CN102494845A - Device and method for measuring inertia product of object - Google Patents

Abstract

The invention relates to a device and method for testing static balance of a machine or a structural component, in particular to measurement of the inertia product of an object. The invention provides a device and method for measuring the inertia product of an object, which are convenient to operate. The device comprises a first flat plate, an overturning plate, three slings arranged at the outer edge of the first flat plate, a bracket connected with the other ends of the slings, tension sensors, a tiny break arranged on the first flat plate, a photoelectric signal sensor arranged at the tiny break, an optical signal reading device connected with the photoelectric signal sensor, wherein the first flat plate is provided with a through hole at the center, the overturning plate is similar to the polygonal through hole in shape and can respectively rotate for any angle along a hinge joint connection line relative to the first flat plate, and a tension sensor is arranged on each sling. The method is based on a simple principle, is easy to control and convenient to operate and is applicable to most of complicated power devices.

Description

Object product of inertia measurement mechanism and method

Technical field

The present invention relates to the orthostatic proving installation and the method for machine or structure member, further relate to the mensuration of the object product of inertia.

Background technology

The object product of inertia is an important physical parameter in the Machine Design, still has nothing to do in the record of this respect in the prior art.Therefore, be badly in need of a kind of easy object mass center measurement mechanism and method.

Summary of the invention

The invention provides a kind of object product of inertia measurement mechanism and method easy and simple to handle.Surpass 500kg for quality, the large-sized power plant that physical dimension surpasses 1.5m has remarkable advantages more.

The technical scheme that the present invention adopted is following:

Object product of inertia measurement mechanism comprises:

First flat board of the unsettled placement of level, the first dull and stereotyped geometric shape is that circle or limit number are the regular polygon of 3N, N is the integer more than or equal to 1; There is 1 through hole the first dull and stereotyped center, and the geometric shape that through hole is is that circle or limit number are the regular polygon of 2N, and N is the integer more than or equal to 2; The turnover panel similar with the regular polygon via hole profile, turnover panel is used to hold testee; At least 1 pair of pin joint in center of the center, 2 sides that is positioned at turnover panel symmetry and the corresponding equilateral through hole of first dull and stereotyped polygon side, said turnover panel can overturn with respect to first flat board respectively along the pin joint line at any angle; Be positioned at the first dull and stereotyped outer rim place, equidistantly distribute, equal length and perpendicular to first dull and stereotyped 3 hoist cables; The support that is connected with the hoist cable other end; Be positioned at the pulling force sensor on the every hoist cable; Be positioned at the small gap on first flat board; Be positioned at the photoelectric sensor of opening position, under the static steady state (SS), said photoelectric sensor and support keep fixing position relation, and when first flat board along the center of circle minor rotation took place, the signal of photoelectric sensor changed; The photosignal reading device links to each other with photoelectric signal sensor.

Said regular polygon through hole is square preferably, and said turnover panel profile is square preferably; Said first dull and stereotyped preferred equilateral triangle of geometric shape or the equilateral hexagon is positioned at the place, summit with the junction of hoist cable.

On said apparatus, realize object product of inertia measuring method, definition: three ropes are respectively first rope, second rope, the 3rd rope, and its length is defined as L; Its corresponding pulling force sensor is respectively first pulling force sensor, second pulling force sensor, the 3rd pulling force sensor; On first flat board, three ropes and the first dull and stereotyped node are defined as first node, second node, the 3rd node respectively, and the first dull and stereotyped center is true origin O; The horizontal range at the hoist cable node distance first dull and stereotyped center is defined as R; The acceleration of gravity of measuring the place is defined as g, and the cycle of rocking is T, and first flat board is I with the common moment of inertia of turnover panel _Pi

Barycenter with testee is true origin O ₁, be the Z axle perpendicular to the turnover panel direction, two other direction that is parallel to turnover panel is X axle and Y axle, sets up the rectangular coordinate system of testee;

Step comprises:

Step 1: the adjustment horizontal stand, guarantee to be in same surface level with the node of rope; Adjust first flat board, make it keep surface level, the adjustment turnover panel is to horizontal level; Testee is placed on the turnover panel, guarantee that the barycenter of testee and the first dull and stereotyped center are on the same perpendicular line; Give first dull and stereotyped small power, make it with a low-angle torsional oscillation, said angle is greater than 0, and smaller or equal to 5 degree; Read torsional oscillation cycle T 1 through photoelectric sensor; At this moment, the reading of first, second, third pulling force sensor is respectively F ₁₁, F ₁₂, F ₁₃First flat board is I with the common moment of inertia of turnover panel _P1

