1、 Reference number ISO 14839-3:2006(E) ISO 2006INTERNATIONAL STANDARD ISO 14839-3 First edition 2006-09-15 Mechanical vibration Vibration of rotating machinery equipped with active magnetic bearings Part 3: Evaluation of stability margin Vibrations mcaniques Vibrations de machines rotatives quipes de
2、 paliers magntiques actifs Partie 3: valuation de la marge de stabilit ISO 14839-3:2006(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are l
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6、t permission in writing from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2006 All right
7、s reservedISO 14839-3:2006(E) ISO 2006 All rights reserved iii Contents 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 Annex A (informative) Case study 1
8、 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 open loop used for a MIMO system
9、33 Bibliography . 35 ISO 14839-3:2006(E) iv ISO 2006 All rights reservedForeword 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 tech
10、nical 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 closely
11、 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 I
12、nternational 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 document
13、 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 applie
14、d 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 Additional
15、 parts are currently in preparation. ISO 14839-3:2006(E) ISO 2006 All rights reserved v Introduction 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
16、 forces. Therefore, a feedback 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 c
17、onstitute an operable AMB system. 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
18、 which are as follows: a) to 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, commissio
19、n and maintenance; c) to serve and collect industry consensus on the requirements of system stability as a design and operating guide for AMB equipped rotors. INTERNATIONAL STANDARD ISO 14839-3:2006(E) ISO 2006 All rights reserved 1 Mechanical vibration Vibration of rotating machinery equipped with
20、active magnetic bearings Part 3: Evaluation of stability margin 1 Scope This part of 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
21、 this index. It is applicable to industrial rotating machines operating at nominal 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 address
22、ed. This part of ISO 14839 concerns the system stability measured during normal steady-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 purcha
23、ser and vendor. This part of ISO 14839 does not address resonance vibration appearing 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
24、 this document. For dated references, only the edition cited applies. For undated references, 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 ro
25、tor should first be evaluated for damping and stability properties for all relevant 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 freque
26、ncies that are within the rotational speed range of the rotor. These eigen frequencies 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 corres
27、ponding to eigen frequencies of the two rigid modes and the first bending mode is evaluated; 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
28、 of ISO 14839. ISO 14839-3:2006(E) 2 ISO 2006 All rights reservedKey X rotational speed Y vibration magnitude Figure 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
29、 speed from the viewpoint of the AMB control. This analysis is critical since it calls for a minimum level of robustness 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 an
30、d higher harmonic forces). To evaluate the stability margin, several analysis tools are available: gain margin, 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 ro
31、tor without mechanical contact, as shown in Figure 2. AMBs are typically located near the two ends of the shaft and usually include adjacent displacement sensors and touch-down bearings. The position control axes are designated x 1 , y 1at side 1 and x 2 , y 2at side 2 in the radial directions and z
32、 in the thrust (axial) direction. In this manner, five-axis control is usually employed. An example of a control network 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 IS
33、O 14839-3:2006(E) ISO 2006 All rights reserved 3Key 1 mechanical plant rotor 2 position sensor, expressed in V/m 3 AMB controller, expressed in V/V 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
34、signal F bAMB force, expressed in newtons F ddisturbance force, expressed in newtons K icurrent stiffness, expressed in newtons per ampere K snegative position stiffness, expressed in newtons per metre x displacement, expressed in metres aSensor signal. bControl signal. cControl current. Figure 3 Bl
35、ock diagram of an AMB system As shown in these figures, each displacement sensor detects the shaft journal displacement in one radial direction in the vicinity of the bearing and its signal is fed back to the compensator. The deviation of the rotor position from the bearing centre is, therefore, rep
36、orted to the AMB controller. The controller drives the power amplifiers to supply the coil current and to generate the magnetic force for levitation and 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
37、 in Figure 4, using the notation of the transfer function, G r , of the AMB control part and the transfer function, G p , of the plant rotor. At a certain point of this closed-loop network, we can inject an excitation, E(s), as harmonic or random signal and measure the response signals, V 1and V 2 ,
38、 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 o , with s = j , as shown in Equation (1): 2 o 1 () () () Vs Gs Vs = (1) Note that this definition of the open-loop transfer function is ver
39、y specific. Most AMB systems have multiple feedback loops (associated with, typically, five axes of control) and testing is typically done with all loops closed. Consequently, the open-loop transfer function for a given control axis is defined by Equation (1) with the assumption that all feedback pa
40、ths 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 signal paths from the plant rotor to the controller are broken. See Annex E for a more detailed discussion of this issue. ISO 1483
41、9-3:2006(E) 4 ISO 2006 All rights reservedThe closed-loop transfer function, G c , is measured by the ratio as shown in Equation (2): 2 c () () () Vs Gs E s = (2) The transfer functions of the closed loop, G c , and open loop, G o , are mutually consistent, as shown in Equations (3): o c o 1 G G G =
42、 +and c o c 1 G G G = (3) The transfer functions, G cand G o , can typically be obtained using a two-channel FFT analyser. The measurement of G ois shown in Figure 4 a). a) Measurement of G ob) Measurement of G sKey G ptransfer function of the plant rotor G rtransfer function of the AMB control part
43、 E external oscillation signal G oopen-loop transfer function G ssensitivity function Figure 4 Two-channel measurement of G oand G s4.2 Bode plot of the transfer functions Once the open-loop transfer function, G o , is measured as shown in Figure 5, we can modify it to the closed-loop transfer funct
44、ion, G c , 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 speeds are regulated by ISO 10814. This part of ISO 14839 e
45、valuates the stability margin of all of the resulting peaks, noted 1= 1, 2= 6 and 3= 30 in this example. ISO 14839-3:2006(E) ISO 2006 All rights reserved 5Key X non-dimensional rotational speed Y1 gain, expressed in decibels. The decibel (dB) scale is a relative measure: 40 dB = 0,01; 20 dB = 0,1; 0
46、 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, G oISO 14839-3:2006(E) 6 ISO 2006 All rights reservedKey X non-dimensional rotational speed Y1 gain, expressed in decibels. The decibel (dB) scale is
47、a relative 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, G c4.3 Nyquist plot of the open-loop transfer function Besides the standard display in a Bode plot (
48、see Figure 5), the open-loop transfer function G o (j ) can also be displayed on a polar diagram in the form of magnitude G o (j ) and phase of G o (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
49、characteristic equation is provided by 1 + G o (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 greater is the system stability. ISO 14839-3:2006(E) ISO 2006 All rights reserved 7a) 1 , 2and 3b) 3enlarged aThe decibel (dB) scale is a relative
