Dynamics of the rotor systemDynamics of the rotor system, ,

supported by the active magnetic supported by the active magnetic

bearingsbearings

LeontievLeontiev M. K.M. K.

Professor Professor MAIMAI, , general director of the engineering & consulting centre general director of the engineering & consulting centre

The III International Scientific and Technical Conference

«Aeroengines of the XXI century»

Professor Professor MAIMAI, , general director of the engineering & consulting centre general director of the engineering & consulting centre

of Alfaof Alfa--TranzitTranzit Co., LtdCo., Ltd

DavidovDavidov A. V.A. V.

Postgraduate student ofPostgraduate student of MAIMAI

DegtyarevDegtyarev S. A.S. A.

Development Development team leader ofteam leader of AlfaAlfa--TranzitTranzit Co.,LtdCo.,Ltd

December 2010December 2010

• high-vacuum turbo-molecular pumps

• precision measuring instruments,

gyroscopes,

test desks etc.

• centrifugal compressors

• grinding and milling spindles

• balancing machines

• flywheels for energy accumulation

• gas generators

• pump stations

• absence of lubrication and wear

• absence of contact and contamination

• active control of stiffness and damping

• rotation speed(up to 800 000 rpm)

• low noise level

• precision of rotor axis position (up to

0.5 µ m)

• work in extreme conditions

(high-vacuum, zero gravity, variable

temperatures )

• limited bearing capacity

• high objective power

• high heat generation

• high weight

• control system is required

Active magnetic bearingsActive magnetic bearings

ProblemsField of application Features of application

The turbo-blower for cooling

a laser (CO2). Speed is 54000

rpm , the

rotor mass is 3.6 kg, the motor

power is 12 kW, the radial

bearing diameter is

48 mm, the

bearing force is 230 N

(TRUMPF/MECOS).

The synchronous

generator supported by

the superconductive

magnetic bearings.

Temperature is 28K,

maximum

speed is 4500 rpm

(SIEMENS).

The compressor HOFIM for

pumping natural gas:

integration of the direct drive

and the magnetic bearing

in the turbomachine, 6 MW,

9000 rpm (MAN Turbo/S2M).

The gas-turbine generator: 4 radial

bearings and 1 thrust bearing,

6010 rpm, 9000 kW, the bearing

diameter is 400 mm (S2M).

Magnetic force:

PID-controller:

The modulusThe modulus –– The magnetic bearingThe magnetic bearing–– for the rotor dynamics tasksfor the rotor dynamics tasks

Ki = 0 Kp = constK = 0 K = const Kp = const Kd = const

Kd = 0

Kd = 30

Kd = 500

Ki = 0 Kp = const

Kd= var

Kp = 20000

Kp = 50000

Kp = 70000

Ki = 0 Kd = const

Kp = var

Kp = const Kd = const

Ki = var

Ki = 400000

Ki = 0Ki = 100000

Ki = 1e+6

The DYNAMICS R4 software for the rotor system analysis The DYNAMICS R4 software for the rotor system analysis

and design in the unsteady and nonand design in the unsteady and non--linear approachlinear approach

F(t)F(t)F(t)F(t)Any types of dynamic loads – internal and external– F(t)F(t)F(t)F(t)

Dynamic model of the rotor system

Dynamics R4

IntegrationIntegration of theof the ““Magnetic bearingMagnetic bearing”” modulus intomodulus into Dynamics R4Dynamics R4

Model of non-linear link (for example, AMB)

The elements for the rotors simulation in Dynamics R4 The elements for the rotors simulation in Dynamics R4

Spring link Ball and roller bearingsDeflection limiter

(clearance)

Magnetic bearing

Representation

Model

Representation

ModelModel

Representation

Model

Representation

Initial data

Initial data

Initial data

Initial data

The rotor model on magnetic suspension in Dynamics R4 The rotor model on magnetic suspension in Dynamics R4

Clearance

Расчетные параметры АМПАМП АМП Зазор

AMBAMB

Unbalance D=5 g cm

Rotor parameters Clearance

Mass, m 23.76 kg

Length, L 852 mm

Ball

bearing

Spring link with

the base

Nominal stiffness, N/m 0.5e +8

Nominal damping, N sec/m 6000

Radial clearance, mm 0.5

Backup bearings parameters

Ball

bearing

Spring link with

the base

Stiffness, N/m 1е+8

Damping, N s/m 800

Radial clearance, mm 0.25

AMB parameters

Length, L 852 mm

Moment of inertia, Jd 0.92 kg m2

Nominal speed, ω 500 Hz

Critical speeds of the rotor supported by AMBCritical speeds of the rotor supported by AMB

k1=0.5e +8 Н/м k2=0.5e +8 Н/м

ForcedForced oscillationsoscillations ooff the the rotorrotor supportedsupported byby AMB AMB

Узел Критические частоты

вращения, об/мин

17373 24637 45303

Вал ротора 15.506 3.843 87.558

АМП1 48.745 43.710 3.602

АМП2 35.749 52.447 8.839

Сумма 100 100 100

Locus chart of logarithmic decrements Distribution of deformations potential energy

3D -

amplitude-frequency rotor response

2D -

amplitude-frequency rotor response.

