Apparatus and method for measuring structural angular acceleration based on dynamic centrifugal force measurement

Abstract

An apparatus and method for measuring a structural angular acceleration based on dynamic centrifugal force measurement belong to the technical field of angular acceleration measurement. The apparatus has a solid ball. The solid ball can move freely along the radial direction of the outer wall packaging hood. The elastic block is used as a stress base. A rod for lateral limit and connection is used for connecting the rigid block and a pulley and limiting the displacement of solid ball so that the solid ball can only move longitudinally along the apparatus. The rigid block can move freely due to the pulley. Measurement of a transient angular acceleration is converted into dynamic measurement of the centrifugal force of the solid ball. Through the above design, the dynamic angular acceleration of the structure caused by dynamic load can be relatively accurately calculated.

Claims

1. An apparatus for measuring a structural angular acceleration based on dynamic centrifugal force measurement, wherein the apparatus for measuring the structural angular acceleration comprises internal core components (2), an outer wall packaging hood (3) and a data acquisition and processing module (12); the internal core components (2) are fixed to a structural outer surface (1) to be measured through the outer wall packaging hood (3); the internal core components (2) are connected with the data acquisition and processing module (12); the outer wall packaging hood (3) is used for protecting the internal core components (2) and limiting the displacement of a solid ball (4) so that the solid ball (4) can only move longitudinally along the apparatus; the internal core components (2) comprise the solid ball (4), a rigid block (5), an elastic block (6), a strain foil (7), a rod for lateral limit and connection (8), a pulley (9) and a track (10); the solid ball (4) is a spherical entity, has uniform material properties and has center of mass at a center of sphere; the solid ball (4) comes into point contact with inner walls of the outer wall packaging hood (3) and the rigid block (5); the solid ball (4) can move freely, but are limited by the outer wall packaging hood (3) and the rigid block (5); in the absence of an external force, the solid ball (4) is stationary relative to the outer wall packaging hood (3); one end of the rigid block (5) comes into point contact with the solid ball (4), and the opposite other end is connected with one end of the rigid block (5) for transmitting the force between the solid ball (4) and the elastic block (6); the rigid block (5) is used to transmit the force between the solid ball (4) and the elastic block (6); two other ends of the rigid block (5) are connected with the pulley (9) through the rod for lateral limit and connection (8); the pulley (9) is limited to the track (10); the track (10) is fixed to the inner walls of the outer wall packaging hood (3) to ensure that the rigid block (5) can move freely under stress; the other end of the elastic block (6) is fixed to a right inner wall of the outer wall packaging hood (3) and is used as a stress base; the strain foil (7) is fixed to a surface of the elastic block (6), and is connected with the data acquisition and processing module (12) for detecting a strain of the elastic block (6); and a centrifugal force produced by the solid ball (4) when the apparatus for measuring the structural angular acceleration is torsional and is calculated.

2. A method for measuring structural angular acceleration using the apparatus according to claim 1, the method comprising the following steps: first step, fixing the apparatus for measuring the structural angular acceleration to the structural outer surface (1) to be measured; enabling a head to face a structural torsional center if the solid ball (4) in the apparatus is deemed as the heads; second step, under a structural torsion condition, the solid ball (4) will act on the rigid block (5) because of a centrifugal force effect; then the rigid block (5) will transmit the force to the elastic block (6) because the rigid block (5) will not deform; measuring, by the strain foil (7), the strain generated after the elastic block (6) is stressed; and obtaining the size of a centrifugal force F from the strain c obtained by the strain foil (7):
F=ε×E×A  (1) where E is an elastic modulus of the elastic block (6) in the apparatus; A is the cross-sectional area of a plane of point contact between the elastic block (6) and the solid ball (4) in the apparatus, and is also numerically equal to the cross-sectional area of the elastic block (6) in the apparatus; ε is the strain of the elastic block (6), and ε=ε.sub.measured−ε.sub.0, where ε.sub.measured is a directly measured strain of the elastic block (6), and ε.sub.0 is an initial strain of the elastic block (6) caused by uneven structural surface; third step, converting measurement of a transient angular acceleration into measurement of dynamic centrifugal force, and calculating angular velocity ω of structural torsion: $\begin{array}{cc}\omega =\sqrt{\frac{F}{m\times r}}& \left(4\right)\end{array}$ where m is the mass of the solid ball (4); ω is the angular velocity of structural torsion, and is also the angular velocity of the solid ball (4) which is along with structural torsion; r is a distance between a structural torsional center and the center of sphere of the solid ball (4); F is the centrifugal force of the solid ball (4); fourth step, calculating the angular acceleration α of structural rotation using formula (6), $\begin{array}{cc}\alpha =\frac{d\omega }{dt}=\frac{{\omega }_2-{\omega }_1}{t_2-t_1}& \left(6\right)\end{array}$ where t.sub.1, t.sub.2 are any two moments of infinite proximity, and ω.sub.1, ω.sub.2 are angular velocities of structural torsion corresponding to t.sub.1, t.sub.2; combining the above four steps to directly obtain: $\begin{array}{cc}\alpha =\frac{\left(\sqrt{{\mathrm{.Math.}}_2}-\sqrt{{\mathrm{.Math.}}_1}\right)\times \sqrt{\frac{E\times A}{m\times r}}}{t_2-t_1}& \left(7\right)\end{array}$ where α is a structural instantaneous angular acceleration, ε.sub.1, ε.sub.2 are strains of the elastic block corresponding to t.sub.1, t.sub.2, and the physical significance of other parameters is as described above.

