1、 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58with active magnetic bearings Part 3: Evaluation of stability marginICS 17.160Mechanical vibration
2、Vibration of rotating machinery equipped BRITISH STANDARDBS ISO 14839-3:2006BS ISO 14839-3:2006This British Standard was published under the authority of the Standards Policy and Strategy Committee on 28 February 2007 BSI 2007ISBN 978 0 580 50150 0Amendments issued since publicationAmd. No. Date Com
3、mentsThis publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.National forewordThis British Standard was published by BSI. It is the UK i
4、mplementation of ISO 14839-3:2006.The UK participation in its preparation was entrusted by Technical Committee GME/21, Mechanical vibration, shock and condition monitoring, to Subcommittee GME/21/5, Vibration of machines.A list of organizations represented on GME/21/5 can be obtained on request to i
5、ts secretary.Reference numberISO 14839-3:2006(E)INTERNATIONAL STANDARD ISO14839-3First edition2006-09-15Mechanical vibration Vibration of rotating machinery equipped with active magnetic bearings Part 3: Evaluation of stability margin Vibrations mcaniques Vibrations de machines rotatives quipes de p
6、aliers magntiques actifs Partie 3: valuation de la marge de stabilit BS ISO 14839-3:2006ii iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references . 1 3 Preceding investigation . 1 4 Outline of feedback control systems 2 5 Measurement procedures 9 6 Evaluation criteria. 11 Ann
7、ex A (informative) Case study 1 on evaluation of stability margin 13 Annex B (informative) Case study 2 on evaluation of stability margin 25 Annex C (informative) Field data of stability margin 28 Annex D (informative) Analytical prediction of the system stability. 32 Annex E (informative) Matrix op
8、en loop used for a MIMO system 33 Bibliography . 35 BS ISO 14839-3:2006iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO te
9、chnical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates close
10、ly with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft
11、 International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this docume
12、nt may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 14839-3 was prepared by Technical Committee ISO/TC 108, Mechanical vibration and shock, Subcommittee SC 2, Measurement and evaluation of mechanical vibration and shock as appl
13、ied to machines, vehicles and structures. ISO 14839 consists of the following parts, under the general title Mechanical vibration Vibration of rotating machinery equipped with active magnetic bearings: Part 1: Vocabulary Part 2: Evaluation of vibration Part 3: Evaluation of stability margin Addition
14、al parts are currently in preparation. BS ISO 14839-3:2006vIntroduction While passive bearings, e.g. ball bearings or oil-film bearings, are essentially stable systems, magnetic bearings are inherently unstable due to the negative stiffness resulting from static magnetic forces. Therefore, a feedbac
15、k control is required to provide positive stiffness and positive damping so that the active magnetic bearing (AMB) operates in a stable equilibrium to maintain the rotor at a centred position. A combination of electromagnets and a feedback control system is required to constitute an operable AMB sys
16、tem. In addition to ISO 14839-2 on evaluation of vibration of the AMB rotor systems, evaluation of the stability and its margin is necessary for safe and reliable operation of the AMB rotor system; this evaluation is specified in this part of ISO 14839, the objectives of which are as follows: a) to
17、provide information on the stability margin for mutual understanding between vendors and users, mechanical engineers and electrical engineers, etc.; b) to provide an evaluation method for the stability margin that can be useful in simplifying contract concerns, commission and maintenance; c) to serv
18、e and collect industry consensus on the requirements of system stability as a design and operating guide for AMB equipped rotors. BS ISO 14839-3:20061Mechanical vibration Vibration of rotating machinery equipped with active magnetic bearings Part 3: Evaluation of stability margin 1 Scope This part o
19、f ISO 14839 establishes the stability requirements of rotating machinery equipped with active magnetic bearings (AMB). It specifies a particular index to evaluate the stability margin and delineates the measurement of this index. It is applicable to industrial rotating machines operating at nominal