The AMB1section

UnsteadyUnsteady analysisanalysis ofof the the rotorrotor supportedsupported byby AMBAMB

Unsteady analysis in consideration of weight,

К=0.5 е+8 =const

Change in current, Iпред = 5 А

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000

Transient response

[mm

]

[1/min]

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000

Transient response

Cu

rre

nt,

I_1

[A

]

[1/min]

Reactions in support Motion orbits, AMB1 section

-1000

-750

-500

-250

0

250

500

750

1000

1250

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000

Transient response

Ph

ys

ica

l fo

rce

, fy

1 [

N]

[1/min]

PD controller PID controller

AMB stiffness and damping controlAMB stiffness and damping control

6000

6500

7000

7500

8000

8500

9000

9500

10000

10500

11000

11500

12000

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000

Transient response

Dam

pin

g in

xx d

irection, C

xx [N*s

/m]

[1/min]

AMB damping control

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000

Transient response

Stiff

ness in

xx d

irection, K

xx [N/m

][e8]

[1/min]

AMB stiffness control

The rThe rotorotor dropdowndropdown onon the the journaljournal bearingsbearings

(Steel on babbit) 0.005

(Steel on graphit) 0.1

-1.00

-0.75

-0.50

-0.25

-0.00

0.25

0.50

0.75

1.00

-0.01 -0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11

Transient response

[mm

]

[s]

Journal bearing 1 Journal bearing 2

Radial clearance in AMB , mm 0.5

Radial clearance in journal bearing,

mm

0.25

AMB stiffness, N/m 0.5e+8

AMB damping, N s/m 6000

Contact stiffness, N/m 1е+10

-0.15

-0.10

-0.05

0.00

0.05

Transient response

[mm

]

Transition period

Going into

backward precession Backward precession-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.01 -0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Transient response

[mm

]

[s]

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.01 -0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Transient response

[mm

]

[s]

-0.35

-0.30

-0.25

-0.20

-0.15

0.015 0.016 0.017 0.018 0.019 0.020 0.021 0.022 0.023 0.024

[mm

]

[s]

The rThe rotorotor dropdowndropdown onon the the rollingrolling bearingsbearings

Going into

whirling motion

Bearing 1 Bearing 2

Radial clearance in AMB , mm 0.5

Radial clearance in rolling bearing,

mm

0

Radial clearance between the shaft

and the rolling bearing, mm

0.25

AMB stiffness, N/m 0.5e+8

AMB damping, N s/m 6000

Contact stiffness in rolling bearing,

N/m

1е+10

The rotor stop.

Rotating speed changes from n = 30000 rpm

up to n = 0 rpm

t= 10 s

Movement before

whirling motion

Rotating speed of

inner ring of rolling

bearing

n = 30000 rpm

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

-0.02 -0.01 -0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

Transient response

[mm

]

[s]

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.02 -0.01 -0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

Transient response

[mm

]

[s]

Full-clearance motion Following stop

The general methodology of designing the rotor The general methodology of designing the rotor

supported by AMBsupported by AMB

Determination of necessary values of AMB stiffness and damping

Determination of the rotor’s damped critical speeds and mode shapes – places of prospective resonances

Calculation of forced oscillations and amplitude values of vibroparameters : displacements, vibrovelocity,

reactions in supporting units. etc.

Estimation of AMB control coefficients and adjustment of the control system

Development of the program of current – AMB stiffness and damping – control for passing systems

resonances and going into the operating range

characteristics at transient regimes

Unsteady analysis of the rotor supported by AMB with the aim of more precise definition of the rotor’s

characteristics at transient regimes

Simulation of the rotor supported by backup bearings. The non-linear unsteady rotor analysis. The aim is to

determine the possibility of the rotor’s going into whirling motion or backward precession

The unsteady rotor analysis after switching off AMB supported by non-linear rolling bearings while the rotor’s

deceleration and determination of resonance regimes

THANK YOU FOR

YOUR ATTENTION!