Stressing of axial impellers
Axial flow fan impellers will also be subject to centrifugal forces and thus the various elements will be “stressed”. As in most cases the blades are “cantilevered” and only supported at the end adjacent to the hub, fluctuating stresses are more important. These are due to aerodynamic forces and vary according to the duty position on the fan characteristic. Fatigue is therefore the important criteria in determining the life to failure.
Figure 7.5 Detailed finite element mesh for a backward aerofoil impeller
True aerofoil blades vary in section along their length. It is preferable for the centroids of each section to lie on a radial line, when the stress at the blade root will be:
I A(r) • rdr
= cross-sectional area of blade root (m2)
= cross-section area of any element (m2) at radius r (often function of r)
The static pressure difference across the blade swept area and the torque combine to give a bending moment on each blade. These should be resolved along the blade to give a bending moment at the blade root normal to a neutral axis for which the section modulus is least. The section modulus may be found by drawing an enlarged aerofoil section, dividing it into a number of strips. A summation of these will give:
I = ^dAxy2
Beyond this it is difficult to particularise as each design will be unique. General equations as for centrifugal fans are not usually possible.
Apart from out-of-balance, the only readily perceived cause of a fluctuating force has been due to aerodynamic effects and these are magnified at unstable parts of the fan characteristic curve.
In the design of any axial flow impeller, it is therefore necessary to ascertain the magnitude of not only the centrifugal stresses that are imposed, but also the fluctuating stresses. The ratio of these will lead to a determination of the operational life. During the last fifty years, vast strides have been made in the advance
of metallurgy, particularly as it relates to the use of non-ferrous alloys. Many of these were developed for the aircraft industry and have a considerable increase in tensile strength, but most importantly, a greater resistance to fatigue.
The use of such new alloys, however, often presents problems in the methods required in the foundry, heat treatment, forge or machine shops. If the full advantages are to be obtained, it is essential that the design engineer is aware of the characteristics of the material being used and how they will be down-rated according to the manufacturing processes involved.
For complete success a three-stage design and testing programme is preferable with appropriate iterations as necessary between each of these stages:
• Finite Element Analysis
• photo-elastic coating tests
• strain gauging
Figure 7.7 shows the stress resulting only from the centrifugal loading and on this must be superimposed the fluctuating stress caused by aerodynamic and other effects. At the present time these are not easily susceptible to mathematical evaluation and it is best to deduce them experimentally. Nevertheless, a fatigue crack will start initially at a point of high stress concentration such as a keyway, toolmark, oil hole, start fillet, inclusion, change of section or any other “stress raiser”. The FEA and
Figure 7.6 FEA mesh of a hub
As with centrifugal impellers, it is not proposed to give a detailed description of the methods used for axial machines. Suffice it to say that such programmes are readily added to CAD systems and are now considered essential if we are to be aware of the highest stress points in a blade or hub, examples of which are shown in Figures 7.6 and 7.7.
CAD programmes assist in the identification of such problem areas and lead to modifications which will improve the design.
In any FEA programme assumptions have been made and, for complete confidence, these should be validated (see Section 7.7.8). Photoelasticity is therefore used to both confirm the overall stress distribution and to enable the high stress points to be immediately identified.
When a photoelastic material is subjected to a load and then viewed with polarised light, coloured patterns are seen which are directly related to the stresses in the material. The colour sequence observed starts at black, (zero) and continues through yellow, red, blue-green, yellow, red, green, yellow, red green with increasing stress and repeating. The transition between the red and green colours is known as a “fringe”. The number of fringes increases in proportion to the increase in stress and is illustrated in Figure 7.8.
Figure 7.8 Photoelastic stress patterr
Whilst photoelastic methods can give quantitative results, strain gauge techniques are preferred, as these also permit the measurement of the fluctuating stresses, so important in the assessment of the fatigue life of the component. High stress points in an impeller blade or hub, as identified in the Finite Element Analysis and confirmed by the photoelastic tests, should then be fitted with strain gauges.
Stress in a material cannot, of course, be measured directly and must be computed from other measurable parameters. We, therefore, use measured strains in conjunction with other properties of the material to calculate the stress for a given loading. Bonded resistance strain gauges are normally used (Figure
7.9) these being cemented to the blade, hub or other part as re-
Triangles grid centre —
Outer gnd Inee
100 mm 1000ЦІ
Figure 7.10 Strain gauge trace
Quired. An initial unstrained gauge resistance is used as a reference measurement. When the fan is run, a change in resistance will occur which can be equated to the strain. The variation in the strain, due to fluctuating forces, can be seen on the trace produced. It is necessary to assess this value as it is far from constant (Figure 7.10).
