JPH01267429A - Measurement of multiple component forces - Google Patents

Abstract

PURPOSE:To achieve a higher measuring accuracy, by performing a proper correction of correctable errors. CONSTITUTION:A detection output is taken out of a multiple component detector. The results of the detection are expressed by a specified formula to determine an interference coefficient from which an interference correction coefficient is obtained from such a condition as to minimize an error function in an arithmetic processing. The resulting interference correction coefficient is introduced to detect multiple components at a specified accuracy by computing the results of the detection. Thus, errors based on various interferences can be corrected sufficiently, thereby enabling implementation of detecting multiple components at a specified measuring accuracy.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a method for detecting component forces acting on an object using a multi-force detector, and particularly relates to a method for detecting component forces acting on an object by using a multi-force detector, and in particular, a method for detecting component forces acting on an object by using a multi-force detector. This invention relates to a method for measuring multiple forces that enables accurate measurement.

[Prior art]

Considering an arbitrary point on an object on which various external forces are acting, the forces FX + Fv, Fz in each axis direction in the X, Y, Z orthogonal coordinate system, and the moment MX around each axis.
It can be decomposed into six independent force components consisting of 1 MYI MZ.

When such a force is separated into force components and measured using a multi-force detector attached to an object, the output of the detector includes an error. This error includes various factors, but it can be broadly classified into correctable errors and difficult-to-correct errors.

However, with recent advances in measurement technology, some errors that were difficult to correct in the past can now be corrected, and although there are some areas that do not appear to be errors, there are still many errors that cannot be corrected. Ta.

[Problems to be solved by the present invention]

The present invention aims to provide a method for measuring multiple forces that can dramatically improve measurement accuracy by appropriately correcting correctable errors.

Here, errors to be corrected include those due to various types of interference. These interferences include (1) interference due to the shape of the object to be measured, (2) interference due to the position of the gauge, and (3) interference when the gauge is deflected, as will be described later.

[Structure of the invention]

The multi-force measuring method according to the present invention extracts the output from a multi-force detector, expresses the detection result in a predetermined formula to obtain an interference coefficient, and minimizes the error function when arithmetic processing is performed using the interference coefficient. The present invention is characterized in that multi-force detection with a predetermined accuracy is performed by determining an interference correction coefficient from conditions, introducing the interference correction coefficient, and calculating the detection result.

〔Effect of the invention〕

According to the method for measuring multiple forces according to the present invention, errors caused by various types of interference can be sufficiently corrected, and multiple forces can be detected with desired measurement accuracy.

〔Example〕

The force acting on the Cartesian coordinate system with the origin at point 0 on the object is
As shown in Figure 1, the forces F,, FY in each axial direction.

It can be considered by breaking it down into component forces of FZ and moments Mx, Mv, and Mz around each axis. Each of these component forces can be measured, for example, by attaching a strain gauge to a required location on the object to be measured. In this case, it is known that interference of component forces occurs depending on the shape and dimensions of the object to be measured, the mounting condition of the strain gauge, and other circumstances, resulting in measurement errors.

Conventionally, in order to reduce this measurement error, correction is performed using a linear equation.

The method will be described below.

First, add a known component force to each component force direction of the multiforce detector,
By reading the output of each component force at that time, the load of each component force, that is, the calibration coefficient of the output of each component force is determined.

This general formula is given by the following formula.

Here, E F x NE M z is the detector output, F,
%Mz is the load applied to the detector, ^1. ~A66 is a matrix for conversion.

When measuring external force acting on an object, output EFx-E
Since the external force FX%MZ is calculated from Mz, the following equation is obtained.

Here, (B) is the inverse matrix of (A), and CB)
There is a relationship of = (A)-'. Note that these matrices are linear matrices.

For interference correction of a multi-force detector used for general measurements, the above-mentioned linear correction, that is, -order correction is sufficient.

However, when the detector is deformed and the attitude of the object to be measured changes, or when high-accuracy measurement performance is required, the above-described method cannot satisfy the required measurement accuracy.

This case will be described below.

(1) When the deformation of the detector cannot be ignored When conducting wind tunnel tests on aircraft etc. using a Sting-type multi-force detector, the rigidity of the detector greatly affects the measurement performance. As more and more capacity is required, the importance of interference correction increases accordingly.When an external force is applied to a wind tunnel test aircraft, the detector and sting deform, and the attitude of the aircraft changes accordingly. Change.

Since the purpose of wind tunnel testing is to measure the aerodynamic force acting on the aircraft, the coordinate system must be constructed with the aircraft as a reference. The same goes for calibrating the detector (Figure 2).
.

