A new method of data presentation for machine vibration analysis
3, Svishtovskaja str., Kremenchug, Poltavskaja region, Ukrain
" The imagination is more important than knowledge"
The objects of the vibration measurements and investigations are first of all the bearing cages. When we consider the vibration of a measurement point in three orthogonal directions, we find that the point during oscillation moves by a trajectory of a complicated, almost always closed loop, the form of which varies in time.
The general theory of image identification is considered to be the theoretical basis of technical diagnostics.
The diagnostic algorithms or the algorithms of identification use the diagnostic models and models of faults. The diagnostic models define the relationship between the system condition and its image in the space of diagnostic symptoms. The models of faults that are investigated in the theory of reliability enable to predict the time of possible failure.
The theory of image identification proposes two main methods - probabilistic and deterministic approaches. The probabilistic approach uses the statistical relationship between the system condition and diagnostic parameters. As a result of realization of some algorithm a most probable diagnosis and if possible its certainty are defined.
The deterministic method defines the relationship between the system condition and the coordinates in the space of diagnostic parameters on the basis of investigated consistent patterns, particularly by the use of theory of oscillations.
Let us use the concept of virtual modeling as a component of deterministic approach.
When we make the measurements of vibration levels by the transducers of the same type, in the same frequency range (as a rule), in the same units, and we know that a point moves in the space by a certain trajectory - orbit, we know that the reciprocal arrangements of measurement points reflects the real configuration of the object in the current time.
Let us consider the movement of a measurement point in a given coordinate system. The vibration levels of the point, for example, t2 are V = 4.5 mm/s, H = 7.1 mm/s, A = 11.2mm/s. On orthogonal measurement directions - vectors we indicate these values. When we connect all the ends of the vectors we get an area - a triangle of the measurement point space position. Take into account the fact that two rotors (for example the driving rotor and the driven rotor) are positioned on the same axis.
As the constructed triangle is arranged under some angle against the main axes and its visual perception is disturbed we shall transfer it from the 3D coordinate to a plane one with the distribution of the vectors under 120 degrees.
For visual demonstration let us use the clock-face. The radial directions – vertical and horizontal we shall use as the basic plane. The vibration vertical vector we shall direct in the 12 o'clock direction, the vector of the horizontal vibration we shall direct in the 4 o'clock direction, and the vector of the axial vibration we shall direct in the 8 o'clock direction.
The graphical transform of the measurement point coordinate is made only to display the information on the monitor screen (the stage of modeling the prism). The real trajectory of the point’s movement looks different.
The zero coordinates of the image scanning planes are laid on the main axes of the machine. Besides this these planes are perpendicular to the shaft line. The triangles that simulate in our case the bearing units reflect the position of the bearing cases: point 1 – the rear bearing of the driver, point 2 – the front bearing of the driver, point 3- the front bearing of the pump, point 4 – the rear bearing of the pump.
The distribution of boundaries between the directions of measurements is made by dividing the triangle into three rhombs. Each rhomb is colored in the color that corresponds the targeted signal level depending on the point’s vibration magnitude in the given direction.
For each case the whole triangle or some of its vertexes toggle its color to red, yellow or green according to the value of the vibration in comparison of the corresponding alert, warning or normal levels of vibration in corresponding directions.
When we conduct this operation for each measurement point we shall make the next stage – signal level settings.
If we connect the vertexes of the triangles with each others (Vt1, Vt2, Vt3, Vt4; Ht1, Ht2, Ht3, Ht4; At1, At2, At3, At4) we shall obtain a space figure – a three edge prism – a space model of a machine.
Depending on the machine construction and the number of measurement points the constructed 3D figure has additional diagnostic symptom – a visual image.
The theory of image identification is enriched by a new visual symptom.
The succeeding vibration measurements conducted on the controlled machine and added to the data base will result in changes of the model condition, its spatial image and signature. Here signature is a standard set of controlled vibration parameters, including the parameters of vibration spectra, that correspond to the normal machine condition.
The part of the prism between the points t2 and t3 does not belong to one solid rotor and requires some arrangement.
Let us discuss an additional area for analysis – the joint coupling. We know the constructive dimensions of the machine and coordinates of the measurement points, the distance between the points on the main machine axes and the height of point on the perpendicular to the shaft. When we have the coordinates of the points t1 (R t1) and t2 (R t2), the radius of the flange of the joint coupling (R jc), the distance between t1 and t2 we can extrapolate these data and obtain an imaginary point t2’ - the place of connection on the driver side. Conducting the same analysis with the points t3 and t4 we get the point t3’ – the connection from the pump side.
As a result of further construction we have two additional space triangles and the boundary of conditional split of the prism.
By using in our measurements a transducer for reference signal we can see the phase of the vibration vector in the space of each support.
The diagnostics defect symptoms of the company “Predict DLI” define the misalignment (parallel) as follows:
- 2X (R) or (T) ? 95 VdB
so the signal exceeds the standard ?2 VdB
on both sides of the joint coupling.
- 2X (R) ? 1X (R) or
2X (T) ? 1X (T)
on one side of the joint coupling.
- Maximum 2X ? 101 VdB or
the sum of the threshold levels crossing 2X ? 18 VdB
at least on one side of the joint coupling.
1., 2., 3., the phase shift is 180 degrees on both sides of the coupling.
The modeling of misalignment on the virtual model is displayed as a convolution of virtual space triangles t2’ and t3’ in points. Visual are only the vectors of vibration that are directed 180 degrees against each other.
When there are no measurements in one of the directions the angular point of the triangle, that corresponds this direction, coincides with the zero point of the coordinates and lays on the main axis of the aggregate.
The system of interactive modeling of a technical condition aggregate – CINEMATES, is a shell that displays on the screen of the computer a spatial model of the aggregate as a whole, all the points, all the measurements simultaneously.
Receiving the results of measurements the computerized program processes the data and displays on the screen a series of moving 3D animated pictures, that reproduce the vibration of the controlled aggregate’s points on the selected frequencies, the prism deviates.
CINEMATES is an alternative to the traditional presentation of the visual data of machine vibration analysis.
- A.S. Goldin Vibration of Rotating Machines.
- Ronald L. Eshleman. Machinery Vibration Analysis I.
- Mechanical Vibration of Machines II. SCHENCK AG.
- Introduction to Machine Vibration by Glenn White, CD-ROM dick, “PREDICT/DLI” (USA), “Octava +” (Russia).
- Power Point Presentation, ExpertALERTTM, “PREDICT/DLI” (USA), “Octava +” (Russia).
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