Rotor Dynamic Analysis Using Xl Rotor

Rotordynamic Analysis Using XLRotor SQi-03A-112008 Technote, SpectraQuest Inc. (Nov. 2008)

ROTORDYNAMIC ANALYSIS USING XLROTOR

Mohsen Nakhaeinejad, Suri Ganeriwala

SpectraQuest Inc., 8227 Hermitage Road, Richmond, VA 23228

Ph: (804)261-3300 Fax: (804)261-3303 Nov 2008

Abstract The rotordynamic analysis of the SpectraQuest Machinery Fault Simulator (MFS) Magnum is performed in

XLRotor to study critical speeds and imbalance response of the machine. MFS Magnum machine including

motor, shaft, disks, coupling and rolling element bearings is modeled and the rotordynamic analysis was

performed using the rotordynamic software XLRotor. The stiffness and damping associated with rolling

element bearings of the motor and shaft are calculated in the software. Different shaft and disk

configurations are introduced to the model, the whole rotating system is solved for damped critical speeds

and mode shapes are obtained. Also, imbalance response is studied, bearing displacements and dynamic

loads on the bearings are obtained and presented. This study clearly shows the power of the XLRotor for

rotordynamic analysis.

Keywords: Rotordynamic Analysis, Critical Speed, Rotating Machinery, Imbalance

Response, XLRotor, MFS Magnum

1. INTRODUCTION

Rotating machinery produces vibration signatures depending on the structure and

mechanism involved. Faults in machine also can increase and excite the vibrations.

Vibration behavior of the machine due to natural frequency and imbalance is one of the

important topics in rotating machinery which should be studied and considered in design.

All objects exhibit at least one natural frequency which depends on the structure of the

object. The critical speed of a rotating system occurs when the rotational speed matches a

natural frequency. The lowest speed at which a natural frequency is encountered is called

the first critical. As the speed increases, additional critical speeds may be observed.

Minimizing rotational unbalance and unnecessary external forces are very important to

reducing the overall forces, which initiate resonance. Due to the enormous destructive

energy and vibration at resonance, the main concerns when designing a rotating machine

are how to avoid operation at or closed to criticals and how to pass safely through the

criticals in acceleration and deceleration. Safely refers not only to catastrophic breakage

and human injury but also to excessive wear on the equipment.

Since the real dynamics of machines in operation is difficult to model theoretically,

calculations are based on the simplified model which resembles the various structural

components. Obtained equations from models can be solved either analytically or

numerically. Also, Finite Element Methods (FEM) is another approach for modeling and

analysis of the machine for natural frequencies. Resonance tests to confirm the precise


frequencies are often performed on the prototype machine and then the design revised as

necessary to assure that resonance does not become an issue.

XLRotor as a rotordynamic software provides powerful, fast and accurate tools to

perform rotordynamic modeling and analysis. Comprehensive capabilities of the software

include analysis of undamped and damped critical speeds, imbalance, stability, mode

shapes, nonlinear transient response, torsion, synchronous and asynchronous force

response, indeterminate static deflection, rolling element bearings and fluid film bearings.

All model inputs are entered on worksheets and several templates and modules are

available to create the model of each part. Completing computations and analysis by the

software, the results are available through tables and charts in Excel worksheets.

The objective of this technical note is to study the rotordynamic behavior of the

SpectraQuest Machinery Fault Simulator (MFS) Magnum including critical speeds and

imbalance responses. To achieve this goal, the MFS Magnum machine shown in Fig. 1

including motor, shaft, disks, coupling and rolling element bearings is modeled and the

rotordynamic analysis was performed using the rotordynamic software XLRotor. The

stiffness and damping associated with rolling element bearings of the motor and shaft are

calculated in the software. Different shaft and configurations are introduced to the model,

the whole rotating system is solved for damped critical speeds and mode shapes are

obtained. Also, imbalance response analysis for the rotor in acceleration is studied and

dynamic load on the bearings are obtained and presented.

2. MODELING AND ANALYSIS PROCEDURES

In this study, the SpectraQuests Machinery Fault Simulator (MFS) Magnum is modeled in the rotordynamic analysis software XLRotor. Undamped and damped critical speeds

and imbalance response are obtained for different rotor/disk configurations.

