According to ISO 1940/1: - ISO 1940/1 defines balance quality grades (G values) that represent the maximum permissible vibration caused by unbalance at operating speeds. Lower G values indicate better balance quality requirements. - Specific unbalance is the product of the rotor's center of gravity displacement and angular velocity. It is measured in units like mm/s. - Maximum permissible residual unbalance (Uper) is calculated based on factors like specific unbalance, rotor weight, balancing radius, and rotor geometry. Formulas are provided to calculate Uper for general, symmetrical, overhung, and narrow rotors.

1. Balancing
Requirement
According to
ISO 1940/1

2. 1. Introduction
1.1 Known as International Standard Organization, ISO 1940/1 – Balance quality
requirements for rigid rotors.
ISO 1940/1 – Balance
quality requirements
for rigid rotors.
ANSI S2.19-1975
BS 6861: Part 1
VDI 2060
1.2 Also adopted by:
- ANSI (American National Standards Institute) S2.19-1975.
- British Standards, BS 6861: Part 1
- German Standards, VDI 2060.
1.3 Other standard
- MIL-STD-167-1
- API 610

3. 2. Balance Quality Grade ISO 1940/1

4. 2. Balance Quality Grade ISO 1940/1
What is mean by G 0.4, G 1.0, G 2.5, G 6.3 and so on?
G is the product of specific unbalance & the angular velocity of the rotor at
maximum operating speed.
What is specific unbalance?
Specific unbalance
- center of gravity displacement of rotor.
- Symbol = eper
- Unit in g.mm/kg or um.

5. 2. Balance Quality Grade ISO 1940/1
What is angular velocity?
- Measure how fast rotor is turning.
-The standard unit for angular velocity is "radians per second“.
- One turn or one revolution:
- 2∏ radians
- 360 degrees
- 60 seconds
- 1 minute
- Unit can be in rpm or Hz
-Symbol is ω (omega)
- Formula = ω = 2 ∏n/60
ω
Back to G 0.1, G 1.0, G 2.5, G 6.3 and so on
Is actually = eper x ω
Unit in mm/s
Meaning G1.0 is the rotor unbalance shall create vibration of 1.0 mm/s at
maximum operating speed at certain center of gravity displacement.

6. 3. Maximum Permissible Specific Residual Unbalance, eper
Is the method to find center of gravity displacement by referring to:
1. Balance quality grade required
2. Operating or maximum rotor speed
Two ways how to find center of gravity displacement
2. Using ISO 1940/1 unbalance nomogram.
1. Calculation by using formula.
Calculation by using formula.
eper = (10 x G) / (n x 1000)
Where
G = Balance quality grade
n = Rotor operating speed in RPM.

7. 3. Maximum Permissible Specific Residual Unbalance, eper
Using ISO 1940/1 unbalance nomogram
Units in:
g.mm/kg
or
= g.mm/kg
= 1/1000 x mm
= 10-3 x 10-3 m
= 10-6 m
= um (microns)

8. 4. Maximum Permissible Residual Unbalance, Uper
Is a function of:
Rotor’s center gravity of displacement (um)
Rotor weight (kg),
Divided into four rules:
1st - General rules
2nd – Rules for symmetrical rotor
3rd – Rules for outboard rotor
4th – Rules for overhung & narrow rotor
Balancing radius (mm).
1st – General rules
Uper = (eper x m) / r
Where
eper = Rotor permissible specific unbalance (g.mm/kg or um)
m = Weight of rotor (kg)
r = Balancing radius (mm) i.e. balancing wieght location.

9. 4. Maximum Permissible Residual Unbalance, Uper
2nd – Rules for symmetrical Rotor
Apply to dynamic balancing requirement for two planes.
Formula
Plane 1 , Uper = [(eper x m) / r] ÷ 2
Plane 2 , Uper = [(eper x m) / r] ÷ 2
If HL = HR
Plane 1 , Uper = [(eper x m) / r] (HR ÷ B)
Plane 2 , Uper = [(eper x m) / r] (HL ÷ B)
If HL ≠HR

10. 4. Maximum Permissible Residual Unbalance, Uper
2nd – Rules for symmetrical Rotor (Cardan shaft example)
Apply to dynamic balancing requirement for two planes.
Calculate: eper
eper = (10 x G) / (n x 1000)
= (10 x 16) / (1272 x 1000)
= 125.7 um
Data:
Balance quality grade = G 16
Weight = 450 kg
Max. speed = 1272 rpm
Balancing radius = 190 mm
Plane 1 , Uper = [(eper x m) / r] ÷ 2
Plane 2 , Uper = [(eper x m) / r] ÷ 2
If HL = HR
Uper = [(125.7 x 450)/190] ÷ 2
= 148.8 grams
Calculate: Uper
Permissible residual unbalance
for each plane = 148.8 grams

11. 4. Calculate Center of Gravity
L
DD
d/2
d/2
e
CG= e = (1/3) x [(3D + 2d)÷(2D+d)] x L
D = 1500
2d + D = 2500
L = 3000
CG= e = 1625 mm
Plane 1 , Uper = [(eper x m) / r] (H2 ÷ B)
Plane 2 , Uper = [(eper x m) / r] (H1 ÷ B)
If H1 ≠H2

12. 5. Maximum Permissible Residual Unbalance, Uper
2nd – Rules for symmetrical Rotor (Pulper rotor example)
Apply to dynamic balancing requirement for two planes.
Calculate: eper
eper = (10 x G) / (n x 1000)
= (10 x 6.3) / (160 x 1000)
= 393.7 um
Data:
Balance quality grade = G 6.3
Weight = 5700 kg
Max. speed = 160 rpm
Balancing radius 1 = 725 mm
Balancing radius 2 = 1200 mm
Calculate: Uper
Permissible residual unbalance for
Plane 1 = 1416 grams
Plane 2 = 1013 grams
Plane 1 , Uper = [(eper x m) / r1] (H2 ÷ B)
= [(393.7 x 5700)/725] (1375/3000)
= 1416 grams
Plane 2 , Uper = [(eper x m) / r2] (H1 ÷ B)
= [(393.7 x 5700)/1200)] (1625/3000)
= 1013 grams
If HL ≠HR

13. 6. Maximum Permissible Residual Unbalance, Uper
Apply to dynamic balancing requirement for one planes.
Formula
Static , Uper = [(eper x m)/r] x (2D/C)
Dynamic, Uper = [(eper x m)/r] x (3D/4C)
4th – Rules for overhung/narrow Rotor

14. 7. Maximum Permissible Residual Unbalance, Uper
4th – Rules for overhung/narrow Rotor (Trim pit blower example)
Apply to dynamic balancing requirement for one planes.
Calculate: eper
eper = (10 x G) / (n x 1000)
= (10 x 6.3) / (2890 x 1000)
= 21.7 um
Data:
Balance quality grade = G 6.3
Weight, m = 155 kg
Max. speed = 2890 rpm
Balancing radius, r = 400 mm
C = 720 mm
D = 490 mm
Calculate: Uper
Permissible residual unbalance for
Dynamic = 4.20 grams
Dynamic, Uper = [(eper x m)/r] (3D/4C)
= 4.20 gram