CN108106952B - Method for measuring impact load of beam with double symmetrical sections - Google Patents

Abstract

The invention relates to a method for measuring impact load of a beam with double symmetrical sections, and belongs to the field of load measurement of airplane design mechanical structures. The method comprises the following steps: A) determining the section of the structural beam to be measured, wherein the section must be a double-symmetrical section; B) selecting a test piece surface through which two symmetrical shafts pass on the determined double-symmetrical section and adhering right-angle strain rosettes; C) measuring strain values of 4 flower sheets under the actual working state of the beam; D) the method comprises the steps of obtaining the elastic modulus E and Poisson ratio mu of a structural beam material for common circular sections and common circular sections, and calculating section load by using a corresponding formula, and E) for more common double-symmetrical sections, except for section torque load, the method is consistent with a circular or circular section calculation method, and section torque needs to be calibrated, and the section load is reversely deduced by calibrating the relation between the load and strain.

Description

Method for measuring impact load of beam with double symmetrical sections

Technical Field

The invention relates to a method for measuring impact load of a beam with double symmetrical sections, and belongs to the field of load measurement of airplane design mechanical structures.

Background

In the mechanical structure, many structures can be assumed as beams, such as automobile frames, airplane arresting hooks, engine piston rods and the like, according to the plane assumption and the assumption that longitudinal fibers have no normal stress. The structural beams are easy to damage when subjected to high-speed impact, and if the impact load of the structure during working can be measured, the load can be used for carrying out optimized design, the force transmission path is improved, and the accident rate is reduced.

The load of the beam refers to the axial force, the shearing force and the bending moment of a certain section. An euler coordinate system is usually established, which is decomposed into three directional forces and three directional bending moments.

The term "double-symmetrical cross section" means that the cross section has two intersecting symmetry axes, such as a common rectangle, circle, I-shape, etc., and such a cross section is mechanically characterized in that the shear center of the cross section coincides with the centroid of the cross section.

The traditional method for measuring impact load is as follows: in a test room, a structure related to the structural rod piece is used as a test piece, the working condition of the structure in actual use is simulated, the structural beam is impacted at a high speed by using a force measuring device, and the load borne by the structural beam is obtained through the load measured by the force measuring device. The method has the following disadvantages:

a. the measurement of the impact load belongs to the structure transient response category, and the impact load has close relation with the mass distribution, rigidity, damping distribution, contact mode and the like of an impact object and an impacted object, so that the actual working state of the structure is difficult to simulate in a test room, and the measured load is not true;

b. the impact occurrence time is usually below millisecond level, and the measurement needs a large-range and high-frequency-response force-measuring element to accurately measure the time history of the load. The force measuring element is made into a force measuring device, the frequency response of the element is difficult to ensure, and the dynamic calibration technology is difficult to achieve.

c. When the structural beam is under the action of impact load, the transient stress wave propagation is complex, only one section loading point is needed, a dynamic model with quite high precision (which is often difficult to come) can be used for simulating the load transfer in the beam, and if the actual measurement loads of a plurality of sections can be obtained, the stress calculation precision can be improved under the condition of the same model precision, and more reliable strength evaluation is given.

Disclosure of Invention

The invention aims to provide a method for measuring impact load of a beam with double symmetrical sections, which solves the problem of load measurement when the beam is impacted at high speed in an actual working state.

In order to achieve the purpose, the invention adopts the following technical scheme:

a method for measuring impact load of a beam with double symmetrical sections comprises the following steps:

A) determining the section of the structural beam to be measured, wherein the section must be a double-symmetrical section;

the number of cross sections is determined according to the measurement purpose and the hardware condition of the measurement equipment. The section with larger estimated stress is recommended to be selected, because the method can measure the strain of the corresponding point of the section while measuring the load of the section, the measurement hardware channel can be saved;

B) selecting a test piece surface through which two symmetrical shafts pass on the determined double-symmetrical section and adhering right-angle strain rosettes;

establishing an Euler coordinate system, selecting the centroid or shear center of the beam as an origin, the length direction of the beam as a z-axis, two symmetrical axes of the cross section as an x-axis and a y-axis respectively, and the coordinate system accords with the right-hand rule; the right-angle strain pattern pieces are adhered to the intersection points of the x axis and the y axis and the surface of the beam, the number of the right-angle strain pattern pieces is 4, and one right-angle side of each pattern piece is parallel to the z axis;

C) measuring strain values of 4 flower sheets under the actual working state of the beam;

D) obtaining the elastic modulus E and Poisson ratio mu of the structural beam material for common circular sections and circular ring sections, and calculating the section load by using a corresponding formula;

E) and for a more general double-symmetrical section, except for the section torque load, the calculation method is consistent with that of a circular or circular section, the section torque needs to be calibrated, and the section load is reversely deduced through calibrating the relation between the load and the strain.

The invention has the beneficial effects that:

the invention solves the problem of load measurement when the beam is impacted at high speed in the actual working state, accurately simulates the actual working state of the structure in the test, and is real and effective; the stress calculation accuracy is improved, and more reliable strength evaluation is given.

Drawings

FIG. 1 is a schematic diagram of a doubly symmetrical cross-section of a beam of the present invention;

FIG. 2 is a schematic view of the plane A-A of FIG. 1;

in fig. 2: 1-a first patch; 2-a second patch; 3-a third patch; 4-a fourth patch;

FIG. 3 is a schematic view of the first patch in the direction B;

FIG. 4 is a schematic view of the direction of the third patch from C;

FIG. 5 is a schematic view of the second patch orientation;

fig. 6 is a schematic view of the fourth patch orientation;

FIG. 7 is a schematic diagram showing the relationship between the measured strain value and the strain in the beam coordinate;

fig. 8 is a schematic view of the torsion calibration of the beam.

