MODAL ANALYSIS OF THE ROTOR SYSTEM TOMÁŠ JAMRÓZ ...

20th SVSFEM ANSYS Users' Group Meeting and Conference 2012
SVSFEM s.r.o
MODAL ANALYSIS OF THE ROTOR SYSTEM
TOMÁŠ JAMRÓZ, KAREL PATOČKA, VLADIMÍR DÁNIEL, TOMÁŠ HORÁČEK
Aerospace research and test establishment
Abstract: The article deals with the issue of modelling of fundamental dynamic
calculations in ANSYS Workbench environment. There are shown discrepancies in the
modal analysis calculation of bodies system using an unstructured grid. It is pointed out
correct choice of function for the contact surface. Furthermore, the article highlights the
problem of preload modal analysis. There is shown the influence of the function "Bolt
Pretension" on the results of a modal analysis.
Keywords: modal analysis, rotor, preload
1 Introduction
This article deals with the issue of modelling of fundamental dynamic calculations in the
ANSYS Workbench environment. Under the term basic dynamic characteristics are
understood modal properties such as natural frequencies and eigenmodes of the system.
These basic dynamic characteristics are obtained for rotor system of free turbine
consisting of 13 parts. The reason for the identification of modal parameters is their
subsequent use in the optimization of the main and distributor gear set.
Fig. 1 Construction of rotor system
http://aum.svsfem.cz
1

20th SVSFEM ANSYS Users' Group Meeting and Conference 2012
SVSFEM s.r.o
Modal properties of above mentioned rotor system were solved in the software Ansys
Workbench environment. There was placed emphasis mainly on torsion modes of system
whose dynamic characteristics have the greatest influence on the dynamics of gearing.
Free free modal analysis of the system was calculated, thus excluding boundary
conditions of rotor system. It was also taken into consideration the mounting requirements
and examined the effect of rotor system preload. Preload of the rotor system was
modelled using multi-bodies and contact functions instead of using one bond solid from a
CAD system.
2 Modeling of preload
As mentioned in the introduction, the rotor assembly is preloaded in the axial direction of
the axial force. This preload is given by torque union nut, which fixed the rotor system of
the rotor shaft in the axial direction. Shift of natural frequencies of the rotor system was
investigated with respect to the axial preload.
The task was solved by two successive analysis: static one followed by modal one with
delegated stiffness matrix from the previous calculation. Preload of rotor shaft was solved
with the help of "Bolt Pretension" function which was applied to the in the halfway crosssection
of the shaft between the bearings. The results of structural analysis of rotor
system with preload are shown in Fig.2. The nominal value of normal stress is 48MPa in
the shaft.
Fig. 2 Normal stress in rotor system from preload
The subsequently performed comparison between modal analyses with and without
pretension proved that the preloading has a negligible effect on the natural frequencies
shift with respect to torsion and bending modes. The frequency increase for these modes
was very small. The only natural frequencies of axial modes were markedly affected
(frequency shift was about 30%). Preload had the opposite effect for the modes (the
natural frequencies were reduced).
As shown in Fig.3, the substantial decrease of the axial natural frequency values is mainly
caused by the elements in a spot, where the "Bolt Pretension" function was applied to.
The „Bolt Pretension“ function was applied in the form of input load.
http://aum.svsfem.cz
2

20th SVSFEM ANSYS Users' Group Meeting and Conference 2012
SVSFEM s.r.o
Application of preload using either thermal boundary conditions or the “Bolt Pretension”
function in the form of displacement or shifts in contacts could prevent unwanted changes
of natural frequencies in the axial direction at preload modal analysis.
Fig. 3 Axial nature frequency
When comparing the eigenmodes of multi-body system with and without preload applied it
was found that the first six rigid modes do not have zero values of natural frequencies.
The frequency values are 155Hz, 155Hz and 285Hz for the rotating modes for the given
rotor set.
Fig. 4 The first torsion nature frequency mode
http://aum.svsfem.cz
3

