle), trial weight measurements are no longer necessary. Only based on the current vibration (amplitude and phase angle), the required balancing weights and positions can be calculated. (The unit weight and radius depend on the units used during the recording of the response matrix: if the weights are given in grams and the radius in mm, then for the interpretation of the response matrix, we take the values of unit weight=1 gram and unit radius=1 mm as a basis.)

Permissible residual imbalance

Since, as mentioned in the introduction, perfectly balanced rotating parts do not exist, we always encounter residual imbalance. The permissible level of residual imbalance for different machine types is defined by ISO 1940 standard. This standard classifies machines based on the circumferential speed of the center of mass displacement of the rotating parts (see our table) and determines the residual specific imbalance (the deviation of the center of mass from the rotation axis during rotation) in the emeg value.

 

Classification of Machines according to ISO 1940

Balancing Class	Types of Rotating Parts (general examples)                                             (source: Energopenta)
G1600	Stable crankshaft drives, rigidly mounted two-stroke engine crankshafts, drives
G630	Rigidly mounted large four-stroke engine crankshafts, drives. Flexibly mounted ship diesel engine crankshafts
G250	Rigidly mounted fast four-cylinder diesel engine crankshafts, drives
G100	Stable crankshaft drives, fast rotating six- or multi-cylinder diesel engine crankshafts, drives, complete engines for cars, trucks, diesel locomotives
G40	Auto parts, wheel discs, drive shafts. Multi-cylinder four-stroke flexibly mounted fast engines
G16	Articulated shafts with special requirements, components of breaking machines and agricultural machinery, certain parts of passenger and commercial vehicle engine crankshafts. Crankshafts of six- or multi-cylinder engines with special requirements
G6.3	Components of processing plant machinery: centrifuge drums, rollers of paper industry machines, fans, assembled rotating parts of aircraft gas turbines, pump impellers, components of machines and machine tools, rotating parts of general electric motors, individual components of motors meeting special requirements
G2.5	Rotating parts of jet engines, gas and steam turbines (including marine main turbines), rigid turbo-generators, rotating parts, turbo compressors, drives of machine tools, medium and large electric armatures meeting special requirements, rotating parts of small motors, turbine-driven pumps
G1	Drives of tape recorders and turntables, grinder drives, small electric armatures meeting special requirements
G0.4	Rotating parts, shafts, and discs of precision grinders, gyroscopes

Rahne Eric (PIM Ltd.) pim-kft.hu, gepszakerto.hu

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