CN107340098A - A kind of four-point method measurement quality, barycenter and the inclined method of matter - Google Patents

A kind of four-point method measurement quality, barycenter and the inclined method of matter Download PDF

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CN107340098A
CN107340098A CN201710555020.9A CN201710555020A CN107340098A CN 107340098 A CN107340098 A CN 107340098A CN 201710555020 A CN201710555020 A CN 201710555020A CN 107340098 A CN107340098 A CN 107340098A
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CN107340098B (en
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宋永端
高瑞贞
谭觅
赖俊峰
何鎏
赵凯
贾晓娟
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Chongqing University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00—Testing static or dynamic balance of machines or structures
    • G01M1/12—Static balancing; Determining position of centre of gravity
    • G01M1/122—Determining position of centre of gravity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D21/00—Measuring or testing not otherwise provided for
    • G01D21/02—Measuring two or more variables by means not covered by a single other subclass
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01G—WEIGHING
    • G01G19/00—Weighing apparatus or methods adapted for special purposes not provided for in the preceding groups
    • G01G19/52—Weighing apparatus combined with other objects, e.g. furniture

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)
  • Nitrogen And Oxygen Or Sulfur-Condensed Heterocyclic Ring Systems (AREA)

Abstract

The present invention relates to a kind of four-point method measurement quality, barycenter and the inclined method of matter, measurand is placed in two V-type support blocks by this method, a weighing sensor is set respectively on two medial slopes of each V-type support block, then the vertical component of four weighing sensors is added as to the quality of measurand；Assuming that the actual barycenter of measurand to reference plane axial distance be LsCalculate LsThe actual barycenter of measurand is calculated in the position of Y-axis, is then calculating measurand barycenter respectively in X axis and Z axis to position, you can learn the actual barycenter of measurand；Calculating actual barycenter coordinate in X-axis and Z axis again, can to calculate radial direction matter inclined.Due to using independent arrangement, the relation that intercouples between multi weighing sensor is avoided；Weighing sensor is directly contacted with measurand, avoids the influence of V-type support block in four-point method；The stress of weighing sensor is normal pressure, and measurement accuracy is high, is advantageous to improve the measurement accuracy of measuring system.

Description

A kind of four-point method measurement quality, barycenter and the inclined method of matter
Technical field
The present invention relates to mass of object feature measurement technical field, and in particular to a kind of four-point method measurement quality, barycenter and The inclined method of matter.
Background technology
Supported at three point method (abbreviation line-of-sight course) is a kind of algorithm of weight reaction method, by three weighing sensors, according to Principle of moment balance completes the measurement to the quality, barycenter parameter of measurand.Its calculating process is as described below.
Mass measurement is typically measured using static weighing principle, and its weighing platform is designed to that one piece of rigidity is overall, puts down Platform is fixed on platform below as certain regular arrangement weighing sensor, measurand, after system is stable, by weighing and sensing Platform deadweight is summed and then subtracted to the indicating value of device, just obtains the weight of measurand.The weighing platform of line-of-sight course is disposed below three Group weighing sensor, as shown in figure 1, platform keep level, tested pair is calculated according to the reading value of this three groups of weighing sensors The quality m of elephant1, calculation formula is as follows：
In formula, m1--- the quality (kg) of measurand；
m2--- the quality (kg) of platform.
Fi' --- the reading value (N) of weighing sensor at each hinge, i=1,2,3；
When unloaded, platform mass is measured by weighing sensor：
m2G=F1+F2+F3 (2-2)
Wherein, Fi--- when unloaded, the reading value (N) of each hinge weighing sensor, i=1,2,3；
Formula (2-2) is substituted into formula (2-1), the quality for obtaining measurand is：
Line-of-sight course measures barycenter：
1st, coordinate system
According to line-of-sight course weighing measurement principle, platform has three strong points, installs weighing sensor respectively.In order to obtain quilt The centroid position of object is surveyed, it is necessary to establish platform coordinate system and measurand disjunctor coordinate system, describes platform and measurand Mutual alignment relation, and power and torque equilibrium equation are established by weighing sensor indicating value, solve the centroid position of measurand.
