On the Calculation of Vibrations of the Frame of DC Machines with Wide Speed Regulation
Abstract Generated abstract
This paper examines vibrations of the frames of series P direct-current motors with wide speed regulation, emphasizing magnetic-origin vibrations as a major component of vibroacoustic performance. Using vibrometer and frequency-analyzer measurements on a model installation, the authors compare frame vibration patterns with and without bearing end shields across the 1500 to 4000 rpm speed range and relate observed resonances to calculated natural frequencies for radial and flexural modes. The study finds that different frame sections have distinct resonant frequencies, so resonating regions can occur throughout the operating range, and that measured spatial deformation patterns often differ from simplified theoretical mode shapes. Bearing end shields reduce vibration levels by about 7 to 10 dB, shift resonant frequencies upward, and substantially alter circumferential vibration distributions, leading the authors to recommend vibration testing at multiple resonant speeds rather than at a single operating speed.
Full Text
ON THE CALCULATION OF VIBRATIONS OF THE FRAME OF DC MACHINES WITH WIDE-RANGE SPEED CONTROL
E. E. DUTLOV, K. A. KHOR'KOV
(Presented by the scientific seminar of the Departments of Electrical Machines and Apparatus and General Electrical Engineering)
The operation of electrical machines is inevitably accompanied by the occurrence of vibrations. Vibrations arise from alternating magnetic forces and from technological defects in the manufacture of the machine (inaccuracy in the installation of ball bearings, displacement and inclination of the shaft rotation axis, etc.).
At present, the vibroacoustic characteristics of a machine are becoming one of the principal indicators of the quality and reliability of electrical machines. From year to year, the requirements imposed on vibration-acceleration levels are steadily increasing.
One of the tasks of work on the modernization of electrical machines for the purpose of reducing vibration levels is to determine the reserves present in the design of existing series.
In this connection, vibrations of magnetic origin are of particular interest, since, as a rule, they predominate in the vibration-acceleration spectrum and are the most difficult to reduce.
The present work is devoted to a study of vibrations of the frame of series “P” DC motors of the fourth frame size with \(2p=4\) and a speed-control range from 1500 to 4000 rpm. The instruments used for measuring vibrations were: an SM-2I vibrometer with a KD-13 pickup, and a Marconi frequency analyzer. The vibrations of the frame were studied on a special model installation with the armature mounted in pedestal bearings. The machine frame was installed on shock absorbers. The elastic mounting of the frame should not substantially distort the spatial form of its deformation. The motor was tested under no-load conditions.
Figure 1 presents typical vibrograms of the three most characteristic sections of the frame, located along the axis of the main pole, along the axis of the interpole, and in the middle of the section between the pole axes, in the absence of bearing shields. Figure 2 presents vibrograms of these same points with bearing shields present.
From Fig. 1 it is evident that there are several resonant speeds for each section of the frame. For the section of the frame along the axis of the main pole, resonances occur at speeds of 1700, 2000, 2300, 2900, and 3750 rpm; for the section of the frame along the axis of the interpole, resonances occur at speeds of 1650, 2000, 2900, and 3850 rpm; and for the section between the poles, resonances occur at 1620, 2020, 2300, 2900, and 3850 rpm.
Fig. 1. Vibration diagram of the frame without bearing shields: a) the sensor is installed along the axis of the main pole, b) the sensor is installed along the axis of the commutating pole, c) the sensor is installed at the center of the interpole space.
These speeds correspond to vibration-acceleration frequencies (measured by a spectrum analyzer and coinciding with the first tooth frequency of the field in the machine air gap): 830, 850, 880, 1030, 1180, 1930, 1990 Hz.
The presented vibration pattern is also valid for other combinations of poles, with some deviations in the resonant frequency and in the amplitude of the vibration acceleration.
In general, for the motor frame the following series of resonant frequencies can be written:
770, 775, 830, 850, 880, 980, 1000, 1030, 1180, 1420, 1450, 1500, 1520, 1550, 1800, 1830, 1880, 1930, 1990, and 2030 Hz.
Thus, the experiments showed that over the entire range of control of the motor rotational speed there are resonating sections of the frame.
Calculation of the natural vibration frequencies of the housing for radial bending, taking into account the masses of the main and commutating poles according to the method of [1], gives the following results for the machine under study:
Fig. 2. Vibration diagram of the frame with bearing shields:
a) the sensor is installed along the axis of the main pole, b) the sensor is installed along the axis of the commutating pole, c) the sensor is installed at the center of the interpolar space
\(f_0\) — frequency of purely radial vibrations, \(f_0 = 6050\) Hz;
\(f_1\) — frequency of vibrations relative to the support points, considering them as hinged [2], \(f_1 = 170\) Hz;
\(f_{2,3,4,5}\) — frequencies of flexural vibrations in a plane when the main poles of the machine are located at the antinodes or at the nodes of vibration, respectively:
\[ \begin{aligned} f_2 &= 316 \text{ or } 460 \text{ Hz}, &\qquad f_3 &= 865 \text{ or } 1060 \text{ Hz},\\ f_4 &= 1620 \text{ or } 1570 \text{ Hz}, &\qquad f_5 &= 2600 \text{ or } 1950 \text{ Hz}. \end{aligned} \]
Taking into account the hinged fastening of the supports, according to [2], for the machine under study we have
\[ \begin{aligned} f_2 &= 445 \text{ or } 646 \text{ Hz},\\ f_3 &= 1000 \text{ or } 1230 \text{ Hz}. \end{aligned} \]
The diagram of the distribution of vibration accelerations around the circumference of the frame is presented in Fig. 3. Points 1, 5, 9, 13 correspond to sections of the frame along the axis of the commutating poles; points 3, 7, 11, 15 correspond to sections along the axis of the main poles, and the machine feet are attached along the line of points 7 and 11. The even-numbered points correspond to interpolar sections. The diagram is plotted for the most clearly expressed resonance frequencies of the frame: 980, 1500, and 1990 Hz.
