Method and apparatus for minimizing vibration

• US 5,243,512 A
• Filed: 05/20/1991
• Issued: 09/07/1993
• Est. Priority Date: 05/20/1991
• Status: Expired due to Term

• Current Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Westinghouse Electric Company LLC (Brookfield Asset Management Incorporated)
• Inventors: Putman, Thomas H., Hill, Peter D.
• Primary Examiner(s): RUGGIERO, JOSEPH F
• Application Number:
  US07/703,330
• Time in Patent Office: 841 Days
• Field of Search: 364/400, 364/508, 364/572, 364/574, 364/148, 318/114, 318/128, 318/629, 318/649, 310/51, 73/583, 73/602, 73/658, 73/666, 73/668, 181/207-209, 381/71, 381/94
• US Class Current: 700/55
• CPC Class Codes: G05D 19/02 characterised by the use of electric means
• CPC Class Codes: G10K 2210/121 Rotating machines, e.g. engines, turbines, motors; Periodic or quasi-periodic signals in general
• CPC Class Codes: G10K 2210/125 Transformers
• CPC Class Codes: G10K 2210/129 Vibration, e.g. instead of, or in addition to, acoustic noise
• CPC Class Codes: G10K 2210/3012 Algorithms
• CPC Class Codes: G10K 2210/3019 Cross-terms between multiple in's and out's
• CPC Class Codes: G10K 2210/3021 Eigenfrequencies; Eigenvalues, e.g. used to identify most significant couplings between actuators and sensors
• CPC Class Codes: G10K 2210/3032 Harmonics or sub-harmonics
• CPC Class Codes: G10K 2210/3046 Multiple acoustic inputs, multiple acoustic outputs
• CPC Class Codes: G10K 2210/3053 Speeding up computation or convergence, or decreasing the computational load

Abstract

Vibration of a system such as a motor and pump on a platform or a transformer is minimized by applying a compensating force to the system. The optimum compensating force is determined by measuring the initial vibration and using that measurement in one of three algorithms to determine an adjustment to be made to the compensating force applied to the system at the time the initial vibration was measured. The adjusted compensating force is applied to the system which changes the vibration. That vibration is measured and applied to the selected algorithm to determine a second adjustment to the compensating force. The process is repeated until a compensating force is found which produces zero vibration, minimum vibration or a desired vibration. A plurality of sensors for measuring vibration and a plurality of actuators for applying a compensating force are preferably used.

Claims

1. An improved method for minimizing vibration of a system represented by a column matrix V_s ] and caused by a disturbing force acting on the system, the disturbing force represented by a column matrix D] the system being characterized by an m×

n transfer admittance matrix [Y] comprising the steps of;

a) providing a compensating force represented by column matrix F_c ] which may initially equal zero, and which can be changed as may be required by this method, such that a change in the compensating force will cause a change in the vibration V_s ];

b) measuring the vibration V_s ];

c) defining a matrix [A]=[Y]*^T [Y] wherein [Y]*^T is a transpose conjugate of the matrix [Y];

d) finding the eigenvalues and vectors of [A] by solving an equation [A]·

X]=Γ

[X] wherein Γ

=Γ

₁ thru Γ

_n are eigenvalues of [A] and X]=ⁿ ] are corresponding eigenvectors;

e) forming a modal matrix

space="preserve" listing-type="equation">[L.sub.a ]=[.sup.1 ], .sup.2 ] . . . .sup.n ]];

f) inverting [L_a ] to create [L_a ]^-1 ;

g) defining [μ

] as matrix ##EQU16## such that μ

₁ thru μ

_n are selected so that -<

(1-2μ

_i Γ

_i)<

1 where i=1, 2, . . . n;

h) solving for H]_i =2 [μ

]L_a ]^-1 [Y]^*T V_s ];

i) solving for Q]_i+1 =Q]_i -H]_i wherein Q]_i may initially equal zero;

j) solving for F_c ]_i+1 =[L_a ] Q]_i+1 ;

k) applying the force F_c ]_i+1 to the system;

l) thereafter measuring the vibration V_s ]; and

m) repeating steps c thru 1 until V_s ] reaches one of a minimum value and a desired value.

2. The method of claim 1 wherein the vibration is measured by m transducers each of which produces a harmonic with complex amplitude V where k=1, 2, . . . m and column matrix V_s ] is comprised of V₁ thru V_m.

3. The method of claim 1 wherein the compensating force is provided by n actuators each of force F_k where k=1, 2, . . . n and values of column matrix F_c ] are comprised of F₁ thru F_n.

4. The method of claim 1 wherein the vibration is measured by sensors, the compensating force is applied by actuators and more sensors than actuators are used.

5. The method of claim 1 wherein the μ

'"'"'s are chosen such that 0<

1-2μ

_i Γ

_i <

1 for i=1, 2, . . . n.