Figure 7.11 As cast specimen for fatigue testing
0 50 100 150 200 250 300
Mean S*r«M (MPa)
Failure under low cycle fatigue is rapid. It is easily recognised and is usually due to the rotational frequency coinciding with the natural frequency of the component. With a blade, it is common to “tap” it with a hammer and measure the acoustic emission and analyse its frequency. It is a simple matter to rectify by local stiffening. Such failures are especially rapid in the “stall” region.
There will however be many other resonances over the whole frequency spectrum which can be captured by the acoustic emission. These resonances become ever closer at increasing frequencies and lead to high cycle fatigue.
The term fatigue is used to describe the failure of a material under a repeatedly applied stress. The stress required to cause failure, if it is applied many times, is, of course, much less than that necessary to break the material in a single “pull”.
As previously stated, fatigue causes many of the failures of axial impeller rotating parts and it is, therefore, necessary to design against this eventuality. To repeat, in an impeller there will be a mean stress, due to centrifugal loading, and a fluctuating stress imposed on this, due to aerodynamic effects.
Experience has shown that for satisfactory correlation with actual behaviour in service, full size blades and hubs should be tested in conditions as close as possible to those encountered during service. Some basic information can however be obtained from simple laboratory tests.
A Roell-Amsler vibraphore resonant frequency machine can be used establish the fatigue strength of the aluminium alloys used. Test samples are cast as shown in Figure 7.11 and these are then subject to high cycle fatigue at various mean stress levels an at variously defined numbers of stress reversals (cycles). A tensile test is also carried out on one of the run-out fatigue specimens in order to give a tensile strength value and thus permit all the data to be plotted on a Goodman diagram (Figure 7.12). Figures 7.13 and 7.14 give typical impeller and impeller hub stresses versus LM25-TF fatigue data. LM25-TF is a heat treated aluminium alloy frequently used for hubs and clamp-plates. It is interesting (and very informative) to compare the as cast data with that published for smooth specimens.
Examination of the fracture surfaces of the failed specimens has shown that in the majority of cases, failure initiates from defects, however minute, in the aluminium casting. It has also been noted that the larger defects correspond to the lower fatigue lives.
Figure 7.12 Goodman diagram for LM25-TF cast aluminium
No of Cycles to failure
Figure 7.14 Typical impeller stresses versus LM25-TF fatigue data
VOLUME FLOW ( mJ/sec )
Figure 7.16 Gottingen design blades — pressure and fluctuating stress against flowrate
This is a relatively new subject which looks at the fracture toughness of cast materials and their rates of fatigue crack growth. This type of research has enabled fan manufacturers to determine design rules which specify acceptable defect sizes under combinations of steady and fluctuating stress. The tests are carried out in accordance with BS 6835:1988 and ASTM E647.
VOLUME FLOW < ip/sec 1
Figure 7.17 NARAD design blades — pressure and fluctuating stress against flowrate
Figure 7.15 is an example of the results obtained from LM25-TF.
Figure 7.15 Defect size and stress in rim of LM25-TF hub
It is convenient during the performance (rating) tests of a fan to also measure the fluctuating stress at various flow rates. From these tests, some interesting conclusions have been deduced.
Whilst the fluctuating stress generally increases towards the stall point at that particular impeller blade pitch angle, the maximum is not necessarily coincident with the stall (Figure 7.16). Furthermore, whilst different aerofoil shapes may give similar aerodynamic results, this does not apply to the fluctuating stress values. For new ranges of metric axial flow fans and also for large special purpose tunnel ventilation units, manufacturers have developed improved sections (Figure 7.17) which have reduced fluctuating stress values away from the stall point.
Note especially, that in reverse rotation high maxima can occur on the negative slope of the characteristic — what would otherwise be assumed to be an acceptable operating point for this condition. Note also that maximum fluctuating stresses generally increase with increasing pitch angles (Figure 7.18). Truly reversible sections have also been developed which not only give virtually the same airflow in each direction (tube axial), but also have extremely low values of fluctuating stress across the whole performance characteristic (Figure 7.19).
Figure 7.18 NARAD design blades — pressure and fluctuating stress against flowrate with varying pitch angles
Figure 7.19 Reversible design blade — pressure and fluctuating stress against flowrate
The techniques described in this Section can act as a powerful tool for obtaining the same integrity with axial flow fans as has been achieved over many years with centrifugal fans.
It is essential that a design and testing procedure is adopted which recognises that a major cause of failure in axial impellers is due to insufficient knowledge of the fatigue criteria and how they are affected by casting quality. Close co-operation between design and production departments is necessary to ensure that the stated operating life is achieved. Constant vigilance is, nevertheless, indicated with continual research to improve knowledge. Reference to Chapter 17, Section 17.6 may be useful for practical solutions and advice.
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