(1) system coordinate system
The centre of gyration for choosing supporting hinge is the origin of coordinates, establishes Descartes rectangular coordinate system OXYZ, as shown in Fig. 2 its Middle OX axles are platform long side direction, and OY axles are platform short side direction, and OZ axles are vertical direction, the dynamometry direction of weighing sensor Along OZ direction of principal axis, meet the right-hand rule.
(2) measurand disjunctor coordinate system
Measurand is fixed on carrying platform, correct position and posture is chosen, establishes disjunctor coordinate system OX1Y1Z1.Quilt Survey relation between object disjunctor coordinate system and platform coordinate system to be determined by the placement location and posture of measurand, by corresponding Sensor measure, determine coordinate conversion matrix.
By above-mentioned analysis, line-of-sight course measurement quality and centroid position have the characteristics that：
1st, line-of-sight course measurement measurand barycenter horizontal level principle it is relatively easy, it is easy to operate, it is necessary to biography of weighing Sensor number is relatively fewer.
2nd, during line-of-sight course measurement height of center of mass position, mechanism is relatively complicated to be driven, it is necessary to apply two movements, and It is required that realization is synchronized with the movement, to keep work top posture.In motion process, because driving hinge and support hinge are low Secondary motion pair, particularly supports hinge, and its kinematic accuracy influences line-of-sight course measurement accuracy.
3rd, during line-of-sight course measurement height of center of mass, it is necessary to measure and the rotational angle theta of control platform, and the levelness of platform, angle Degree measurement accuracy has a great influence to mass property parameter measurement precision.
4th, when line-of-sight course measures, positioning accuracy request hinge of the measurand on platform is high.
Existing four-point method is compared with line-of-sight course, has the advantage of three aspects.First, it is adapted to the survey of cylindrical measurand Amount.Under the support of V-block, measurand is being placed with rotary movement, has automatic centering function.Second, 4 points Method is relatively easy with respect to positioning action and coordinate system the measurement operation of measurand.3rd, four-point method measurement radial disbalance When, it is necessary to which initial position and dextrorotation turn 90 degrees the quality information of two positions, 90 degree of position measurements, which are compared in line-of-sight course, appoints The measurement of meaning angle, θ, precision will height.But there is also the deficiency of following three aspects for four-point method：First, in four-point method, support The V-block of measurand, the X axis of its barycenter and Y-axis position can be measured by zero load, still, Z axis to can not measure, Need to obtain by theoretical calculation.Second, in four-point method, four weighing sensors are in contact with V-type support block simultaneously, V-type branch Bracer is contacted with measurand again, and this layout structure causes four weighing sensors to intercouple, not independent reaction Stressing conditions at measurand contact point, symmetrical accuracy of measurement produce certain influence.3rd, it can produce after force acting on transducer A certain amount of deformation, when particularly weighing large-scale measurand, the influence of related variation amount factor is not accounted for.Weighing and sensing The deformation of device can cause V-type support block position and attitudes vibration, and then symmetrical accuracy of measurement produces considerable influence.
The content of the invention
In view of the above-mentioned problems existing in the prior art, first purpose of the invention is to provide a kind of four-point method measurement quality Method.
Second object of the present invention is to provide a kind of method of four-point method measurement barycenter.
Third object of the present invention is to provide a kind of inclined method of four-point method measurement matter.
