## Abstract

Conventional rotordynamic analyses generally treat the rotor as a continuous body without considering effect of clamped joints. However, in modern rotating machines, rotors are often assembled with multiple complex-shaped parts and joints, which may significantly affect rotordynamic behavior. Several authors have proposed methods for implementing contact effects in rotordynamic analysis, but a more general modeling method for handling arbitrary contact geometries with various levels of surface roughness is needed. The present paper suggests a new contact model for rotordynamic analysis of an assembled rotor-bearing system with multiple parts connected by multiple joints. A contact element formulation is presented using solid finite elements and statistics-based contact theories. A test arrangement was developed to validate the proposed contact model for varying interface surface roughness and preloads. An iterative computation algorithm is introduced to solve the implicit relation between contact stiffness and stress distribution. Prediction results, using the contact model, are compared with measured natural frequencies for multiple configurations of a test rotor assembly. A case study is performed for an overhung type rotor-bearing system to investigate the effect of contact interfaces, between an overhung impeller and a rotor shaft, on critical speeds.

## References

1.
Abramowitz
,
M.
, and
Stegun
,
I. A.
,
1965
,
Handbook of Mathematical Functions
,
General Publishing Company, Ltd
,
Toronto, Ontario
.
2.
,
A. C.
, and
Kirk
,
R. G.
,
2004
, “
Part II—Case Studies for a Synchronous Thermal Instability Operating in Overhung Rotors
,”
Int. J. Rotating Mach.
,
10
(
6
), pp.
477
487
. 10.1155/S1023621X04000478
3.
Bhushan
,
B.
,
1998
, “
Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact
,”
Tribol. Lett.
,
4
(
1
), pp.
1
35
. 10.1023/A:1019186601445
4.
Brake
,
M. R.
,
2017
,
The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics
,
Springer
,
Cham, Switzerland
.
5.
Brake
,
M. R.
,
Reuss
,
P.
,
Segalman
,
D. J.
, and
Gaul
,
L.
,
2014
, “
Variability and Repeatability of Jointed Structures with Frictional Interfaces
,”
32nd International Modal Analysis Conference (IMAC XXXII)
,
Orlando
, FL, pp.
245
252
.
6.
Budynas
,
R. G.
, and
Nisbett
,
J. K.
,
2008
,
Shigley's Mechanical Engineering Design
,
McGraw-Hill
,
New York
.
7.
Combescure
,
D.
, and
Lazarus
,
A.
,
2008
, “
Refined Finite Element Modelling for the Vibration Analysis of Large Rotating Machines: Application to the Gas Turbine Modular Helium Reactor Power Conversion Unit
,”
J. Sound Vib.
,
318
(
4-5
), pp.
1262
1280
. 10.1016/j.jsv.2008.04.025
8.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
2002
,
Concepts and Applications of Finite Element Analysis
,
John Wiley & Sons. Inc
., Hoboken,
NJ
.
9.
Fantetti
,
A.
,
Tamatam
,
L. R.
,
Volvert
,
M.
,
Lawal
,
I.
,
Liu
,
L.
,
Salles
,
L.
, and
Nowell
,
D.
,
2019
, “
The Impact of Fretting Wear on Structural Dynamics: Experiment and Simulation
,”
Tribol. Int.
,
138
, pp.
111
124
. 10.1016/j.triboint.2019.05.023
10.
Festjens
,
H.
,
Chevallier
,
G.
, and
Dion
,
J. L.
,
2014
, “
Nonlinear Model Order Reduction of Jointed Structures for Dynamic Analysis
,”
J. Sound Vib.
,
333
(
7
), pp.
2100
2113
. 10.1016/j.jsv.2013.11.039
11.
Firrone
,
C. M.
, and
Zucca
,
S.
,
2009
, “
Underplatform Dampers for Turbine Blades: The Effect of Damper Static Balance on the Blade Dynamics
,”
Numer. Anal.-Theory Appl.