20th SVSFEM ANSYS Users' Group Meeting and Conference 2012
SVSFEM s.r.o
Tab. 1 Natural frequencies (number 7-10 are the bending modes, 11 is first torsion mode and 12 is
the axial mode)
No. preload Without preload
1 0.55776 4.26E-03
2 0.55809 6.07E-03
3 0.55812 6.28E-03
4 155 154
5 156 155
6 212 212
7 739 739
8 742 742
9 2020 2019
10 2023 2022
11 2850 2853
12 3893 5037
3 Rigid modes issues
As already mentioned in the previous chapter, Ansys Workbench environment in
"standard setting" computes the non-zero rigid modes for the analysis of the system of
bodies connected by contact functions with unstructured mesh.
Another finding was the discrepancy in the values of the natural frequencies for the
system imported into Ansys environment as a single body and for system imported in
Ansys as an assembly and afterwards connected by contact functions in
Ansys/DesignModeler environment. When using the contact function "Bonded-Pure
Penalty" the difference was about 5% w.r.t. single body model. The latter value also
roughly corresponds to the value of the frequency shift of rigid modes. In case of the first
two bending modes and torsion mode the differences were 18% and 12%, respectively.
Fig. 5 The rigid rotation modes
As recommended by representatives of Ansys software, MPC method was used for
contacts. Using such a contact the natural frequencies differences changed from 18% to
5% and from 15% to 2% for the first two bending modes and the first torsion mode,
respectively. The frequency shift was equal about 5% for all other modes. There was also
a significant decrease in the frequency values of the rotating rigid modes - from about
285Hz to about 25Hz.
http://aum.svsfem.cz
4

20th SVSFEM ANSYS Users' Group Meeting and Conference 2012
SVSFEM s.r.o
Tab. 2 Comparison of natural frequencies for contact functions Pure Penalty, Augmented lagrange
and MPC (number 7-10 are the bending modes, 11 is first torsion mode and 12 is the axial mode)
No. One-body
Multi-body system
system
Pure Penalty Augmented
MPC
lagrange
Frequency
[Hz]
Frequency
[Hz]
Shift
[%]
Frequency
[Hz]
Shift
[%]
Frequency
[Hz]
Shift
[%]
1 0 0 0 0
2 0 0 0 0
3 0 0 0 0
4 0 203 203 14
5 0 205 205 24
6 0 285 285 26
7 755 894 18 894 18 795 5
8 756 898 19 898 19 799 6
9 2179 2321 6 2321 6 2284 5
10 2182 2323 6 2323 6 2289 5
11 3480 3850 12 3850 12 3532 1
12 4819 5047 5 5047 5 5044 5
4 Displacement in the gear tooth
In the introduction it was mentioned that the several dynamic variables are needed to
optimize the gearbox. One of the dynamic variables is the average tangential
displacement of the diametral pitch for torsion mode.
The path along the tooth could not be defined by two points for this type of gear because
of helical gearing. Deviation from a straight line is small, but the resulting tangential
displacement values are significantly different.
2,9400
2,9200
2,9000
2,8800
2,8600
2,8400
2,8200
2,8000
2,7800
2,7600
Pure Penalty
2,7400
0,0000 0,0050 0,0100 0,0150 0,0200
Fig. 6 Diagram of tangential displacement along the gear tooth for torsion mode
http://aum.svsfem.cz
5

20th SVSFEM ANSYS Users' Group Meeting and Conference 2012
SVSFEM s.r.o
The curves showing tangential displacement values along the length of the tooth for
different contact function are compared in the Fig. 6. The graph shows that the curve
shape does not change for different contact functions. The curves are only shifted. In
addition, the difference is negligible.
Tab. 3 Comparison of mean value of tangential displacement among contact functions
Body (Contact functions)
Mean value of tangential disp.
[m]
Difference
[%]
One body (no contact function) 2.7925 0.00
Multi-body („Pure Penalty“) 2.9041 3.99
Multi-body („Lagrange“) 2.9041 3.99
Multi-body( „MPC“) 2.8766 3.01
5 Conclusion
In our case the preload has no effect on the natural frequency of the torsion mode but it
can affect the frequency shift of axial modes for particular contact function used. Only if
"Bolt Pretension" in the form of load input is used the frequencies decrease significantly
for all axial modes. This undesirable effect can be avoided by application of preload using
either thermal boundary conditions or the “Bolt Pretension” function in the form of
displacement or shifts in contacts.
In case of modal analysis calculation of multi-body system (where contact function have to
be used), MPC contact function should be used to minimize the shift of natural
frequencies and to bring the natural frequencies of rigid modes near to zero. Then the
frequency deviations are also relatively small compared to one-body system. The nonzero
rigid modes issue does not exist when structured mesh is used.
Acknowledgement
The work was performed with support of EC FP7 project Efficient Systems and Propulsion
for Small Aircraft – ESPOSA. Project number: 284 859
Contact address:
Ing. Tomáš Jamróz
VZLÚ
Beranových 130
19905 Praha – Letňany
jamtoz@vzlu.cz
tel: +420 225115593
- The whole document is written in Arial
- The whole document follows singe lines
- Page margins: left 3 cm, others 2.5 cm
- Image, table and equation numbering is automatic by Seq fields named Image, Tab and Eqv. You
can just copy mentioned fields in this template. Bookmarks and Cross-references should form Field
references.
- symbol of free line
http://aum.svsfem.cz
6