CN106289492A - A kind of counterweight value component combination checking method - Google Patents

Abstract

The open a kind of counterweight value component combination checking method of the present invention, is compared with a whole set of tested counterweight based on a standard test weight, according to standard test weight value calibration tested counterbalance mass value by the counterweight value component combination checking method using invention to provide.This method requires the counterweight of each specification is carried out measurement repeatedly.During measurement, tested counterweight combination nominal value is identical with standard test weight nominal value, and weigh equation number will be more than the number of unknown counterweight simultaneously.The advantage of the method is, containing unnecessary measurement, to improve measurement results reliability, improves measurement result uncertainty, thus obtains accurate testing result.

Description

A kind of counterweight value component combination checking method

Technical field

The present invention relates to fields of measurement, particularly relate to a kind of counterweight value component combination checking method.

Background technology

Counterweight is the counterweight such as used as standard test weight in calibration authority or in corresponding certified company, with Just scale, especially precision steelyard are verified, or other counterweights of more low accuracy grade are calibrated.

The degree of accuracy of counterweight is limited by so-called accuracy class.These accuracy classs determine each permission Maximum error.Accuracy class is divided into nine grades, wherein, grade E₁It is the most accurate counterweight grade, and grade M₃It is Coarse counterweight grade.When the counterweight amount of carrying out to each other passes, high-grade counterweight value is conclusive, namely all the time Say, after the counterweight that a counterweight is connected on higher accuracy class and compare therewith and obtain its value.It is directed to this Benchmark be international prototype kilogram, the most so-called original kilogram.This international prototype kilogram represents mass metrology unit.It is by platinoiridita Cylinder is constituted, and is saved in the BIPM near Paris.By different copy, it is followed of at this original kilogram Country's weight standard, and the most finally it is followed by the counterweight of accuracy class E1, this counterweight is again the most more The benchmark of the counterweight of low accuracy class.

Counterweight amount passes and must extremely carefully preserve and operate.Counterweight such as can not take with hand-held or touch, this is because This inevitably leads to check on counterweight deposit, and this may cause again aoxidizing on the surface of inspection counterweight, and And therefore nature can cause counterweight value to change.Even dust granule does not allows to be attached on this inspection counterweight.

There are different so-called counterweight groups, it has a counterweight of different stage, such as 1 gram, 2 grams, 5 grams, 10 grams, 20 Gram, 50 grams, 100 grams, 200 grams, 500 grams.

What China generally used have 5,2,2*, the combination of 1；Namely 5 grams, 2 grams, 2 grams, 1 gram；Or 5 milligrams, 2 milligrams, 2 milligrams, 1 milligram；The like.

The most domestic counterweight detection device major part is all manually detection, intervenes enterprising at mass comparator by personnel Row quality Determination.When particularly carrying out the calibrating of counterweight component combination, personnel are all used to have been manually done.But, this manually The error that detection device produces when operation due to operator, or misread data and the error that causes all can have a strong impact on inspection Determine result.Especially milligram group counterweight, because milligram group counterweight is to be bent to form by specific shape by tinsel, volume is relatively Little, it is very easy to when operator grip with clip cause counterweight to deform, thus affects the detection of counterweight, and milligram group weight Code is typically to carry out on the high accuracy comparator block of 1/10000000th to detect, and any trickle personal error can have a strong impact on Verification result.

In prior art, in prior art, the calibration method to counterweight has relative method and combination relative method one to one, but In China JJG99-2006 " weight detecting code ", the E1 grade transmission E2 grade milligram group counterweight of regulation is to use combination Relative method carries out detecting.But, when this automatic detection device uses combination relative method to measure, it is that counterweight is put down It is placed on comparator block to paving formula, so different owing to combining counterweight position on comparator block, therefore it is introduced into uneven loading error, so And the existence of uneven loading error can affect final verification result.