20、power greater than 15 kW, and not limited by size or operational rated speed. It covers both rigid AMB rotors and flexible AMB rotors. Small-scale rotors, such as turbo molecular pumps, spindles, etc., are not addressed. This part of ISO 14839 concerns the system stability measured during normal ste
21、ady-state operation in-house and/or on-site. The in-house evaluation is an absolute requirement for shipping of the equipment, while the execution of on-site evaluation depends upon mutual agreement between the purchaser and vendor. This part of ISO 14839 does not address resonance vibration appeari
22、ng when passing critical speeds. The regulation of resonance vibration at critical speeds is established in ISO 10814. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated r
23、eferences, the latest edition of the referenced document (including any amendments) applies. ISO 10814, Mechanical vibration Susceptibility and sensitivity of machines to unbalance 3 Preceding investigation The AMB rotor should first be evaluated for damping and stability properties for all relevant
24、 operating modes. There are two parts to this assessment. First, the run-up behaviour of the system should be evaluated based on modal sensitivities or amplification factors (Q-factors). This concerns all eigen frequencies that are within the rotational speed range of the rotor. These eigen frequenc
25、ies are evaluated by the unbalance response curve around critical speeds measured in a rotation test. When the unbalance vibration response is measured as shown in Figure 1, the sharpness of each vibration peak corresponding to eigen frequencies of the two rigid modes and the first bending mode is e
26、valuated; this is commonly referred to as Q-factor evaluation. These damping (stability) requirements for an AMB system during run-up are covered by ISO 10814 (based on Q-factors), and are not the subject of this part of ISO 14839. BS ISO 14839-3:20062 Key X rotational speed Y vibration magnitude Fi
27、gure 1 Q-factor evaluation by unbalance vibration response The second part, which is covered by this part of ISO 14839, deals with the stability of the system while in operation at nominal speed from the viewpoint of the AMB control. This analysis is critical since it calls for a minimum level of ro
28、bustness with respect to system variations (e.g. gain variations due to sensor drifts caused by temperature variations) and disturbance forces acting on the rotor (e.g. unbalance forces and higher harmonic forces). To evaluate the stability margin, several analysis tools are available: gain margin,
29、phase margin, Nyquist plot criteria, sensitivity function, etc. 4 Outline of feedback control systems 4.1 Open-loop and closed-loop transfer functions Active magnetic bearings support a rotor without mechanical contact, as shown in Figure 2. AMBs are typically located near the two ends of the shaft
30、and usually include adjacent displacement sensors and touch-down bearings. The position control axes are designated x1, y1at side 1 and x2, y2at side 2 in the radial directions and z in the thrust (axial) direction. In this manner, five-axis control is usually employed. An example of a control netwo
31、rk for driving the AMB device is shown in Figure 3. a) Axial view b) Rotor system Key 1 AMB 2 sensor aSide 1. bSide 2. Figure 2 Rotor system equipped with active magnetic bearings BS ISO 14839-3:20063Key 1 mechanical plant rotor 2 position sensor, expressed in V/m 3 AMB controller, expressed in V/V
32、4 power amplifier, expressed in A/V 5 electromagnet, expressed in N/A 6 AMB actuator 7 negative position stiffness, expressed in N/m 8 AMB E excitation signal FbAMB force, expressed in newtons Fddisturbance force, expressed in newtons Kicurrent stiffness, expressed in newtons per ampere Ksnegative p
33、osition stiffness, expressed in newtons per metre x displacement, expressed in metres aSensor signal. bControl signal. cControl current. Figure 3 Block diagram of an AMB system As shown in these figures, each displacement sensor detects the shaft journal displacement in one radial direction in the v
34、icinity of the bearing and its signal is fed back to the compensator. The deviation of the rotor position from the bearing centre is, therefore, reported to the AMB controller. The controller drives the power amplifiers to supply the coil current and to generate the magnetic force for levitation and
35、 vibration control. The AMB rotor system is generally described by a closed loop in this manner. The closed loop of Figure 3 is simplified, as shown in Figure 4, using the notation of the transfer function, Gr, of the AMB control part and the transfer function, Gp, of the plant rotor. At a certain p