Description

DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a stereographic schematic diagram when an apparatus is fixed to a structure;

(2) FIG. 2 is a plan schematic diagram when an apparatus is fixed to a structural surface;

(3) FIG. 3 is a plan schematic diagram of internal core components of an apparatus;

(4) FIG. 4 is a schematic diagram of A-A section of internal core components of an apparatus; and

(5) FIG. 5 is a schematic diagram of B-B section of internal core components of an apparatus.

(6) In the figures: 1 structural external surface; 2 internal core component; 3 outer wall packaging hood; 4 solid ball; 5 rigid block; 6 elastic block; 7 strain foil; 8 rod for lateral limit and connection; 9 pulley; 10 track; 11 conducting wire; and 12 data acquisition and processing module.

DETAILED DESCRIPTION

(7) Specific embodiments of the present invention are described below in detail in combination with the technical solution and drawings.

(8) An apparatus for measuring a structural angular acceleration based on dynamic centrifugal force measurement is provided. The apparatus comprises internal core components 2, an outer wall packaging hood 3 and a data acquisition and processing module 12. The internal core components 2 are fixed to a structural outer surface 1 to be measured through the outer wall packaging hood 3; the internal core components 2 are connected with the data acquisition and processing module 12 through a conducting wire 11; and the outer wall packaging hood 3 is used for protecting the internal core components 2 and limiting the displacement of solid ball 4 so that the solid ball 4 can only move longitudinally along the apparatus.

(9) The internal core components 2 comprise the solid ball 4, a rigid block 5, an elastic block 6, a strain foil 7, a rod for lateral limit and connection 8, a pulley 9 and a track 10. The solid ball 4 is a spherical entity, has uniform material properties and has center of mass at the center of sphere. The solid ball 4 comes into point contact with five surfaces of the inner walls of the outer wall packaging hood 3 (based on FIG. 3, including upper inner wall, lower inner wall, front inner wall, rear inner wall and left inner wall) and the rigid block 5; the solid ball 4 can move freely, but is limited by the outer wall packaging hood 3 and the rigid block 5; and in the absence of external force, the solid ball 4 is stationary relative to the outer wall packaging hood 3. One end (left side surface) of the rigid block 5 comes into point contact with the solid ball 4, and the opposite other end (right side surface) is connected with one end of the elastic block 6. The rigid block 5 is used to transmit the force between the solid ball 4 and the elastic block 6. Two other opposite ends (upper side surface and lower side surface in FIG. 3) of the rigid block 5 are connected with the pulley 9 through the rod for lateral limit and connection 8; the pulley 9 is limited to the track 10; and the track 10 is fixed to the inner wall of the outer wall packaging hood 3 to ensure that the rigid block 5 can longitudinally move freely under stress. The other end of the elastic block 6 is fixed to the right inner wall of the outer wall packaging hood 3 and is used as a stress base; The strain foil 7 is fixed to the surface of the elastic block 6, and is connected with the data acquisition and processing module 12 through a conducting wire 11 for detecting the strain of the elastic block 6; and a centrifugal force produced by the solid ball when the structure is torsional is calculated.

