RU2562273C2 - Test bench for measurement of mass-inertia characteristics of item - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: invention relates to measurement equipment, namely to measurement of mass-inertia characteristics of different items. A test bench includes a bed, three frames installed on hinges, a dynamometric platform, springs and devices for setting oscillations, fasteners and three high-selective angular acceleration sensors installed on the frame to which the item is attached, the axes of which are oriented parallel to rotation axes of movable internal, external and lower frames of the test bench.

EFFECT: improvement of measurement accuracy.

15 dwg

Description

The invention relates to the field of mechanical measurements, in particular to the measurement of mass, coordinates of the center of mass and moments of inertia of products.

The task of controlling the high-speed movement of products of space and rocket technology, land and sea transport systems requires a knowledge of the mass, coordinates of the center of mass and moments of inertia of the products. The most reliable method for determining the complex of these parameters is measurement.

A known complex for measuring mass, coordinates of the center of mass and moments of inertia of engineering products (see VV Bogdanov, BC Volobuev and others. "Complex for measuring masses and moments of inertia of engineering products", Measuring technique No. 2, 2002, S. 37 -39).

The complex includes two stands, one of which is designed to measure the mass and coordinates of the center of mass, the other - to measure the moments of inertia of the products. The stand for measuring mass and coordinates of the center of mass consists of two frames, on the horizontal beams of which, with the help of special clamps, a cylindrical product extended over the length is installed. Using vertical rods, the beams are connected to four dynamometers. The bases of the dynamometers are connected to the support posts, which are rigidly fixed to the power foundation. Along the rods are reaction forces, which are measured by dynamometers.

The mass of the product is measured by the sum of the reactions of the dynamometers, and by the combination of reactions and the known coordinates of the dynamometers, two horizontal coordinates of the center of mass. To measure the vertical coordinate, you must rotate the product 90 ° around the longitudinal axis of the product.

The stand for measuring moments of inertia is a frame with four vertical springs, on which the product is installed using special clamps. In places where the springs are attached to the clamps, displacement sensors are located that measure the deformation of the springs. To prevent these points from moving horizontally, guide bushings are provided in the stand design. Thus, the movement of the product is possible only in three degrees of freedom.

Prior to the measurement, a force is applied to the springs, which is then immediately removed and the system begins to make free oscillations in three degrees of freedom. As a result of digital signal processing of each of the sensors, the frequencies and amplitudes of oscillations are used to determine the moments of inertia of the product. To obtain three axial moments of inertia, it is necessary to rotate the product 90 ° around the longitudinal axis.

The main disadvantages of this complex are the following:

- the need to rotate the product through an angle of 90 ° to obtain a measurement result (in many cases, such a rotation is unacceptable according to the technical conditions for the product);

- the mass and coordinates of the center of mass are measured on one stand, and the moments of inertia on another, which leads to additional measurement errors due to inaccurate alignment (mismatch) of the product axes with the axes of the stand.

In connection with the creation of a number of stands, TsAGI has gained some experience in the technique of measuring the inertia moments of various bodies and it has become possible to further improve the methodology for creating such measuring instruments.

The closest constructive solution is the stand created at FSUE TsAGI for measuring the mass, coordinates of the center of mass and inertia tensor of an engineering product (see patent for invention No. 2368880, IPC G01M 1/10, 2008, “Sensors and systems” No. 5, 2010 Page 24-28; 29-33), containing the frame to which the product is attached, dynamometers, angle sensors, springs, a bed, a dynamometric platform with a frame rotation unit, an oscillation setting device consisting of movable internal, external and lower frames interconnected with the bed with hinges and a spring system in, connected to the frames, while the axis of the hinges are connected to the axes of the angle sensors.

All necessary measurements are performed on one stand without changing the installation position of the product.

The stand has two modes of operation - static and dynamic.

In static mode, the mass and three coordinates of the center of mass of the product are measured using a dynamometer platform. The horizontal coordinates of the center of mass are determined by the forces measured by the dynamometers. To measure the vertical coordinate of the product using a rotation node, a series of consecutive tilt angles is specified. From the moments measured using the dynamometer platform and the measured tilt angles, the vertical coordinate of the product’s center of mass is determined.

