At present,there are two ways to measure small-rolling-moment in wind tunnel tests. One is the using conventional multi-component balance[1] or double cross elasticity of flexure structure balance[2, 3],and the other is using air balance system[4, 5]. As for micro-rolling-moment whose value of quantity is below 0.5N·m,the conventional [JP]multi-component balance or double cross elasticity of flexure structure balance is not able to conduct the measurement. The air balance can measurte the micro-rolling-moment,but it is a single component balance,so it can’t implement six components measurement at the same time.
In some special high-speed wind tunnel tests,the rolling moment of the balance is much lower than the loads of other components[6]. Take the ratio of normal force Y to rolling moment for example,for conventional six-component balance,the ratio ranges from 50/m to 120/m,whereas for the micro-rolling-moment six-component balance it is about 250/m. In either case,the measurement accuracy would be affected due to the fact that the interference of the other components on the rolling moment cannot be totally corrected. It’s necessary to develop a micro-rolling-moment six-component strain gauge balance that will not only help achieve the goal of simultaneous measurement of six components,but also improve the accuracy of the wind tunnel testing. 1 Technical key points and difficulties 1.1 Small rolling moment balances
In the past,HSAI of CARDC developed quite a few five-component balances,which can measure small Mx ranging from 0.3N·m to 0.5N·m or above. Table 1 lists HSAI’s conventional balances with Mx≤1N·m,including their specified load and Mx sensitivities. As is shown in Table 1,there is just one six-component balance in the stock,whose Mx sensitivity is only 1.0mV/(N·m).
Balance type | X /N | Y /N | Z /N | Mx /(N·m) | My /(N·m) | Mz /(N·m) | Mx Sensitivity /(mV·(N·m)-1) |
|
Single- Component Balance | 0.2 | 32.5 | |||||
| 5N5-24-Mx | 200 | 130 | 0.5 | 2 | 3 | 9.6 | |
| 5N5-24A | 200 | 70 | 0.3 | 1 | 5 | 18.0 | |
| 5N5-24B | 200 | 70 | 0.4 | 1 | 5 | 14.0 | |
| 2N5-24A | 300 | 200 | 0.5 | 1 | 10 | 6.0 | |
| 3N5-24A | 550 | 200 | 1 | 10 | 30 | 2.9 | |
| 2N5-20B | 500 | 60 | 1 | 3 | 20 | 4.6 | |
| 5N6-24E | 850 | 580 | 100 | 1 | 3 | 6.5 | 1.0 |
The key technical problem in the balance development is the design of strength and sensitivity for the rolling moment component[7, 8].
At present the component that is sensitive to Mx load normally is of a “米”-shaped structure and is positioned at the geometric center of symmetry of the balance to reduce the stresses exerted by other components on the Mx component[9]. Figure 1 shows a typical five-component small Mx balance. The structure has greatly reduced the stresses by Y and Z components on Mx component,thus having guaranteed component strength.
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| 图 1 典型的五分量小Mx天平结构 Fig. 1 Typical structure of a five-component with small Mx balance |
Normally,to take both axial force and rolling moment into consideration,the axial force component and rolling moment component of the six-component balance for relatively small rolling moment assume a tandem structure with the two components separated from each other (Fig. 2). However,in the case of the balance with micro-rolling-moment,the same structure would lead to contradiction between sensitivity and strength for the rolling moment component and an increase in the length of the balance. If the rolling moment is measured with normal force or side force component,the sensitivity requirement cannot be met.
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| 图 2 串联结构型式 Fig. 2 Tandem structure with two components |
To solve the problems,we conjured up a composite structure that integrates axial force and rolling moment components as shown in Fig. 3. The Mx component consists of three pairs of symmetrically arranged beams forming a“米”-shaped structure. Based on calculation and analysis,the angles between the central planes of each beam and the horizontal plane being 90°,20° and -20° respectively(1#,2#,3#). In this case,axial force is measured by the spring and rolling moment is measured by the “米”-shaped structure in the middle of the axial force component. With this design,the sensitivity of Mx component has been greatly improved,and the stresses acted on the Mx component by other components,especially by Y and Z,have been reduced to ensure component strength and reduce interference on rolling moment component deformation which indicates greater anti-interference ability.
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| 图 3 复合结构型式 Fig. 3 Composite structure with six components |
Due to the presence of normal force and side force,with the same electrical bridge output,if the rolling moment component is a separate part,then the distance between its root and the reference center of the balance moment will be lengthened. In contrast,the bending moment stress induced by normal force or side force at the root of the rolling moment component will be reduced. 3 Application and results analysis 3.1 Major technical parameters
There is a six-component internal balance with a diameter (D) of 24mm and a component length (L) of 80mm. The balance is primarily intended for measuring test model’s rolling moment at micro level (Mx0) with the angle of attack near zero. The basic measurement requirement is Δmx0＜5×10-6,and we try to achieve Δmx0＜3×10-6.The specified loads for the components are shown in Table 2.
component | X /N | Y /N | Z /N | Mx /(N·m) | My /(N·m) | Mz /(N·m) |
| load | 200 | 50 | 50 | 0.2 | 2 | 2 |
The material for the balance and supportis F141,whose limit of bending strength is σb=1862N/mm2,longitudinal elastic modulus is E=1.8725×105N/mm2,and shear elastic modulus is G=0.72×105N/mm2[10].