To realize above-mentioned first purpose, the present invention adopts the following technical scheme that：A kind of method of four-point method measurement quality, its It is characterised by, comprises the following steps：
S1：Measurand is placed in two V-type support blocks, on two medial slopes of each V-type support block respectively One weighing sensor is set；
S2：If the measured value of four weighing sensors is respectively P1V,P2V,P3V,P4V, corresponding vertical component is designated as respectively P1⊥,P2⊥,P3⊥,P4⊥, then：
Wherein, α=45 °；
S3：The weight P of measurand has formula (2) to be calculated：
P=P1⊥+P2⊥+P3⊥+P4⊥ (2)。
=P1Vcosα+P2Vcosα+P3Vcosα+P4Vcosα
To realize above-mentioned second purpose, the present invention adopts the following technical scheme that：A kind of method of four-point method measurement barycenter, its It is characterised by, comprises the following steps：
Step 1：Measurand is placed in two V-type support blocks, divided on two medial slopes of each V-type support block She Zhi not a weighing sensor；
Step 2：Establish system coordinate system：
If the straight line in a V-type support block where two weighing sensors is X-axis, for fixing two V-type support blocks The length direction of base be Y-axis, the radial direction of measurand is Z axis, any in two weighing sensors for determining X-axis The center of one weighing sensor is the former heart, if on the basis of right side face under measurand；
Step 3：Y-axis centroid position is calculated as follows：
I the measured value for) setting four weighing sensors (24) is respectively P1V,P2V,P3V,P4V, corresponding vertical component difference It is designated as P1⊥,P2⊥,P3⊥,P4⊥, then：
Wherein, α=45 °；
(P1⊥+P2⊥)ly=(P3⊥+P4⊥)(L2-ly) (3)；
Wherein, L2The distance between weighing sensor center being mounted in two V-type support blocks, lyRepresent barycenter in Y Coordinate on axle；
II) assume the actual barycenter of measurand to reference plane axial distance be Ls, then：
Wherein, Piv(i=1,2,3,4) is respectively the measured value of four weighing sensors, α=45 °, L0For X-axis to benchmark The vertical range in face；
Step 4：Measurand barycenter is in X axis and Z axis to position：
1) initial position of measurand meets formula below：
Wherein,I=1,2,3,4 be measurand in initial position, the measured value of i-th of weighing sensor,I=1,2,3,4 be measurand in initial position, the vertical component of i-th of weighing sensor measured value；l'xIt is tested Object is in initial position, coordinate value of the measurand barycenter along Y-axis, L1For two weighing sensor centers on V-block it Between along X axis distance；
2) measurand is turned clockwise 90 ° of positions, coordinate value l of the measurand barycenter along Y-axisx", meet following Formula：
Wherein,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, the measurement of i-th weighing sensor Value,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, vertical point of i-th weighing sensor measured value Amount；
3) according to the measurement twice of step 1) and step 2), you can obtain the X-axis and Z axis coordinate position of barycenter：
Wherein, LzFor in coordinate system, the Z axis coordinate of measurand rotation axis.
To realize above-mentioned 3rd purpose, the present invention adopts the following technical scheme that：A kind of inclined method of four-point method measurement matter, its It is characterised by, comprises the following steps：
A) measurand is placed in two V-type support blocks, set respectively on two medial slopes of each V-type support block Put a weighing sensor；
B) initial position of measurand meets formula below：
Wherein,I=1,2,3,4 be measurand in initial position, the measured value of i-th of weighing sensor,I=1,2,3,4 be measurand in initial position, the vertical component of i-th of weighing sensor measured value；l'xIt is tested Object is in initial position, coordinate value of the measurand barycenter along Y-axis, L1For two weighing sensor centers on V-block it Between along X axis distance；
C) measurand is turned clockwise 90 ° of positions, coordinate value l of the measurand barycenter along Y-axisx", meet following Formula：
Wherein,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, the measurement of i-th weighing sensor Value,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, vertical point of i-th weighing sensor measured value Amount；
D) according to step b) and step c) measurement twice, you can obtain the X-axis and Z axis coordinate position of barycenter：
Wherein, LzFor in coordinate system, the Z axis coordinate of measurand rotation axis.