Fig. 1 SpectraQuests Machinery Fault Simulator (MFS) Magnum used for the critical speed test

The Machinery Fault Simulator (MFS) Magnum illustrated in Fig. 1 can be used to

introduce, simulate and study rotating machinery faults. Rotating parts consist of


1/2 shaft

UCS1 DE/MS2 IR3

UCS

DE/MS

IR

5/8 shaft

UCS

DE/MS

IR

UCS

DE/MS

IR

rotor/bearings of the motor, beam coupling, and the rotating shaft supported by two

rolling element bearings. The span between two bearings is 28.5 inches. Disks can be

mounted on the shaft at different locations and the unbalance can be introduced on disks.

The simulator can run experiments with different size and configuration of bearings, shaft

and disks. In this study, several configurations of rotating parts of the MFS Magnum with

two disks and two shafts 1/2" and 5/8" are modeled. Dimensions and material properties

used in the model were chosen to be closed to the real machine as much as possible.

Since the beam coupling shown in Fig. 2(b) is a structure rather than a simple beam, the

material properties were obtained by running a force/displacement experiment.

(a)

(b)

(c)

Fig. 2 The rotating parts of the MFS Magnum. (a): the rotor of the motor supported on two bearings (b):

beam coupling which connects the motor to the rotating shaft (c): bearings and housings which supports the

rotating shaft of the machine

XLRotor is a powerful and fast software to perform any kind of rotordynamic analysis on

rotor bearing system models. Comprehensive capabilities of the software include

analysis of undamped and damped critical speeds, imbalance, stability, mode shapes,

nonlinear transient response, torsion, synchronous and asynchronous force response,

indeterminate static deflection, rolling element bearings and fluid film bearings. All

model inputs are entered on worksheets and several templates and modules are available

to create the model of each part. Completing computations and analysis by the software,

the results are available through tables and charts in Excel worksheets.

Table 1 Different disk/rotor configurations used for modeling of the MFS Magnum machine in XLRotor

1 UCS: Undamped Critical Speed Analysis 2

DE/MS: Damped Eigenvalue and Mode Shape Analysis 3

IR: Imbalance Response Analysis


Modeling has been done for different shaft/disks configuration. The whole sets of

modeling configurations and analysis are summarized in Table 1. Two different shaft

sizes of and 5/8 were modeled and for each model two different disks configurations were considered as shown in Table 1. For each case undamped critical speed, damped

eigenvalue, mode shape and imbalance response analysis has been done. Table 2 shows

the parameters and specifications of the MFS rotor which was modeled in XLRotor.

Table 2 Specifications of the MFS Magnum machine modeled in XLRotor

motor: Marathon Four In One CAT No - D 391

beam coupling stiffness obtained by experiment 1800 (psi)

shaft diameter 0.625 (inch)

shaft length 36.25 (inch)

shaft overhung from outboard bearing 3.5 (inch)

rotor bearings span 28.5 (inch)

disks diameter (aluminum): 6 (inch)

disks thickness 0.625 (inch)

rolling element bearings used for the 5/8 shaft ER-10K

rolling element bearings used for the 1/2 shaft ER-8K

3. ROLLING ELEMENT BEARING ANALYSIS

Rotors are supported by bearings and lateral vibration of the machine depends on the

stiffness and damping behavior of bearing. Therefore structural analysis of the bearings is

necessary for rotordynamic analysis. XLRotor performs bearing analysis and compute

structural charactresitics of the bearing to be linked to the rotor model.

3.1. Rolling Element Bearings of the Motor

Rotor of the motor is supported by two rolling element bearings. The bearings

specifications shown in Table 3 are used in XLRotor for modeling.