Summary of the invention

In order to overcome above-mentioned deficiency of the prior art, it is an object of the invention to, it is provided that a kind of counterweight value component group Close checking method, select the standard test weight of following nominal value and tested counterweight:

---standard test weight A:1 × 10ⁿ(n=1,2,3 or-1 ,-2 ,-3), unit g；

---tested counterweight B:(5,2,2*, 1) × 10^n-1, unit g；

---check standard counterweight C:1* × 10^n-1, unit g；

---standard test weight A:1 × 10ⁿ(n=1,2,3 or-1 ,-2 ,-3), unit g；

---tested counterweight B:(5,2,2*, 1) × 10^n-1, unit g；

---check standard counterweight C:1* × 10^n-1, unit g；

Wherein, verification step includes:

1) standard test weight A (1 × 10ⁿ) and tested counterweight B [(5+2+2*+1) × 10^n-1] combination on relatively instrument compare Relatively, difference DELTA m1 is obtained；

2) standard test weight A (1 × 10ⁿ) and tested counterweight B [(5+2+2*) × 10ⁿ-¹]+C(1*×10^n-1) combination than Compare on relatively instrument, obtain difference DELTA m2；

3) tested counterweight B (5 × 10^n-1) and tested counterweight B [(2+2*+1) × 10^n-1] combination on relatively instrument compare Relatively, difference DELTA m3 is obtained；

4) tested counterweight B (5 × 10^n-1) and tested counterweight B [(2+2*) × 10^n-1]+C(1*×10^n-1) combination comparing Compare on instrument, obtain difference DELTA m4；

5) tested counterweight B (2+1) × 10^n-1Combination and tested counterweight B (2* × 10^n-1)+C(1*×10^n-1) combination exist Relatively compare on instrument, obtain difference DELTA m5；

6) repeat, tested counterweight B [(2+1) × 10^n-1] combination and tested counterweight B (2* × 10^n-1)+C(1*×10^n-1) Combination compare on relatively instrument, obtain difference DELTA m6；

7) tested counterweight B (2 × 10^n-1)+C(1*×10^n-1) combination and tested counterweight B [(2*+1) × 10^n-1] combination exist Relatively compare on instrument, obtain difference DELTA m7；

8) repeat, tested counterweight B (2 × 10^n-1)+C(1*×10^n-1) combination and tested counterweight B (2*+1) × 10^n-1's Combination is compared on relatively instrument, obtains difference DELTA m8；

9) tested counterweight B (2 × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at relatively instrument Upper comparison, obtains difference DELTA m9；

10) tested counterweight B (2 × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at relatively instrument Upper comparison, obtains difference DELTA m10；

11) tested counterweight B (2* × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at comparator block Compare on device, obtain difference DELTA m11；

12) tested counterweight B (2* × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at comparator block Compare on device, obtain difference DELTA m12；

Obtain following measurement pattern:

Standard test weight A	Relatively	5+2+2*+1
			Standard test weight A	Relatively	5+2+2*+C
5	Relatively	2+2*+1
			5	Relatively	2+2*+C
2+1	Relatively	2*+C
			2+1	Relatively	2*+C
2+C	Relatively	2*+1
			2+C	Relatively	2*+1
2	Relatively	1+C
			2	Relatively	1+C
2*	Relatively	1+C
			2*	Relatively	1+C

If: m_AFor standard test weight A mass value, standard test weight A is known standard value；

x₁-tested counterweight (5) mass value；

x₂-tested counterweight (2) mass value；

x₃-tested counterweight (2*) mass value；

x₄-tested counterweight (1) mass value；

x₅-check standard counterweight C mass value；

Can draw two groups of linear equation:

By resolving above-mentioned two equation, available x₁、x₂、x₃、x₄、x₅Numerical value, i.e. obtain tested counterweight 5,2,2*, 1 Actual amplitudes；

The most first list the augmented matrix of equation:

The augmented matrix P of equation one:

$P=\left[\begin{array}{cccccc}1& 1& 1& 1& 0& {\mathrm{\Δm}}_1+{\mathrm{mc}}_A\\ -1& 1& 1& 1& 0& {\mathrm{\Δm}}_3\\ 1& -1& -1& 0& 1& {\mathrm{\Δm}}_4\\ 0& 1& -1& 1& 1& {\mathrm{\Δm}}_5\\ 0& 1& -1& -1& -1& {\mathrm{\Δm}}_7\\ 0& 1& 0& -1& 1& {\mathrm{\Δm}}_9\\ 0& 0& 1& -1& 1& {\mathrm{\Δm}}_{11}\end{array}\right]$

The augmented matrix Q of equation two:

