RU2535645C1 - Determination of long object bending stiffness with help of curvature gage - Google Patents

Abstract

FIELD: test equipment.

SUBSTANCE: object is secured in cantilever at bearing column to use mechanical curvature gage for measurement of object curvature at its separate sections at objected bending under preset load applied to its free end. Curvature of separate parts in different cross-sections over the object length is measured by sequential transfer of curvature gage from cross-section to another one along reference washers, first, at initial flexed state under initial load and, then, at flexure after application of preset extra load curvature of every section corresponding to appropriate bending moment is defined as the difference between curvatures measured at two said strained states of the object. Bending stiffness at design cross-section is defined as the quotient of division of bending moment at section mid cross-section by measured curvature multiplied by correction factor. The latter is predetermined by calculations of known functions of nominal bending stiffness distribution set at tests as the relationship between nominal mean curvature to that at object mid section.

EFFECT: higher accuracy, lower labour input.

2 cl, 4 dwg

Description

The invention relates to a test technique and aims to increase accuracy and reduce the complexity of the method for determining bending stiffness using the curvature of extended objects with a variable length stiffness.

A known method for determining the bending stiffness of samples of constant cross-section (Deformation of structural materials. Textbook. - Ministry of Education and Science of the Russian Federation Tomsk Polytechnic University. - Tomsk ed. TPU, 2004 - Pages 8-12), in which one end of the sample is pinched a device mounted on a fixed base, a transverse load is applied to its free end, linear or angular displacements of the end section of the sample relative to the base coordinate system associated with the base are measured, and, using the known calculated dependences for the displacements of the console of constant cross section determine the value of bending stiffness. For example, when measuring linear displacement h, the bending stiffness of the sample is determined by the formula EI = P'L ³ / 3h, where L is the distance of the point of application of force P from the seal.

The specified method has the following disadvantages that make it difficult to use to determine the stiffness characteristics of extended objects with a variable length stiffness: the measured deflection of the end section of the sample during cantilever bending is an integral function of the bending stiffness of the entire bending section and the bending stiffness determined by this method characterizes some average stiffness of the sample in general, while the stiffnesses in its specific sections remain unknown; to measure in this way the bending stiffness of segments of an extended object located in its various sections along the length, it is necessary to appropriately move the places of embedment and application of the load, which is associated with large labor costs; the accuracy of measuring the elastic deflection of the end section of the sample relative to the fixed base can be significantly affected by deformations of the fixture and the attachment points of the sample, causing linear and angular displacements of the sample as a solid, which leads to the appearance of corresponding errors in measuring the elastic deflection, which require labor-intensive to take into account or compensate precision measurements.

For the above reasons, the scope of the known method for determining bending stiffness, based on measurements of the displacements of individual points of the object, is limited mainly to laboratory tests of small samples.

The closest analogue of the claimed invention is a method for determining the bending stiffness of an object such as a wing (Manual for laboratory work on the discipline "Design and strength of aircraft". Laboratory work No. 1. Experimental and computational study of deformations of aircraft structures - Ministry of Transport of the Russian Federation. Moscow State Technical University Civil Aviation. - M .: MGTUGA, 2006 - p. 5-11), which consists in the fact that the object is cantilevered on a power column and with the help of ivomera Upadysheva measured curvature of its individual portions flexural object under a given lateral load applied to the free end thereof, and determine the bending stiffness as the quotient of the bending moment in the middle portion of the cross section to the measured curvature.

The considered method for determining bending stiffness from the measured curvature is based on the beam bending equation known from the resistance of materials in the form of:

$$k\left(x\right)=\mathrm{one}/\rho \left(x\right)=M\left(x\right)/EI\left(x\right),\text{(one)}$$

establishing a functional dependence of the curvature k (x) (radius of curvature ρ (x)) of the elastic axis of the beam in the current section x on the bending moment M (x) and rigidity EI (x) in this section. For known values of curvature and bending moment in the calculated section from equations (1), bending stiffness can be determined:

$$EI\left(x\right)=M\left(x\right)/k\left(x\right),\text{(2)}$$

The Upadyshev’s curve gauge is a three support frame, one of the supports of which is movable and is equipped with an indicator for measuring its movement due to the bending of the controlled area of the object. The magnitude of the measured displacement determines the curvature of the arc of the controlled area, as the curvature of the arc of a circle drawn through three points of contact of the support of the gauge with the surface of the object according to the formula:

$$ko=\mathrm{four}h/a^2,\text{A.}\text{(3)}$$

where h is the movement of the movable support of the gauge, measured by the indicator, a is the base of the gauge, equal to the distance between its extreme supports.