Table 3 Motor Ball Bearings Specification

Model: NSK 620 3, Bore 5/8 Number of Balls: 8

OR Curvature: 0.53 Ball Diameter: 0.2656 (in)

IR Curvature: 0.516 Pitch Diameter: 1.122 (in)

Contact Angle: 0 Material Density: 0.283 (lb/in3)

Poisson's Ratio: 0.3 Elastic Modulus: 2.9E+7 (psi)

Stiffness and damping parameters of the bearings as well as rotordynamic coefficients for

different speeds are calculated and illustrated. Curve fitting is also done by the software

to estimate stiffness and damping parameters of the bearings.


sti

ffn

ess

(lb

/in

)

dam

pin

g (

lb.s

/in

)

Table 4 Calculated stiffness and damping parameters of the motor bearings

Speed

rpm

Kxx

lb/in

Kxy

lb/in

Kyx

lb/in

Kyy

lb/in

Cxx

lb-s/in

Cxy

lb-s/in

Cyx

lb-s/in

Cyy

lb-s/in

0 80249 0 0 80249 3 0 0 3 10000 83049 0 0 83049 3 0 0 3

20000 86774 0 0 86774 3 0 0 3

30000 82396 0 0 82396 3 0 0 3

40000 83417 0 0 83417 3 0 0 3

50000 85353 0 0 85353 3 0 0 3

100000.

90000.

80000.

70000.

60000.

50000.

40000.

30000.

20000.

10000.

0.

Kxx

Kxy

Kyx

Kyy

0 10000 20000 30000 40000 50000 60000

speed (rpm)

(a)

4 3 3

Cxx

2 Cxy

2 Cyx

1 Cyy

1

0

0 10000 20000 30000 40000 50000 60000

speed (rpm)

(b)

Fig. 3 Stiffness (a) and damping (b) behavior of the motor bearings

3.2. Rolling Element Bearings of the Shaft

The rotating shaft is supported by two rolling element bearing. The bearings are modeled

and rotordynamic coefficients associated with the bearings are calculated to be used in

the main model.

Table 5 Rotor Ball Bearings Specification: ER-10K

Model: ER-10K, Bore 5/8 Number of Balls: 8

OR Curvature: 0.53 Ball Diameter: 0.3125 (in)

IR Curvature: 0.516 Pitch Diameter: 1.319 (in)

Contact Angle: 0 Material Density: 0.283 (lb/in3)

Poisson's Ratio: 0.3 Elastic Modulus: 2.9E+7 (psi)

Table 6 Calculated stiffness and damping parameters of the bearings supporting the shaft

Speed

rpm

Kxx

lb/in

Kxy

lb/in

Kyx

lb/in

Kyy

lb/in

Cxx

lb-s/in

Cxy

lb-s/in

Cyx

lb-s/in

Cyy

lb-s/in

0 84718 0 0 84718 3 0 0 3 10000 89385 0 0 89385 3 0 0 3

20000 85898 0 0 85898 3 0 0 3

30000 86560 0 0 86560 3 0 0 3

40000 89373 0 0 89373 3 0 0 3

50000 93506 0 0 93506 3 0 0 3


sti

ffn

es

s (

lb/i

n)

dam

pin

g (l

b.s

/in

)

100000.

90000.

80000.

70000.

60000.

50000.

40000.

30000.

20000.

10000.

0.

Kxx

Kxy

Kyx

Kyy

0 10000 20000 30000 40000 50000 60000

speed (rpm)

4 3 3

Cxx 2

Cxy 2

Cyx

1 Cyy

1 0

0 10000 20000 30000 40000 50000 60000

speed (rpm)

(a)

Fig. 4 Stiffness (a) and damping (b) of the 5/8 rotor bearings (ER-10K) (b)

In bearing analysis, damping force is very small compare to other structural forces.

Therefore for calculations small values are chosen for the damping parameters. Also, in

bearing analysis, it is assumed that cross stiffness values are zero.

4. CRITICAL SPEEDS AND MODE SHAPES

As shown in Table 1 several configuration of the shaft (1/2 and 5/8) and disks (located closed to the bearings and at the shaft center) are modeled. In this section for each case

undamped and damped critical speeds, and mode shapes are calculated. First critical

speeds of the rotor as a function of bearing stiffness obtained and results are illustrated in

graphs as Undamped Critical Speed Map. It is clear that bearing stiffness can increase or

decrease the critical speeds. Damped eigenvalues for lateral rotor model is obtained by

the software and presented as Damped Natural Frequency Map. This plot shows how the

natural frequencies of the model vary with running speed. Gyroscopics and speed

dependent bearing coefficients are what cause the natural frequencies to depend on speed.

