機械振動測試系統(tǒng)的設(shè)計【含CAD圖紙、說明書】
振動系統(tǒng)動態(tài)測試虛擬儀器的研究摘要:通過把振動系統(tǒng)動態(tài)分析理論與數(shù)字信號處理方法相結(jié)合,提出并系統(tǒng)地論述了振動系統(tǒng)動態(tài)測試虛擬儀器的開發(fā)原理。1 引言 隨著數(shù)字計算機仿真技術(shù)的發(fā)展,虛擬儀器技術(shù)的應(yīng)用越來越廣泛,所謂虛擬儀器就是在通用計算機上增加一組軟件和相關(guān)硬件,使使用者在操縱這臺計算機時,就像是在操作一臺他自己設(shè)計的專用傳統(tǒng)電子儀器。在虛擬儀器系統(tǒng)中,硬件僅僅是為了解決信號的輸入輸出,而軟件才是整個儀器系統(tǒng)的關(guān)鍵。任何一個使用者都可以通過修改軟件的方法,很方便地調(diào)整儀器系統(tǒng)的功能與規(guī)模。虛擬儀器技術(shù)給用戶一個充分發(fā)揮自己才能及想象力的空間,用戶(而不是儀器廠家)可以根據(jù)自己的需求隨心所欲地設(shè)計自己的儀器系統(tǒng)。因此有軟件就是儀器的說法。 本文正是根據(jù)數(shù)字計算機仿真技術(shù)和虛擬儀器技術(shù)的思想,從簡單實用的角度出發(fā),把振動系統(tǒng)的動態(tài)測試理論和數(shù)字信號處理方法相結(jié)合,提出并系統(tǒng)地論述了振動系統(tǒng)動態(tài)測試虛擬儀器的開發(fā)原理。2 動態(tài)測試的基本概念 工程中大多數(shù)實際系統(tǒng)均用線性系統(tǒng)來描述,而線性系統(tǒng)的輸入輸出之間存在著簡單的因果關(guān)系。因此,可以通過對被測系統(tǒng)輸入輸出物理量的測量和分析來確定系統(tǒng)的動態(tài)特性,這就是動態(tài)測試。動態(tài)特性的數(shù)學(xué)模型有多種形式:時域中常用的有微分方程、差分方程和狀態(tài)方程;復(fù)數(shù)域中有傳遞函數(shù)、結(jié)構(gòu)圖;頻域中有頻率響應(yīng)函數(shù)等。對機械振動系統(tǒng)進行動態(tài)特性辨識的主要目的是得到系統(tǒng)的頻域特性或傳遞函數(shù),并進一步獲得機械振動力學(xué)系統(tǒng)的模態(tài)參數(shù)。頻率響應(yīng)函數(shù)用頻率響應(yīng)數(shù)據(jù)和曲線來表示,可以把頻率響應(yīng)函數(shù)看成是描述線性系統(tǒng)的非參數(shù)模型。對于機械振動系統(tǒng),其動態(tài)特性常用“固有頻率、阻尼比和振型”等所謂的模態(tài)參數(shù)來描述。在頻率響應(yīng)函數(shù)測試的基礎(chǔ)上,可以通過參數(shù)識別的方法,即試驗?zāi)B(tài)分析來建立機械振動系統(tǒng)的模態(tài)參數(shù)。 動態(tài)測試技術(shù)的主要內(nèi)容就是對被測振動系統(tǒng)進行激勵,通過振動測試、數(shù)據(jù)采集和信號分析,由輸入和輸出確定機械振動系統(tǒng)的動態(tài)特性??梢?,動態(tài)測試分為兩大部分:頻率響應(yīng)函數(shù)的測繪和模態(tài)參數(shù)的識別。機械振動系統(tǒng)動態(tài)特性測試與分析的重點是,如何利用測試分析所得的頻率響應(yīng)函數(shù)曲線,通過模態(tài)識別的方法,求解出表征機械振動系統(tǒng)動態(tài)特性的模態(tài)參數(shù)。模態(tài)識別可分為單模態(tài)識別和多模態(tài)識別,單模態(tài)識別是建立在小阻尼、弱耦合假設(shè)的基礎(chǔ)上。對于模態(tài)密集的復(fù)雜結(jié)構(gòu)或大阻尼情況,則需采用多模態(tài)分析。隨著數(shù)字計算機技術(shù)的深入發(fā)展,現(xiàn)代模態(tài)參數(shù)識別大都采用多模態(tài)識別。3 振動系統(tǒng)動態(tài)測試虛擬儀器的設(shè)計3.1 虛擬儀器的提出和組成原理圖虛擬儀器的優(yōu)點在于能夠共享計算機輔助測試系統(tǒng)的硬件資源和輸入輸出接口軟件,用戶只需設(shè)計有關(guān)的應(yīng)用軟件便可以實現(xiàn)相應(yīng)的測試分析功能。這樣不僅節(jié)約成本,而且還具有“實用性強,準(zhǔn)確度高,效價比良,靈活性好,全自動化”的特點?;跀?shù)字計算機仿真技術(shù)和虛擬儀器技術(shù)的快速發(fā)展,通過把機械振動系統(tǒng)動態(tài)測試技術(shù)和數(shù)字信號處理方法相結(jié)合,提出了一種構(gòu)建“振動系統(tǒng)動態(tài)測試虛擬儀器”的原理和方法。振動系統(tǒng)動態(tài)測試虛擬儀器的設(shè)計過程是:首先按流程圖布置好振動系統(tǒng)動態(tài)測試虛擬儀器的硬件系統(tǒng);然后,在個人計算機上開發(fā)相應(yīng)的應(yīng)用軟件;最后,振動系統(tǒng)動態(tài)測試與模態(tài)識別的全過程,都是在個人計算機上通過軟面板對話框和適當(dāng)?shù)目刂瓢粹o來完成。3.2 激振方式、激振器和振動傳感器的布置激振方式可分為正弦穩(wěn)態(tài)掃頻和寬頻帶激振兩大類。通常采用“正弦穩(wěn)態(tài)掃頻激振”,其優(yōu)點是激振能量集中,信噪比高,對于線性系統(tǒng)的動態(tài)特性測試具有很高的測量精度。首先,根據(jù)測試分析要求及振動系統(tǒng)的機械結(jié)構(gòu)特點,確定激振點的位置和測量點的數(shù)量N及各測量點的位置。對于空間結(jié)構(gòu)系統(tǒng),往往需要測量1個點的3個方向,這時應(yīng)選用三軸振動傳感器。安裝激振器時,必須注意激振力的正確施加。在安裝測振傳感器時,應(yīng)保證傳感器能正確感受被測體的振動。小型振動系統(tǒng)必須選用微型傳感器,以避免傳感器附加質(zhì)量影響振動系統(tǒng)動態(tài)特性。3.3 振動系統(tǒng)動態(tài)測試應(yīng)用軟件的總體研究 根據(jù)對前面振動系統(tǒng)動態(tài)測試虛擬儀器原理圖的分析可知,振動系統(tǒng)動態(tài)測試應(yīng)用軟件的設(shè)計流程分為如下步驟: (1)計算機發(fā)出指令控制“信號發(fā)生器”產(chǎn)生激勵信號,再通過“激振器”施加于被測振動系統(tǒng)。激勵信號的數(shù)字序列為X(n)。 (2) 等待被測振動系統(tǒng)穩(wěn)定一定時間,然后計算機再發(fā)出指令同步采集數(shù)據(jù)序列X(n)和Y1(n),Y2(n), ,YN(n) 。采樣時間間隔或采樣頻率應(yīng)符合采樣定理及頻率分辨率的要求。 (3)利用按本原理設(shè)計的專用軟件分析處理X(n)和Y1(n),Y2(n),YN(n), 就可得出被測振動系統(tǒng)的模態(tài)參數(shù)和相應(yīng)數(shù)學(xué)模型。顯然,整套應(yīng)用軟件應(yīng)包括兩大部分,即操作控制部分和數(shù)據(jù)處理部分。由于目前計算機控制技術(shù)和虛擬儀器技術(shù)的發(fā)展,已足以解決此應(yīng)用軟件中的操作控制部分,且鑒于篇幅有限,所以筆者對應(yīng)用軟件的操作控制部分不再作進一步討論,下面重點研究應(yīng)用軟件的數(shù)據(jù)處理部分。