Bending stiffness is defined as the quotient of dividing the bending moment in the middle section of the controlled area by the measured curvature according to the formula:

$$EIo=M/ko,\text{(four)}$$

where the bending moment is defined as the product of the force applied to the free end of the object by the shoulder relative to the middle section of the section.

The known method is implemented as follows: the object is cantilevered on the power column, in the initial state when the object is bent under its own weight, a curvature is installed on one of its specified design sections, the object is loaded with a bending moment by applying a concentrated force P to its free end, then determine the difference in the readings Δλ of the gauge indicator when the load changes from 0 to P and the displacement h = Δλ corresponding to the deformation of the controlled area during bending by the force ρ о initial state, further by the formula (3) calculating a curvature ko and the formula (4) determine the bending stiffness RIo.

To determine the bending stiffness in another design section, the object is unloaded and the cycle of all the above operations on loading the object, measuring the displacement h and calculating the curvature ko is performed again.

This method, if used to determine the stiffness characteristics of an extended object with a variable length bending stiffness, has the following disadvantages: greater complexity, due to the need to perform multiple loading cycles of the object to measure the curvature of the controlled sections located in different sections along its length, for example, at the rotor blades, the number of such sections may be 20 or more; no measures are foreseen to prevent possible displacements of the gauge along the surface of the object during its deformation during loading, which cause the appearance of uncontrolled errors of measurement of curvature; the bending stiffness, determined by formula (4) through the curvature ko, characterizes the average bending stiffness of the entire controlled section, while the desired stiffness in the average (calculated) section of the section remains unknown. This is due to the fact that when deriving formula (4) in the original expression (2) for the bending stiffness EI (x), instead of the curvature k (x) in the middle section of the section, the curvature ko (3) is introduced, which, like the curvature of the circle, has a constant the value along the length of the section, and in the general case with variable stiffness of the controlled section will not be equal to the stiffness in its middle section. In view of this, the known method does not allow to evaluate the correspondence of the actual (measured) stiffnesses of an object with a variable stiffness in length to the calculated data specified by the stiffness values in a number of calculated sections of the object.

The aim of the invention is to reduce the complexity and improve the accuracy of determining the characteristics of the distribution of bending stiffness along the length of an extended object, using a gauge to measure the bending deformation of its individual sections.

The problem is solved in that in the method for determining the characteristics of the bending stiffness of extended objects, where the object is cantilever mounted on the power column and using the mechanical curvature meter, the curvature of its individual sections, the middle sections of which are located in predetermined design sections, is measured when the object is bent under a given load, applied to its free end, bending stiffness is determined as the quotient of dividing the bending moment in the middle section of the section by the measured curvature, respectively In accordance with the claimed invention, the curvature of individual sections located in different sections along the length of the object is measured by sequentially rearranging the curvature number from section to section along reference washers previously glued to the surface of the object, first in the initial deformed state when bent under a certain initial load, and then during bending after application of a given additional load, after which the curvature of each section corresponding to the bending moment from a given load is calculated as the difference between the values of the curvature measured by the curvature meter in the two indicated deformed states of the object, and determine the bending stiffness in the calculated section as the quotient of the division of the bending moment in the middle section of the section by the measured curvature, multiplied by the correction coefficient, which is previously found by calculation using known distribution functions nominal bending stiffnesses of the object and bending moments specified during the test, as the ratio of the nominal value of the average curvature of the plot to n in the nominal value of the average curvature in its cross section.

Reference washers are used to ensure accurate installation and fixation of the curvature meter relative to the calculated cross section, while the reference washers are glued onto the surface of the object in pairs at the locations of the two extreme supports of the curvature meter, one of the washers paired with a tapered centering surface and the other with a longitudinal wedge-shaped groove .

Figure 1 presents a diagram of the measurement of bending deformation of a section of an object with a curvature meter.

Figure 2 presents the layout of the curvature meter on the object.

Figure 3 presents a view in longitudinal section of the extreme supports of the curvature meter installed by spherical tips in the reference washers.

Figure 4 presents a top view of a pair of reference washers with a conical hole and a wedge-shaped longitudinal groove.

The method is implemented as follows.