$Q=\left[\begin{array}{cccccc}1& 1& 1& 0& 1& {\mathrm{\Δm}}_2+{\mathrm{mc}}_A\\ -1& 1& 1& 1& 0& {\mathrm{\Δm}}_3\\ 1& -1& -1& 0& 1& {\mathrm{\Δm}}_4\\ 0& 1& -1& 1& 1& {\mathrm{\Δm}}_6\\ 0& 1& -1& -1& -1& {\mathrm{\Δm}}_8\\ 0& 1& 0& -1& 1& {\mathrm{\Δm}}_{10}\\ 0& 0& 1& -1& 1& {\mathrm{\Δm}}_{12}\end{array}\right]$

Augmented matrix P and Q is resolved, utilizes Gaussian elimination method to produce one " row echelon form "；Echelon matrix Acquisition means that unknown number tries to achieve solution, the most just obtains the value of tested counterweight；

By the parsing to matrix P and Q, draw following echelon matrix:

$P=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1-{\mathrm{\Δm}}_3)/2\\ 0& 1& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9)/5\\ 0& 0& 1& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_{11})/5\\ 0& 0& 0& 1& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5+4{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9+5{\mathrm{\Δm}}_{11})/10\\ 0& 0& 0& 0& 1& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4+4{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9+5{\mathrm{\Δm}}_{11})/10\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7+2{\mathrm{\Δm}}_9-2{\mathrm{\Δm}}_{11})/2\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-3{\mathrm{\Δm}}_7+2{\mathrm{\Δm}}_9-2{\mathrm{\Δm}}_{12})/10\end{array}\right]$

$Q=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_4)/2\\ 0& 1& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10})/5\\ 0& 0& 1& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{12})/5\\ 0& 0& 0& 1& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_6+4{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{12})/10\\ 0& 0& 0& 0& 1& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+4{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{12})/10\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{12})/2\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_6-3{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{12})/10\end{array}\right]$

For obtaining the numerical value of more high precision, the meansigma methods generally taking two groups of numerical value is final result, i.e. takes the flat of two matrixes Average is final result matrix, it may be assumed that

$\begin{array}{c}X=(P+Q)/2\\ =\\ \left[\begin{array}{cccccc}1& 0& 0& 0& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4)/4\\ 0& 1& 0& 0& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10})/10\\ 0& 0& 1& 0& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12})/10\\ 0& 0& 0& 1& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6+4{\mathrm{\Δm}}_7+4{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{11}+5{\mathrm{\Δm}}_{12})/20\\ 0& 0& 0& 0& 1& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4+4{\mathrm{\Δm}}_5-4{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{11}+5{\mathrm{\Δm}}_{12})/20\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_9+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{11}-2{\mathrm{\Δm}}_{12})/4\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-3{\mathrm{\Δm}}_7-3{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_9+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{11}--2{\mathrm{\Δm}}_{12})/20\end{array}\right]\end{array}$

The most i.e. obtain tested counterbalance mass correction value:

x₁=mc₅=(2mc_A+Δm₁+Δm₂-Δm₃-Δm₄)/4

x₂=mc₂=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄-Δm₅-Δm₆-Δm₇-Δm₈-Δm₉-Δm₁₀)/10

x₃=mc_2*=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄+Δm₅+Δm₆+Δm₇+Δm₈-Δm₁₁-Δm₁₂)/10

x₄=mc₁=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄-Δm₅-Δm₆+4Δm₇+4Δm₇-Δm₉-Δm₁₀+5Δm₁₁ +5Δm₁₂)/20

x₅=mc_C=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄+4Δm₅-4Δm₆-Δm₇-Δm₈-Δm₉-Δm₁₀+5Δm₁₁ +5Δm₁₂)/20

As calculated tested counterweight value listed in next counterweight metering, simplification process can be done by above-mentioned, it may be assumed that

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{\mathrm{11}}+{\mathrm{\Δm}}_{\mathrm{12}}}{4};$

By

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3\mathrm{+2}{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

The numerical value of the check standard counterweight of available every series counterweight group；

Due in this series counterweight 5,2,2*, 1 be all tested counterweight B, and check standard counterweight C is the core of known quality value Looking into standard, therefore after a series is finished, calculated C mass value can compare with its mass value, thus obtains The correctness of this series data；