Moments of inertia are measured in dynamic mode. In this case, the frame with the product make free damped oscillations sequentially around the three orthogonal axes of the stand. Using a dynamometric platform, three dynamic moments are measured, according to which, using the data of angle sensors, the known mass and coordinates of the center of mass, the moments of inertia of the product are determined using the digital signal processing apparatus. With damped frame vibrations, using the angle sensors, the current values of the frame rotation angle are measured, which are used to calculate the angular accelerations of the corresponding frame.

The vector of the measured moment acting on the dynamometric platform is the sum of three moments.

where M _k is the inertial moment due to product vibrations around the center of mass;

M _F - inertial moment due to fluctuations in the mass m of the product around the axis of rotation;

M _P - positional moment due to the action of gravity of the product during its rotation around the axis of rotation.

The moments M _F and M _P are inherently complementary, and the moment M _k is basic.

The main point is obtained by subtracting additional moments from the measured moment.

The vector of the main moment is related to the angular acceleration vector by the dependence:

where T is the inertia tensor

where J _x , J _y , J _z are axial, and J _{x · y} = J _{y · x} ; J _{x z} = J _{z x} ; J _{y · z} = J _{z · y} are the centrifugal moments of inertia;

- вектор углового ускорения с составляющими:

- vector of angular acceleration with components:

Oscillations of the frame frames of the stand with the product around three rectangular axes are sequentially excited and the components of the moment M _k along the indicated axes are simultaneously measured. After subtracting the components from the two additional moments, we obtain the following nine equations to determine the six moments of inertia:

The first indices in the notation of moments indicate the name of the moment component, and the second - on the axis around which the product oscillates. To obtain the final results, it is necessary to measure angular accelerations in addition to the moment components.

Previously, a method was developed for determining the angular acceleration from the readings of the angle sensor, see "Sensors and Systems" No. 5, 2012, p. 29 ... 32.

The main disadvantage of this stand is the lack of accuracy in measuring angular acceleration, because the damped oscillatory signal from the output of the angle sensor after sampling and coding is fed to the input of the notch digital filter, the filter is automatically tuned to unknown vibration frequency and attenuation coefficient. According to the known settings, the oscillation frequency, attenuation coefficient and the initial oscillation amplitude, necessary for calculating the angular acceleration, are found.

The method makes it possible to measure angular acceleration with high accuracy if the oscillation frequency remains constant throughout the entire signal attenuation time. Often, due to the nonlinear restoring force of the stand springs, the frequency changes during the damping process. The oscillatory system of the stand is non-isochronous, its frequency depends on the amplitude of the oscillations.

As a result, a damped frequency-modulated signal acts at the input of the notch filter, which makes the filter settings go awry. An inaccurate filter setting causes an error in measuring the frequency and, as a result, insufficient accuracy of measuring angular acceleration, and then insufficient accuracy of determining the moments of inertia.

The technical result of the invention is to increase the accuracy of measuring angular acceleration by direct (without calculating the second derivative of the angle of rotation over time) measuring the current angular acceleration when the product vibrates around the axis of rotation of the stand.

The technical result is achieved by the fact that the stand for measuring the mass-inertial characteristics of the product, containing the frame to which the product is attached, dynamometers, angle sensors, springs, bed, dynamometer platform, frame rotation unit, oscillation setting device, consisting of movable internal, external and lower frames connected to each other and to the bed by hinges and a system of springs, while the axis of the hinges are connected to the axes of the angle sensors, is equipped with clamps that allow the product to oscillate only around that axis, relative which is currently measuring the moment of inertia, and mounted on the frame to which the product is attached, three highly selective angular acceleration sensors, each of which consists of a housing, a shaft, two flywheels, mounted on the rim of a tensometric element consisting of a hub, a rim and connecting their two signal and two auxiliary racks located along mutually perpendicular axes, while the ratio of the radius of the hub to the length of the signal beam does not exceed 0.5, and on the inner faces of the signal struts in the root sections from the hub side are glued with strain gauges integrated in a bridge circuit, and the axes of highly selective angular acceleration sensors are oriented parallel to the rotation axes of the movable inner, outer and lower frames of the stand.

For a more detailed explanation of the invention, we consider the layout of the stand, its design and principle of operation.

In FIG. 1 shows a perspective view of a bench structure.

In FIG. 2 - stand design in two orthogonal projections.

In FIG. 3 is a perspective view of a highly selective angular acceleration sensor.