In the proposed method, a curvature meter 1 (FIGS. 1 and 2) is used, which schematically represents a frame with three supports 2, 3, 4 (FIGS. 1 and 2), two of which supports 2 and 3 (FIGS. 1 and 2) are rigid , and one of the extreme supports — the support 4 (FIGS. 1 and 2) is movable and is equipped with an indicator 5 (FIG. 2) for measuring its linear displacement h (FIG. 1) due to the bending of the controlled area of the object 6 (FIG. 2) . The size a of the distance between the extreme supports 2 and 4 (Figs. 1 and 2) determines the base of the curvature number 1 (Figs. 1 and 2) and the length of the controlled section.

Curvature number 1 (Figs. 1 and 2) as a means of measuring bending deformation is characterized by the following properties: curvature number 1 (Figs. 1 and 2) directly measure the deflection arrow f of the arc of the surface surface of the deformed section in the longitudinal plane of the object, while the amount of displacement h measured by indicator 5 (figure 2) curvature number 1 (figures 1 and 2) is equal to twice the magnitude of the arrow deflection: h = 2f (figure 1); curvature number 1 (figures 1 and 2) determine the curvature of the arc of the controlled area, as the curvature of the circular arc with the arrow of the deflection f drawn through three points x ₁ , x ₂ , x ₃ (figures 1, 2) of the contact supports 2, 3, 4 (Fig. 1, 2) of the curvature number 1 (Figs. 1 and 2) with the surface of the object 6 (Fig. 2), while the relationship between the curvature and the size a of the base of the curvature number 1 (Figs. 1 and 2) and the measured displacement h formula of curvature number:

$$ko=\mathrm{four}h/a^2,\text{(5)}$$

Using the formula of the curvature number, the second differential derivative function of the deflections of the controlled section is also calculated according to the coordinates of three points on the grid with a step equal to a / 2:

$$\text{y ''}=\text{four}\left({\text{y}}_{\text{one}}-{\text{<figure-callout id="2" label="2y" filenames="00000011.png,00000012.png" state="{{state}}">2y</figure-callout>}}_{\text{2}}+{\text{y}}_{\text{3}}\right){\text{/ a}}^{\text{2}}\text{,}\text{(6)}$$

while in the coordinate system OXY associated with the curvature number 1 (figure 1), the points x ₁ , x ₂ and x ₃ (figure 1 and 2) in sections along the supports 2, 3, 4 (figure 1 and 2) of the curvature number 1 (figures 1 and 2) have the following ordinates: y ₁ = y ₂ = 0, y ₃ = h. As a result, formula (6) for the second difference derivative takes the form equivalent to formula (5) for the curvature ko:

$$y\text{'}\text{'}\text{'}\text{'}=ko=\mathrm{four}h/a^2\text{(7)}$$

Measurement of curvature and determination of bending stiffness in the present method is performed in the following order.

Object 6 (figure 2), for example, a blade, is mounted on a power column (not shown). On the longitudinal axis of the object mark the position of the calculated sections 7 (Fig. 2), as well as points x ₁ , x ₂ and x _{3 of the} contact of the supports 2, 3, 4 (Figs. 1 and 2) of curvature number 1 (Figs. 1 and 2) with the surface object 6 (figure 2), while the middle support 3 (figures 1 and 2) of curvature number 1 (figures 1 and 2) is located at point x _{2 of the} calculated section 7 (figure 2).

To ensure accurate installation and fixing the position of the curvature number 1 (Fig.1 and 2) relative to the calculated cross section x ₂ when measuring the curvature of individual sections of the object 6 (Fig.2) using reference washers 8 and 9 (Fig.2, 3, 4). They are glued onto the surface of the object 6 (Fig. 2) in pairs using a double-sided adhesive substrate 10 (Figs. 3, 4) at the points x ₁ and x _{2 of the} contact of the two extreme supports 2 and 4 (1 and 2) of curvature number 1 (Fig. 1) and 2). In this case, the washer 8 (Figs. 3 and 4) has a conical centering surface, and the washer 9 (Figs. 3 and 4) has a longitudinal wedge-shaped groove, which, when the washers 8 and 9 (Fig. 2) are installed, are oriented along the longitudinal axis of the object.

The curvature of the sections is measured first in the initial deformed state of the object 6 (Fig. 2) under the action of some initial load, for example, its own weight, and then after applying to the free end of the object 6 (Fig. 2) an additional specified transverse load, in each of deformed states of measurement are carried out immediately in all calculated sections, by sequentially rearranging curvature number 1 (Fig. 1, 2) along the length of the object 6 (Fig. 2) from section to section along reference washers 8 and 9 (Figs. 2, 3, 4) .

