How using thermal images can optimize strain gage positioning for the experimental modal analysis of composite rotors
The described method of optimizing strain gage measuring point positions on propellers was primarily developed to define suitable strain gage positions, for situations where there is no, or only limited, documentation available on the construction and physical properties of the rotor blades.
Symbols
ΔQ, Δq | Increase in temperature, specific increase in temperature | [J, J/kg] |
C, c | Thermal capacity, specific thermal capacity | [J/K, J/kgK] |
ΔT | Temperature change | [K, °C] |
m | Mass | [kg] |
ΔU | Strain energy increment | [J] |
S | Area | [m2, mm2] |
t | Thickness | [m, mm] |
ρ | Density | [kg/m3] |
ζ | Loss coefficient | [1] |
Δl | Deflection, bending amplitude | [m, mm] |
1. Introduction
Deflection, bending amplitude optimum performance. A crucial step towards vibration-free propeller operation requires the suitable fine-tuning of the natural frequencies of the rotor blade.There is a challenge, however, because only a limited number of data channels are ever available for testing aircraft propellers.
This is because of the restrictions imposed by telemetric data transmission and the considerable effect of strain gage (SG) preparation on the aerodynamic properties of the rotor blades. These aspects make it desirable to have a reduced number of strain gages with minimal negative aerodynamic consequences.
The positioning of the strain gages is conditional since there must be no impact on the natural vibrations that occur during operation. Figure 1 shows an example of the installation of HBM strain gages on fiber-composite propeller blades, with telemetric measurement transmission.
Fig. 1: Fiber-composite propeller blades with LY41-6/350 strain gages from HBM, with telemetric data transmission
The following two basic situations can occur in experimental modal analysis based on strain gage measuremen
- Testing rotors and rotor blades of a known construction, where technical documentation is available. In this case, the strain gages can be installed at measuring points calculated by standard numerical methods, such as the Finite Element Method (FEM).
- Testing of old rotors, as well as rotors of unknown origin and from third-party suppliers, where there is no available documentation of the structural design.
The second case is challenging, as the physical properties of the composites are unknown and it is a highly complicated process to determine them. It is not usually possible to obtain a sample of the composite without damaging the test specimen such as the composite rotor blade. A sample would allow a detailedexamination of the fiber reinforcement orientation to be carried out or ensure that the proportion by volume of the composite components could be measured. Calculations are not possible without reliable material data, so neither is it possible to measure strain, based on FEM analysis, for example.
Normally a detailed experimental modal analysis is performed to determine the significant natural frequencies and vibration forms. Results and years of experience teach us that a large number of strain gages are attached to all those positions that could provide an adequate signal for most forms of vibration. Those strain gages that detect at least the first five or six forms of vibration are then selected for the modal analysis of the entire rotor.
This type of procedure is cost-intensive and also requires a great deal of time.
Not only that, but because of the change in flow conditions brought about by the large number of strain gage measuring points and their associated cabling, results are adversely affected or distorted.
A new and relatively fast method of selecting the optimum strain gage positions has been developed and successfully used at the Aerospace Research and Test Institute in Prague. This method is based on taking infrared images of the vibrating component and assuming that suitable attachment positions for strain gages in the individual natural frequencies can be detected by a localized increase in temperature.
2. Theoretical background
For the rise in material temperature, the generally assumed relationship is
with the increase in temperature coming from the product of thermal capacity and temperature change. As this is a fiber composite consisting of several individual layers, the equation (1) must be modified so that the thermal capacity of the layer as a whole is expressed as the sum of the capacities of the individual layers
If equation (2) is adopted for a mass fraction of an element "e" of area "S" with a given thickness and density, this produces
From this, it is possible to derive the specific thermal capacity of an element of the individual layer
The temperature increase of the element is expressed by
In vibrating bodies, some of the stored mechanical energy is converted into heat by internal losses. By restricting the observations to forms of natural vibration and their associated frequencies, the analyzed element "e" has two amplitudes within a period. It can therefore be assumed that there is a relationship between the heat loss and the doubled value amount of the maximum strain energy contained
From the heat loss, it is assumed that it represents a multiple of this value, with this factor being expressed as the loss coefficient ζ
From equations (5) and (7), the change in temperature, subject to the physical properties of the material and the strain energy of the element, follows to
Equation (8) gives the increase in temperature that corresponds to the stationary state of the vibrating component. It is not dependent on anisotropy directions, on symmetry or on the layer material having a balanced composition.
Furthermore, variations in the stationary temperature fields should be calculated subject to the change in bending amplitude. It is theoretically possible to determine the specific thermal capacity and density of every layer.