3.4 數(shù)據(jù)處理專用軟件的設(shè)計原理3.4.1 濾波方法 由于數(shù)據(jù)序列在采集過程中難免會受到各種干擾, 所以必須采取有效的濾波算法對采集得到的數(shù)據(jù)序列Y1(n),Y2(n),YN(n)進行修正。通常應(yīng)采用相關(guān)濾波算法,因為相關(guān)濾波可以有效地把真正由X(n)通過振動系統(tǒng)產(chǎn)生的信號從Y1(n),Y2(n),YN(n)中分離出來。將經(jīng)過濾波算法處理后的數(shù)據(jù)序列記為YN1(n),YN2(n),YNN(n) ,n=1,2, ,D 。D為采樣點數(shù)量。3.4.2 頻率響應(yīng)函數(shù)的確定 將確定性信號看成隨機信號,采用離散數(shù)字隨機信號的相關(guān)譜分析原理。 XK(k) = FFT X(n) YK(k) = FFT YN(n) SX(k) = XK(k)2 /D SY(k) = YK(k)2 /D SXY(k) = XK*(k)YK(k) /D XK*(K)為XK(k)的共軛復(fù)數(shù)。 為減少數(shù)據(jù)處理誤差,要對SX(k),SY(k),SXY(k)采取平滑處理算法。分段時,相鄰兩段重疊50的效果最佳,即將記錄段X(n),YN(n)分成多個樣本,分別進行上述運算后再求平均值。VXY2(k) = SXY(k)2 / SX(k) SY(k), 相干系數(shù)VXY越接近1效果越好。H(k) =SXY(k) / SX(k), 由變量代換關(guān)系“k/(DTS) =f(TS為采樣時間間隔)”可得到測試出的頻率響應(yīng)函數(shù)H(f) 。 對每一個數(shù)據(jù)序列Y1(n),Y2(n),YN(n)均用上述方法處理,就可以得到測試出來的N個頻率響應(yīng)函數(shù)H1(f),H2(f),HN(f) 。3.4.3 擬合求解模態(tài)參數(shù)機械振動系統(tǒng)模態(tài)參數(shù)識別,又稱為曲線擬合,即采用最小二乘法將測試所得的頻率響應(yīng)值與系統(tǒng)模型值進行曲線擬合。優(yōu)化準(zhǔn)則就是使實測的頻率響應(yīng)值與理論數(shù)學(xué)模型對應(yīng)值的總均方誤差E極小。最小二乘曲線擬合過程中存在的有關(guān)問題,如方程組的病態(tài)問題,可根據(jù)數(shù)值分析理論,采用正交多項式的方法加以解決。通常機械振動系統(tǒng)的“理論數(shù)學(xué)模型”可用有理分式形式的傳遞函數(shù)來表示,即 H(s) = N(s)/D(s) = a0sm+a1sm-1+am-1s+am/ sn+b1sn-1+bn-1s+bn上式中,mn,n=2q,q為系統(tǒng)的自由度數(shù)。一般選定一個具體q值,令m=2q-1,然后循環(huán)擬合,直到滿足E控制精度Eg。 對于每一個頻率響應(yīng)函數(shù),設(shè)由D個采樣點得到的D個測試頻率響應(yīng)值記為HC(f),對應(yīng)的D個理論模型值記為HL(f),則總方差為E=(k=1,D)| HC(f)HL(f)|2。這是非線性優(yōu)化問題,為使用方便和保證精度,可轉(zhuǎn)化為線性優(yōu)化問題。令s=jw=j2f,誤差e=N(f) D(f)HC(f),則總方差轉(zhuǎn)化為E=|N(f) D(f)HC(f)|2。此時,總方差函數(shù)為待求系數(shù)的線性函數(shù),最小二乘解已變成線性優(yōu)化問題。首先通過最小二乘擬合識別出有理分式的系數(shù)ai(i=1,2,m)和bi(i=1,2,n),然后由特征方程D(s)0解得極點sr及sr*(r=1,2,q),由留數(shù)公式ArH(s)(s-sr)| S=Sr”求出留數(shù)Ar及Ar* 。則傳遞函數(shù)可表示為H(s)r=1 , N Ar/(s-sr) + Ar*/(s-sr*)最后以sr= -r wr +j wr (1- r2)1/2,sr為共軛復(fù)數(shù),求得各階模態(tài)固有頻率wr和阻尼比r 。對于線性系統(tǒng),模態(tài)固有頻率和阻尼比是系統(tǒng)的總體固有參數(shù),理論上應(yīng)該不隨測量點而改變。依次對N個測量點的頻率響應(yīng)函數(shù)進行曲線擬合,可得到N組模態(tài)固有頻率和阻尼比,再求出平均值作為系統(tǒng)的模態(tài)固有頻率和阻尼比,進而,再求出各階振型r 。3.4.4 其它輸出振動系統(tǒng)動態(tài)測試所得的系統(tǒng)固有的各階模態(tài)參數(shù)和用模態(tài)參數(shù)表示的各測量點,對應(yīng)于輸入點的數(shù)學(xué)模型。振動系統(tǒng)動態(tài)測試數(shù)據(jù)處理的全過程,可以用目前流行的程序設(shè)計語言VC+或Java2開發(fā)成專用的數(shù)據(jù)處理程序軟件包,然后通過相關(guān)程序語言接口方法嵌入到用LabVIEW或LabWindows平臺開發(fā)的振動系統(tǒng)動態(tài)測試虛擬儀器中。采用本虛擬儀器,可以很容易通過計算機多次重復(fù)振動系統(tǒng)動態(tài)測試的整個過程,進一步提高振動系統(tǒng)動態(tài)特性的測試精度。利用動態(tài)測試得到的數(shù)學(xué)模型,通過Matlab6.1仿真環(huán)境(或自己編制程序)可求出激振點處各種輸入信號各測量點處的輸出響應(yīng)信號。4 結(jié)論經(jīng)過實踐檢驗,振動系統(tǒng)動態(tài)測試虛擬儀器在具體運用中具有“實用性強、準(zhǔn)確度高、效價比良、重復(fù)性好及全自動化等優(yōu)點??梢詫?shù)據(jù)采集功能和數(shù)據(jù)處理功能的軟硬件集成在一起,生產(chǎn)出智能化振動系統(tǒng)動態(tài)測試虛擬儀器,也可以把數(shù)據(jù)處理軟件單獨形成專用的振動系統(tǒng)動態(tài)測試數(shù)據(jù)處理軟件包,無論采取何種方式都具有廣闊的應(yīng)用前景。Virtual Instrument Research for Dynamic Testing of Vibration SystemAbstract: Through combining dynamic analyzing theory of vibration system with digital singles process method, developing principle of virtual instrument for dynamic test of vibration system is proposed and discussed.1. INTRODUCTIONWith the development of digital computer simulation technology, virtual instrument technology applications become wider, and the so-called virtual instrument is on the increase in the general computer a group of related hardware and software, so that users