E) according to measurand barycenter in X-axis and Z axis coordinate inclined, the radial disbalance e that can calculate radial direction matter11Calculation formula is such as Under：
Relative to prior art, the invention has the advantages that：
1st, because four weighing sensors are independently arranged in measuring system, avoid mutual between four groups of weighing sensors Coupled relation.
2nd, weighing sensor is directly contacted with measurand, is not contacted, is kept away with measured piece indirectly by supporting plate The influence of supporting plate is exempted from.
3rd, the stress of weighing sensor is normal pressure, and measurement accuracy is high, is advantageous to improve the measurement accuracy of measuring system.
Brief description of the drawings
Fig. 1 is that four-point method measures the inclined front view of barycenter, matter.
Fig. 2 is that four-point method measures the inclined top view of barycenter, matter.
In figure, 1-V types support block, 2- measurands, 3- weighing sensors.
Embodiment
The present invention is described in further detail below.
The method that a kind of 1 four-point method of embodiment measures quality, comprises the following steps：
S1：Measurand is placed in two V-type support blocks, on two medial slopes of each V-type support block respectively One weighing sensor is set；
S2：If the measured value of four weighing sensors is respectively P1V,P2V,P3V,P4V, corresponding vertical component is designated as respectively P1⊥,P2⊥,P3⊥,P4⊥, then：
Wherein, α=45 °；
S3：The weight P of measurand has formula 2 to be calculated：
P=P1⊥+P2⊥+P3⊥+P4⊥ (2)。
=P1Vcosα+P2Vcosα+P3Vcosα+P4Vcosα
Embodiment 2：A kind of method of four-point method measurement barycenter, comprises the following steps：
Step 1：Measurand is placed in two V-type support blocks, divided on two medial slopes of each V-type support block She Zhi not a weighing sensor；
Step 2：Establish system coordinate system：
If the straight line in a V-type support block where two weighing sensors is X-axis, for fixing two V-type support blocks The length direction of base be Y-axis, the radial direction of measurand is Z axis, any in two weighing sensors for determining X-axis The center of one weighing sensor is the former heart, if on the basis of right side face under measurand；
Step 3：Because the weighing sensor for improving four-point method directly contacts measurand, the pressure of contact point is directly obtained Power, so, according to statical moment equilibrium principle, Y-axis centroid position is calculated as follows：
I the measured value for) setting a pair of left weighing sensors 23 and a pair of right weighing sensors 24 is respectively P1V,P2V,P3V,P4V, Corresponding vertical component is designated as P respectively1⊥,P2⊥,P3⊥,P4⊥, then：
Wherein, α=45 °；
(P1⊥+P2⊥)ly=(P3⊥+P4⊥)(L2-ly) (3)；
Wherein, L2The distance between weighing sensor center being mounted in two V-type support blocks, lyRepresent barycenter in Y Coordinate on axle；
II) assume the actual barycenter of measurand to reference plane axial distance be Ls, then：
Wherein, Piv(i=1,2,3,4) is respectively the measured value of four weighing sensors, α=45 °, L0For right weighing and sensing The center of device 24 to reference plane vertical range,；
Step 4：Measurand barycenter is in X axis and Z axis to position：
Measurand barycenter is measured when X axis and Z axis are to position, it is necessary to measure the original position of measurand respectively first With the information for being rotated by 90 ° two positions around Y-axis axis both clockwise, then carry out calculating acquisition quality, longitudinal barycenter, radial direction matter Deviator.
