Field Balancing의절차와방법

최 성 필박사

㈜터보링크

한국수자원공사교육자료(2005. 9. 8)

2

Balancing 이란?

ISO 1925

회전체의질량분포를조사하고필요하다면저널의진동과베어링의작용력들이

운전속도에대응하는주파수에서특정한한계내에있도록조정하는절차

3

Balancing Machine

Shop Balancing Field Balancing

Low Speed

Balancing Machine

Soft Mount Type

Hard Mount Type

High Speed

Balancing Machine

Soft Mount Type

Hard Mount Type

Balancing

4

불평형원인

Manufacturing (제작)

소재밀도(material density) 의불균일

가공정밀도

비대칭형상

Etc.

Assembly (조립)

조립공차

Operation

부식

이물질부착

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회전체분류(ISO)

Rigid Rotor(강성회전체)

양면밸런싱으로수정가능한로터로써, 로터의최대운전속도까지

승속하여도잔류불평형량이변하지않는로터.

Flexible Rotor(탄성회전체)

Rigid Rotor를제외한모든로터

Rigid Rotor Flexible Rotor

Speed (N)

Am

plitu

de

1st Critical Speed for Flexible Mode

6

밸런싱용어

Unbalance

Unit: g·mm

U = m x r

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밸런싱용어

Unbalance

Static Unbalance

Couple Unbalance

Dynamic Unbalance

F

Cg

e

F1

F2

Cg

F1

F2

Static

Unbalance

Couple

Unbalance

Dynamic

Unbalance

Principle inertia axis

Shaft axis

Cg

Principle inertia axis

Shaft axis

8

허용잔류불평형

Balancing Grade for Rigid Rotor

ISO 1940

API

max 6350 [g mm]

Journal static load [kg]

Max. speed [rpm]

WU

N

W

N

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허용잔류불평형

Balancing Grade for Rigid Rotor

ISO 1940

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허용잔류불평형

Example for Turbine Rotor

Rotor Weight 400 kg

Max. Speed 10,000 rpm

ISO 1940 G2.5

API

max

2006350

10000

= 127.0 [g mm]

kgU

rpm

max 2.4 400

= 960.0 [g mm]

U m kg

11

밸런싱방법

Graphic Method: Single Plane

Vector method

4 Run method

Static couple method

Influence Coefficient Method: Multi Plane

Standard influence coefficient method

Least square influence coefficient method

Modal Method

Critical speed mode shape, Modal influence balancing coefficients

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밸런싱방법

Phase Angle

High Spot

Phase Angle

High Spot

Phase Reference

Pickup

Vibration Pickup

Phase Angle (θ)

T

t

360t

T

Heavy Spot Angle (θ)

Heavy Spot

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밸런싱방법

Phase Angle

High Spot

+ Phase Angle

High Spot

Phase Reference

Pickup

Vibration Pickup

Heavy Spot Angle (θ)

T

t

360t

T - 90˚

- 90˚

Phase Angle (θ)

360t

T

Heavy Spot

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밸런싱방법(Single plane)

Vector Method

Zo : 초기진동벡터

ZT : 시험질량을취부한 진동벡터

= Zo+ T.W

Zo

ZT

T.W

ZT - ZO

q

q

C.WZo – ZT : 시험질량만의효과

T.W : 시험질량

C.W : 수정질량

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밸런싱방법(Single plane)

Vector Method

0

0

0

0

0

T T

T

T

a U

a U

a

Z

Z U

U

Z U

U a

a

0T

T

Z

Ua

Z

0

0

T

T

a UU

Z Z

0

T

Z

Z

0

( )T TU W

U

a

초기진동벡터

시험질량을취부한진동벡터

초기불평형량

시험질량을취부한불평형량

영향계수

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밸런싱방법(Single plane)

Vector Method

0 25 95Z

30 175TZ

35 220TW

10 180Tm g

10 :35 : 25

10 25

35

7.14

C

C

c

g m m m

g mm

m

g m

0 25 95Z

30 175TZ 35 220TW

35 220TW

10 180Tm g

7.14 55Cm g 235o

q

0Z

0

0 0 0 0 0

0

( )

( ) 180 (95 180 ) 220 235

c T T

c T T

m m Z W

m m Z W

7.14 235Cm g

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밸런싱방법(Two plane)

Pick Up Pick Up

Phase

Plane 2 Plane 1

F N

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밸런싱방법(Two plane)

180o0o

90o

360o

180o

N

Plane 1

d

Initial vibration

0o

90o

360o

F

Plane 2

g

Rotation

Phase

19

밸런싱방법(Two plane)

90o

360o

180o

N2

Plane 1

Trial weight – plane 1

0o

90o

360o

180o

F

Plane 2

g

d2

A

F2

aAN

0o

Rotation

Phase

20

밸런싱방법(Two plane)

90o

360o

180o

Plane 1

d3

Trial weight – plane 2

0o

90o

360o

180o

F

Plane 2

g3

F3

B

bBN3 N

0o

Rotation

Phase

21

밸런싱방법(Two plane)

90o

360o

180o

- N

Plane 1

Trial weight – plane 2

0o

90o

360o

180o

F

Plane 2

bB

B

N

- F

aAA

f

f

q q

qA + f (bB) = - N fB + q (aA) = - F

0o

Rotation

Phase

22

0 deg

90

180

270

o

No.1 end

Static component

No. 1 end No. 2 ends

N0. 1 dynamic component

N0. 2 dynamic component

A

C

BNo.2 end

N0. 2 dynamic component

N0. 1 dynamic component

B

A

밸런싱방법

Static/Couple Method

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밸런싱방법

Modal Balancing

Mode Shape

Modal Distribution

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밸런싱프로그램

Input Module

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밸런싱프로그램

Input Module

26

밸런싱프로그램

Input Module

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밸런싱프로그램

Output Module

28

회전체분류(ISO)

Class 1 : Rigid Rotor : These rotors may be balanced in any two

arbitrary axial planes and will remain in balance throughout the

operating speed range

(ex., Gear wheel etc.)

Class 2 : Quasi-flexible Rotors : These rotors are not perfectly rigid but

may be adequately balanced in a low-speed balancing machine and

will maintain smooth operation throughout the speed range

(ex., Shaft with grinding wheel, Jet-engine compressor rotor, Printing-

press roller, Computer memory drum, Five-stage centrifugal pump,

Multistage pump impeller, Impeller pump, Steam turbine rotor)

Single and two plane constant-speed balancing is usually adequate

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회전체분류(ISO)

Class 3 : Flexible Rotors : These rotors cannot be balanced in a

low-speed balancing machine and require one or more high-speed

trim plane corrections

( ex : Generator rotor etc.)

Class 4 : Flexible-attachment Rotors : These rotors have

components within themselves or flexibly attached

(ex : Rotor with centrifugal switch)

Class 5 : Single-speed Flexible Rotors : These rotors could be class

3 flexible rotors but are balanced for operation at one speed only

(ex : High-speed motor)

A least-squared-error influence coefficient

or combined modal technique is preferred