The five main causes of errors in torsional vibration testing of shafts.

Five main causes of errors in torsional vibration testing of shafts

Source: Excerpted from "Journal of Tsinghua University (Natural Science Edition)" Vol. 37, 1997, "Research on Torsional Vibration Testing Errors and Their Correction Methods"

Author:Tiancheng Testing

If using an equal division gear disk or other equal division structure on the shaft, and measuring torsional vibration using the time measurement method, a pulse train can be generated on the gear disk using a sensor. If the graduation of the gear disk is uneven, the time intervals of the pulse train cannot accurately reflect the time taken to rotate through the ideal equal division angle, leading to errors in calculating the instantaneous angular velocity of the shaft. In practice, due to manufacturing precision, there are always errors in the graduation of the gear disk. Taking standard involute gears as an example, if the pitch circle diameter of the gear is d=200mm, the accumulated error of the pitch tE and the corresponding uneven graduation Δθ at different precision levels can be seen in Table 1.

Even without considering other factors, assuming the measurement system is ideal, the measurement accuracy can only reach this limit. In many actual machines, when the torque applied to the rotating shaft is very small, the amplitude of torsional vibration is often only a few percent or a few thousandths of a degree. When measuring these small amplitude vibrations, the uneven graduation error of the gear will make the measurement results completely distorted.

From the above formula, it can be seen that ki will fluctuate between 1/1+λ and 1/1-λ. If k=k(h) is expanded, it can be seen that it will contain cosh, cos2h, cos3h, and higher-order terms. This indicates that even if the rotating shaft does not have torsional vibration, signals of the same frequency and higher-order frequencies will still appear.

In reference [2], it is mentioned that two torsional vibration sensors with a phase difference of 180° can be used to eliminate the influence of lateral vibration. That is, sensors are installed at points A and C, and when Si exists, the time from B to A increases while the time from D to C decreases. Based on the measured times, the influence of lateral vibration can be eliminated, which is an effective and simple method. However, sometimes when using optical code disks, it is inconvenient to install a second sensor on the same code disk. To eliminate the influence of lateral vibration, this paper proposes another numerical calculation method.

A displacement sensor is installed at the cross-section near the code disk to measure the lateral vibration of the shaft. Its direction is perpendicular to the position of the torsional vibration sensor (without loss of generality, set as horizontal direction). Generally speaking, in discrete cases, the number of collection points for lateral vibration and the number of graduations for torsional vibration will not be the same. For example, in torsional vibration measurement, the code disk uses 1024 lines (or 1000, 512 lines, etc.), while the number of collection points for lateral vibration, when applying full cycle collection, is generally 16 points or 32, 64 points.

Let the number of graduations of the code disk be n, the rotational speed be N, the clock pulse frequency during counting be fc, and the number of counting pulses for one graduation be nf, then we have

Since nf must be an integer, while the right side of the above formula may be a decimal, rounding errors exist. The smallest unit of pulse count is 1, so the counting error is at most ±1, and the relative error will be

From the above formula, it can be seen that as the number of graduations n and the rotational speed N increase, the relative error becomes larger; as the clock frequency increases, the relative error becomes smaller. For example, when fc= 6 MHz, N=3000r/min, n=1024, X=0.853%.

It should be noted that if the number of graduations n is reduced to decrease quantization error, it will reduce the sampling points for torsional vibration, which is unfavorable for high-frequency torsional vibration testing.

In addition, if there is rounding error in each scale interval, the cumulative error will be quite large. The total cycle collected after one turn will have a significant error. To solve the cumulative error problem, hardware is used in this system to prevent cumulative errors.

Based on the common errors mentioned above, corresponding software has been developed. In the torsional vibration testing system, it is listed under the general menu for error correction, and through error calibration, the testing accuracy of torsional vibration will be improved.

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