The Synchronous Line on this plot identifies the synchronous critical speeds of the

damped rotor system. The mode shapes for each critical speed are calculated by the

software and illustrated in graphs as Damped Mode Shapes. For each mode shape the

geometry of the rotating parts is also overlaid to the graph to clearly show the nodes and

displacements of the rotor.

Two different shaft size and 5/8 are considered and for each shaft two disks configurations are modeled. Therefore four models are created and for each model, first

the model configuration is shown, then undamped critical speed plots are shown. The

natural frequencies are plotted as function of rotor speed. Finally, the mode shapes are

illustrated.


Critic

al

Sp

ee

d,

cp

m

Sh

aft

Ra

diu

s, in

S

ha

ft R

ad

ius

, in

Na

tura

l F

requ

en

cy, cpm

S

ha

ft R

ad

ius

, in

0

0 0

4.1. Model with Shaft

1/2 Shaft

Fig. 5 Model configuration including rotor of the motor, motor bearings, coupling, 1/2 shaft, two ER8K bearings of the shaft and two gold disks closed to the housings.

Undamped and Damped Critical Speed Analysis

Undamped Critical Speed Map SpectraQuest Machinery Fault Simulator (MFS) Magnum

1/2" shaf t w ith gold disks closed to the housings

100000

cpm1

cpm2

cpm3

18000

16000

14000

Rotordynamic Damped Natural Frequency Map

SpectraQuest Machinery Fault Simulator (MFS) Magnum


12000

10000

1000

1000. 10000. 100000. 1000000.

Bearing Stiffness, lb/in

10000

8000

6000

4000

2000

0

cpm1

cpm2

cpm3

Sy nchronous

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Rotor Speed, rpm

Fig. 6 Undamped critical speed map (left) as a function of bearing stiffness and damped natural frequency

map (right) as a function of rotor speed

Damped Mode Shapes

Damped 1st Mode Shape


1/2" shaft with gold disks closed to the housings


Spec traQues t Mac hinery Fault Simulator (MFS) Magnum

1/2" shaft w ith gold disks closed to the housings

15

f =3008.9 cpm

10 d=.0001 z eta

5

2 4 6

8 10 12 14 16 18 20 22 24

-5

-10

-15

0 10 20 30 40 50

Axial Location, in

f=3008.9 cpm

d=.0001 zeta

(a) (b)

Damped 2nd Mode Shape



15

f =8174.5 cpm 15

d=.0003 z eta

10 10

Damped 3rd Mode Shape



f =15344.5 cpm

d=.0003 z eta

5

2 4 6

8 10 12 14 16 18 20 22 24

5

2 4 6

8 10 12 14 16 18 20 22 24

-5 -5

-10

-10

-15

0 10 20 30 40 50

Axial Location, in

-15

0 10 20 30 40 50

Axial Location, in

(c) (d) Fig. 7 Damped mode shape of MFS Magnum machine with 1/2 shaft and two gold disks closed to the housings. (a) damped 1

st mode, (b) 3D damped 1

st mode (c) damped 2

nd mode, (d) damped 3

rd mode shape


Sh

aft

Rad

ius

, in

C

ritic

al S

pe

ed

, cp

m

Sh

aft

Ra

diu

s,

in

Na

tura

l F

requ

en

cy, cpm

S

ha

ft R

ad

ius

, in

0

0

1/2 Shaft

Fig. 8 Model configuration including rotor of the motor, motor bearings, coupling, 1/2 shaft, two gold disks closed to the center and two ER8K rotor bearings.

Undamped and Damped Critical Speed Analysis Undamped Critical Speed Map



100000 cpm1

cpm2

cpm3

18000

16000

14000

1/2" shaft w ith gold disks closed to the center

10000

1000

1000. 10000. 100000. 1000000.


12000

10000

8000

6000

4000

2000

0

cpm1

cpm2

cpm3

Sy nchronous

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Rotor Speed, rpm

Fig. 9 Undamped critical speed map as a function of bearing stiffness (left) and damped natural frequency

map as a function of rotor speed (right).

