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Balancing and Diagnostic Systems

consequences, causes, definitions ...

Unbalance

Fundamentals - Part 1 unbalance, C.o.G., eccentricity, centrifugal force, vektor ...

Fundamentals - Part 2 axial unbalance distribution on rigid rotors, types of unbalances ...

Tolerances quality grade, allocation of balancing planes ...

balancing machines, accomodation, drive, measuring principles ...

Measuring Unbalance

balancing maschine, rotor, economy, safety ...

Balancing speed determined by

Correction of Unbalance types of correction (add, remove, shift), economy, errors, tolerance ...

Errors phenomena, causes, types, cure (typical examples) ...

rigid rotor (constant behaviour), other rotors (variable ~ ) ...

State of a Rotor

articles ...

Addentum

Balancing and Diagnostic Systems

Unbalance Description u unbalance mass r radius U unbalance

according ISO 1925

*1)

Unit g mm gmm

U

r Formula

Unit

U=ur

gmm

u

kgmm kgm gcm mgmm *1) u

unbalance mass often called m u also

Veit Bleistein - 08.08.2000

Seminar-Chapter-Subject-Page 11-02-01-01

Balancing and Diagnostic Systems

Fundamentals

according ISO 1925

Center of Gravity (C.o.G.) of Unbalance Mass

r

u The centre of gravity of the unbalance mass “u“ acts at the radius “r“

Veit Bleistein - 08.08.2000

Seminar-Chapter-Subject-Page 11-02-01-02

Fundamentals eccentricity “e“ of the rotor

Balancing and Diagnostic Systems

Is the distance between rotating axis and center of gravity Description u r U e m

Unit

unbalance mass radius unbalance (mass) eccentricity mass (rotor) *1)

g mm gmm um kg

U

u

r Formula

according ISO 1925

Unit

U=ur =me

e=

*1) m

U ur = m m

g mm = µm kg

m

mg mm g

rotor mass often called m R also

Author VB - 23-Feb-2001

Seminar-Chapter-Subject-Page 11-02-01-03

Fundamentals

Balancing and Diagnostic Systems

Rotation

according ISO 1925

Description u unbalance mass r radius U unbalance ω angular velocity n speed v circumferential speed Formula

ω=

2 nπ 60

Unit g mm gmm rad/s minm/s 1

v

n

ω

u

r

Unit n

≈ 10

rad/s

where n is measured in [rpm]

v = rω

m/s

m

where r is measured in meters [m]

*1) n also common in [1/min, rpm] Veit Bleistein - 22-Feb-2001

Seminar-Chapter-Subject-Page 11-02-02-01

Balancing and Diagnostic Systems

Fundamentals Centrifugal Force

Force(s)

Description Unit u unbalance mass g r radius mm U unbalance gmm ω angular velocity rad/s n speed minv circumferential speed m/s

F

v U

1

F centrifugal force *

F=urω

2

F=u v r

2

(with: v = r

) [m/s]

n 10

U

N

n ω

u

r

2

N N m

use u [kg], r [m] 2

* Newton: 1 N = 1 kg m/s Veit Bleistein - 23-Feb-2001

Seminar-Chapter-Subject-Page 11-02-02-02

Balancing and Diagnostic Systems

Fundamentals

Exercises

Exercises 1. How much is the unbalance of a screw weighing 15 g at a radius of 300 mm? 2. What centrifugal force is generated at 1 000 rpm? 3. The rotor weight is 225 kg. By how much is the c.o.g. displaced from the shaft axis? 4. An Unbalance correction reduces this eccentricity to 3 :m. Calculate the residual unbalance. 5. If the centrifugal force is the limiting factor, what is the max. per. speed now? 6. A 100 ton roll was produced with an eccentricity of 3 mm. How much is the initial unbalance? 7. The correction radius is 1.5 m. Calculate the necessary correction mass. 8. The max. per. eccentricity of a 30 g gyroscope is 0.01:m. What is that in terms of unbalance? 9. Its correction radius is 15 mm. Welche What unbalance mass may remain?

Veit Bleistein - 08.08.2000

Seminar-Chapter-Subject-Page 11-02-02-10

Balancing and Diagnostic Systems

Fundamentals

Line of Action (Vector)

Vector Unbalance is a Vector quantity; like a Force it has a Direction. It can be shifted linearly on its Line of Action.

U r r

u

U

u

r

U

Hatto Schneider, 9.2.98 -VB 23-Feb-2001

Seminar-Chapter-Subject-Page 11-02-03-01

u

Balancing and Diagnostic Systems

Fundamentals

90 deg. components (H-,V-components)

Vector Split into 90deg. - components (H- and V- components ) 0°

0°

U0°

U

U

U90°

90°

Vector (-forces, -unbalances) can be split into Component (-forces, -unbalances) In this case the original vector has been split into 90° (deg.) components in the vertical and horizontal axis. Hatto Schneider, 9.2.98 VB 23-Feb-2001

Seminar-Chapter-Subject-Page 11-02-03-02

90°

Balancing and Diagnostic Systems

Fundamentals

90 deg. components 30 deg. off 0 deg.

Vector Split up into 90 deg.- (90°) components Rotor coordinates offset by 30 deg. against angular reference system of balancing machine 30°

30°

U30° U

U U120° 120°

120°

Hatto Schneider, 9.2.98 VB 27-Sep-2000

Seminar-Chapter-Subject-Page 11-02-03-05

Balancing and Diagnostic Systems

Fundamentals

120 deg. components (Vector)

Vector Split up into 120 deg. (120°) - components

0°

0°

U0° U

U U120°

120°

120°

Hatto Schneider, 9.2.98 VB 27-Sep-2000

Seminar-Chapter-Subject-Page 11-02-03-07