Step 2: let testee at first around O ₁Angle of Z axle rotation lets turnover panel along rotating a certain angle around pin joint then, lets testee translation in reprint, guarantees true origin O ₁Be on the same perpendicular line with the first dull and stereotyped center, measure O this moment ₁X axle, O ₁Y axle, O ₁The angle of Z axle and vertical direction ₁, β ₁, γ ₁Give first dull and stereotyped small power then, make it with a low-angle torsional oscillation, said angle is greater than 0, and smaller or equal to 5 degree; Read the torsional oscillation cycle T through photoelectric sensor ₂At this moment, the reading of first, second, third pulling force sensor is respectively F ₂₁, F ₂₂, F ₂₃

Step 3: turnover panel recovers horizontal, and repeating step two records other at least four groups of different angle _i, β _i, γ _i, read the torsional oscillation cycle T _i, read the reading F of first, second, third pulling force sensor _I1, F _I2, F _I3

Step 4: according to formula $I_Z=\frac{(F_{11}+F_{12}+F_{13})*R^2*{T_1}^2}{4{\mathrm{\π}}^2*L}-I_{p1}$ Calculate and obtain Iz, under other anglec of rotation, at first calculate and obtain first flat board and the common moment of inertia I of turnover panel _Pi,

I _iNumerical computation method following: $I_i=\frac{(F_{i_1}+F_{i2}+F_{i3})*R^2*{T_i}^2}{4{\mathrm{\π}}^2*L}-I_{\mathrm{Pi}}$

Then with I ₂, I ₃, I ₄, I ₅, I ₆Numerical value and corresponding angle α _i, β _i, γ _iValue is brought equation into,

$I_i=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_i& {\cos \mathrm{\β}}_i& \cos {\mathrm{\γ}}_i\end{array}\right]*\left[\begin{array}{ccc}{I}_x& -I_{\mathrm{xy}}& -I_{\mathrm{xz}}\\ -I_{\mathrm{yx}}& I_y& -I_{\mathrm{yz}}\\ -I_{\mathrm{zx}}& -I_{\mathrm{zy}}& I_z\end{array}\right]*\left[\begin{array}{c}\cos {\mathrm{\α}}_i\\ \cos {\mathrm{\β}}_i\\ \cos {\mathrm{\γ}}_i\end{array}\right]$

At I _zUnder the known situation, simultaneous equations are tried to achieve other five variate-value: I _x, I _y, I _Xy, I _Xz, I _Yz

And then, can obtain the ellipsoid of inertia equation of testee about barycenter.

Use in the engineering that this method finally can record object and use more the center principal moment of inertia and the center principal axis of inertia.This method principle is simple, is easy to control, is convenient to operation, is suitable for the power-equipment of most of complicacies.

Description of drawings

Fig. 1 is the synoptic diagram of embodiment.1 represents support among the figure, and 2 represent pulling force sensor; 3 represent testee, and 4 represent hoist cable, and 5 represent the rope lengths regulating device, and 6 represent first flat board, and 7 represent charge amplifier, and 8 represent computing machine, and 9 represent photoelectric sensor, and 10 represent turnover panel.

Fig. 2 is the synoptic diagram that rotates to an angle.

Fig. 3 is the local enlarged drawing of A among Fig. 2.

Embodiment

Map 1 explanation embodiment of the present invention.

Object product of inertia measurement mechanism comprises:

First dull and stereotyped 6, the first dull and stereotyped geometric shape of the unsettled placement of level is circular; There is 1 through hole the first dull and stereotyped center, and the geometric shape that through hole is is a rectangle; With the turnover panel 10 of rectangular through-hole appearance similar, turnover panel is used to hold testee 3; At least 1 pair of pin joint in center of the center, 2 sides that is positioned at turnover panel symmetry and the first corresponding dull and stereotyped rectangular through-hole side, said turnover panel can overturn with respect to first flat board respectively along the pin joint line at any angle; Be positioned at the first dull and stereotyped outer rim place, equidistantly distribute, equal length and perpendicular to first dull and stereotyped 3 hoist cables 4; The support 1 that is connected with the hoist cable other end; Be positioned at the pulling force sensor 2 on the every hoist cable; Be positioned at the small gap on first flat board; Be positioned at the photoelectric sensor 9 of opening position, under the static steady state (SS), said photoelectric sensor and support keep fixing position relation, and when first flat board along the center of circle minor rotation took place, the signal of photoelectric sensor changed; Photosignal reading device---computing machine 8 links to each other with photoelectric signal sensor.