36、oint of this closed-loop network, we can inject an excitation, E(s), as harmonic or random signal and measure the response signals, V1and V2, directly after and before the injection point, respectively. The ratio of these two signals in the frequency domain provides an open-loop transfer function, G
37、o, with s = j, as shown in Equation (1): 2o1()()()VsGsVs= (1) Note that this definition of the open-loop transfer function is very specific. Most AMB systems have multiple feedback loops (associated with, typically, five axes of control) and testing is typically done with all loops closed. Consequen
38、tly, the open-loop transfer function for a given control axis is defined by Equation (1) with the assumption that all feedback paths are closed when this measurement is made. This definition is different from the elements of a matrix open-loop transfer function defined with the assumption that all s
39、ignal paths from the plant rotor to the controller are broken. See Annex E for a more detailed discussion of this issue. BS ISO 14839-3:20064 The closed-loop transfer function, Gc, is measured by the ratio as shown in Equation (2): 2c()()()VsGsE s= (2) The transfer functions of the closed loop, Gc,
40、and open loop, Go, are mutually consistent, as shown in Equations (3): oco1GGG=+and coc1GGG=(3) The transfer functions, Gcand Go, can typically be obtained using a two-channel FFT analyser. The measurement of Gois shown in Figure 4 a). a) Measurement of Gob) Measurement of GsKey Gptransfer function
41、of the plant rotor Grtransfer function of the AMB control part E external oscillation signal Goopen-loop transfer function Gssensitivity function Figure 4 Two-channel measurement of Goand Gs4.2 Bode plot of the transfer functions Once the open-loop transfer function, Go, is measured as shown in Figu
42、re 5, we can modify it to the closed-loop transfer function, Gc, as shown in Figure 6. Assuming here that the rated (non-dimensional) speed is N = 8, the peaks of the gain curve at 1= 1, 2= 6 are distributed in the operational speed range so that the sharpness, i.e. Q-factor, of these critical speed
43、s are regulated by ISO 10814. This part of ISO 14839 evaluates the stability margin of all of the resulting peaks, noted 1= 1, 2= 6 and 3= 30 in this example. BS ISO 14839-3:20065Key X non-dimensional rotational speed Y1 gain, expressed in decibels. The decibel (dB) scale is a relative measure: 40 d
44、B = 0,01; 20 dB = 0,1; 0 dB = 1; 20 dB = 10; 40 dB = 100. Y2 phase, , expressed in degrees N rated non-dimensional speed aGain. bPhase. Figure 5 Open-loop transfer function, GoBS ISO 14839-3:20066 Key X non-dimensional rotational speed Y1 gain, expressed in decibels. The decibel (dB) scale is a rela
45、tive measure: 40 dB = 0,01; 20 dB = 0,1; 0 dB = 1; 20 dB = 10; 40 dB = 100. Y2 phase, , expressed in degrees N rated non-dimensional speed aGain. bPhase. Figure 6 Closed-loop transfer function, Gc4.3 Nyquist plot of the open-loop transfer function Besides the standard display in a Bode plot (see Fig
46、ure 5), the open-loop transfer function Go(j) can also be displayed on a polar diagram in the form of magnitude Go(j)and phase of Go(j) as shown in Figure 7 (note the dB polar diagram employed). Such a diagram is called the Nyquist plot of the open-loop transfer function. Since the characteristic eq
47、uation is provided by 1 + Go(s) = 0, the distance between the Nyquist plot and the critical point A at ( 1, 0) is directly related to the damping of the closed-loop system and its relative stability. Generally, it can be stated that the larger the curves minimum distance from the critical point, the
48、 greater is the system stability. BS ISO 14839-3:20067a) 1, 2and 3b) 3enlarged aThe decibel (dB) scale is a relative measure: 40 dB = 0,01; 20 dB = 0,1; 0 dB = 1; 20 dB = 10; 40 dB = 100. Figure 7 Nyquist plot of the open-loop transfer function (dB polar diagram) The enlargement of this Nyquist plot
49、 on a linear polar diagram is drawn in Figure 8, focusing on the critical point (1, 0). The shortest distance measured from the critical point is indicated by lAB= Dmin, where a circle of radius Dmincentred at ( 1, 0) is the tangent to the locus. For this example in Figure 8, the gain margin is the distance, lAG(an intersection between the locus and the real axis), and the phase margin is the angle, , (between the real axis and a line extending from the origin to the