There are two independent rolling moment components in design,namely,Mx1 and Mx2,and the superposition of which makes Mx3. The calculation formulae of the output for the Mx1 and Mx2 are traditional. The output Mx3 is the sum of outputs of the Mx1 and Mx2.
When in use,the components can either work separately or function as one measuring component by double bridges. The output of the three components can be compared and crosschecked,therefore improving the credibility of balance measurement.
Bridge Mx1 is composed of 16 strain gauges attached to Beam 2 and Beam 3,and Bridge Mx2 is composed of 8 strain gauges attached to Beam 1. The bridge voltages are 24V and 12V respectively. The full scale output voltage for Mx1 is approximately 7.0mV,which is a relatively higher value; whereas that for Mx2 is around 2.5mV,which is a bit lower. Comparatively speaking,with a value of about 9.5mV,the full scale output voltage for Mx3 is the highest. The sensitivity of Mx3 is 47.5mV/(N·m),it is higher than that of all the other present small Mx balances. The results comparison of calculation and calibration for different components are shown in Table 3.
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| X | Y (M1) | Z (M5) | Mx1 | Mx2 | Mx3 | My (M6) | Mz (M2) |
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Design Load /(N or N·m) | 200 | 50 | 50 | 0.2 | 0.2 | 0.2 | 2 | 2 |
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Mean strain/με | 376 | 335 | 335 | 157 | 118 | 144 | 372 | 372 |
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Bridge voltage/V | 12 | 6 | 6 | 24 | 12 | 6 | 6 | |
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Calculated maximum output/mV | 9.02 | 8.04 | 8.04 | 7.55 | 2.83 | 10.38 | 8.93 | 8.93 |
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Actual Maximum output/mV | 9.24 | 7.49 | 7.65 | 7.02 | 2.55 | 9.57 | 8.02 | 7.88 |
The balance is intended for use in hypersonic wind tunnel with Ma=5～8. Projector is used in the test. Impulsive factor n=3,safety factor K=2,allowable stress is as follows:
The result of strength analysis is shown in Fig. 4. The maximum stress of 220.1 N/mm2 occurs at the lateral side,on top of Beam 1,and at the root of the Mx component. The max stress is below the allowable value and therefore can meet the strength requirement[11, 12].
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| 图 4 天平强度分析结果 Fig. 4 Balance strength analysis result |
The static calibration of the balance was conducted with a body axis calibration rig[13, 14, 15, 16]. A special loading device was applied in the process so that the interference of different components on Mx can be accurately corrected. Table 4 is a list of loads and calibration uncertainty for the components.
| X | Y | Z | Mx1 | Mx2 | Mx3 | My | Mz | |
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Design load /(N or N·m) | 200 | 50 | 50 | 0.2 | 0.2 | 0.2 | 2 | 2 |
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Calibrated load /(N or N·m) | 200 | 50 | 50 | 0.2 | 0.2 | 0.2 | 2 | 2 |
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Calibrated uncertainty/% | 0.1 | 0.1 | 0.1 | 0.3 | 0.3 | 0.3 | 0.2 | 0.2 |
Four repeatability tests were performed at Ma=5 to verify the performance of the new balance. Table 5 gives the limit deviations of the rolling moment components. The limit deviations of the other components are the same with that of conventional balances.
It is indicated by repetitive tests that all the technical parameters of the balance have met the design requirement. At Ma=5,the mean limit deviation for Mx1 and Mx3 is Δmx0＜1×10-6; for Mx2,the mean limit deviation is Δmx0＜2.2×10-6 due to its comparatively lower sensitivity and output signal.
α | β | Δmx1 | Δmx2 | Δmx3 |
| -2 | 0 | 5.00×10-7 | 2.50×10-6 | 10.00×10-6 |
| -1 | 0 | 10.00×10-6 | 2.00×10-6 | 12.00×10-6 |
| 0 | 0 | 10.00×10-6 | 1.80×10-6 | 10.00×10-6 |
| 1 | 0 | 4.00×10-7 | 1.80×10-6 | 7.00×10-7 |
| 2 | 0 | 8.00×10-7 | 1.80×10-6 | 8.00×10-7 |
| 0 | 0 | 9.00×10-7 | 2.30×10-6 | 10.00×10-6 |
| 0 | 2 | 13.00×10-6 | 2.30×10-6 | 12.00×10-6 |
| 0 | 1 | 10.00×10-6 | 2.80×10-6 | 13.00×10-6 |
| 0 | 0 | 10.00×10-6 | 2.60×10-6 | 11.00×10-6 |
| 0 | -1 | 6.00×10-7 | 2.10×10-6 | 7.00×10-7 |
| 0 | -2 | 4.00×10-7 | 1.90×10-6 | 6.00×10-7 |
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Mean limit deviations | 8.09×10-7 | 2.17×10-6 | 9.64×10-7 | |
In the testing process,the balance demonstrated good anti-interference ability owing to itscomposite structure. At Ma=5,mean limit deviation for Δmx0 is very small and at Ma=8,Δmx0＜1.1×10-6,which suggests stable performance. The value of Mx0 is a little lower than that of single-component small rolling moment balances used in prior tests at HSAI,primarily because the latter cannot be deducted of the influence of normal force (side force) on Mx0 measurement as the former. 4 Conclusions
It is proven by test results that the newly-developed composite structured balance is a successful improvement,which has addressed the contradiction between strength and sensitivity as well as accomplishing accurate measurement of six components simultaneously. The balance boasts a rolling moment component of high sensitivity,good anti-interference,repeatability and stability.
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