Determine the uncertainty of measurement result again；

If: m_AFor standard test weight A mass value, standard test weight A is known standard value；

x₁-tested counterweight (5) mass value；

x₂Tested counterweight (2) mass value；

x₃Tested counterweight (2*) mass value；

x₄Tested counterweight (1) mass value；

x₅Check standard counterweight C mass value；

By a pair four linear mathematical models:

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{\mathrm{11}}+{\mathrm{\Δm}}_{\mathrm{12}}}{4}$

Determine that quality difference △ m is:

${\mathrm{\Δm}}_i=\frac{I_{iB}-I_{iA}+I_{(i+1)B}-I_{(i+1)A}}{2}$

It is to complete on same weighing apparatus owing to weighing, so the uncertainty that quality difference introduces is identical, Its expanded uncertainty is for weighing instrument interval half-breadth, and obedience is uniformly distributed, it may be assumed that

$u\left(\mathrm{\Δ}m\right)=u\left({\mathrm{\Δm}}_i\right)=u\left(I_{A1}\right)=u\left(I_{A2}\right)=u\left(I_{B1}\right)=u\left(I_{B2}\right)=\frac{d}{2\sqrt{3}}$

Then:

$\begin{array}{c}u\left({\mathrm{mc}}_5\right)=\sqrt{{\left(\frac{u\left({\mathrm{mc}}_A\right)}{2}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_1}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_2}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_3}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_4}{4}\right)}^2}\\ =\sqrt{{\left(\frac{u\left({\mathrm{mc}}_A\right)}{2}\right)}^2+{\left(\frac{u(\mathrm{\Δ}m}{4}\right)}^2}=\frac{1}{2}\sqrt{u^2\left({\mathrm{mc}}_A\right)+u^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_2\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)\\ +u^2\left({\mathrm{\Δm}}_6\right)+u^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_8\right)+u^2\left({\mathrm{\Δm}}_9\right)+u^2\left({\mathrm{\Δm}}_{10}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{5}\right({\mathrm{mc}}_A\left)\right)}^2+\frac{1}{10}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_{2*}\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)\\ +u^2\left({\mathrm{\Δm}}_6\right)+u^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_8\right)+u^2\left({\mathrm{\Δm}}_{11}\right)+u^2\left({\mathrm{\Δm}}_{12}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{1}{10}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_1\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{20}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{20}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)+u^2\left({\mathrm{\Δm}}_6\right)\\ +4^2{u}^2\left({\mathrm{\Δm}}_7\right)+4^2{u}^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_9\right)+u^2\left({\mathrm{\Δm}}_{10}\right)+5^2{u}^2\left({\mathrm{\Δm}}_{11}\right)+5^2{u}^2\left({\mathrm{\Δm}}_{12}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{90}{{20}^2}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}.$

As can be seen from the above technical solutions, the invention have the advantages that

By using the counterweight value component combination checking method inventing offer tested with a whole set of based on a standard test weight Counterweight compares, according to standard test weight value calibration tested counterbalance mass value.This method requires to enter the counterweight of each specification Row measurement repeatedly.During measurement, tested counterweight combination nominal value is identical with standard test weight nominal value, weighs equation simultaneously Number will be more than the number of unknown counterweight.The advantage of the method is, containing unnecessary measurement, to improve measurement results reliability, carry High measurement result uncertainty, thus obtain accurate testing result.

Accompanying drawing explanation

In order to be illustrated more clearly that technical scheme, will the accompanying drawing used required in describing be made simple below Ground is introduced, it should be apparent that, the accompanying drawing in describing below is only some embodiments of the present invention, for ordinary skill From the point of view of personnel, on the premise of not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings.

The counterweight value component combination checking method that Fig. 1 provides for the present invention and JJG99-2006 " counterweight " code test method The comparison of measurement result uncertainty.

Detailed description of the invention

For making the goal of the invention of the present invention, feature, the advantage can be the most obvious and understandable, concrete by using below Embodiment and accompanying drawing, be clearly and completely described the technical scheme of present invention protection, it is clear that enforcement disclosed below Example is only a part of embodiment of the present invention, and not all embodiment.Based on the embodiment in this patent, the common skill in this area All other embodiments that art personnel are obtained under not making creative work premise, broadly fall into the model of this patent protection Enclose.