,
36
(
4
), pp.
515
522
.
12.
Gao
,
J.
,
Yuan
,
Q.
,
Li
,
P.
,
Feng
,
Z.
,
Zhang
,
H.
, and
Lv
,
Z.
,
2012
, “
Effects of Bending Moments and Pretightening Forces on the Flexural Stiffness of Contact Interfaces in Rod-Fastened Rotors
,”
ASME J. Eng. Gas Turbines Power
,
134
(
10
), p.
102503
. 10.1115/1.4007026
13.
Gastaldi
,
C.
, and
Gola
,
M. M.
,
2016
, “
On the Relevance of a Microslip Contact Model for Under-Platform Dampers
,”
Int. J. Mech. Sci.
,
115-116
, pp.
145
156
. 10.1016/j.ijmecsci.2016.06.015
14.
Gaul
,
L.
, and
Lenz
,
J.
,
1997
, “
Nonlinear Dynamics of Structures Assembled by Bolted Joints
,”
Acta Mech.
,
125
(
1-4
), pp.
169
181
.
15.
Genta
,
G.
,
2005
,
Dynamics of Rotating Systems
,
Springer
,
New York
.
16.
Greenwood
,
J. A.
, and
Williamson
,
J. B.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proceedings of the Royal Society A: Mathematical, Physical, Engineering Sciences
,
295
(
1442
), pp.
300
319
.
17.
Guyan
,
R. J.
,
1965
, “
Reduction of Stiffness and Mass Matrices
,”
AIAA J.
,
3
(
2
), p.
380
.
18.
Kessel
,
R.
,
Kacker
,
R.
, and
Berglund
,
M.
,
2006
, “
Coefficient of Contribution to the Combined Standard Uncertainty
,”
Metrologia
,
43
(
4
), pp.
S189
S195
. 10.1088/0026-1394/43/4/S04
19.
Liu
,
X.
,
Yuan
,
Q.
,
Liu
,
Y.
, and
Gao
,
J.
,
2014
, “
Analysis of the Stiffness of Hirth Couplings in Rod-Fastened Rotors Based on Experimental Modal Parameter Identification
,”
Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition
,
Duesseldorf, Germany
.
20.
Lu
,
M.
,
Geng
,
H.
,
Xu
,
G.
, and
Yu
,
L.
,
2013
, “
Analytical and Experimental Study of Dynamic Characteristics of Rod Fastened Rotor-Bearing System Under Preload Saturation
,”
Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition
,
San Antonio, TX
.
21.
Mayer
,
M. H.
, and
Gaul
,
L.
,
2007
, “
Segment-to-Segment Contact Elements for Modelling Joint Interfaces in Finite Element Analysis
,”
Mech. Syst. Signal Process.
,
21
(
2
), pp.
724
734
. 10.1016/j.ymssp.2005.10.006
22.
McCool
,
J. I.
,
1986
, “
Comparison of Models for the Contact of Rough Surfaces
,”
Wear
,
107
(
1
), pp.
37
60
. 10.1016/0043-1648(86)90045-1
23.
Müser
,
M. H.
,
Dapp
,
W. B.
,
Rugnicourt
,
R.
,
Sainsot
,
P.
,
Lesaffre
,
N.
,
Lubrecht
,
T. A.
,
,
B. N.
,
Harris
,
K.
,
Bennett
,
A.
,
Schulze
,
K.
, and
Rohde
,
S.
,
2017
, “
Meeting the Contact-Mechanics Challenge
,”
Tribol. Lett.
,
65
(
4
), p.
118
. 10.1007/s11249-017-0900-2
24.
Oh
,
J.
,
Palazzolo
,
A. B.
, and
Hu
,
L.
,
2020
, “
Stability of Non-Axisymmetric Rotor and Bearing Systems Modeled With Three-Dimensional-Solid Finite Elements
,”
ASME J. Vib. Acoust.
