piping harmonic analysis

8/10/2019 Piping Harmonic Analysis

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forced harmonic motion.mcd

Effects of damping on system response to harmonic loading

Omega n (n) is a system natural frequeny, omega () is a range of forcingfrequencies, zeta () is critical damping ratio and A is the amplitude of the response.

from Theory of Vibration with Applications byWilliam Thompson pg. 49:n 10:=

0 .1

, 50

..:= A , n,( ) 1

1

n

2

2

2

n

2

+

:=

0 0.5 1 1.5 2 2.50

10

20

30

40

50

A .01 , n,( )

A .03 , n,( )

A .05 , n,( )

A .10 , n,( )

n

Tablulate amplification for a range of frequency ratios (r=/n) and various damping ratios:

r .55 .6, 1.1..:= A r,( ) 1

1 r( )2

2

2 r( )2

+

:=

r0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

= A 0.01 r,( )1.434

1.562

1.731

1.96

2.284

2.775

3.597

5.24

10.067

50

9.558

4.736

= A 0.03 r,( )1.432

1.56

1.728

1.954

2.274

2.753

3.544

5.063

8.854

16.667

8.312

4.543

= A 0.05 r,( )1.429

1.556

1.721

1.943

2.253

2.712

3.446

4.757

7.346

10

6.815

4.218

=


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Illustrating a Phase Relationship in a Damped System (TDRP

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 3

Angle

Amplitude(

normalized)

Node 5

Node 20 (la- report


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ASME Section VIII, Division 2, Mandatory Appendix 5 Design Based on Fa

Figure 5-110.1 Design Fatigue Curves for Carbon, Low Alloy, Series 4XX, High A

High Tensile Steels for Temperatures not exceeding 700F


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s is ASME VIII-2 polishedbar S-N curve (amplitude);

s/2 reflects a safety factorof 2 on stress or 20 on

number of cycles;

S(N) is Markl's fatiguecalculation for carbon steel

SA(N)/2 is expansionallowable adjusted fromrange to amplitude;

OM3 and API618 arerecommended maximumstress amplitudes

10 100 1 .103 1 .104 1 .105 1 .10610

100

1 .103

1 .104

s

s

2

S N( )

SA N( )

2

OM3

API618

n n, N, N, n, n,

API618 DATA 3 := API 44.8

OM 53.0OM3 DATA 2

:=

s DATA 1 :=The allowable vibration amplitude can be calculated based on

the endurance limit. OM3(Pre-operational and Initial StartupVibration Testing of Nuclear Power Plant Piping Systems)specifies 68.9 MPa zero to peak as the allowable endurancelimit for carbon steel and specifies that the minimum safety

factor is 1.3 which equates to 53.0 MPa zero to peak. API 618(Reciprocating Compressors for General Refinery Services)states that stresses shall be less than 179 MPa peak to peak,or 89.6 MPa zero to peak, and is normally used with a safetyfactor of 2. - Piping Vibration Analysis - a tutorial from the19th Turbomachinery Symposium

n DATA 0 :=

The ASME fatigue curves show stress as anamplitude (as do the harmonic results fromCAESAR II). These values are derived fromstrains multiplied by the elastic modulus and adesign margin. This allowable stress amplitude,therefore, is directly comparable to calculatedstress intensity and stress amplitude. Thesevalues are adjusted to include the maximum effectof mean stress. - ASME VIII - 2 Para. 5-101

DATA

101

102

103

104

105

106

107

108

3999

1413

572

262

138

86.2

86.2

86.2

OM

OM

OM

OM

OM

OM

OM

OM

API

API

API

API

API

API

API

API

:=

Section VIII, VDiv 2 Appx.5FatigueCurve Fig.5-110.1(a)UTSif

1.2 N 3125

piping harmonic analysis

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