1) initial position of measurand meets formula below：
Wherein,I=1,2,3,4 be measurand in initial position, the measured value of i-th of weighing sensor,I=1,2,3,4 be measurand in initial position, the vertical component of i-th of weighing sensor measured value；l'xIt is tested Object is in initial position, coordinate value of the measurand barycenter along Y-axis, L1For two weighing sensor centers on V-block it Between along X axis distance；
2) measurand is turned clockwise 90 ° of positions, coordinate value l of the measurand barycenter along Y-axisx", meet following Formula：
Wherein,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, the measurement of i-th weighing sensor Value,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, vertical point of i-th weighing sensor measured value Amount；
3) according to the measurement twice of step 1 and step 2, you can obtain the X-axis and Z axis coordinate position of barycenter：
Wherein, LzFor in coordinate system, the Z axis coordinate of measurand rotation axis.
Embodiment 3：A kind of inclined method of four-point method measurement matter, comprises the following steps：
A) measurand is placed in two V-type support blocks, set respectively on two medial slopes of each V-type support block Put a weighing sensor；
B) initial position of measurand meets formula below：
Wherein,I=1,2,3,4 be measurand in initial position, the measured value of i-th of weighing sensor,I=1,2,3,4 be measurand in initial position, the vertical component of i-th of weighing sensor measured value；l'xIt is tested Object is in initial position, coordinate value of the measurand barycenter along Y-axis, L1For two weighing sensor centers on V-block it Between along X axis distance；
C) measurand is turned clockwise 90 ° of positions, coordinate value l of the measurand barycenter along Y-axisx", meet following Formula：
Wherein,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, the measurement of i-th weighing sensor Value,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, vertical point of i-th weighing sensor measured value Amount；
D) according to step b) and step c) measurement twice, you can obtain the X-axis and Z axis coordinate position of barycenter：
Wherein, LzFor in coordinate system, the Z axis coordinate of measurand rotation axis.
E) according to measurand barycenter in X-axis and Z axis coordinate inclined, the radial disbalance e that can calculate radial direction matter11Calculation formula is such as Under：
Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with The present invention is described in detail good embodiment, it will be understood by those within the art that, can be to the skill of the present invention Art scheme is modified or equivalent substitution, and without departing from the objective and scope of technical solution of the present invention, it all should cover at this Among the right of invention.

Claims (3)

  1. A kind of 1. method of four-point method measurement quality, it is characterised in that comprise the following steps：
    S1：Measurand is placed in two V-type support blocks, set respectively on two medial slopes of each V-type support block One weighing sensor；
    S2：If the measured value of four weighing sensors is respectively P1V,P2V,P3V,P4V, corresponding vertical component is designated as P respectively1⊥, P2⊥,P3⊥,P4⊥, then：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mi>V</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    Wherein, α=45 °；
    S3：The weight P of measurand has formula (2) to be calculated：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>P</mi> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  2. A kind of 2. method of four-point method measurement barycenter, it is characterised in that comprise the following steps：
    Step 1：Measurand is placed in two V-type support blocks, set respectively on two medial slopes of each V-type support block Put a weighing sensor；
    Step 2：Establish system coordinate system：
    If the straight line in a V-type support block where two weighing sensors is X-axis, for fixing the bottom of two V-type support blocks The length direction of seat is Y-axis, and the radial direction of measurand is Z axis, and any one in two weighing sensors for determining X-axis claims The center for retransmitting sensor is the former heart, if on the basis of right side face under measurand；
    Step 3：Y-axis centroid position is calculated as follows：
    I the measured value for) setting four weighing sensors (24) is respectively P1V,P2V,P3V,P4V, corresponding vertical component is designated as respectively P1⊥,P2⊥,P3⊥,P4⊥, then：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mi>V</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    Wherein, α=45 °；
    (P1⊥+P2⊥)ly=(P3⊥+P4⊥)(L2-ly) (3)；
    Wherein, L2The distance between weighing sensor center being mounted in two V-type support blocks, lyRepresent barycenter in Y-axis Coordinate；
    II) assume the actual barycenter of measurand to reference plane axial distance be Ls, then：
    <mrow> <msub> <mi>L</mi> <mi>s</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>l</mi> <mi>y</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>)</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    Wherein, Piv(i=1,2,3,4) is respectively the measured value of four weighing sensors, α=45 °, L0Reference plane is arrived for X-axis Vertical range；