On said apparatus, realize object product of inertia measuring method, definition: three ropes are respectively first rope, second rope, the 3rd rope, and its length is defined as L; Its corresponding pulling force sensor is respectively first pulling force sensor, second pulling force sensor, the 3rd pulling force sensor; On first flat board, three ropes and the first dull and stereotyped node are defined as first node, second node, the 3rd node respectively, and the first dull and stereotyped center is true origin O; The horizontal range at the hoist cable node distance first dull and stereotyped center is defined as R; The acceleration of gravity of measuring the place is defined as g, and the cycle of rocking is T, and first flat board is I with the common moment of inertia of turnover panel _Pi

Barycenter with testee is true origin O ₁, be the Z axle perpendicular to the turnover panel direction, two other direction that is parallel to turnover panel is X axle and Y axle, sets up the rectangular coordinate system of testee;

Step comprises:

Step 1: the adjustment horizontal stand, guarantee to be in same surface level with the node of rope; Adjust first flat board, make it keep surface level, the adjustment turnover panel is to horizontal level; Testee is placed on the turnover panel, guarantee that the barycenter of testee and the first dull and stereotyped center are on the same perpendicular line; Give first dull and stereotyped small power, make it with a low-angle torsional oscillation, said angle is greater than 0, and smaller or equal to 5 degree; Read the torsional oscillation cycle T through photoelectric sensor ₁At this moment, the reading of first, second, third pulling force sensor is respectively F ₁₁, F ₁₂, F ₁₃First flat board is I with the common moment of inertia of turnover panel _P1

Step 2: let testee at first around O ₁Angle of Z axle rotation lets turnover panel along rotating a certain angle around pin joint then, lets testee translation in reprint, guarantees true origin O ₁Be on the same perpendicular line with the first dull and stereotyped center, measure O this moment ₁X axle, O ₁Y axle, O ₁The angle of Z axle and vertical direction ₁, β ₁, γ ₁Give first dull and stereotyped small power then, make it with a low-angle torsional oscillation, said angle is greater than 0, and smaller or equal to 5 degree; Read the torsional oscillation cycle T through photoelectric sensor ₂At this moment, the reading of first, second, third pulling force sensor is respectively F ₂₁, F ₂₂, F ₂₃

Step 3: turnover panel recovers horizontal, and repeating step two records other at least four groups of different angle _i, β _i, γ _i, read the torsional oscillation cycle T _i, read the reading F of first, second, third pulling force sensor _I1, F _I2, F _I3

Step 4: according to formula $I_Z=\frac{(F_{11}+F_{12}+F_{13})*R^2*{T_1}^2}{4{\mathrm{\π}}^2*L}-I_{p1}$ Calculate and obtain Iz, under other anglec of rotation, at first calculate and obtain first flat board and the common moment of inertia I of turnover panel _Pi,

I _iNumerical computation method following: $I_i=\frac{(F_{i_1}+F_{i2}+F_{i3})*R^2*{T_i}^2}{4{\mathrm{\π}}^2*L}-I_{\mathrm{Pi}}$

Then with I ₂, I ₃, I ₄, I ₅, I ₆Numerical value and corresponding angle α _i, β _i, γ _iValue is brought equation into,

$I_i=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_i& {\cos \mathrm{\β}}_i& \cos {\mathrm{\γ}}_i\end{array}\right]*\left[\begin{array}{ccc}{I}_x& -I_{\mathrm{xy}}& -I_{\mathrm{xz}}\\ -I_{\mathrm{yx}}& I_y& -I_{\mathrm{yz}}\\ -I_{\mathrm{zx}}& -I_{\mathrm{zy}}& I_z\end{array}\right]*\left[\begin{array}{c}\cos {\mathrm{\α}}_i\\ \cos {\mathrm{\β}}_i\\ \cos {\mathrm{\γ}}_i\end{array}\right]$

At I _zUnder the known situation, simultaneous equations are tried to achieve other five variate-value: I _x, I _y, I _Xy, I _Xz, I _Yz

And then, can obtain the ellipsoid of inertia equation of testee about barycenter.

Claims (4)

1. object product of inertia measurement mechanism is characterized in that, comprising:

First flat board of the unsettled placement of level, the first dull and stereotyped geometric shape is that circle or limit number are the regular polygon of 3N, N is the integer more than or equal to 1;

There is 1 through hole the first dull and stereotyped center, and the geometric shape that through hole is is that circle or limit number are the regular polygon of 2N, and N is the integer more than or equal to 2;

The turnover panel similar with the regular polygon via hole profile, turnover panel is used to hold testee;

At least 1 pair of pin joint in center of the center, 2 sides that is positioned at turnover panel symmetry and corresponding 2 sides of the first dull and stereotyped regular polygon through hole, said turnover panel can overturn with respect to first flat board respectively along the pin joint line at any angle;

Be positioned at the first dull and stereotyped outer rim place, equidistantly distribute, equal length and perpendicular to first dull and stereotyped 3 hoist cables;

The support that is connected with the hoist cable other end;

Be positioned at the pulling force sensor on the every hoist cable;

Be positioned at the small gap on first flat board;

Be positioned at the photoelectric sensor of opening position, under the static steady state (SS), said photoelectric sensor and support keep fixing position relation, and when first flat board along the center of circle minor rotation took place, the signal of photoelectric sensor changed;

The photosignal reading device links to each other with photoelectric signal sensor.