Detailed Description

The invention is described in detail below with reference to the attached drawing figures:

for the selected structural beam double-symmetrical section, a beam element coordinate system is established, the original point of the coordinate system is selected at the centroid O point of the section, the x axis and the y axis are respectively two symmetrical axes of the section, and the z axis is along the beam direction, which is shown in the attached figure 1.

In the cross section shown in fig. 2, the first patch 1, the second patch 2, the third patch 3 and the fourth patch 4 are adhered with right-angle flower strain gauges, and the adhering direction of the right-angle flower strain gauges is defined as shown in fig. 3, 4, 5 and 6. Selecting a right-angle side of the right-angle pattern piece from the original + z-axis direction, and defining the right-angle side as epsilon i _0 DEG, namely epsilon i in the beam element coordinate system_z(ii) a Is ε i-90 DEG in the direction of the cross section, ε i in the coordinates of the beam element_xOr ε i_y(ii) a The strain gauge with the direction of epsilon I-0 degrees and epsilon I-90 degrees forming 45 degrees is epsilon i-45 degrees.

From FIG. 7, it can be seen that the strain gauge measuresEpsilon i _0 deg., epsilon i _45 deg., epsilon i _90 deg., and the positive strain of the beam element coordinate system

And shear strain γ i_xz、γi_yzThe relationship of (1) is:

when i is 1, 3

When i is 2, 4

For a common circular cross-section, the ring cross-section, the cross-sectional load can be calculated as follows. The beam material has an elastic modulus E, a Poisson's ratio μ, a shear modulus G, and

these material constants can be found according to the materials handbook or by experimentation. A is the area of the cross section, I_xIs the moment of inertia of the cross-section to the x-axis, I_yIs the moment of inertia of the cross-section to the y-axis, I_pAnd R is the polar inertia moment of the cross section to the point O, and is the distance R from the points 1, 2, 3 and 4 to the origin.

It is clear that for a circular (circular) cross-section, M_xCalculating y ═ R, M in the formula_yX ═ R in the formula was calculated.

For a more general bi-symmetric cross-section, the cross-sectional twist M_zThe shear strain of the induced section is not simple formula and can be calculated, and the relation between the load and the shear strain can be given only by a calibration method. The remaining cross-sectional loads are all in agreement with the circular (circular) cross-section and can be calculated by the formula. The calibration method is shown in figure 8. And (3) mounting the target beam at an included angle theta with the horizontal direction, fixedly connecting one end of a horizontal rigid beam and the target measuring beam to the point A, and hanging weights on the point B at the other end of the horizontal rigid beam. The section to be calibrated is at point O on the target beam. The distance between AO and AB is L and b. And (4) placing weights at the point B, loading step by step, and measuring the strain values of the 4 strain gauge flowers. When the mass of the hanging weight at the point B is m, the local gravity acceleration g and the torque converted into the cross section are as follows:

M_z＝-mgbcosθ

the linear range of the structure exists:

M_z＝K1·(γ_3xz-γ_1xz)＝K2·(γ_4yz-γ_2yz)

obtaining a set of gamma by using the mass m of a set of weights_3xz-γ_1xzAnd gamma_4yz-γ_2yzRegression analysis was performed to obtain the least squares of K1 and K2.

During actual working condition measurement, the section torsional load is obtained by using calibrated K1 and K2: m_z＝[K1·(γ_3xz-γ_1xz)+K2·(γ_4yz-γ_2yz)]/2。

Claims (1)

1. A method for measuring impact load of a beam with double symmetrical sections is characterized by comprising the following steps:

A) determining the section of the structural beam to be measured, wherein the section must be a double-symmetrical section;

B) selecting a test piece surface through which two symmetrical shafts pass on the determined double-symmetrical section and adhering right-angle strain rosettes;

establishing an Euler coordinate system, selecting the centroid or shear center of the beam as an origin, the length direction of the beam as a z-axis, two symmetrical axes of the cross section as an x-axis and a y-axis respectively, and the coordinate system accords with the right-hand rule; the right-angle strain pattern pieces are adhered to the intersection points of the x axis and the y axis and the surface of the beam, the number of the right-angle strain pattern pieces is 4, and one right-angle side of each pattern piece is parallel to the z axis;

C) measuring strain values of 4 flower sheets under the actual working state of the beam;

D) for the circular section and the circular ring section, obtaining the elastic modulus E and the Poisson ratio mu of the structural beam material, and calculating the section load by using a corresponding formula;

E) for the double-symmetrical cross sections except the circular or ring cross sections, except for the cross section torque load, the method is consistent with the circular or ring cross section calculation method, the cross section torque needs to be calibrated, and the cross section load is reversely deduced through calibrating the relation between the load and the strain;

calculating the section load in the step D:

the beam material has an elastic modulus E, a Poisson's ratio μ, a shear modulus G, and

；

a is the area of the cross section,

is the moment of inertia of the cross-section to the x-axis,

is the moment of inertia of the cross-section to the y-axis,

the polar inertia moment of the cross section to the point O is shown, and R is the distance R from the points 1, 2, 3 and 4 to the origin;

is the positive strain of the coordinate system of the beam element,

the positive strain shear strain of the beam element coordinate system is obtained;

for a circular or circular cross-section,

the calculation of y = R in the formula,

calculated x = R in the formula.

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