Virtual Rotor Balancing in Magnetic Bearings

This application is related to commonly-owned application Ser. No. 521,158, filed May 7, 1990.

This invention pertains to the balancing and stabilizing of rotating machinery through the control of active magnetic bearings.

The advantages of active magnetic bearings include no contact between moving parts, no lubricant and small power loss. Active magnetic bearings are also known for their versatility in controlling rotor vibrations. The stiffness and damping of active magnetic bearings can be adjusted through electronic means for specific rotordynamic applications.

For example, it is well-known to use a tracking notch filter in the control electronics of an active magnetic bearing. The notch filter blocks the bearing response to synchronous vibration (i.e., at the rotating frequency), and essentially makes the magnetic bearing very soft at only the rotating frequency. The rotor experiencing no resistance in rotation tends to spin about its inertial axis (which passes through the center of gravity) rather than the geometric axis, and therefore generates no imbalance force.

However, the balancing approach using a notch filter is subject to system instabilities as there is a limit to how soft the active magnetic bearing response can be made at the synchronous frequency without causing an unstable mode near the frequency. See H. M. Chen, "Magnetic Bearing Stiffness Control Using Frequency Band Filtering", Rotordynamics Instability Problems in High-Performance Turbomachinery, 1988, NASA Conference Publication 3026, pages 341-352. Similar approaches have used modified filter schemes with a tracking differential notch filter or a disturbance estimator. See B. G. Johnson et al., "Active Synchronous Response Control of Rigid-Body Rotors", C290/88, I Mech. E., 1988; and K. D. Reinig and A. A. Desrochers, "Disturbance Accommodating Controllers for Rotating Mechanical Systems", A.S.M.E., Journal of Dynamic Systems, Measurement, and Control, Vol. 108, pp. 24-31, March 1986. When two or more vibrational modes are involved, the implementation of the estimator approach can be complicated.

The object of this invention is to provide a method and apparatus for the balancing and stabilization of rotating machinery through the control of active magnetic bearings allowing an unbalanced rotor to rotate about its inertial axis, transmitting no imbalance forces to the active magnetic bearing housing without causing an unstable mode near the synchronous frequency, and which is not overly complex to implement.

This invention uses straightforward balancing which treats each magnetic bearing as a balancing plane. The rotor is forced to rotate on its inertial axis at all speeds. Therefore, the rotational frequency of the rotor can be changed without encountering critical imbalance responses. Furthermore, the additional bearing control associated with this method and apparatus is equivalent to generating rotating forces on the rotor, not manipulating the bearing stiffness and damping. Thus, no inherent instability problem occurs.

The apparatus identifies the rotor mass eccentricities (vectors) of the inertial axis at the active magnetic bearings as the rotor spins on its geometric axis. The eccentricities of the rotor are identified using an influence-coefficient method similar to the conventional two-plane balancing method. Each active magnetic bearing axis is controlled by a Proportional Integral Derivative (hereinafter "PID") controller, and additional control is provided to shift the rotating axis from the geometric axis to the inertial axis. The sine-wave generator produces a sine-wave in synchronization therewith. The output of the sine-wave generator is adjusted in amplitudes and phases according to the eccentricity vectors and then subtracted from the displacement measurements before feeding to the PID controllers. The signal subtraction moves the active magnetic bearing control reference to the inertial axis. The rotor freely cranks with the mass eccentricity. The displacement probes sees the eccentricity. The controller does not respond to it. Thus, there is no imbalance force transmitted to the housing of the active magnetic bearing.

The advantages of the invention will become apparent from the following description and claims, and from the accompanying drawings, wherein:

FIG. 1a is a side view of an imbalance rotor supported by active magnetic bearings.

FIG. 1b is a cross-sectional view of the invention, showing the relationship of the probes to the rotor.

FIG. 2 is a schematic of the control system of the invention.

Referring now to the drawings in detail wherein like numerals indicate like elements throughout the several views, FIG. 1a shows a rotor 10 with a speed/phase indicator 11 and two disks 12, 14 which include imbalances 16, 18. Rotor 10 is supported by two active magnetic bearings 20, 22. Each active magnetic bearing 20, 22 is controlled in two independent axes Without the special control of this invention, rotor 10 would whirl around geometric axis 24 in the presence of imbalances 16, 18 and transmit imbalance forces to bearings 20, 22.