(10) A method for measuring structural angular acceleration using the apparatus comprises the following steps:

(11) First step, fixing the apparatus for measuring the structural angular acceleration to the structural outer surface 1 to be measured; enabling a head to face a structural torsional center if the solid ball 4 in the apparatus is deemed as the heads;

(12) Second step, under the structural torsion condition, the solid ball 4 will act on the rigid block 5 because of the centrifugal force effect. Then the rigid block 5 will transmit the force to the elastic block 6 because an ideal rigid block 5 will not deform. Therefore, measuring, by the strain foil 7, the strain generated after the elastic block 6 is stressed; and obtaining the size of the centrifugal force F from the strain ε obtained by the strain foil 7:
F=ε×E×A  (1)

(13) where E is an elastic modulus of the elastic block 6 in the apparatus; A is the cross-sectional area of a plane of point contact between the elastic block 6 and the solid ball 4 in the apparatus, and is also numerically equal to the cross-sectional area of the elastic block 6 in the apparatus; ε is the strain of the elastic block 6, and ε=E.sub.measured−ε.sub.0, where ε.sub.measured is a directly measured strain of the elastic block 6, and ε.sub.0 is an initial strain caused by uneven structural surface.

(14) A derivation process is as follows: a material mechanics formula

(15) $\begin{array}{cc}\frac{\sigma }{\mathrm{.Math.}}=E& \left(2\right)\end{array}$

(16) where σ is a stress of the cross section of an elastic object, ε is a strain produced due to the stress of the elastic object, and E is an elastic modulus of the material.

(17) $\begin{array}{cc}\sigma =\frac{F}{A}& \left(3\right)\end{array}$

(18) where F is an external force of the cross section of the elastic block, and A is the cross section acted upon by an external force.

(19) Substituting formula (3) into (2) to obtain a relational expression (1).

(20) Third step, converting measurement of a transient angular acceleration into measurement of dynamic centrifugal force, and calculating angular velocity ω of structural torsion:

(21) $\begin{array}{cc}\omega =\sqrt{\frac{F}{m\times r}}& \left(4\right)\end{array}$

(22) where m is the mass of the solid ball 4; ω is the angular velocity of structural torsion, and is also the angular velocity of the solid ball 4 which is along with structural torsion; r is a distance between the structural torsional center and the solid ball 4; F is the centrifugal force of the solid ball 4.

(23) Derivation process: when an object makes circular motion around a point, a centrifugal force is produced, making the object tend to leave the center of rotation. In the present invention, ω is the angular velocity of structural torsion, and is also the rotational angular velocity of the solid ball 4; m is the mass of the solid ball 4; r is a distance between the structural torsional center and the solid ball 4; F is the centrifugal force of the solid ball 4. Then
F=mω.sup.2r  (5)

(24) Obtaining a relational expression (4) from (5).

(25) Fourth step, calculating the angular acceleration α of structural rotation using formula (6), i.e.,

(26) $\begin{array}{cc}\alpha =\frac{d\omega }{\mathrm{dt}}=\frac{{\omega }_2-{\omega }_1}{t_2-t_1}& \left(6\right)\end{array}$

(27) where t.sub.1, t.sub.2 are any two moments of infinite proximity, and ω.sub.1, ω.sub.2 are angular velocities of structural torsion corresponding to t.sub.1, t.sub.2.

(28) Combining the above four steps to directly obtain:

(29) $\begin{array}{cc}\alpha =\frac{\left(\sqrt{{\mathrm{.Math.}}_2}-\sqrt{{\mathrm{.Math.}}_1}\right)\times \sqrt{\frac{E\times A}{m\times r}}}{t_2-t_1}& \left(7\right)\end{array}$

(30) where α is a structural instantaneous angular acceleration, ε.sub.1, ε.sub.2 are strains of the elastic block corresponding to t.sub.1, t.sub.2, and the physical significance of other parameters is as described above.

(31) Derivation process:

(32) $\begin{array}{c}\alpha =\frac{d\omega }{dt}=\frac{{\omega }_2-{\omega }_1}{t_2-t_1}\\ =\frac{\sqrt{\frac{F_2}{m\times r}}-\sqrt{\frac{F_2}{m\times r}}}{t_2-t_1}=\frac{\sqrt{\frac{{\mathrm{.Math.}}_2\times E\times A}{m\times r}}-\sqrt{\frac{{\mathrm{.Math.}}_1\times E\times A}{m\times r}}}{t_2-t_1}\\ =\frac{\left(\sqrt{{\mathrm{.Math.}}_2}-\sqrt{{\mathrm{.Math.}}_1}\right)\times \sqrt{\frac{E\times A}{m\times r}}}{t_2-t_1}\end{array}$

(33) F.sub.1, F.sub.2 are external forces of the cross section of the elastic block corresponding to t.sub.1, t.sub.2, and are numerically equal to the centrifugal force of the solid ball; and the physical significance of other parameters is as described above.

(34) Because the transient angular acceleration at a point can be determined by the present invention, on one hand, the angular acceleration in a key position of the structure can be accurately measured; and on the other hand, the whole angular acceleration of the structure can also be determined by measuring at multiple points.