Harmonic Displacements Tab - CAESAR II - Help

CAESAR II Users Guide

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English
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CAESAR II
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CAESAR II Version
13

This tab is available when Harmonic is selected for Analysis Type in the Dynamic Analysis window.

Values must be entered on either the Harmonic Forces tab or the Harmonic Displacements tab.

Harmonic Phasing

Phasing is important if more than one force or displacement is included. The phase angle (entered in degrees) relates the timing of one load or displacement to another. For example, if two harmonic loads act along the same line but at different nodes, the loads can be directed towards each other (that is, in opposite directions), producing no net dynamic imbalance on the system. The loads can also act in the same direction (that is, to the right or to the left together), producing a net dynamic imbalance in the system equal to the sum of the two forces. The phase angle determines this relationship. For example, the following load data is defined to specify loads that are operating in unison and at the same phase angle at nodes 10 and 105.

Force

Direction

Phase

Start Node

1500

X

0

10

1500

X

0

105

The next harmonic load input example shows the same load vectors applied at nodes 10 and 105 but with opposing phase angles.

Force

Direction

Phase

Start Node

1500

X

0

10

1500

X

180

105

The two most common phased loadings are those due to rotating equipment and reciprocating pumps.

Rotating equipment can have an eccentricity, a speed, and a mass. These items must be converted into a harmonic load acting on the rotor at the theoretical mass centerline. The magnitude of the harmonic load is calculated from:

Fn = (mass)(speed)2(eccentricity)

where speed is the angular velocity of the shaft in cycles per second. This load is applied along both axes perpendicular to the shaft axis and at a 90º phase shift.

In the case of a reciprocating pump, the pump introduces a pressure wave into the line at some regular interval that is related to the pump valving and speed. This pressure wave moves away from the pump at the speed of sound in the fluid. These pressure waves cause loads at each bend in the piping system. The load on each subsequent elbow in the system, starting from the first elbow, is phase-shifted by an amount that is a function of the distance between the elbows, from the first elbow to the current elbow. The amount of phase shift between elbow-elbow pairs produces the net unbalanced dynamic load in the piping. The phase shift, in degrees from the first elbow, is calculated from:

phase (in degrees) = [(frequency)(length) / (speed of sound)]360º

where frequency is the frequency of wave introduction at the pump, and length is the distance from the first elbow to the current elbow under study. The magnitude of the pressure load at each elbow is:

Harmonic Force = 0.5 (peak-to-peak pressure variation) (Area)

With phasing considerations, all specified loads are considered to act together at each applied frequency.