Fig. 3. Distribution of vibration accelerations around the circumference of the frame without bearing end shields:
△ — · — · — \(n = 3850\) rpm, \(\; f_z = 1990\) Hz,
⊙ — — — \(n = 2900\) rpm, \(\; f_z = 1500\) Hz,
× ——— \(n = 1900\) rpm, \(\; f_z = 980\) Hz
According to theory, these frequencies should correspond to vibrations of the plane bending of the frame of the third, fourth, and fifth orders.
The curve of the distribution of vibration accelerations around the circumference of the machine at a frequency of 980 Hz corresponds to vibrations of plane bending of the third order, with clamping of the frame arcs at the points where the feet are attached. We have an almost analogous picture at a frequency of 1500 Hz, and an even more indeterminate picture at a frequency of 1990 Hz, from which it is impossible to establish the order of the frame vibrations with any certainty.
It is interesting to compare the vibrograms of the frame without bearing end shields and with shields. With bearing end shields present, the vibration level decreased by 7–10 dB. Noticeable changes occurred in the values of the resonant speeds. The resonant frequencies most clearly expressed for the points of the frame under consideration are:
930, 970, 1180, 1230, 1290, 1500, 1620, 1700, and 2060 Hz. Only two frequencies, 1180 and 1500 Hz, occur in both series of frequencies.
On the whole, the following series of resonant frequencies is obtained for the machine frame: 930, 970, 1110, 1130, 1180, 1230, 1290, 1340, 1450, 1470, 1500, 1550, 1620, 1650, 1680, 1700, 1730, 1750, 2020, 2040, 2060 Hz.
Thus, the bearing end shields of the machine lead to a reduction in the vibration level of the frame and to a shift of the resonant frequencies toward higher values.
Figure 4 presents a diagram of the distribution of vibration accelerations around the circumference of the frame in the presence of bearing end shields for the most clearly expressed resonant frequencies, 1180, 1680, and 2040 Hz.
Fig. 4. Distribution of vibration accelerations around the circumference of the frame with bearing shields:
| Mark | Line | \(n\) | \(f_z\) |
|---|---|---|---|
| △ | dash-dot | \(3950\ \text{rpm}\) | \(2040\ \text{Hz}\) |
| ⊙ | dashed | \(3270\ \text{rpm}\) | \(1680\ \text{Hz}\) |
| × | solid | \(2270\ \text{rpm}\) | \(1180\ \text{Hz}\) |
If the obtained diagram is compared with Fig. 3, then significant changes are evident in the distribution of vibration accelerations around the circumference of the frame, changes that occurred under the influence of the bearing shields. At a frequency of 1180 Hz (in comparison with the diagram at 980 Hz without shields), the vibrations of the left half of the housing—points 16, 13, 12, and also point 3—decreased significantly, which led to an entirely different appearance of the diagram. The diagrams changed significantly at a frequency of 1680 Hz (in comparison with the diagram at 1500 Hz) and 2040 Hz (in comparison with the diagram at 1990 Hz).
It may be said that the spatial forms of deformation of the machine housing with shields and without shields have almost nothing in common with one another.
It is interesting to note that the magnitude of the vibrations of the feet, measured at the bolt heads, at most frequencies considerably exceeds the vibrations of the frame points when bearing shields are present, and is practically equal to the vibrations of the feet when the armature is mounted in pedestal bearings.
As a result of the analysis performed on the data of the experimental investigation of vibrations of the frame of a direct-current machine, the following conclusions may be drawn:
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Individual sections of the frame have their own natural resonant frequencies, differing from one another, as a result of which resonating elements are present practically at any armature rotational speed.
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The spatial form of deformation of the frame differs significantly from generally accepted theoretical constructions corresponding to higher \((i>1)\) orders of vibration.
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Bearing end shields introduce substantial changes into the pattern of the distribution of vibration accelerations around the circumference of the frame and lead to distortion of the shape of the spatial deformations of the frame.
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In studying the vibrations of DC machines, and also during factory testing of machines, when it is necessary to determine the highest vibration level, one must not confine oneself to vibration measurements at any single rotational speed of the armature. Vibrations should be measured at a number of resonant speeds occurring within the operating range of variation of the motor rotational speed.
REFERENCES
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J. P. Den Hartog. Mechanical Vibrations. GIFML, Moscow, 1960.
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B. B. Voronetskii. Calculation of the natural vibration frequencies of the yoke of DC machines. — VEP, 1957, No. 9.