Damped Mode Shapes



1/2" shaft with gold disks closed to the center


Spec traQuest Mac hinery Fault Simulator (MFS) Magnum

1/2" s haf t w ith gold dis ks c losed to the c enter

15

f =1785.0 cpm

d=.0 zeta

10

5

16

2 4 6

8 10 12 14 16 18 20 22 24

-5

-10

-15

0 10 20 30 40 50

Axial Location, in

f=1785.0 cpm

d=.0 zeta

(a) (b)




15 15

f =10839.7 cpm

d=.0001 zeta 10 10




f =16316.2 cpm

d=.0008 zeta

5 16

2 4 6

8 10 12 14 16 18 20 22 24

5

2 4 6

8 0

16

10 12 14 16 18 20 22 24

-5 -5

-10

-10

-15

0 10 20 30 40 50

Axial Location, in

-15

0 10 20 30 40 50

Axial Location, in

(c) (d)

Fig. 10 Damped mode shapes of MFS Magnum machine with 1/2 shaft and two gold disks closed to the shaft center. (a) damped 1


st mode, (c) damped 2


rd mode


Critica

l S

pe

ed

, cpm

S

ha

ft R

ad

ius,

in

Sh

aft

Ra

diu

s, in

Natu

ral F

req

ue

ncy, cp

m

Sh

aft

Ra

diu

s, in

4 6

4.2. Model with 5/8 Shaft

5/8 Shaft

Fig. 11 Model configuration including rotor of the motor, motor bearings, coupling, 5/8 shaft, two ER10K bearings of the shaft and two gold disks closed to the housings.

Undamped and Damped Critical Speed Analysis

Undamped Critical Speed Map SpectraQues t Machinery Fault Simulator (MFS) Magnum

5/8" shaf t w ith gold dis ks closed to the bearings

100000

cpm1

cpm2

cpm3

10000

25000

20000

15000

10000


SpectraQues t Mac hinery Fault Simulator (MFS) Magnum

5/8" shaf t w ith gold disks c los ed to the bearings

cpm1

cpm2

cpm3

Synchronous

5000

1000

1000. 10000. 100000. 1000000.


0

0 5000 10000 15000 20000 25000

Rotor Speed, rpm

Fig. 12 Undamped critical speed map (left) as a function of bearing stiffness and damped natural frequency

map (right) as a function of rotor speed

Damped Mode Shapes



5/8" shaft with gold disks closed to the bearings

Damped 1st Mode Shape 3D Plot

Spec traQues t Mac hinery Fault Simulator (MFS) Magnum

5/8" s haf t w ith gold dis ks closed to the bearings

15

10 f =3654.1 cpm

d=.0001 zeta

5

2 4 6

8 10 12 14 16 18 20 22 24 0

-5

-10

-15

0 10 20 30 40 50

Axial Location, in

f=3654.1 cpm

d=.0001 zeta

(a) (b)




15 15

f =11003.8 cpm

d=.0006 z eta

10 10




f =20266.6 c pm

d=.0018 z eta

5

2 4 6

8 10 12 14 16 18 20 22 24 0

5

0 2 8 10

12 14

16 18

20 22 24

-5 -5

-10

-10

-15

0 10 20 30 40 50

Axial Location, in

-15

0 10 20 30 40 50

Axial Location, in

(c) (d) Fig. 13 Damped mode shape of MFS Magnum machine with 5/8 shaft and two gold disks closed to the bearings. (a) damped 1


st mode (c) damped 2


rd mode shape


Sh

aft

Ra

diu

s,

in

Sh

aft

Ra

diu

s,

in

Critica

l Sp

eed

, cpm

Sh

aft

Ra

diu

s,

in

Na

tura

l Fre

que

ncy, c

pm

5/8 Shaft

Fig. 14 Model configuration including rotor of the motor, motor bearings, coupling, 5/8 shaft, two gold disks closed to the center and two ER10K rotor bearings.

Undamped and Damped Critical Speed Analysis U ndamped Critical Speed Map

SpectraQues t Machinery Fault Simulator (MFS) Magnum

100000

cpm1

cpm2

cpm3

10000

25000

20000

15000

10000


SpectraQues t Mac hinery Fault Simulator (MFS) Magnum

cpm2

cpm3

Synchronous

5000

1000

1000. 10000. 100000. 1000000.


