5.7.3 Verification of estimated natural frequencies and wheel chamber tests
After a prototype blade has been designed on paper, a single blade is made in mild steel so that the calculation of natural frequencies can be checked. Provided that cantilever vibration tests confirm that the single-blade frequencies are in accordance with requirements, a complete bladed disc is manufactured. The bladed disc is then tested by fitting piezoelectric crystals at selected positions on the wheel and recording the modal shapes and natural frequencies.
Since the natural frequencies of all blade rows, except the last few LP stages, are generally above the eighth engine order (400 Hz for a 3000 r/min machine), static testing is usually sufficient to confirm that possible resonances will be well removed from excitations which the blades will experience in service. The natural frequencies of the longer LP blades, however, are lower and may coincide with harmonics of rotational frequency below the eighth order. Also, since the flexibility of longer twisted blades changes slightly with speed, the bladed discs must be tested over the running range to ensure that natural frequencies do not coincide with synchronous harmonics.
Driving large bladed wheels in air would absorb large amounts of power and would require large prime movers. Also windage, particularly near the blade tips, would cause overheating and make the results difficult to interpret. For these reasons, the complete bladed disc is run in a vacuum wheel chamber, where an array of magnets is used to stimulate impulses acting on each blade as it passes. The disc is run up to 115% synchronous speed and the blade vibration is detected by strain gauges or crystals. Signals are brought out either through sliprings on the shaft or, more recently, by telemetry and the frequency and amplitude recorded.
By examining particular resonances, it is possible to trace families of modes over the speed range. These are drawn on a 'Campbell Diagram' similar to that shown in Fig 1.90. Radial order lines through the origin represent events that occur a fixed number of times in each revolution. Where the vibrational frequency trace for a particular mode crosses an order line, there is the prospect of resonance occurring during service. It is usual to confine attention to within ±6% of synchronous speed (i.e., 2820 to 3180 r/min). Within this speed range, the specified requirement is to have no resonances up to the eighth engine order. Experience has shown that, if resonances are avoided in this speed range, the blade assembly will experience minimal alternating stress during service.