RU1777092C - Method of detection of solid body point linear acceleration - Google Patents

Abstract

The invention relates to the field of metrology and instrumentation and can be used in measuring and testing techniques to determine the linear acceleration of any point in a solid body. The inventive method involves placing on a solid two linear accelerometers whose measuring axes are parallel to the coordinate axis, and the centers of inertia of the sensing elements and the measuring point are located on one straight line at known distances from each other in a plane perpendicular to the coordinate axis 2 or

Description

The invention relates to the field of metrology and instrument engineering and can be used in measuring and testing techniques to determine the linear acceleration of any point in a solid body, for example, an automation device.

Known for measuring linear acceleration of points of a solid body, it consists of installing four linear accelerometers on its working surface, the measuring axes of which are oriented parallel to the coordinate axis, and the centers of inertia of the sensing elements are located at the vertices of the quadrangle, the plane of which is perpendicular to the coordinate axis, and acceleration is defined as the arithmetic mean of the readings of the accelerometers 1.

This method has insufficient accuracy in measuring linear acceleration at a particular point in a solid.

performing a complex movement, as well as an insufficient measuring range not exceeding the upper limit of the measuring range of the linear accelerometers used.

Closest to the invention is a method of measuring the acceleration of a point of a solid body, which consists in installing a linear accelerometer with known metrological characteristics on a solid body, so that its measuring axis is oriented parallel to the coordinate axis, and the center of inertia of its sensor is located near that point of the solid in which acceleration is measured and also includes mathematical processing of the readings of the accelerometer 2.

The disadvantage of this method is the low measurement accuracy in the case of a complex law of motion of the solid gel, which is due to the presence of methodology C

x | x | about y

Yu

This is due to the fact that it is impossible for structural reasons to precisely match the center of inertia of the sensitive element of the linear accelerometer with that point of the solid at which the acceleration should be measured. This drawback arises, for example, in the case when the measuring point is inside the solid and is not accessible for placing the accelerometer in it, or when it is necessary to measure three projections of the linear acceleration vector of the solid point on the coordinate axes at once, because it is impossible to place three accelerometers at once in one point of a solid body.

A second disadvantage of the known method is the impossibility of taking measurements if the measured acceleration is so great that its value at the measurement point exceeds the upper limit of the measuring range of the used or known linear accelerometers.

The aim of the invention is to increase the accuracy of determining acceleration in the case of the complex law of motion of a solid body and to expand the measuring range. a The goal is achieved in that in the known method, determining the linear acceleration of a point of a solid body, which consists in installing a linear accelerometer with known metrological characteristics on a solid body, the measuring axis of which is oriented parallel to the coordinate axis, and in the subsequent mathematical processing of the accelerometer readings a second linear accelerometer with known metrological characteristics is installed on a solid body, the measuring axis of which is oriented by parallel to the coordinate axis, and the centers of inertia of the sensitive elements of linear accelerometers are located at distances hi and h2 of the measurement point, respectively, and on one straight line passing through the measurement point perpendicular to the coordinate axis, and the linear acceleration of the solid point is determined from the Ratio

./M..iattA2J V (A1) .. „)

where ay (A1), ay (A2) are the accelerations at points A1 and A2, measured by the first and second linear accelerometers, respectively, and determined by mathematical processing of their readings; the + sign refers to the case when the accelerometers are located on different sides of the measuring point, and the sign - to the case when the accelerometers are located on one side of the measuring point.

In the proposed measurement method

the use of a second linear accelerometer with known metrological characteristics, the center of inertia of the sensitive element of which is located on a straight, perpendicular coordinate axis, and passing through the measuring point and the center of inertia of the sensitive element of the first accelerometer, and the measuring axis is parallel to the coordinate

axis, allows, together with the listed features of the known method, to eliminate the above methodological measurement error in the case of a complex law of motion of a solid body, as well as to expand the measurement range.

Figure 1 shows a rigid body moving in a complex law, at the point M of which the projection of the linear acceleration vector onto a rigidly connected

the body coordinate axis O Y; figure 2 as an example of the implementation of the method for determining the acceleration of a point of a solid body presents a channel for measuring the projection of the linear acceleration vector ax (M) of point M

complex centrifuge platforms.

In Fig. 1, the following notation is adopted: M is the point of the solid at which it is necessary to measure the projection a / (M) of the eyelids

a linear acceleration torus S (M) to the axis O of the coordinate system O X Y Z rigidly connected to the body; n is a plane passing through a point M of a solid body perpendicular to the coordinate axis O Y; A1.-A2 are the points at which the centers of inertia of the sensing elements are located, respectively, of the first and second linear accelerometers; hi, h2 are the distances from point M to points A1 and A2, respectively; MX straight parallel to axis 0 of the XY;

a is the angle between the straight MX and A1A2; PAL GAS. Pm, respectively, the radius vectors of the points A1, A2 and M.