The curvature of each section corresponding to the bending moment from a given load is determined as the difference between the values of curvature measured by curvature number 1 (Figs. 1 and 2) in the two indicated deformed states of object 6 (Fig. 2).

The bending stiffness in the middle section x _{2 of the} controlled section is determined as the quotient of the division of the bending moment in the middle section by the measured curvature multiplied by the correction factor:

$$\mathrm{<figure-callout\; id="2"\; label="E\; I"\; filenames="00000011.png,00000012.png"\; state="\{\{state\}\}">E\; </figure-callout>}{I}_{}{}_2=\left({\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="00000011.png,00000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_2/k_0\right)F_k,\text{(8)}$$

The correction factor F _k compensates for the error in determining the bending stiffness in a known manner. The appearance of this error is due to the fact that in the known method the average bending stiffness of the controlled section is determined as the ratio of the bending moment in the middle section to the average curvature of the section measured by the curvature meter: EIo = M ₂ / ko, while the desired rigidity in the middle section of the controlled section must be defined as the ratio of the bending moment in the middle section of the plot to the curvature in this section: EI ₂ = M ₂ / k ₂ . EI relationship ₂ / EIo = ko / k ₂ establishes a connection between these two stiffnesses, whose value is calculated from the nominal values of the average curvature _prefecture ko and k _2nom curvature in the middle section of the controlled section, defines the value of the correction coefficient in the formula (8):

$$F_k=k{o}_{n\mathrm{about}m}/{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="00000011.png,00000012.png"\; state="\{\{state\}\}">k</figure-callout>}}_{2.n\mathrm{about}m}\text{(9)}$$

When this curvature k _2nom defined as the quotient of the bending moment in the middle portion of the cross section to a nominal value of bending stiffness in this section k _2nom = M ₂ / EI _2nom and curvature ko _prefecture are in the form of a second difference derivative (7) is calculated according to the coordinates three points of the calculated function of the deflections of the controlled area in sections along the supports of the curvature meter.

The correspondence of the actual (measured) stiffnesses of the object to the calculated data is estimated by the value of the relative difference between the measured and nominal values of the bending stiffness in the middle section of the controlled area.

The combination of these new features of the proposed method for determining bending stiffness using a mechanical curvature provides increased accuracy and a radical decrease in labor intensity, and also expands its capabilities and applications. So, in relation to the rotor blades, this method can be used to solve a wide range of tasks for controlling the stiffness characteristics at all stages of the cycle of their development, production and operation:

a) at the development stage in the laboratory conditions of pilot production: to assess the compliance of the stiffness characteristics of the prototype blades with the design data, to check the effect of the introduced new design solutions on the change in the stiffness characteristics of the blades, to monitor the condition of the blades after various kinds of tests (thermal, strength, etc. .);

b) in the field of mass production: to identify the stiffness characteristics of each produced blade, to control the stability of the quality of manufacture of the blades; to assess the impact of the introduced refinements or possible deviations of the technological process modes on the change in the stiffness characteristics of the blades;

c) in operation: to assess the impact on the stiffness characteristics of the blades of operational factors (heating by solar radiation, high humidity, etc.).

Claims (2)

1. A method for determining the characteristics of the bending stiffness of extended objects, which consists in the fact that the object is cantilevered on the power column and the mechanical curvature meter measures the curvature of its individual sections, the middle sections of which are located in predetermined design sections, when the object is bent under the action of a given load applied to its free end, and bending stiffness is determined as the quotient from dividing the bending moment in the middle section of the section by the measured curvature, characterized in that the curves the knowledge of individual sections located in different sections along the length of the object is measured by sequentially rearranging the curvature number from section to section by reference washers previously glued to the surface of the object, first in the initial deformed state when bent under the influence of a certain initial load, and then when bent after application predetermined additional load, after which the curvature of each section corresponding to the bending moment from the given load is calculated, as the difference between the values of curvature curvature meter in the two indicated deformed states of the object, and bending stiffness in the calculated section is determined as the quotient of dividing the bending moment in the middle section of the section by the measured curvature multiplied by the correction coefficient, which is previously found by the calculation method from the known distribution functions of the nominal bending stiffnesses of the object and bending moments set during the test, as the ratio of the nominal value of the average curvature of the plot to the nominal value of the curvature in the medium I eat it section. 2. The method according to claim 1, characterized in that for accurate installation and fixing of the curvature meter relative to the calculated cross section, the reference washers are glued onto the surface of the object in pairs at the locations of the two extreme supports of the curvature meter, while one of the washers in pair is made with a conical centering surface, and the other with a wedge-shaped longitudinal groove.

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