In FIG. 4 is a perspective view of a strain gauge element of a highly selective angular acceleration sensor.

In FIG. 5 is a diagram of the deformation of the struts of a tensometric element under the action of an inertial moment.

In FIG. 6 is a diagram of a strain of a signal rack of a strain gauge element.

In FIG. 7 - deflection y and rotation angle φ under the action of force Y and moment M _Z.

.In FIG. 8 is a graph of the dependence of the coefficient K on

.

In FIG. 9 is a diagram of moments acting in cross sections of a signal rack.

In FIG. 10 is a diagram of the installation of strain gages on signal racks.

In FIG. 11 is an electrical diagram of the strain gauge connections to the measuring bridge.

In FIG. 12 - increment of resistance of strain gages under the action of the moment M _And .

In FIG. 13 - increment of resistance of the strain gages under the action of the force F _Y.

In FIG. 14 - increment of resistance of strain gages under the action of forces F _Z.

In FIG. 15 is a photograph of a highly selective angular acceleration sensor.

The product 1 (Fig. 1 and Fig. 2) is mounted on a frame 2 connected by a turning unit 3 with a dynamometer platform 4, which is supported by four vertical 5 and two horizontal 6 dynamometers on the inner frame 7 of the oscillation setting device, consisting of movable internal 7, external 8, lower 9 frames and frame 10. The internal frame 7 is connected to the external frame 8 using two horizontal hinges 11 mounted on brackets 12 and 13, mounted on the inner and outer frames, respectively. The outer frame 8 is connected to the bottom 9 using two horizontal hinges 14 mounted on brackets 15 and 16, mounted on the outer and lower frames, respectively. The lower frame 9 is connected to the frame 10 using a vertical hinge 17. The axis of the hinges 11, 14 and 17 are directed along the coordinate axes 0XYZ of the stand so that the inner frame 7 can oscillate around the Z axis, the outer frame 8 around the Y axis, and the lower frame 9 is about the X axis. The inner frame 7 is connected to the outer frame 8 by a pair of springs 18. The outer frame 8 is connected to the lower frame 9 by a pair of springs 19. The lower frame 9 is connected to the frame 10 by two pairs of springs 20. Angle sensors are mounted on the shafts of the three hinges 21, 22 and 23. As a result, three independent olebatelnye systems, each of which can oscillate about one of the three orthogonal axes of the stand. To prevent arbitrary angular movements of the product, the stand is equipped with clamps 24, 25 and 26, which ensure the product oscillates only around the axis relative to which the moment of inertia is currently being measured.

The main feature of this stand is the presence of three highly selective angular acceleration sensors (VDUU) 27, 28 and 29 located on the frame 2, so that the VDUU 27 axis is parallel to the bench axis Y, the VDUU 28 axis is parallel to the X axis and the VDUU 29 axis is parallel to the Z axis stand, i.e. each VDUU measures the angular acceleration during product vibrations around one of the axes of the stand. To ensure balance, a counterweight of 30 is installed on frame 2.

The VDUU (Fig. 3) consists of a housing 31 in which a shaft 32 is mounted. A strain gauge element 33 is mounted on the shaft, to the rim of which two flywheels 34 are fixedly mounted. The housings 31 of the sensors 27, 28, and 29 are fixedly mounted on the frame 2 (FIG. 1 and Fig. 2). The strain gauge element (Fig. 4) is a hub 35 and a rim 36 connected by two signal 37 and two auxiliary 38 racks. Strain gages 39 are glued on the signal posts. Four threaded holes 40 are made on the outer cylindrical surface of the strain gauge element for mounting calibration devices.

The stand works as follows.

Like the prototype, it has two operating modes - static and dynamic.

In static mode, the mass and three coordinates of the center of mass of the product are measured using a dynamometer platform. The horizontal coordinates of the center of mass are determined by the forces measured by dynamometers 5 (Fig. 1 and Fig. 2). To measure the vertical coordinate of the product using the rotation node 3, a series of consecutive tilt angles is specified. From the moments measured using the dynamometer platform 4 and the measured tilt angles, the vertical coordinate of the center of mass of the product is determined.

Moments of inertia are measured in dynamic mode. In this case, the frame 2 with the product 1 make free damped oscillations sequentially around the three orthogonal axes of the stand. Using a dynamometer platform 4, three dynamic moments are measured, according to which, using the acceleration values obtained from the angular acceleration sensors 27, 28, 29, the known mass and coordinates of the center of mass, using the digital signal processing apparatus, the moments of inertia of the product relative to the axes of the stand are determined.