Figure 2 indicates: 1 - the first linear accelerometer; 2. - the second linear accelerometer; 3 - centrifuge platform; 4 - current collector; 5 is an acceleration calculation unit. The remaining symbols are similar.

The linear acceleration vector, which

In principle, it can be measured using accelerometers a (M), and its projection onto the coordinate axis OV can be written as

a (M) ghgm + 5- (w-hm) -i) 2 hm-g + ao v.

(2)

ay (M) ezv-ex z + o / (ods x +

tuy y + ufe z) - wzy Qy. + 3oy (3) where B, Ex, Јz are the angular acceleration vector of a solid and its projection onto the coordinate axes ОХ and О Z, respectively:

and, ft). , ftfe, respectively, the angular velocity vector of a solid and its projection on the axis of the coordinate system O X Y Z

x, y, g - the coordinates of the point M in the axis x O

xVz;

g, gy is the vector of acceleration of gravity and its projection onto the O Y axis;

ao, ao - linear acceleration vector of point 0 of a solid body (origin) and its projection onto the axis O Y,

Based on figure 1, the coordinates of the points A1, A2 can be written in the form of Al (hicosa + x. Y, hisin rz + z) / A2 (-h2Cosa + x .y.-H2Sina + Z /). (4) Substituting expressions (4) into relation (3), we can write the following expressions for linear accelerations measured by the first and second linear accelerometers, respectively

ay (A1) a / (M) hib. (5)

ay (A2) ay (M) - h2 b (6)

Where

B

(ez + "x) cos a + (c / y - Јx) sin a From expressions (5) and (6) it follows that the values of the accelerations ay (A1) and a - / (A2) differ from the desired acceleration at point M by the amount of methodological errors hi & and h2b, respectively. Solving the system of equations (5), (6) with respect to ay (M), we obtain

а / (m), ЛШ11 «1 1А11 (7)

Formulas (5), (6) and (7) are written for the case shown in Fig. 1, where points A1 and A2 are located on opposite sides of the measurement point M. Similar calculations show that in the case where points A1, A2 are located along one side of the measuring point M in the formula (7), it is necessary to change the minus sign either before hi or before Ii2, which is natural, since the first and second accelerometers are equal. For definiteness, we assume that the minus sign with a one-sided arrangement of accelerometers is placed in the formula (7) before h2. Thus, we arrive at the general expression (I) for determining the acceleration of a point of a solid with both types of arrangement of accelerometers.

The extension of the measuring range can be achieved, for example, in cases where the accelerometers are located on

°

5

0

5

0

n s

solid body on one side of the measuring point M and the inequalities

a / (A1) a / (A2). )

h2 hi 0, J (8)

or

ay (A2) ay (A1) .1

111 P2 0./(9)

Consider the case characterized by expression (8). As

hi 0, it follows from (8) that

hiay (A1) hiay (A2). (10)

Subtract from both sides of inequality (10) the term h2a / (A1). As a result, we get

hiay (A1) -h2a / (A1)

hiay (A2) -h2ay (A1), (11)

where from

ay (A1) (hi-h2) hiay (A2) - h2ay (A1). (12)

Since, according to (8), hi - h2 0, it follows from (12) that

a / (A1). (thirteen)

The right-hand side of inequality (13) is an expression for determining ay (M), i.e. taking into account (8), we have

ay (M) ay (A1) eu (A2).

Similar reasoning for the case characterized by relations (9),

lead to the following result ay (M) a / (A2) ay (A1).

Thus, this method provides higher measurement accuracy and also allows the determination of acceleration values that exceed the upper limit of the range of linear accelerometers used.

Claims (1)

SUMMARY OF THE INVENTION A method for determining the linear acceleration of a point of a solid body, which consists in installing a linear accelerometer with known metrological characteristics on a solid body, the measuring axis of which is oriented parallel to the coordinate axis, and in the subsequent mathematical processing of the accelerometer readings, characterized in that, in order to increase the accuracy of determining the acceleration in the case of a complex law of motion of a solid body and expansion of the measuring range, they are pre-installed on a solid body in Ora linear accelerometer with known metrological characteristics, the measurement axis of which is oriented parallel to the coordinate axis, the centers of mass elements chuvst- vitel.nyh linear accelerometers are located at a distance hi from the point PA and the measurement at one and a straight line passing through the measuring point perpendicular to the coordinate axis. and the magnitude of the linear acceleration of a solid point is determined from the relation a / (M) .V (A2) ± teay- (AU where a / (A1) and a / (A2) are the accelerations of points of a solid measured by the first and second linear 5 accelerometers, respectively. FIG. 2 a (M)