When calibrating the detector, use CAL, B instead of the aircraft.
When using ODY, each time the load is applied, CAL, BODY
Read the output while keeping the position constant.

At this time, the postures of CAL and BODY are constant, but since the detector has low rigidity, interference occurs due to its deformation.

Let's consider an example of interference caused by this deformation. In the following description, the axial force is Fx, the lift force is FZ, and the pitching moment is MY.

(i) Effect of Fz load on FX.

When the inclination angles of CAL and BODY when F2 is loaded are corrected, and the inclination angle that occurs in the Fx sensing section is θ1 as shown in FIG. 3, the following relationship exists.

θ1 = 1・FZ Here, is a proportionality constant.

In this case, the FX acting on the FX sensing section is expressed as in the following equation.

FX =Fz-sinθl #FZ'θ1=, -F
Z2 That is, the tilt of the detector due to the F2 load causes secondary interference with px.

(ii) Effect of Fz and M7 load on FX (a
l When the tilt angle of CAL and BODY when MY acts is corrected, if the tilt angle generated in the FX sensing part is θ as shown in Figure 3, then the following relationship is established as in (i) above. .

θ2=2・F2 (bl Furthermore, when FZ load is applied in this state,
θ1 is expressed as in the following equation.

1・F2 for θ1# Further, the overall slope θ3=θ1+θ2.

In this case, the FX acting on the FW sensing section is expressed as in the following equation.

FX #Fz−sinθ3 =Fzsin(θ1+θ
2)”-Fz(K+・Fz+Kz・My)#K
+・Fz” +Kz・Fz−Mv, that is, Fz S
When My acts, it also generates secondary interference with px. Note that this calculation ignores higher-order interference.

[2] Strain gauges should be attached to the detector when the effects of complex stress acting on the part cannot be ignored.

When various forces are acting on the multi-force detector, a fairly large stress is acting on the sensitive part to which the strain gauge is attached. This stress is not a single stress, but stresses corresponding to axial force, bending force, and shearing force are generated.

According to elasticity, for example, when a bending force is applied while an axial force is acting, the change in stress due to the bending force does not match the stress when only the bending force is applied, but is due to the change in stress caused by the bending force applied in advance. It is known that it changes depending on the axial force. In this way, the change in stress due to the composite load is not due to -order interference, but
Naturally, high-order interference is generated.

The general formula when there are various high-order interferences as described above is as follows.

In the following description, the loads Fx xllllz applied during the calibration test are assumed to be F1 to F6, and the outputs EFX to EMZ at that time are assumed to be EFI to EF.

The relationship between load and output is as follows.

EFI = ΣAIJ'FJ (-order interference)
=ΣA2jk-F, [secondary interference] =ΣA:1Jkl·F, ·Fk-Fl (tertiary interference) When measuring aerodynamic force using such a detector, the following formula is used.

Fl = ΣB, j-EFj = ΣB□, -EF, 4Pk = ΣB3Jkl·EF, ·EFk, EFl, where (B) = (A) -'.

Note that even when performing high-order correction, it is usually sufficient to perform secondary correction. The calculation formula at this time is as follows if the above formula is expanded for FX.

FX=B.

+B114Fx+Btz4Fy+---+B+6・EM
z+Bz++・EF,”+8!+2・EFX・EFY+
...+Bz+6・EFx4Mz +Bz224Fy2+...”・+Bzz64P+i”
EMz+Bza64Mz2 Based on these circumstances, a method for calculating the interference coefficient will be disclosed below.

Here, similarly to the above, the magnitude of the component force applied in the calibration test is F1 to F6, and the output at that time is EF, -
Let it be EF.

Suppose that the test results in this case are obtained as shown in the table below.

n F1nF6n EF+n EFbn
The interference coefficient obtained from this test result is assumed to be (A), and the following relationship is assumed.

AFi=^. (li +Ao+tF+ +AoztFz+・・・・・・+AO
61F&+A, eye F, 28121FIFZ+...
...+Al61FIFl.

+AzziFI2+”...+Az61FzF6+A,,
6tFzF6” Since measurement inevitably involves errors, the condition for finding (A) is that the solution is the coefficient that minimizes the sum of squares of the difference between the measured value and the value calculated by substituting the coefficient. In other words, the least squares method is used.

Let the sum of the squares of the differences between the calculated values AFL using the above calculation formula be an error function D1.

Dl = Σ(AFilIEFtn)'' The condition for this error function Di to be minimized is the solution of the simultaneous equations according to the following equations.

In this equation, since i is independent, it will be omitted in the following explanation.