in the manipulation of this computer, as in the operation of a his design for the traditional electronic devices. In the virtual instrument system, the hardware simply to solve the input and output signals, and software is the key to the whole instrument. Any user can modify the software through the method, it is very easy to adjust the function of the system and apparatus scale. Virtual instrument technology to users a fully display their talent and imagination of space, users (rather than equipment manufacturers) can be arbitrary in accordance with their own needs and design their own instrument system. It is software is the apparatus argument. In this paper, in accordance with the digital computer simulation and virtual instrument technology ideas, from simple practical point of view, the vibration theory of the dynamic test and digital signal processing method, and proposed a systematic exposition vibration system dynamic testing Virtual Instrument development principle.2. The basic concept of dynamic testingMost of the actual system works were used to describe the linear system, the input-output linear system exists between the simple causal relationship. Therefore, it can be measured by the input-output system physical measurement and analysis to determine the dynamic characteristics, and this is dynamic testing. Dynamic characteristics of the mathematical model takes many forms: the time domain is commonly used differential equations, differential equations and equation of state; a complex domain transfer function, structure diagram; frequency domain, such as a frequency response function. Mechanical vibration system of the dynamic characteristics is the main purpose of identification by the system or frequency domain characteristics of the transfer function, and further mechanical vibration mechanical system modal parameters. Frequency response function with data and the frequency response curve, frequency response function can be described as a non-linear system parameter model. The mechanical vibration system, the dynamic characteristics of common natural frequency, damping and mode shape than the so-called modal parameters to describe. In the frequency response function test on the basis of parameters can be identified, that is, experimental modal analysis to establish the mechanical vibration system modal parameters. Dynamic testing technology is the main content of the measured vibration of the incentive system, through vibration testing, data acquisition and signal analysis, input and output determined by the mechanical vibration system dynamic characteristics. Thus, dynamic test is divided into two parts: the frequency response function mapping and identification of the modal parameters. Dynamic mechanical vibration system of testing and analysis of the key is how to use the proceeds of testing frequency response function curves through modal identification method for the characterization of mechanical vibration system dynamic characteristics of modal parameters. Modal Recognition state recognition can be divided into single-mode and multi-modal identification, identification of single-mode state is built on small damping loose on the basis of assumptions. The modal-intensive complex structure or