0

0 5000 10000 15000 20000 25000

Rotor Speed, rpm

Fig. 15 Undamped critical speed map as a function of bearing stiffness (left) and damped natural frequency

map as a function of rotor speed (right).

Undamped Mode Shapes



5/8" shaft with gold disks closed to the shaft center

Damped 1st Mode Shape 3D Plot


5/8" shaf t w ith gold disks closed to the shaf t center

15 f =2444.4 c pm

d=.0 zeta

10

5

16

2 4 6

8 10 12 14 16 18 20 22 24 0

-5

-10

-15

0 10 20 30 40 50

f=2444.4 cpm

d=.0 zeta

(a) Axial Location, in (b)




15

f =13485.4 c pm 15

d=.0001 zeta

10 10




f =20714.0 cpm

d=.003 zeta

5

16

2 4 6

8 10 12 14 16 18 20 22 24 0

5 16

2 4 6

8 10 12 14 16 18 20 22 24 0

-5 -5

-10 -10

-15

0 10 20 30 40 50

Axial Location, in

-15

0 10 20 30 40 50

Axial Location, in

(c) (d)

Fig. 16 Damped mode shapes of MFS Magnum machine with 5/8 shaft and two gold disks closed to the shaft center. (a) damped 1


st mode, (c) damped 2


rd mode


Critical speeds for each model are extracted from the Damped Natural Frequency Maps

and presented in Table 7 For these configurations, the MFS Magnum can reach the first

mode and the higher modes are too far from the operating range of the machine.

Changing the configuration with different shaft and disks might allow higher modes to be

seen on the MFS Magnum.

Table 7 Critical speeds of the SpectraQuest MFS Magnum machine calculated by XLRotor

1st

CS1 (cpm) 2

nd CS (cpm) 3

rd CS (cpm)

1/2 shaft

3008 8174 15344

1785 10839 16316

5/8 shaft

1 CS: Critical Speed

3654 11003 20266

2444 13485 20714

5. IMBALANCE RESPONSE ANALYSIS

Rotor imbalance causes lateral vibration and creates dynamic force on the supporting

bearings. Also, the imbalance in rotating machinery can excite the natural frequency of

the machine and cause resonance. XLRotor allows studying the imbalance response of

the model. First imbalance weights are defined and the observation station on the rotor

for monitoring the displacement and dynamic loads are specified. Running the model for

imbalance response, displacements on desired stations as well as dynamic forces on

bearings are calculated and plotted as function of rotor speed.

In this report, for each model defined in Table 1 imbalance weight is introduced on the

disk closed to the inboard bearing and displacements of the motor bearings and shaft

bearings are calculated and presented in form of bode plots. Also dynamic forces on the

bearings due to imbalance weight are obtained and presented. The imbalance responses

are function of rotor speed. At critical speeds when machine passes the natural

frequencies, the increase in magnitude and changing the phased is observed from the

bode plots. Also, based on the structural parameters of the bearings such as stiffness and

damping which calculated before, dynamic forces on bearings are created. The force

picks are when machine passes the critical speeds.


Resp

on

se,

mil

s p

-p

Beari

ng

L

oad

, lb

pk

Beari

ng

L

oad

, lb

pk

Resp

on

se,

mil

s p

-p

Beari

ng

L

oad

, lb

pk

Beari

ng

L

oad

, lb

pk

5.1. Model with Shaft

1/2 Shaft

(a)

160

140

120

Rot or dynam ic Re sponse Plot



Sta. No. 12: Inboar d bearing housing abs. disp.

360

270

180

90 Major A mp 0

160

140

120




Sta. No. 23: Outboard bearing housing abs. disp.