But it is a very demanding task to provide the mathematical expression for the loss coefficient ζ. To simplify matters, equation (8) can also be realized as
with constant Ae for a given composite having to be defined experimentally by a thermography system. On condition that the specific thermal capacity, the density and thickness of the layers are known, this also makes it possible to determine the loss coefficient ζ. These characteristics are regarded as material constants independently of bending, frequency and temperature.
The conversion of the temperature fields in relation to the level of bending amplitude occurs in accordance with the proportion of strain energy at the element subject to the bending ratio
By including equations (9) and (10), reference temperature Tref and the increment of experimentally measured temperature ΔTexp at nominal bending (amplitude) Δlexp, it is possible to determine temperature T2 for the new nominal bending Δl2 of the system as follows
Temperature field calculation, based on FEM modal analysis and a thermographic analysis used as a reference base, thus follows in accordance with the equation
The following illustrations (Figs. 2 and 3) show a comparison of the temperature distributions on the suction face of rotor blade VZLU V45 as the result of numerical analysis (FEM) and as the result of measurement (thermography). The results correspond very well. Consequently, the correlation between the increase in temperature and the strain amplitude makes it possible to determine suitable strain gage positions for calculating forms of natural vibration. This can either be based on the calculated temperature distribution or on the measured temperature distribution.
Fig. 2: Thermal image of the third natural vibration mode, suction face of rotor blade VZLU V45.
Fig. 3: FEM analysis of the temperature fields of the third natural vibration mode, suction face of rotor blade VZLU V45.
3. Determining strain gage positions, measurement results
The practical procedure for selecting suitable strain gage positions is described using a composite fan blade as an example. The fan blade is clamped in a special device, which is also used to initiate vibration. In Figure 4, the fan blade with the vibration generator is shown top left. The image top right shows the temperature distribution for vibration in a natural frequency, recorded by a thermography system. The strain gage measuring points (T1 - T3) for strain measurement are visible below.
Fig. 4: Fan blade in a device for initiating vibration, the measured temperature distribution and the strain gage measuring point positions
Note that the increase in temperature occurring at the upper left tip of the blade is not relevant to modal analysis. It arises from a fault in the blade, caused by collision with a foreign body while the blade was in operation. This is important for non-destructive material defect testing, a further application for the thermal imaging camera.
Following analysis of the temperature distribution, three type LY41-6/350 strain gages from HBM were installed at the points of maximum temperature, at the base of the blade.
A further experimental modal analysis was then performed on rotating blades, with only strain gages T1 and T2 being chosen for measurement. This showed that each of them was capable of recording all the relevant natural frequencies of the blade.
The data link from the running fan motor was made by type SK12 slip rings from HBM. Because of the special conditions, only two rotor blades were fitted with strain gages for this test. Figure 5 shows an example of the measured Campbell diagram. On the left-hand side, the strain amplitudes of strain gage T1 are given in µm/m (maximum values, average values, etc.) over speed. The actual Campbell diagram determined from this is shown on the right-hand side. The natural frequencies are applied over speed as abscissa
Fig. 5: Example of the Campbell diagram recorded by strain gage strain gage T1 (see Fig. 4)
4. Conclusions
The described method of optimizing strain gage measuring point positions on propellers was primarily developed to define suitable strain gage positions, for situations where there is no, or only limited, documentation available on the construction and physical properties of the rotor blades. Because of the high conformity between the measured thermal images and the temperature distributions calculated using FEM (see Figs. 2 and 3), the procedure described can be applied in both cases. This means that strain gages can be positioned on the basis of both measured and calculated results.
With experimental determination, the rotor blade must be excited in several resonance frequencies, in order to obtain the requisite infrared images for selecting the strain gage positions. This procedure reaches the limits of its usefulness if the test specimen is too big, as is the case with large fans, or with the rotor blades of wind turbines, and for technical reasons, excitation in the higher natural frequencies is too complicated. FEM calculation is then the only remaining option for determining temperature fields.
The main advantages of the new method of strain gage measuring point optimization are that it takes far less time and costs less. Reducing the number of strain gages for each rotor blade has other advantages. The free strain gage channels can be used for synchronous measurements on other rotor blades.
This makes it possible to handle additional problems, such as determining the phase shifts between the forms of vibration on various rotor blades and recording differences in vibration amplitude.
This study was subsidized by the Ministry for Education, Youth and Sport of the Czech Republic, Research Project MSM0001066904 "Research into the behavior of composites in the primary structure by devices based on the principle of rotating bearing surfaces".
