Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T09:17:21.036Z Has data issue: false hasContentIssue false
  • English
  • Français

The Analysis of Radial Flow Impellers by the Matrix Finite Element Method

Published online by Cambridge University Press:  04 July 2016

A. S. L. Chan  and
R. K. Henrywood
A. S. L. Chan
Affiliation:
Department of Aeronautics, Imperial College, London
R. K. Henrywood
Affiliation:
Department of Aeronautics, Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Extract

The stress analysis of an axisymmetrical body under the influence of a field of centrifugal body force is of considerable importance to the design of rotating machinery. The classical problem of the rotating disc of uniform thickness was considered by Maxwell as long ago as 1850. For this, the simplifying assumption that the stresses are functions of the distance from the centre only, with no change across the thickness, was made. Since then, the same basic analysis has been extended to discs of conical and hyperbolical cross-section profile, with or without a central hole, references to which may be found in a number of text books. The analysis of a disc with an elliptical cross-section was published by Chree in 1895. The solution for a disc of constant thickness has been refined to allow stress variation across the thickness. Although these solutions, in common with many analytical solutions in the theory of elasticity, do not satisfy all the boundary conditions exactly, they serve as very good approximations in practice.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 75 , Issue 732 , December 1971 , pp. 850 - 860
Copyright
Copyright © Royal Aeronautical Society 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Maxwell, J. C. On the Equilibrium of Elastic Solids. Paper read to the Royal Society of Edinburgh, 1850.Google Scholar
2. Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, Third Edition, McGraw Hill, New York, 1970.Google Scholar
3. Prescott, J. Applied Elasticity. Dover. New York, 1946.Google Scholar
4. Biezeno, C. B. and Grammel, R. Engineering Dynamics. Vol 3, Steam Turbines, Blackie, London, 1954.Google Scholar
5. Chree, C. Isotropic Elastic Solid Ellipsoids under Forces Derivable from a Potential of the Second Degree. Proc Roy Soc London. Vol 58, 1895.Google Scholar
6. Kobayashi, A. S. and Trumpler, P. R. Elastic Stresses in a Rotating Disc of General Profile. Int J Mech Sci, Vol 2, No 1, 1960.Google Scholar
7. Hooke, C. J. Numerical Solution of Axisymmetric Stress Problems by Point Matching. J Strain Analysis, Vol 5, No 1, January, 1970.Google Scholar
8. Guernsey, R. Photoelastic Study of Centrifugal Stresses in a Single Wheel and Hub. Proc Soc for Exp Stress Analysis Vol 18, No 1, January, 1961.Google Scholar
9. Fessler, H. and Thorpe, T. E. Centrifugal Stresses in Rotationally Symmetrical Gas Turbine Discs. J Strain Analysis Vol 3, No 2, April, 1968.Google Scholar
10. Thurgood, D. A., Givan, V. E. F. and McEwan, J. R. Stress Analysis of the Asymmetric Profile Rotating Disc. Hawker Siddeley Dynamics Ltd, Stress Office Report No 619, December, 1967.Google Scholar
11. Thurgood, D. A. Stresses in Asymmetric Discs. J Strain Analysis Vol 4, No 1, January, 1969.Google Scholar
12. Givan, V. E. F. and Thurgood, D. A. Comparison of Stress Analysis Methods for Radial Flow Rotors, Hawker Siddeley Dynamics Ltd, Stress Office Report No 630, November, 1969.Google Scholar
13. Schilhansl, M. J. Stress Analysis of a Radial Flow Rotor. Trans ASME Ser A Vol 84, No 1, January, 1962.Google Scholar
14. Rimrott, F. P. J. and Bell, D. Stress and Strain Determination in Impellers of Asymmetrical Profile. Canadian Aeronautics and Space Journal Vol 9, No 3, March, 1963.Google Scholar
15. Swansson, N. S. The Stress Analysis of a Radial Flow Impeller. Australian Defence Scientific Service. ARL ME Note 259, August, 1963.Google Scholar
16. Meriam, J. L. Centrifugal Stresses in Impellers. Aircraft Engineering Vol 15, No 175, September, 1943.Google Scholar
17. Argyris, J. H. Energy Theorems and Structural Analysis. Part 1 General Theory. Aircraft Engineering Vol 26, 1954, Vol 27, 1955. (Now published Butterworths, Fourth Edition, London, 1971).Google Scholar
18. Stordahl, H. and Christensen, H. Finite Element Analysis of Axisymmetric Rotors. J Strain Analysis Vol 4, No 3, July, 1969.Google Scholar
19. Argyris, J. H. Tetrahedron Elements with Linearly Varying Strain for the Matrix Displacement Method. Aeronautical Journal Vol 69, No 660, December, 1965.Google Scholar
20. Argyris, J. H. Triangular Elements with Linearly Varying Strain for the Matrix Displacement Method. Journal of the Royal Aeronautical Society Vol 69, No 658, October, 1965.Google Scholar
21. Argyris, J. H., Kamel, H., Sorenson, M., Schmid, G. and Pretsch, H. Automatic System for Kinematic Analysis (ASKA). ISD Report No 8. Stuttgart. October, 1965.Google Scholar
22. Chan, A. S. L. and Firmin, A. The Analysis of Cooling Towers by the Matrix Finite Element Method. Part 1. Small Displacements. Aeronautical Journal of the Royal Aeronautical Society Vol 74, No 718, October, 1970.Google Scholar
23. Westlake, J. R. Numerical Matrix Inversion and Solution of Linear Equations. John Wiley. New York, 1968.Google Scholar
24. Berezin, I. S. and Zhidkov, N. P. Computing Methods Vol 1, Pergamon, London, 1965.Google Scholar
25. Argyris, J. H. The TRIAX 6 Element for Axisymmetric Analysis by the Matrix Displacement Method. Aeronautical Journal of the Royal Aeronautical Society Vol 70, No 672, December, 1966.Google Scholar