The various components of large industrial fan impellers, such as kiln I.D. fans for the cement industry, have natural resonant frequencies. If excited during operation, these natural resonant frequencies may cause vibratory stress and fatigue, resulting in the cracking or destruction of certain components. Fortunately, simple field tests performed with fairly inexpensive equipment can measure the vibration response of the various components and anticipate frequencies that will be excited in the field installation. This article describes one such test, the impact (or impulse) excitation technique, which has several advantages over the swept-sine wave excitation test. Further, the article recommends corrections that can be introduced to prevent natural frequency excitation.

Natural frequency excitation

Component parts of an industrial fan — such as the shroud (rim), webplate (center disk), or impeller blade — have a natural frequency of vibration, which is based on their geometry, material of construction, and points of connection with other components. It is possible, but not desirable, to excite this natural frequency by some outside force. A simple example would be the blade of an axial flow impeller vibrating as a cantilever beam. This type of vibration is not to be confused with unbalance, bearing vibration or shaft natural frequency.

A short case study may help to explain. A 98-in.-diam axial flow impeller from a large sintering plant developed cracks in several blades. One blade tore completely loose from the hub. A vibration analysis showed that there were three important natural frequencies (or modes) associated with blade movement:

• In the first mode at a frequency of 92 Hz, the blade vibrated as a cantilever, i.e., with base anchored, the entire blade moved up and down.

• In the second mode at a frequency of 124 Hz, there was one node, near the transition point between the thicker and thinner sections of the blade (Figure 1).

  Figure 1: The blade of a 98-in. axial flow impeller is shown in the first mode at 92 Hz, with the blade vibrating as a cantilever.

• In the third mode at a frequency of 372 Hz, there were two nodes, one at the base of the blade and one just beyond the transition point between the thicker and thinner sections.

The impeller had ten blades and had been operating between 680 and 750 rpm, which means the blade passage frequency was between 113 and 125 cycles per second. In other words, the blade passage frequency — or the operationally induced frequency — coincided with the natural frequency in the second mode of 124 Hz. As a result, cracks had developed in the blade in the node location indicated in the vibration analysis above (second mode). A blade redesign with a stiffer cross section raised the natural frequency of the primary mode to 152 Hz and solved the problem.

Additional variables

Determining the natural frequencies of the component parts is only part of the job when preventing failures. The fan engineer must also anticipate which frequencies are likely to be excited in the field. Among the variables to consider are the following:

• Operating speed;

• Blade passage frequency;

• Rotating stall caused by partially closed inlet dampers;

• Duct-induced vibration due to stack length, duct work turns, etc.

• Mechanical drive vibration caused by bearing problems, coupling misalignment, etc.; and

• Shaft torsional frequency, especially in variable speed drive applications.

Impeller test preparation

To prepare the impeller for testing, it should be suspended on two crane straps or other soft supports so the shaft centerline is on a horizontal plane. There should be no contact between the fan and the floor or other obstruction and the test area should be free of ambient noise and vibration.

Measurement locations

On centrifugal fans, the following locations are usually tested:

• Shroud O.D., midway between two blades;

• Should I.D., midway between two blades;

• Web O.D., midway between two blades;

• Blade tip, midway between two blades; and

• Blade inlet, midway between hub and shroud.

On axial fans, only the blades are tested but they should be tested at several points to determine mode shapes at each resonance.

Testing procedure

With the testing equipment set up in accord with Figure 2, the accelerometer should be attached to one face of a metal component while the hammer strikes on the opposite face of the same component. Where there are hollow sections or where tight clearances prohibit access to both faces of the component, the hammer can strike directly beside the accelerometer with minimal effect on accuracy. However, it should be noted that the phase will be shifted 180°.

Figure 2: The blade of 98-in. axial flow impeller is shown in the second mode at a frequency of 124 Hz, with one node near the transition point between the thicker and thinner sections of the blade.

The most convenient way to effectively mount the accelerometer is with beeswax. This method is reliable under most circumstances up to 1 KHz. The use of a magnet is not recommended because there is some risk that the accelerometer will jump upon hammer impact. Under conditions where beeswax is not suitable, such as extreme temperatures or high frequency measurements, other methods may be employed, such as a screw stud or an adhesive.

The hammer should strike each location several times (typically four or eight), allowing time between each hit for the vibration to dissipate. By taking several averages, the effects of ambient vibrations and non-linearities are greatly reduced.

The output of the impact hammer's integral force transducer is connected to Channel A of the spectrum analyzer, which should be equipped with a threshold signal trigger. The output of the accelerometer is connected to Channel B of the analyzer via the charge amplifier. A graph of transfer function vs. frequency will be displayed on the screen of the spectrum analyzer (Figure 3). Transfer function is, essentially, Channel B input (acceleration) divided by Channel A input (force). This information can be used to calculate compliance vs. frequency using a standard formula:

Compliance, C = m/N

m=(mV_B/(2Pi² (S_B)

mV_B = millivolts of Channel B (accelerometer)

S_B = accelerometer sensitivity, mV_B/m/s²

N = (mV_A)/(S_A)

mV_A = millivolts of Channel A (hammer)

S_A = hammer sensitivity, mV_A/N

C = (mV_B) (S_A)/(2PiHz² (S_B) (mV_A)

X = mV_B/mV_A

S_A = 2.00 mV/N

S_B = 10 mV/m/sec²

C= X/197.2 (Hz)²

The analyzer also may be used to generate useful information about mode shapes, such as those illustrated in Figure 1. The technician should move the accelerometer to different points on the impeller while keeping the excitation point constant. Alternatively, the technician may vary the excitation point while keeping the accelerometer at one location. By comparing the phase values of all the points at each resonance, a mode shape can be defined.

Analysis of test results

In the graph of transfer function vs. frequency (Figure 4), one is looking for high vibration at or near the point of operationally induced excitation frequencies, such as the blade passage frequency noted in Figure 3. To determine whether vibration is too high at any given point, one must have predetermined limits as to the maximum compliance within a specified percent of an excitation frequency.

In terms of corrective action, an extra brace or liner bar may be added to increase stiffness and, consequently, raise the natural frequency of a component. The mode shape determination described above is quite useful when deciding where to place a stiffener and what type to use. Another solution, less desirable from the standpoint of time and expense, is to redesign the impeller with a different material thickness or cross-section.

This article was adapted from materials provided by Robinson Industries, Inc., Zelienople, Pa.