6. The method of claim 1 wherein all μ

_i Γ

_i are equal to one another such that ##EQU17##

7. The method of claim 1 wherein the system is a transformer.

8. An improved method for minimizing vibration of a system represented by a column matrix V_s ] and caused by a disturbing force acting on the system, the disturbing force represented by a column matrix D] the system being characterized by an m x n transfer admittance matrix [Y] comprising the steps of:

a) providing a compensating force represented by column matrix F_c ] which may initially equal zero, and which can be changed as may be required by this method, such that a change in the compensating force will cause a change in the vibration V_s ];

b) measuring the vibration V_s ];

c) defining a matrix [A]=[Y]*^T [Y] wherein [Y]*^T is a transposed conjugate of the matrix [Y];

d) solving for [X] in the equation [A]·

X]=Γ

[X] wherein Γ

=Γ

₁ thru Γ

_n which are eigenvalues of [A] and X]=^k ] is an eigenvector associated with the eigenvalue Γ

_k

e) forming a modal matrix

space="preserve" listing-type="equation">[L.sub.a ]=[.sup.1 ] .sup.2 ] . . . .sup.n ]];

f) inverting [L_a ] to create [L_a ]^-1 ;

g) defining [μ

] as matrix ##EQU18## such that the μ

'"'"'s are selected so that -1<

1-2μ

_i Γ

_i <

1

where i=1, 2 . . . n;

h) solving for

space="preserve" listing-type="equation">H].sub.i =2 [L.sub.a ] [μ

] [L.sub.a ].sup.-1 [Y].sup.*T V.sub.s ];

i) solving for F_c ]_i+1 =F_c ]_i -H]_i wherein F_c ]_i may initially equal zero and when this step is repeated F_c ]_i equals the F_c ] determined when this step was previously performed;

j) applying the force F_c ]_i+1 to the system;

k) thereafter measuring the vibration V_s ]; and

l) repeating steps h thru k until V_s ] reaches one of a minimum value and a desired value.

9. The method of claim 8 wherein the vibration is measured by m transducers each of which produces a harmonic with a complex amplitude V_k where k=1, 2, . . . . m and column matrix V_s ] is comprised of V₁ thru V_m.

10. The method of claim 8 wherein the compensating force is provided by n actuators each of which produce a harmonic force F_k where k=1, 2, . . . n with a complex amplitude and column matrix F_c ] is comprised of F₁ thru F_n.

11. The method of claim 8 wherein the vibration is measured by sensors, the compensating force is applied by actuators and more sensors than actuators are used.

12. The method of claim 8 wherein

0<

(1-2μ

_i Γ

_i)<

1.

13. The method of claim 8 wherein all μ

_i Γ

_i are equal to one another such that ##EQU19## and 0<

α

<

1.

14. The method of claim 8 wherein the system is a transformer.

15. An improved method for minimizing vibration of a system represented by a column matrix V_s ] and caused by a disturbing force acting on the system, the disturbing force represented by a column matrix D] the system being characterized by an m×

n transfer admittance matrix [Y] comprising the steps of;

a) providing a compensating force represented by column matrix F_c ] which may initially equal zero, and which can be changed as may be required by this method, such that a change in the compensating force will cause a change in the vibration V_s ];

b) measuring the vibration V_s ];

c) defining a matrix [A]=[Y]*^T [Y] wherein [Y]*^T is a transposed conjugate of the matrix [Y];

d) selecting some α

where 0<

α

<

1;

e) determining H] by solving the equation H]=(1-α

)[A]^-1 [Y]*^T V_s ] wherein [A]^-1 is an inverse of [A];

f) solving for F_c ]_i+1 =F_c ]_i -H]_i ;

g) applying the force F_c ]_i+1 to the system;

h) thereafter measuring the vibration V_s ]; and

i) repeating steps b, e, f, g and h until V_s ] reaches one of a minimum value and a desired value.

16. The method of claim 15 wherein the vibration is measured by m transducers each of which produces a harmonic with a complex amplitude V_k where k=1, 2, . . . m and column matrix V_s ] is comprised of V₁ thru V_m.

17. The method of claim 15 wherein the compensating force is provided by n actuators each of which produce a harmonic with a complex amplitude F_k where k-1, 2, . . . n and the values of column matrix F_c ] is comprised of F₁ thru F_n.

18. The method of claim 15 wherein the vibration is measured by sensors, the compensating force is applied by actuators and more sensors than actuators are used.

19. The method of claim 15 wherein the system is a transformer.

20. An improved transformer of the type having walls which vibrate during operation of the transformer wherein the improvement comprises

a) a plurality of sensors attached to the walls and connected to control means which sensors each generate a signal corresponding to a vibration of the wall to which the sensor is attached;

b) control means for receiving input from sensors and calculating forces from that input in accordance with at least one of Q-coordinate method, F-coordinate method and equal eigenvalues method and outputting directions to actuators to apply those forces; and

c) a plurality of actuators connected to the control means and attached to the walls of the transformer for applying forces to the walls as directed by the control means.

21. An apparatus for reducing vibrations in a system comprising

a) a plurality of sensors attached to the system for measuring vibration of the system at a point where the sensor is attached and generating a signal corresponding to that vibration;

b) control means connected to the sensors and receiving signals therefrom for calculating forces according to at least one of Q-coordinate method, F-coordinate method and equal eigenvalues method and directing actuates to apply the calculated forces to the system; and

c) a plurality of actuators connected to the control means and attached to the system for applying forces to the system as directed by signals from the control means.