,
142
(
1
), p.
011010
. 10.1115/1.4045099
25.
Palazzolo
,
A. B.
,
2016
,
Vibration Theory and Applications With Finite Elements and Active Vibration Control
,
Wiley
,
Chichester, UK
.
26.
Peng
,
H.
,
Liu
,
Z.
,
Wang
,
G.
, and
Zhang
,
M.
,
2011
, “
Rotor Dynamic Analysis of Tie-Bolt Fastened Rotor Based on Elastic-Plastic Contact
,”
Proceedings of ASME Turbo Expo 2011
,
.
27.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2003
, “
Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks
,”
ASME J. Turbomach.
,
125
(
2
), pp.
364
371
. 10.1115/1.1539868
28.
Peyret
,
N.
,
Chevallier
,
G.
, and
Dion
,
J. L.
,
2013
, “
Dynamics of Assembled Structures: Taking Into Account the Surface Defects in Interfaces
,”
ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Portland, France
.
29.
Rimpel
,
A. M.
, and
Leopard
,
M.
,
2020
, “
Simple Contact Stiffness Model Validation for Tie Bolt Rotor Design With Butt Joints and Pilot Fits
,”
ASME J. Eng. Gas Turbine Power
,
142
(
1
), p.
011014
. 10.1115/1.4045102
30.
Sherif
,
H. A.
, and
Kossa
,
S. S.
,
1991
, “
Relationship Between Normal and Tangential Contact Stiffness of Nominally Flat Surfaces
,”
Wear
,
151
(
1
), pp.
49
62
. 10.1016/0043-1648(91)90345-U
31.
Stender
,
M.
,
Papangelo
,
A.
,
Allen
,
M.
,
Brake
,
M. R.
,
Schwingshackl
,
C.
, and
Tiedemann
,
M.
,
2016
, “
Structural Design With Joints for Maximum Dissipation
,”
Shock Vibration, Aircraft/Aerospace, Energy Harvesting, Acoustics & Optics
,
9
, pp.
179
187
.
32.
Süß
,
D.
, and
Willner
,
K.
,
2015
, “
Investigation of a Jointed Friction Oscillator Using the Multiharmonic Balance Method
,”
Mech. Syst. Signal Process.
,
52-53
, pp.
73
87
. 10.1016/j.ymssp.2014.08.003
33.
Vannini
,
G.
,
2014
, “
Rotordynamic Validation of an Ultra High Speed Multistage Centrifugal Compressor Stacked Rotor
,”
Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition
,
Duesseldorf, Germany
.
34.
Yang
,
J.
, and
Palazzolo
,
A. B.
,
2019
, “
Three-Dimensional Thermo-Elasto-Hydrodynamic Computational Fluid Dynamics Model of a Tilting Pad Journal Bearing—Part I: Static Response
,”
ASME J. Tribol.
,
141
(
6
), p.
061702
. 10.1115/1.4043349
35.
Yang
,
J.
, and
Palazzolo
,
A. B.
,
2019
, “
Three-Dimensional Thermo-Elasto-Hydrodynamic Computational Fluid Dynamics Model of a Tilting Pad Journal Bearing—Part II: Dynamic Response
,”
ASME J. Tribol.
,
141
(
6
), p.
061703
. 10.1115/1.4043350
36.
Zhang
,
Y.
,
Du
,
Z.
,
Shi
,
L.
, and
Liu
,
S.
,
2010
, “
Determination of Contact Stiffness of Rod-Fastened Rotors Based on Modal Test and Finite Element Analysis
,”
ASME J. Eng. Gas Turbine Power
,
132
(
9
), p.
094501
. 10.1115/1.4000591
37.
Zhuo
,
M.
,
Yang
,
L. H.
, and
Yu
,
L.
,
2016
, “
Contact Stiffness Calculation and Effects on Rotordynamic of Rod Fastened Rotor
,”
Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition
,
Phoenix, AZ
.