damping, required a multi-modal analysis. With the in-depth development of the digital computer technology, the modern modal parameters to identify most of a multi-modal identification.3 Virtual Instrument Desire for Dynamic Testing of Vibration System3.1 Virtual Instrument made and composed schematicVirtual instrument has the advantage of being able to share computer-aided test the systems hardware resources and input-output interface software, users design of the application software will be able to achieve the corresponding test analysis functions. This will not only save costs, but also had a practical, accurate and high-titer, flexibility, and the fully automated features. Based on digital computer simulation and virtual instrument technology and the rapid development of the mechanical vibration system through dynamic testing technology, and digital signal processing method, the proposed construction of a dynamic vibration test system virtual machines the principles and methods. Dynamic vibration testing virtual instrument design process are as follows: First flow chart layout by good dynamic vibration test system hardware Virtual Instrument System; Then, in the corresponding development of personal computer software applications; Finally, the dynamic vibration testing and modal identification the entire process is in the personal computer through the soft panel dialog and appropriate control button.3.2 Vibration, vibration and vibration sensor layoutSinusoidal excitation mode can be divided into static and broadband excitation Swept two categories. Usually adopts a sine steady Sweep exciting, the merits of excitation energy is concentrated, high signal to noise ratio for linear dynamic characteristics of the test system with high precision. First, in accordance with requirements analysis and testing of mechanical vibration system structure, determine the location and vibration measurement points N and the number of the location of measurement points. The spatial structure system, often requires a measurement point three directions, then should use three-axis vibration sensors. Exciter installed, it should be noted excitation of the right to impose. Vibration sensors in the installation, should ensure that the sensor can accurately measured feelings of the vibration. Small vibration system to select micro-sensors, in order to avoid affecting the quality vibration sensors additional dynamic characteristics of the system.3.3 Dynamic vibration tests on the overall application softwareUnder the previous system dynamic vibration testing Virtual Instrument schematic analysis, we can see the dynamic vibration test application software design process is divided into the following steps: (1) directive issued computer control signal generator, produced encouraging signals, and through the Vibrator imposed on the measured vibration system. Encouraging signals in the digital sequence X (n). (2) the measured vibration system is stable for a certain period of time, and then issued instructions to the computer data acquisition synchronization sequence X (n) and Y1 (n), Y2 (n), YN (n). Sampling frequency or time interval should be consistent with the sampling theorem and frequency resolution requirements. (3) make use of the