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实际工作中有不少场合采用扫频(连续变更激励源的频率)的方法测试系统的频率特性或寻找机械系统的谐振点。本文通过对二阶系统动态激励的数字仿真研究,对这种方法的合理性作了初步探讨,认为在同样扫频速度下,小阻尼系统的测试误差较大,动态响应较快的系统的测试误差相对小些;对于一定阻尼的系统,扫频速度应有一个限度,以免引起过大的误差。通常,测取系统频率特性是通过逐点测试正弦输入下的稳态输出,将输出的幅值、相位与输入的幅值、相位相比较得到系统频率特性。但是,实际工作中,很多地方采用扫频方法测试系统的频率特性(扫频仪就是这样测试频率特性的一类仪器)或寻找机械系统的谐振点。在旋转轴系中,动不平衡转子在加速或减速时的强迫振动也常被用来对系统的模态进行识别。这种强迫振动是由变振幅的变频正弦激励力造成的。我们把连继变更频率的这一类输入称作扫频激励。尽管扫频激励被广泛地使用在测取频率特性和系统模态识别上,但是,这一方法的合理性没有引起足够的注意。严格地说,不管扫频速度多么慢,系统总是处于暂态。因此,如果用扫频激励来画系统的奈氏图,即使不计测量仪器和X-Y记录仪的动态响应(它们是测试系统中的串联环节,其动态特性也影响所得结果)所得的也不是系统真实的奈氏图。扫频速度越大,差别也就越大。另外,被测系统本身的动态特性也影响所得的结果。任何一个多自由度线性系统,不管用什么激励方式,在任何一个测点上都可以测得系统的各阶固有频率和阻尼率。任一测点的输出可以认为是多个单自由度系统(反映系统相应的模态)输出的并联叠加。因此,我们将对具有典型代表性的单自由度系统在扫频激励下的响应进行初步的考察。对一个二阶系统在扫频激励的条件下进行数字仿真的结果表明,测试的误差受如下两个因素的影响:(1)系统的阻尼率ζ。相同扫频速度下,阻尼率较小的系统测试误差较大;(2)扫频速度。相同阻尼的系统,扫频速度越高,测试误差越大。
There are many occasions in practical work using frequency sweep (continuous change of excitation frequency) method to test the frequency characteristics of the system or find the resonance point of the mechanical system. In this paper, we study the rationality of this method by simulating the dynamic excitation of second-order system. It is considered that under the same sweep speed, the test error of the system with small damping is larger and the dynamic response is faster The error is relatively small; for a certain damping system, the sweep rate should have a limit, so as not to cause too much error. Usually, the frequency characteristic of the measuring system is obtained by measuring the steady-state output under sine input point by point and comparing the amplitude and phase of the output with the amplitude and phase of the input to obtain the system frequency characteristic. However, in practice, many places use the frequency sweep method to test the frequency characteristics of the system (the frequency sweeper is a type of instrument that tests the frequency characteristics) or look for the resonance point of a mechanical system. In the rotating shaft system, the forced vibration of the dynamic imbalance rotor during acceleration or deceleration is also often used to identify the mode of the system. This forced vibration is caused by a variable amplitude sinusoidal excitation force. We refer to this type of input as the frequency-swept stimulus. Although swept frequency excitation is widely used in the measurement of frequency characteristics and system modal identification, the reasonableness of this method has not attracted enough attention. Strictly speaking, no matter how slow the sweep is, the system is always in a transient state. Therefore, if we use the sweep excitation to draw the system’s Knit plot, it is not true that the dynamic responses of measuring instruments and XY recorders, which are the dynamic characteristics of the test system, affect the results Knight’s Figure. The greater the sweep speed, the greater the difference. In addition, the dynamic nature of the system under test also affects the results obtained. For any linear system with multiple degrees of freedom, no matter what kind of excitation method is used, the system natural frequency and damping rate can be measured at any measuring point. The output of either measurement point can be considered as a parallel overlay of the outputs of multiple single-degree-of-freedom systems (reflecting the corresponding modalities of the system). Therefore, we will conduct a preliminary investigation of the response of a typical single-degree-of-freedom system under sweeping excitation. The numerical simulation of a second-order system under swept-frequency excitation shows that the test error is affected by two factors: (1) the damping rate ζ of the system. Under the same sweep speed, the system test error with smaller damping rate is larger; (2) Sweep speed. The same damping system, the higher the frequency sweep, the greater the test error.