A kind of counterweight value component combination checking method that the present invention provides, the present invention is based on a pair four component combination methods, So-called a pair four component combination methods are that a standard test weight compares with the tested counterweight combination that the highest number is four, and sequence is measured in design Row and mathematical model, by known standard test weight value and standard test weight and the comparison difference of tested combination counterweight, draw the whole series The actual reduced mass value of counterweight.Owing to being a standard test weight and the counterweight combination that the highest number of combinations is four, therefore this side Method is referred to as a pair four component combination checking methods.

In the present embodiment, select the standard test weight of following nominal value and tested counterweight:

---standard test weight A:1 × 10ⁿ(n=1,2,3 or-1 ,-2 ,-3), unit g；

---tested counterweight B:(5,2,2*, 1) × 10^n-1, unit g；

---check standard counterweight C:1* × 10^n-1, unit g；

Wherein, combining with the counterweight of n=1 and compare citing, standard test weight A (10), check standard counterweight C are check standard weight Code 1*.

Total following operating procedure:

Wherein, verification step includes:

1) standard test weight A (1 × 10ⁿ) and tested counterweight B [(5+2+2*+1) × 10^n-1] combination on relatively instrument compare Relatively, difference DELTA m1 is obtained；

2) standard test weight A (1 × 10ⁿ) and tested counterweight B [(5+2+2*) × 10^n-1]+C(1*×10^n-1) combination than Compare on relatively instrument, obtain difference DELTA m2；

3) tested counterweight B (5 × 10^n-1) and tested counterweight B [(2+2*+1) × 10^n-1] combination on relatively instrument compare Relatively, difference DELTA m3 is obtained；

4) tested counterweight B (5 × 10^n-1) and tested counterweight B [(2+2*) × 10^n-1]+C(1*×10^n-1) combination comparing Compare on instrument, obtain difference DELTA m4；

5) tested counterweight B (2+1) × 10^n-1Combination and tested counterweight B (2* × 10^n-1)+C(1*×10^n-1) combination exist Relatively compare on instrument, obtain difference DELTA m5；

6) repeat, tested counterweight B [(2+1) × 10^n-1] combination and tested counterweight B (2* × 10^n-1)+C(1*×10^n-1) Combination compare on relatively instrument, obtain difference DELTA m6；

7) tested counterweight B (2 × 10^n-1)+C(1*×10^n-1) combination and tested counterweight B [(2*+1) × 10^n-1] combination exist Relatively compare on instrument, obtain difference DELTA m7；

8) repeat, tested counterweight B (2 × 10^n-1)+C(1*×10^n-1) combination and tested counterweight B (2*+1) × 10^n-1's Combination is compared on relatively instrument, obtains difference DELTA m8；

9) tested counterweight B (2 × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at relatively instrument Upper comparison, obtains difference DELTA m9；

10) tested counterweight B (2 × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at relatively instrument Upper comparison, obtains difference DELTA m10；

11) tested counterweight B (2* × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at comparator block Compare on device, obtain difference DELTA m11；

12) tested counterweight B (2* × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination at comparator block Compare on device, obtain difference DELTA m12；

The present embodiment uses following concrete numerical value the calibrating to tested counterweight is described, but be not limited to saying of following data Bright.

1) combination of standard test weight A (10) and tested counterweight B (5+2+2*+1) is compared on instrument comparing, and obtains difference DELTA m1；

2) combination of standard test weight A (10) and tested counterweight B (5+2+2*+1*) is compared on instrument comparing, and obtains difference DELTA m2；

3) combination of tested counterweight B (5) and tested counterweight B (2+2*+1) is compared on instrument comparing, and obtains difference DELTA m3；

4) combination of tested counterweight B (5) and tested counterweight B (2+2*+1*) is compared on instrument comparing, and obtains difference DELTA m4；

5) combination of the combination of tested counterweight B (2+1) and tested counterweight B (2*+1*) is compared on instrument comparing, and obtains difference Δm5；

6) repeating, the combination of the combination of tested counterweight B (2+1) and tested counterweight B (2*+1*) is compared on instrument comparing, Obtain difference DELTA m6；

7) combination of the combination of tested counterweight B (2+1*) and tested counterweight B (2*+1) is compared on instrument comparing, and obtains difference Δm7；

8) repeating, the combination of the combination of tested counterweight B (2+1*) and tested counterweight B (2*+1) is compared on instrument comparing, Obtain difference DELTA m8；

9) combination of tested counterweight B (2) and tested counterweight B (1*+1) is compared on instrument comparing, and obtains difference DELTA m9；

10) combination of tested counterweight B (2) and tested counterweight B (1*+1) is compared on instrument comparing, and obtains difference DELTA m10；

11) combination of tested counterweight B (2*) and tested counterweight B (1*+1) is compared on instrument comparing, and obtains difference DELTA m11；

12) combination of tested counterweight B (2*) and tested counterweight B (1*+1) is compared on instrument comparing, and obtains difference DELTA m12.