principle of design analysis software for X (n) and Y1 (n), Y2 (n), YN (n), measured vibration system can arrive at the modal parameters and the corresponding mathematical model . Obviously, application software package should include two parts, namely, operational control and data-processing part of some. As computer control technology and the development of virtual instrument technology has been sufficient to resolve this application in the operational control of light and space is limited, so the author on the application of software is no longer part of the operational control for further discussion below focuses on the application software data-processing part.3.4 Data processing software for the design principle3.4.1 filtering method The sequence data in the acquisition process will inevitably be all kinds of interference, it is necessary to take effective filtering algorithm to the data acquisition sequence Y1 (n), Y2 (n), YN (n) be amended. Usually associated filtering algorithm should be used, because the relevant filter can effectively from the real X (n) through the vibration signal from the system Y1 (n), Y2 (n), YN (n) separated. After filtering algorithm will be dealt with after the sequence data recorded as YN1 (n), YN2 (n), YNN (n), n = 1,2, D. D is the number of sampling points. 3.4.2 determine the frequency response function Signal will be uncertainty as random signal, a number of discrete random signals in the spectrum analysis of the relevant principles. XK (k) = FFT X (n) YK (k) = FFT YN (n) SX (k) = | XK (k) | 2 / D SY (k) = | YK (k) | 2 / D SXY (k) = XK * (k) YK (k) / D XK * (K) XK (k) Conjugate complex. In order to reduce data processing error, the SX (k), SY (k), SXY (k) to smoothing algorithm. Subparagraph, the two overlap adjacent 50 best results, the forthcoming record of the X (n), YN (n) is divided into a number of samples, respectively, to carry out such operations after seeking average. VXY2 (k) = | SXY (k) | 2 / SX (k) SY (k), the more coherent coefficient close to 1 VXY better results. H (k) = SXY (k) / SX (k), variable substitution k / (DTS) = f (TS for the sampling time interval) available to test the frequency response function H (f). For each data series Y1 (n), Y2 (n), YN (n) are dealing with the above method, it can be tested by the frequency response function of N H1 (f), H2 (f), HN (f).3.4.3 Fitting Solution modal parameters Mechanical vibration system modal parameter identification, also known as curve fitting, that is, using the least square method will test the frequency response of the system model and the value curve fitting. Optimization criterion is the value of the measured frequency response corresponds with the theoretical mathematical model of the total value of the minimum mean square error E. Least-squares fitting in the course of the relevant issues, such as the sick equations, numerical analysis according to theory, orthogonal polynomials method used to solve the problem. Usually mechanical vibration systems theory mathematical model can be rational fraction of the transfer function to indicate that H (s) = N (s) / D (s) = + a0sm a1sm-1 + + + am-1s am / sn-1 + + b1sn-1s + + bn bn - On, m n, n = 2q, q freedom of the system. Q general selected a specific value of