2. according to the said object product of inertia of claim 1 measurement mechanism, it is characterized in that said regular polygon through hole is a square, said turnover panel profile is a square.

3. according to the said object product of inertia of claim 1 measurement mechanism, it is characterized in that the said first dull and stereotyped geometric shape is equilateral triangle or regular hexagon, be positioned at the place, summit with the junction of hoist cable.

4. on any one said device of claim 1 to 3, realize object product of inertia measuring method; Definition: three ropes are respectively first rope, second rope, the 3rd rope; Its length is defined as L, and its corresponding pulling force sensor is respectively first pulling force sensor, second pulling force sensor, the 3rd pulling force sensor, on first flat board; Three ropes and the first dull and stereotyped node are defined as first node, second node, the 3rd node respectively; The first dull and stereotyped center is true origin O, and the horizontal range at the hoist cable node distance first dull and stereotyped center is defined as R, and the acceleration of gravity of measuring the place is defined as g; The cycle of rocking is T, and first flat board is I with the common moment of inertia of turnover panel _Pi

Barycenter with testee is true origin O ₁, be the Z axle perpendicular to the turnover panel direction, two other direction that is parallel to turnover panel is X axle and Y axle, sets up the rectangular coordinate system of testee;

It is characterized in that step comprises:

Step 1: the adjustment horizontal stand, guarantee to be in same surface level with the node of rope; Adjust first flat board, make it keep surface level, the adjustment turnover panel is to horizontal level; Testee is placed on the turnover panel, guarantee that the barycenter of testee and the first dull and stereotyped center are on the same perpendicular line; Give first dull and stereotyped small power, make it with a low-angle torsional oscillation, said angle is greater than 0, and smaller or equal to 5 degree; Read the torsional oscillation cycle T through photoelectric sensor ₁At this moment, the reading of first, second, third pulling force sensor is respectively F ₁₁, F ₁₂, F ₁₃First flat board is I with the common moment of inertia of turnover panel _P1

Step 2: let testee at first around O ₁Angle of Z axle rotation lets turnover panel along rotating a certain angle around pin joint then, lets testee translation in reprint, guarantees true origin O ₁Be on the same perpendicular line with the first dull and stereotyped center, measure O this moment ₁X axle, O ₁Y axle, O ₁The angle of Z axle and vertical direction ₁, β ₁, γ ₁Give first dull and stereotyped small power then, make it with a low-angle torsional oscillation, said angle is greater than 0, and smaller or equal to 5 degree; Read the torsional oscillation cycle T through photoelectric sensor ₂At this moment, the reading of first, second, third pulling force sensor is respectively F ₂₁, F ₂₂, F ₂₃

Step 3: turnover panel recovers horizontal, and repeating step two records other at least four groups of different angle _i, β _i, γ _i, read the torsional oscillation cycle T _i, read the reading F of first, second, third pulling force sensor _I1, F _I2, F _I3

Step 4: according to formula $I_Z=\frac{(F_{11}+F_{12}+F_{13})*R^2*{T_1}^2}{4{\mathrm{\π}}^2*L}-I_{p1}$ Calculate and obtain Iz, under other anglec of rotation, at first calculate and obtain first flat board and the common moment of inertia I of turnover panel _Pi,

I _iNumerical computation method following: $I_i=\frac{(F_{i_1}+F_{i2}+F_{i3})*R^2*{T_i}^2}{4{\mathrm{\π}}^2*L}-I_{\mathrm{Pi}}$

Then with I ₂, I ₃, I ₄, I ₅, I ₆Numerical value and corresponding angle α _i, β _i, γ _iValue is brought equation into,

$I_i=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_i& {\cos \mathrm{\β}}_i& \cos {\mathrm{\γ}}_i\end{array}\right]*\left[\begin{array}{ccc}{I}_x& -I_{\mathrm{xy}}& -I_{\mathrm{xz}}\\ -I_{\mathrm{yx}}& I_y& -I_{\mathrm{yz}}\\ -I_{\mathrm{zx}}& -I_{\mathrm{zy}}& I_z\end{array}\right]*\left[\begin{array}{c}\cos {\mathrm{\α}}_i\\ \cos {\mathrm{\β}}_i\\ \cos {\mathrm{\γ}}_i\end{array}\right]$

At I _zUnder the known situation, simultaneous equations are tried to achieve other five variate-value: I _x, I _y, I _Xy, I _Xz, I _Yz

And then, can obtain the ellipsoid of inertia equation of testee about barycenter.

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