Claims
- 1. A method for improving the vibrational characteristics of a device having a rotating element, the method comprising:
(a) in a computer, generating a computer model of a first version of a device having a rotating element; (b) selecting a set of independent vibration shape functions for the rotating element; (c) calculating the stationary natural frequencies of the rotating element corresponding to the independent vibration shape functions; (d) calculating gyroscopic coefficients of the rotating element from the independent vibration shape functions; (e) solving gyroscopic equations of motion to obtain some of the vibrational characteristics of the rotating element through generalized coordinates corresponding to the independent vibration shape functions; (f) transforming the obtained vibrational characteristics from modal space into three-dimensional physical space; and (g) using the transformed vibrational characteristics to modify the first version of the device.
- 2. The method of claim 1, wherein the computer model comprises a mesh suitable for finite element analysis.
- 3. The method of claim 1, wherein the independent vibration shape functions are stationary vibration mode shapes of the rotating element.
- 4. The method of claim 2, wherein at least some of the natural frequencies and said independent vibration shape functions are determined using a finite element analysis applied to the computer model wherein the rotating element is stationary, undamped, and subject to free boundary conditions.
- 5. The method of claim 1, wherein the set of equations of motion includes externally applied generalized forces, damping forces, and centrifugal stiffening effects from the rotating element.
- 6. The method of claim 1, wherein the coefficient of the set of equation of motion are derived from the natural frequencies and the gyroscopic coefficients.
- 7. The method of claims 5 wherein the damping forces are modeled in the form of modal viscous damping factors.
- 8. The method of claim 1, wherein the equations of motion comprise constant coefficients.
- 9. A method for improving the vibrational characteristics of a device, the method comprising the steps of:
(a) in a computer, generating a computer model of a first version of a device having a rotating element, a stationary element, and at least one bearing disposed between the rotating element and the non-rotating element; (b) selecting a first set of independent vibration shape functions for the rotating element; (c) calculating the stationary natural frequencies of the rotating element corresponding to the first set of independent vibration shape functions; (d) calculating gyroscopic coefficients of the rotating element from the first set of independent vibration shape functions; (e) selecting a second set of independent vibration shape functions for the non-rotating element; (f) calculating natural frequencies of the non-rotating element corresponding to the second set of independent vibration shape functions; (g) solving a set of gyroscopic equations of motion to obtain some of the vibrational characteristics of the rotating element through generalized coordinates corresponding to the first and second sets of independent vibration shape functions; (h) transforming the obtained vibrational characteristics from modal space into three-dimensional physical space; and (i) modifying the first version of the device using the vibrational characteristics to generate a second version of the device.
- 10. The method of claim 9, wherein the computer model or part of the computer model is a mesh suitable for finite element analysis.
- 11. The method of claim 9, wherein the first set of independent vibration shape functions are stationary vibration mode shapes of the rotating element.
- 12. The method of claim 9, wherein the first set of independent vibration shape functions is a portion of the vibration mode shapes, defined over the rotating part, of the device while the rotating part of the device is stationary.
- 13. The method of claim 9, wherein the second set of independent vibration shape functions is vibration mode shapes of the non-rotating element.
- 14. The method of claim 9, wherein the second set of independent vibration shape functions is a portion of vibration mode shapes, defined over the non-rotating part, of the device while the rotating part of the device is stationary.
- 15. The method of claim 9, wherein the non-rotating part is rigid.
- 16. The method of claim 10, wherein at least some of the natural frequencies and said independent vibration shape functions of the rotating part are determined using a finite element analysis applied to the model of the rotating element, wherein the rotating element is stationary, undamped, and subject to free boundary conditions.
- 17. The method of claim 9, wherein the set of equations of motion includes externally applied generalized forces, damping forces, and centrifugal stiffening effects from the rotating element.
- 18. The method of claim 9, wherein the set of equations of motion includes externally applied generalized forces, damping forces, and externally prescribed motion of the non-rotating element.
- 19. The method of claim 9, wherein the set of equation of motion includes generalized forces from the bearings.
- 20. The method of claim 9, wherein the coefficient of the set of equation of motion are calculated from the natural frequencies of the rotating element and the non-rotating element and from the gyroscopic coefficients of the rotating element.
- 21. The method of claims 17, wherein the damping forces of the rotating element and the non-rotating element are modeled as modal viscous damping factors.
- 22. The method of claim 9, wherein the equations of motion comprise constant coefficients.
- 23. The method of claim 9, wherein the bearing model is a linear combinations of spring forces and damping forces.
- 24. The method of claim 23, wherein the spring forces and damping forces are nonlinear.
- 25. The method of claim 9, wherein the rotating element and the non-rotating element are modeled as linearly elastic elements.
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of Provisional Applications No. 60/473,748, filed May 27, 2003, and No. 60/517,684, filed Nov. 6, 2003, the benefit of which is hereby claimed under 35 U.S.C. § 119.
STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH OR DEVELOPMENT
[0002] The present invention was made in the course of research that was supported by the National Science Foundation under grants CMS-0244116 and CMS-9820745. The United States Government may have certain rights to the invention herein.
Provisional Applications (2)
|
Number |
Date |
Country |
|
60473748 |
May 2003 |
US |
|
60517684 |
Nov 2003 |
US |