To ensure that blade stress levels are within the fatigue life requirementsof the compressor， it is usual practice to strain-gauge the blading on oneor two prototype machines， measure the stresslevels， and generate a Camp-bell diagram showing the plotted test data. To measuredata， an impeller can also be mounted on a shaker table with a variable frequency output(0-10，000 Hz). Accelerometers can be mounted at various positions on the impeller to obtain the frequency responses in conjunction with a spectrum analyzer (Figure 5-26).
Initially， tests are run to identify the major critical frequencies of the impeller. Mode shapes are then determined visually at each of the criticalfrequencies. To obtain these mode visualizations， salt is sprinkled evenly onthe disc surface. The shaker is maintained at a particular frequency， at which value a given critical frequency is excited for a certain length of time so that the salt particles display the mode shape. The salt accumulates in the nodal regions. Photographs are taken at lower values of these critical frequencies. Photography allows a qualitative identification of the appropriate mode shapes corresponding to each frequency. Figure 5-27 shows an impeller with the mode shapes.
The next step in the testing procedure is to record accelerometer readingsat variousdisc，blade， and shroud locations at lower critical frequencies. The objective of this test is to quantitatively identify the high and low excitation regions.For thistest， a six-or five-blade region is considered sufficiently large to be representative of the entire impeller. The results of these tests are plotted on aCampbell diagram， as shown for one such impeller in Figure 5-28. Lines of excitation frequencies are then drawn vertically onthe Campbell diagram， and a line corresponding to the design speed is drawn horizontally. Where the lines of excitation frequencies and multiples ofrunning speed intersect near the line of design rpm， a problem area may exist.If， for instance， an impeller has 20 blades， a design speed of 3000 rpm (50 Hz)，and a critical frequency of 1000Hz， the impeller is very likely to be severelyexcited， since the critical is exactly 20 .. On a Campbell diagram the previous example will correspond to anexact intersect of the running speedline，1000 Hz frequencyline， and the line of slope 20 ..
A shrouded impeller was tested containing 12 blades and a design speed of 3000 rpm. The 12-bladed impeller's first excitation mode occurred at afrequency of 150Hz， resulting in a single-umbrella mode occurring at the contact point between the two back shrouds. At 350 Hz a coupled mode existed. At these two frequencies it is the back shroud that is the exciting force. At 450 Hz a two-diameter mode existed. This mode is characterized by four nodal radial lines and in many instances can be the most troublesome mode. This mode is excited by the front shroud and the impeller eye. Adouble-umbrella mode occurred at 600 Hz. At the last two frequencies， the blade eye experienced high excitation. The Campbell diagram (Figure 5-28) showed that at design speed this frequency coincided with the 12. line. Thiscoincidence is undesirable， since the number of blades is 12 and may be theexciting force needed to cause a problem. At 950Hz， a three-diameter modeexisted， and at 1100 Hz a four-diameter mode existed. At 1100 Hz the blade-tip frequency is the predominant forcing function. This impeller seemed tobe in trouble at 600Hz， since this frequency coincided with the number ofblades. To remove this problem， it was recommended that either the number of blades should be increased to 15 or the blades should be made out of a thicker stock. This type of analysis is useful mostly in the design stages so that problems may be prevented. An analysis may also be helpful in the field.If a problemexists， the machine can be run at a different speed to avert a catastrophe.
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