the m = 2q-1, and then cycle fitting, until the E control accuracy Eg. For each frequency response function, a sampling from D-D tests by the frequency response of mind for HC (f), the corresponding value of D-theoretical model in mind for the HL (f), the total variance for E = (k = 1, D) | HC (f)-HL (f) | 2. This is the non-linear optimization problem, as easy to use and guarantee accuracy, and can be transformed to a linear optimization problem. Order s = = j2 f jw error e = N (f) - D (f) HC (f), the total variance into E = | N (f) - D (f) HC (f) | 2. At this time, the total variance function question for coefficient of linear functions, linear least squares solutions have become optimization problem. First identified by the least square fitting rational fraction of the coefficient ai (i = 1, 2, m) and the bi (i = 1, 2, n), and then by the characteristic equation D (s) = 0 Solutions in the pole sr and sr * (r = 1,2, q), by the residue formula Ar = H (s) (s-sr) | S = Sr sought stay of Ar and Ar *. will transfer function can be expressed as H (s) = r = 1, N Ar / (s-sr) + Ar * / (s-sr *) Finally, sr = - r wr + j wr (1 - r2) 1 / 2, sr for complex conjugate, and get the band Modal wr natural frequency and damping ratio r. For linear systems, modal natural frequency and damping ratio is inherent in the overall system parameters, in theory, should not change with the measurement point. N followed by the measurement point to the frequency response curve fitting function, can be inherent in group N modal frequencies and damping ratio, then calculated the average as a modal system natural frequency and damping ratio, in turn, obtained the order again r mode.3.4.4 Other Output System Dynamic vibration test systems inherent in the band modal parameters and the use of modal parameters of the measurement point, corresponding to the input point of the mathematical model. Dynamic vibration test data-processing system in the whole process can be used currently popular programming language VC + + or Java2 developed into a dedicated data processing package, and then through the relevant procedures language interface method using LabVIEW embedded development platform or LabWindows Dynamic vibration testing virtual instruments. Using the virtual instrument, can be easily repeated by the computer system dynamic vibration testing of the whole process, and further enhance the dynamic characteristics of vibration test system accuracy. The use of dynamic testing mathematical model through Matlab6.1 simulation environment (or their own development process) can be derived exciting point of the input signal measurement point response to the output signal. 4 Conclusion After the test of practice, vibration, dynamic testing system in the specific application of virtual instruments in a practical, accurate and high-titer, good repeatability, and the entire automation, etc. can function data acquisition and data processing hardware and software integration together to produce intelligent system dynamic vibration testing virtual instrument, can also form a separate data processing software for the system dynamic vibration test data-processing package, no matter in what ways have broad prospects.
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