360

270

180

90 Major A mp 0

100

80

60

40

20

0

-90

-180

-270

-360

-450

-540

-630

-720

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(b)

Horz Amp

Vert Amp

Horz Phs

Vert Phs

100

80

60

40

20

0

-90

-180

-270

-360

-450

-540

-630

-720

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(c)

Horz Amp

Vert Amp

Horz Phs

Vert Phs

Rotordynam ic Be ar ing Load Plot Rotordynam ic Be ar ing Load Plot

7000

6000

5000

4000

3000

2000

1000

Spectr aQuest Machinery Fault Simulator (MFS) Magnum


Brg at Stn 12: Inboard Brg 1/2"

Max Load

Horz Load

Vert Load

6000

5000

4000

3000

2000

1000



Brg at Stn 23: Outboard Brg 1/2"

Max Load

Horz Load

Vert Load

0

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(d)

0

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(e)


800

700

600

500

400

300

200

100

0



Brg at Stn 3: Motor Bearings 6203

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(f)

Max Load

Horz Load

Vert Load

2500

2000

1500

1000

500

0




0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(g)

Max Load

Horz Load

Vert Load

Fig. 17 Imbalance response plots for 16 (gm-in) imbalance weight on the left disk which is closed to the

inboard bearing. (a): model configuration, (b): phase and amp. disp. of inboard housing, (c): phase and

amp. disp. of outboard housing, (d), (e), (f) and (g): dynamic loads on shaft inboard bearing, shaft outboard

bearing, motor outboard bearing and motor inboard bearing respectively.

Tech Note, SpectraQuest Inc.

Rotordynamic Analysis using XLRotor

SQI03-02800-0811

Resp

on

se,

mil

s p

-p

Beari

ng

L

oad

, lb

pk

Beari

ng

L

oad

, lb

pk

Resp

on

se,

mil

s p

-p

Beari

ng

L

oad

, lb

pk

Beari

ng

L

oad

, lb

pk

1/2 Shaft

(a)



1/2" shaf t w ith gold disks closed to the center

Sta. No. 12: Inboard bearing housing abs. disp.

6 360

270

5 180

90 Major A mp 4 0

2.5

2





360

270

180

90 Major A mp 0

-90

3 -180

Horz Amp

Vert Amp

1.5 -90

-180

Horz Amp

Vert Amp

-270 Horz Phs 1 2 -360

-270 Horz Phs -360

-450

1 -540

-630

0 -720

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(b)

Vert Phs 0.5

0

-450

-540

-630

-720

0 2000 4000 6000 8000 10000

Rotor Spe ed, r pm

(c)

Vert Phs


250

200

150

100

50

0



Brg at Stn 12: Inboard Brg 1/2"

0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(d)

Max Load

Horz Load

Vert Load



Brg at Stn 23: Outboard Brg 1/2"

90

80

70

60

50

40

30

20

10

0

0 2000 4000 6000 8000 10000

Rot or Spe ed, r pm

(e)

Max Load

Horz Load

Vert Load





45

40

35

30

25

20

15

10

5

0

0 2000 4000 6000 8000 10000

Rot or Spe ed, r pm

(f)

Max Load

Horz Load

Vert Load

140

120

100

80

60

40

20

0




0 2000 4000 6000 8000 10000

Rotor Spee d, r pm

(g)

Max Load

Horz Load

Vert Load


inboard bearing. (a): model configuration, (b): phase and amp. disp. of inboard housing, (c): phase and





SQI03-02800-0811

5.2. Model with 5/8 Shaft

Res

po

nse,

mils p

-p

Beari

ng

L

oad

, lb

pk

B

eari

ng

L

oad

, lb

pk

Res

po

nse,

mils p

-p

Beari

ng

L

oad

, lb

pk

B

eari

ng

L

oad

, lb

pk

5/8 Shaft

(a)



5/8" shaf t w ith gold disks closed to the bearings


6 360

270

5 180

90 Major A mp

4 0

4

3.5

3





360

270

180

90 Major A mp

0

-90

3 -180

Horz Amp

Vert Amp

2.5

2

-90

-180

Horz Amp

Vert Amp

-270 Horz Phs 2 -360

1.5 -270 Horz Phs -360

-450

1 -540

-630

0 -720

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(b)

Vert Phs 1

0.5

0

-450

-540

-630

-720

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(c)

Vert Phs


250



Brg at Stn 12: Inboard Brg 5/8

140



Brg at Stn 23: Outboar d Brg 5/8

200

150

100

50

Max Load

Horz Load

Vert Load

120

100

80

60

40

20

Max Load

Horz Load

Vert Load

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spe ed, r pm

(d)

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spe ed, r pm

(e)





30

25

20

15

10

5

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(f)