FIG. 1b discloses x-probe 28 and y-probe 30 of a bearing and a speed/phase probe 32 which detects speed mark 34 and phase marks 35 on the speed phase indicator.

FIG. 2 discloses the schematic of the control system of the invention showing only details of one of four independently controlled axes. X-probe 28 (parallel circuitry is provided for y-probe 30) provides a first input to adder 36. Probe 32 provides a once-per-revolution signal .omega. to sine-wave generator 38. Influence coefficient calculation module 40 provides values of E and .PHI. to sine-wave generator 38. Sine-wave generator 38 outputs a value of e.sub.x =E cos(.omega.t+.PHI.) which is subtracted by adder 36 from the displacement measurement by probe 28. The output of sine-wave generator 38 is also input to feed forward path 42 (which includes gain .DELTA.C.sub.d).

The output of adder 36 is received by magnetic bearing PID controller 44. Magnetic bearing PID controller 44 functionally includes four multipliers 45, 46, 47 and 48, each receiving the output of adder 36. The function of multipliers 45, 46, 47, 48 will become apparent from the forthcoming derivation. The outputs of multipliers 46, 47 and 48 are received and added by adder 50. The outputs of multiplier 45, adder 50, and feed forward path 42 are received and subtracted by adder 52. The output of adder 52 is received by power amplifier 54 which has a transfer function of G.sub.a (s). The output of power amplifier 54 is received by the coils of active magnetic bearing 20 or 22.

In operation, influence coefficient calculation module 40, preferably a digital computer, identifies the eccentricity (expressed as a vector) of the inertial axis at each active magnetic bearing 20, 22. The influence-coefficient method is similar to conventional two-plane rotor balancing and is well-known in the prior art. To apply this method, trial eccentricity vectors (E,.PHI.) can be provided by module 40 to sine-wave generators 38. Module 40 then measures the changes of output voltage signals V of all adders 50. A trial eccentricity vector is applied to one controller each time and the output changes of all adders 50 due to the trial vector are recorded. The relation between the trial vectors and adder 50 output changes is called an influence coefficient matrix. The matrix, once determined, will be used to calculate the eccentricity vectors which will eliminate the synchronods signals in all adder 50 output. Feed forward path 42 serves to null the negative spring effect of the magnetic field due to the bias currents of active magnetic bearings 20, 22.

The active magnetic bearing regulating force in the control axis of FIG. 2 is:

where:

k.sub.1 =current stiffness as a function of the bias current and air gap

k.sub.m =negative stiffness as a function of the bias current and air gap

x=active magnetic bearing journal displacement

The regulating current is:

where:

.DELTA.C.sub.d =proportional gain for nulling negative stiffness K.sub.m

C.sub.d =proportional gain for dynamic stiffness control

C.sub.e =integral gain for static stiffness control

C.sub.v =derivative gain for damping control

G.sub.p (s)=displacement probe gain and low-pass filter

G.sub.a (s)=amplifier/coil gain including low-pass effect due to slew-rate limit

e.sub.x =E cos(.omega.+.PHI.)

Substituting the above equation for i.sub.x into the above equation for the equation for F.sub.x and defining .DELTA.C.sub.d as K.sub.m /(K.sub.i G.sub.p G.sub.a) in rotating frequency range, and T(s) as C.sub.d +C.sub.e /(.tau..sub.i s+1)+C.sub.v s/(.tau..sub.v s+1), the following equation is derived:

Where the first term is the normal active magnetic stiffness and damping whereas the second term is the sinusoidal force generated in the active magnetic bearing. This second term is a forcing term because e.sub.x has constant amplitude and phase. The addition of the sine-wave generator 38 and associated components does not change the active magnetic bearing stiffness and damping. Therefore, the system stability is not affected the apparatus of this invention. The adjustment of E and .PHI. can be made automatically. The influence coefficients can be stored for periodically updating the eccentricity vectors. If a blade is lost, for example, new eccentricity vectors can be calculated immediately.

Thus the several aforementioned objects and advantages are most effectively attained. Although a single preferred embodiment of the invention has been disclosed and described in detail herein, it should be understood that this invention is in no sense limited thereby and its scope is to be determined by that of the appended claims.