When measuring the axial moment of inertia about the Y axis, the latch 24 (Fig. 1 and Fig. 2) is open and allows the product to oscillate around the Y axis, and the latches 25 and 26 are closed and prevent angular movement of the product around the X and Z axes. External frame 8 with installed on it, the inner frame 7, the dynamometer platform 4 and the frame 2 with the product 1 deviates by an angle φ _Y about the axis Y of the stand and under the action of the springs 19 makes angular damped oscillations. The moments attached to the product are measured with vertical dynamometers 5, and angular acceleration, in contrast to the prototype, with a highly selective angular acceleration sensor 27 (Fig. 1 and Fig. 2)

When measuring the axial moment of inertia about the Z axis, the latch 25 (Fig. 1 and Fig. 2) is open, and the latches 24 and 26 are closed and prevent angular movement of the product around the X and Y axes. The inner frame with a dynamometer platform 4, frame 2 and product 1 deviates by an angle φ _Z around the axis Z of the stand and under the action of the springs 18 (Fig. 1 and Fig. 2) performs damped angular oscillations. The moments applied to the product are measured with vertical dynamometers 5, and angular acceleration with a highly selective angular acceleration sensor 29 (Fig. 1 and Fig. 2).

When measuring the axial moment of inertia about the X axis, the latch 26 (Fig. 1 and Fig. 2) is open, and the latches 24 and 25 are closed and prevent angular movement of the product around the Y and Z axes. The lower frame 9 with external 8, internal 7 frames, with dynamometer platform 4, frame 2 and product 1 is deflected by an angle φ _X around the axis X of the stand and under the action of the springs 20 (Fig. 1 and Fig. 2) performs damped angular oscillations. The moments applied to the product are measured with horizontal dynamometers 6, and angular acceleration with a highly selective angular acceleration sensor 28 (Fig. 1 and Fig. 2).

Further, using expressions (3) and the measured components of the moments and angular acceleration, unknown moments of inertia are determined.

An important distinguishing feature of this invention is the presence of three highly selective angular acceleration sensors, which operate as follows. In FIG. 5 schematically shows the deformation of the signal 37 and auxiliary 38 racks of the strain gauge element under the influence of the inertial moment M _And acting on the hub 35 from the side of the rim 36.

The magnitude of the moment:

where J is the total axial moment of inertia of the flywheels of the sensor and the rim and other elements of the strain gauge element;

- измеряемое угловое ускорение вала стенда;

- the measured angular acceleration of the stand shaft;

M _C - part of the inertial moment applied to one signal rack;

M _In - part of the inertial moment applied to one auxiliary rack;

In FIG. 6 shows a diagram of the deformation of a strut of length l when turning a hub of radius R by an angle φ.

;Where

;

и $$c_{{\varphi }_B}$$

- коэффициенты угловой жесткости сигнальной и вспомогательной стоек. $$c_{{\varphi }_C}$$

and $$c_{{\varphi }_B}$$

- coefficients of angular stiffness of the signal and auxiliary racks.

For a signal rack with a width of b _C , a thickness of h _C , a length of l _C and a hub of radius R (Fig. 4), c _φ is expressed by the dependence:

In FIG. 7 shows the deflection y and the angle of rotation φ _{C of the} root section of the signal rack under the action of force Y _B and moment M _B. The latter is related to the moment M _{C by the} ratio:

where K is the moment transmission coefficient

. На фиг. 8 представлен график зависимости коэффициента передачи момента K от отношения

, где штриховкой выделен интервал изменения отношения

, внутри которого K≥1.From the expression (8) it follows that the moment transmission coefficient varies depending on the ratio

. In FIG. 8 is a graph of the moment transmission coefficient K from the ratio

where the shading indicates the interval of change in the ratio

inside which K≥1.

коэффициент передачи момента имеет максимальное значение K_max=1,16.With respect

the moment transmission coefficient has a maximum value of K _max = 1.16.

Thus, in order to obtain a high sensitivity of the sensor to the measured angular acceleration, the ratio of the hub radius to the length of the signal rack should be no more than 0.5.

An important factor ensuring the high sensitivity of the VDUU is the choice of the location of the strain gauges on the signal rack.