    Step 4：Measurand barycenter is in X axis and Z axis to position：
    1) initial position of measurand meets formula below：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> <mo>(</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mo>(</mo> <mn>5</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> <mo>;</mo> </mrow>
    Wherein,I=1,2,3,4 be measurand in initial position, the measured value of i-th of weighing sensor,I=1, 2,3,4 be measurand in initial position, the vertical component of i-th of weighing sensor measured value；l'xIt is measurand first During beginning position, coordinate value of the measurand barycenter along Y-axis, L1Along X axis between two weighing sensor centers on V-block Distance；
    2) measurand is turned clockwise 90 ° of positions, coordinate value l " of the measurand barycenter along Y-axisx, meet formula below：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>)</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>=</mo> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>)</mo> <mo>(</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mo>(</mo> <mn>6</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> <mo>;</mo> </mrow>
    Wherein,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, i-th of weighing sensor measured value, I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, the vertical component of i-th of weighing sensor measured value；
    3) according to the measurement twice of step 1) and step 2), you can obtain the X-axis and Z axis coordinate position of barycenter：
    <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>-</mo> <mfrac> <msub> <mi>L</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>+</mo> <msub> <mi>L</mi> <mi>z</mi> </msub> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mo>(</mo> <mn>7</mn> <mo>)</mo> <mo>;</mo> </mrow>
    Wherein, LzFor in coordinate system, the Z axis coordinate of measurand rotation axis.
  3. 3. a kind of inclined method of four-point method measurement matter, it is characterised in that comprise the following steps：
    A) measurand is placed in two V-type support blocks, one is set respectively on two medial slopes of each V-type support block Individual weighing sensor；
    B) initial position of measurand meets formula below：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> <mn>0</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> <mo>(</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mo>(</mo> <mn>5</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> <mo>;</mo> </mrow>
    Wherein,I=1,2,3,4 be measurand in initial position, the measured value of i-th of weighing sensor,I=1, 2,3,4 be measurand in initial position, the vertical component of i-th of weighing sensor measured value；l'xIt is measurand first During beginning position, coordinate value of the measurand barycenter along Y-axis, L1Along X axis between two weighing sensor centers on V-block Distance；
    C) measurand is turned clockwise 90 ° of positions, coordinate value l " of the measurand barycenter along Y-axisx, meet formula below：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mi>V</mi> </mrow> <mn>1</mn> </msubsup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>1</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>4</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>)</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>=</mo> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mn>2</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>+</mo> <msubsup> <mi>P</mi> <mrow> <mn>3</mn> <mo>&amp;perp;</mo> </mrow> <mn>1</mn> </msubsup> <mo>)</mo> <mo>(</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mo>(</mo> <mn>6</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> <mo>;</mo> </mrow>
    Wherein,I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, i-th of weighing sensor measured value, I=1,2,3,4 be measurand turn clockwise 90 ° of positions when, the vertical component of i-th of weighing sensor measured value；
    D) according to step b) and step c) measurement twice, you can obtain the X-axis and Z axis coordinate position of barycenter：
    <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>-</mo> <mfrac> <msub> <mi>L</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>+</mo> <msub> <mi>L</mi> <mi>z</mi> </msub> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mo>(</mo> <mn>7</mn> <mo>)</mo> <mo>;</mo> </mrow>
    Wherein, LzFor in coordinate system, the Z axis coordinate of measurand rotation axis.
    E) according to measurand barycenter in X-axis and Z axis coordinate inclined, the radial disbalance e that can calculate radial direction matter11Calculation formula is as follows：
    <mrow> <msub> <mi>e</mi> <mn>11</mn> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>L</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>-</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>l</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>-</mo> <mfrac> <msub> <mi>L</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> 3
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