Max Load

Horz Load

Vert Load




90

80

70

60

50

40

30

20

10

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(g)

Max Load

Horz Load

Vert Load

Fig. 19 Imbalance response plots for 16 (gm-in) imbalance weight on the left gold disk which is closed to

the inboard bearing. (a): model configuration, (b): phase and amp. disp. of inboard housing, (c): phase and





SQI03-02800-0811

Resp

on

se,

mil

s p

-p

Beari

ng

L

oad

, lb

pk

Beari

ng

L

oad

, lb

pk

Resp

on

se,

mil

s p

-p

Beari

ng

L

oad

, lb

pk

Beari

ng

L

oad

, lb

pk

5/8 Shaft

(a)

4

3.5

3





360

270

180

90 Major A mp 0

2.5

2





360

270

180

90 Major A mp 0

2.5

2

1.5

1

0.5

0

-90

-180

-270

-360

-450

-540

-630

-720

Horz Amp

Vert Amp

Horz Phs

Vert Phs

1.5

1

0.5

0

-90

-180

-270

-360

-450

-540

-630

-720

Horz Amp

Vert Amp

Horz Phs

Vert Phs

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spe ed, r pm

(b)

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spe ed, r pm

(c)


140

120

100

80

60

40

20

0



Brg at Stn 12: Inboard Brg 5/8

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spe ed, r pm

(d)

Max Load

Horz Load

Vert Load



Brg at Stn 23: Outboar d Brg 5/8

80

70

60

50

40

30

20

10

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(e)

Max Load

Horz Load

Vert Load





25




70

60 20

50

15 Max Load 40

Horz Load

10 Vert Load 30

20

5 10

Max Load

Horz Load

Vert Load

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(f)

0

0 1000 2000 3000 4000 5000 6000 7000

Rotor Spee d, r pm

(g)


inboard bearing. (a): model configuration, (b): phase and amplitude disp. of inboard housing, (c): phase and





SQI03-02800-0811

6. SUMMARY AND CONCLUSION

In this technical note, the rotordynamic analysis of rotating machinery including

undamped critical speed, damped eigenvalues, mode shapes and imbalance responses

were studied. XLRotor, which is a powerful software for rotordynamic analysis was used

for modeling and analysis. The SpectraQuest Machinery Fault Simulator (MFS) Magnum

was considered as the rotating machine and the model of the machine including all

rotating parts and rolling element bearings was created in the software. Two different

shaft size of and 5/8 were modeled and for each case two different disks configurations were considered. First rolling element bearing of the motor and the shaft

were modeled. Stiffness and damping effects of the bearings were obtained as the

function of rotational speed and reconstructed by curve fitting to be used for critical

speed analysis. Then each case of the shaft and disks configuration including rolling

element bearings was modeled and solved for undamped critical speeds, damped

eigenvalues and mode shapes. Also, the imbalance response of the model given an

imbalance weight on one of the disks was studied using the XLRotor. In imbalance

response analysis, displacement amplitude and phase for the outboard and inboard

bearings were obtained and illustrated as a function of rotor speed. Dynamic forces on

four bearings also were illustrated as function of speed.

From the results it can be observed that the effect of rotor geometry and configurations

on critical speed and vibration of the machine is significant. At critical speeds vibration

and displacements increase. Therefore the dynamic forces on the bearing supports

increase. Simulation results on rolling element bearing show the changes of the bearing

stiffness when the rotor speed changes. This effect happens because of centrifugal effect

in rolling elements. This nonlinear behavior can change the natural frequency of the

rotating machine supported on bearings when the rotor speed change.

The mode shape plots illustrate the maximum and minimum displacement and

deformation of the rotor. Nodes and the shapes of deformation can be observed clearly

using the simulation results created by XLRotor. Overall, this technical report clearly

shows the power of the XLRotor for rotordynamic analysis. In this study few capabilities

of the XLRotor were used to accomplish the job. The software has many more tools

available for comprehensive rotordynamic analysis such as tensional analysis, linear and

nonlinear analysis, synchronous and asynchronous force response, indeterminate static

deflection, nonlinear transient response, fluid film bearing analysis.

Documents

Rotor Dynamic Analysis Using Xl Rotor