In FIG. Figure 9 shows a plot of moments acting in cross sections along a signal rack. The moment M _about in the root section of the rack from the side of the rim is connected with the moment M _stup from the side of the hub by the dependence:

whence it follows that for any R and l _{C, in} order to increase the sensitivity of the VDUU to the measured angular acceleration, it is necessary to place the strain gauges in a place directly adjacent to the root section of the signal rack from the hub side.

In addition to high sensitivity, an equally important requirement is the high selectivity of the sensor. Usually it is not possible to constructively align the axis of the sensor with the axis of rotation of the frame 2 (Fig. 1 and Fig. 2), to which the product is attached. When misaligned, the sensor, in addition to angular, is subject to linear acceleration and, as a result, along with the moment M _AND (Fig. 10), the vector of inertial force F _And appears.

In FIG. 10 shows the layout of the strain gages R ₁ , R ₂ , R ₃ and R ₄ on the signal racks of the strain gauge element. Said strain gauges are connected according to the bridge circuit shown in FIG. 11, where U _P is the supply voltage of the bridge, and ΔU is the output signal.

With tensile strain, the resistance of the strain gauge increases, i.e. the resistance of the strain gage will be R + ΔR, with compression deformation it will decrease, i.e. the resistance of the strain gage will be R-ΔR.

The ratio of the output voltage increment to the supply voltage of the bridge is expressed by the formula:

where R is the initial resistance of the strain gages.

Under the action of the moment M _AND (Fig. 12), the strain gauges receive the same in absolute value and different in sign increments:

where k is the coefficient of strain sensitivity;

ε is the relative strain

where σ is the mechanical stress under the strain gauge;

E is Young's modulus;

M _C is the moment in the cross section of the signal rack at the installation site of the strain gauge;

W _C is the moment of resistance of the cross section of the signal rack at the installation site of the strain gauge.

As a result, from (4), (5) and (8) we find:

The inertial force component F _Y (Fig. 13) compresses the upper and stretches the lower signal racks.

As a result, the strain gages R ₁ and R ₂ receive equal in magnitude negative increments of resistance, and the strain gages R ₃ and R ₄ positive increments. As a result:

In this case:

;

;

where S _C is the cross-sectional area of the signal rack.

Substituting (14) into (10), we find:

The sensor is not sensitive to the component of the inertial force F _Y.

The component of the inertial force F _Z (Fig. 14) bends the signal posts, while the strain gages R ₁ and R ₄ receive equal in value positive increments of resistance, and the strain gages R ₂ and R ₃ are negative.

As a result:

Wherein:

- момент от силы F_Z в сечении сигнальной стойки в месте установки тензорезисторов;Where

- the moment of force F _Z in the cross section of the signal rack at the installation site of the strain gauges;

W _C is the moment of resistance of the signal rack section at the installation site of the strain gauges;

E is Young's modulus.

Substituting (16) in (10), we find:

The sensor is not sensitive to the component of the inertial force F _Z.

Given that:

we can conclude that the sensor is insensitive to the inertial force vector arbitrarily oriented in the plane of the sensor.

The sensor readings in accordance with (13) are proportional exclusively to angular acceleration, which confirms the high selectivity of the angular acceleration sensor.

Claims (1)

A stand for measuring the mass-inertial characteristics of the product, containing a frame to which the product is attached, dynamometers, angle sensors, springs, a bed, a dynamometric platform, a frame rotation unit, an oscillation setting device consisting of movable internal, external and lower frames interconnected and with a bed with hinges and a system of springs, while the axis of the hinges are connected with the axes of the angle sensors, characterized in that the stand is equipped with clamps that only allow the product to oscillate around the axis relative to which At present, the moment of inertia is measured, and installed on the frame to which the product is attached, three highly selective angular acceleration sensors, each of which consists of a housing, a shaft, two flywheels, mounted on the rim of a tensometric element consisting of a hub, a rim and two connecting them signal and two auxiliary racks located along mutually perpendicular axes, while the ratio of the hub radius to the length of the signal beam does not exceed 0.5, and on the inner faces of the signal racks in the root sections of the hub-side glued strain gauges, combined in a bridge circuit, wherein the axis of angular acceleration sensor of highly oriented parallel to the axes of rotation of the movable inner, outer and bottom stand frames.

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