0Ffl= AFn-EFn = (＾oo +AotF+n+AoJzn+ ・・・・
...+AO6F&! 10A1+F+n"+^tzF+n
Fzn+...+A+J+nFbr++＾zJzn2
+..."+AzJznF6n+A, hF, nF, n -EF, ), it becomes as follows. Here, the total of 2
28 yuan with 8 unknowns (^.O””A66)
The following simultaneous equations are obtained.

If you solve this simultaneous equation, the solution is A 011 ” A 66
is obtained.

If this calculation is performed for the output i = 1 to 6 of each component force,
28×6=168 coefficients A001 to A661 are obtained.

〇 to these coefficients. ~A66 is a coefficient for determining the output of a component force when a load component force is given, and cannot be used as is to determine the fluid force from the output obtained from the detector during a wind tunnel test.

In the case of a linear (-order) matrix, an inverse matrix can be easily obtained, but in this case, since it is quadratic, it is troublesome to obtain an inverse matrix.

Therefore, the following method may be used.

It is assumed that the calculation program for i, interference coefficient 11oo %Ai6 has been completed.

ii. If we look at the above test results not as physical quantities but as mere tables, F, ~F6 and EF, ~11iF are nothing more than arrays.

iii.Therefore, F and EF may be interchanged.

iv, iii, 1. When you run the program ^. . ~A66 inverse matrix B0°~B66
is required.

A calibration test method for determining a secondary interference coefficient to correct the interference expressed as above will be disclosed below.

The calibration device, CAL, and BODY that perform such a calibration test are required to have the following functions.

(1) Angle adjustment that allows the reference plane of CAL and BODY to be kept horizontal regardless of the load condition when performing a load test by attaching the sting, detector, CAL, and BODY to a calibration device. Equipped with a mechanism.

(2) When a vertical load is applied and the reference planes of CAL and BODY are made horizontal, it must be equipped with a function that can apply a force in the direction F horizontally.

(3) It should be equipped with a function that allows loads of different magnitudes to be applied for 6 minutes, that is, a combined load test function.

In addition, in the case of a calibration test to determine the -order interference coefficient, the weight and moment of CAL and BODY can be eliminated by moving the zero point without causing an error.
This causes a large error when determining interference coefficients of second order or higher order. Therefore, it is necessary to measure accurately in advance. This measurement is carried out as follows using the detector itself.

(For each component force of the 11 detectors, calibrate against simple component force and find the sensitivity.

(2) Attach the detector alone to the calibration device, read and average the output for each reference direction.

(3) Attach CAL and BODY to the detector and set it so that combined testing can be performed.

(4) Read the output of each component force when CAL and BODY are horizontal for each reference plane.

(5) From the results of (11) above and the data of (4) above, C
A.L.

Calculate the weight and moment of BODY, etc.

In this case, since the weight of CAL, BODY, etc. is considerably smaller than the measured capacity, the secondary characteristic of the output in (4) above can be ignored.

After preparing as above, conduct a combined load test. If the magnitude of the composite load is changed and six component forces are applied in combination at the same time, the number of combinations will be extremely large. Therefore, it is necessary to devise ways to conduct tests efficiently with fewer tests. Therefore, it is convenient to use the orthogonal array method, which is often used in ordinary experiments.

(Assemble the 11 detector, CAL, and BODY, and set them so that a combined load test can be performed.

(2) Load is applied by a combination of orthogonal array methods. Note that adding a load that includes the weight of CAL, BODY, etc. requires a complicated method of applying weights, so it is better to keep the load amount as simple as possible and add the weight of CAL, BODY, etc. during the data processing process. .

(3) Read the output of each force component. In this case, the standard is the zero point of the single detector, so it is necessary to either not move the zero during the test, or to correct it when it is moved so that the change from the original zero position can be read.

(4) Repeat the steps (2) and (3) above while changing the conditions.

(5) Obtain the interference correction coefficient CB) using the interference correction coefficient calculation method described above.

By performing arithmetic processing on the detection results using the interference correction coefficients obtained in this way, the intended purpose is achieved.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram showing the state of multiple forces in an orthogonal coordinate system. FIG. 2 is an explanatory diagram when the detector is bent. FIG. 3 is an explanatory diagram when a force in the Z-axis direction is applied to the object to be measured.

Claims (1)

[Claims] In a method of detecting multiple forces using a multiple force detector placed at a predetermined position of an object to be measured, the interference coefficient is determined by extracting an output from the multiple force detector and expressing the detection result in a predetermined formula. , find an interference correction coefficient from the condition that minimizes the error function when arithmetic processing is performed using the interference coefficient, and perform multiforce measurement with a predetermined accuracy by introducing the interference correction coefficient and calculating the detection result. A method for measuring multiple forces characterized by the following.