Standard test weight	Relatively	5+2+2*+1
			Standard test weight	Relatively	5+2+2*+1*
5	Relatively	2+2*+1
			5	Relatively	2+2*+1*
2+1	Relatively	2*+1*
			2+1	Relatively	2*+1*
2+1*	Relatively	2*+1
			2+1*	Relatively	2*+1
2	Relatively	1+1*
			2	Relatively	1+1*
2*	Relatively	1+1*
			2*	Relatively	1+1*

According to process of measurement, being intended to obtain tested counterweight value, the calibration method of the present invention can provide the survey of tested counterweight B Measure result and determine the uncertainty of measurement result；

The measurement process of tested counterweight B is:

If: m_A--standard test weight (10) mass value (known)；

x₁Tested counterweight (5) mass value；

x₂Tested counterweight (2) mass value；

x₃Tested counterweight (2*) mass value；

x₄Tested counterweight (1) mass value；

x₅Check standard counterweight (1*) mass value；

Two groups of linear equation can be drawn according to operating process:

By resolving above-mentioned two equation, available x₁、x₂、x₃、x₄、x₅Numerical value, i.e. obtain tested counterweight 5,2,2*, 1 amount Value.Utilize higher mathematics linear algebra matrix theory analytic equation.

List the augmented matrix of equation

The augmented matrix P of equation one:

$P=\left[\begin{array}{cccccc}1& 1& 1& 1& 0& {\mathrm{\Δm}}_1+{\mathrm{mc}}_A\\ -1& 1& 1& 1& 0& {\mathrm{\Δm}}_3\\ 1& -1& -1& 0& 1& {\mathrm{\Δm}}_4\\ 0& 1& -1& 1& 1& {\mathrm{\Δm}}_5\\ 0& 1& -1& -1& -1& {\mathrm{\Δm}}_7\\ 0& 1& 0& -1& 1& {\mathrm{\Δm}}_9\\ 0& 0& 1& -1& 1& {\mathrm{\Δm}}_{11}\end{array}\right]$

The augmented matrix Q of equation two:

$Q=\left[\begin{array}{cccccc}1& 1& 1& 0& 1& {\mathrm{\Δm}}_2+{\mathrm{mc}}_A\\ -1& 1& 1& 1& 0& {\mathrm{\Δm}}_3\\ 1& -1& -1& 0& 1& {\mathrm{\Δm}}_4\\ 0& 1& -1& 1& 1& {\mathrm{\Δm}}_6\\ 0& 1& -1& -1& -1& {\mathrm{\Δm}}_8\\ 0& 1& 0& -1& 1& {\mathrm{\Δm}}_{10}\\ 0& 0& 1& -1& 1& {\mathrm{\Δm}}_{12}\end{array}\right]$

Resolve augmented matrix

Augmented matrix P and Q is resolved, utilizes Gaussian elimination method to produce one " row echelon form ".Echelon matrix Acquisition means that unknown number tries to achieve solution, the most just obtains the value of tested counterweight.

By the parsing to matrix P and Q, draw following echelon matrix:

$P=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1-{\mathrm{\Δm}}_3)/2\\ 0& 1& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9)/5\\ 0& 0& 1& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_{11})/5\\ 0& 0& 0& 1& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5+4{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9+5{\mathrm{\Δm}}_{11})/10\\ 0& 0& 0& 0& 1& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4+4{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9+5{\mathrm{\Δm}}_{11})/10\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7+2{\mathrm{\Δm}}_9-2{\mathrm{\Δm}}_{11})/2\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-3{\mathrm{\Δm}}_7+2{\mathrm{\Δm}}_9-2{\mathrm{\Δm}}_{12})/10\end{array}\right]$

$Q=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_4)/2\\ 0& 1& 0& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10})/5\\ 0& 0& 1& 0& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{12})/5\\ 0& 0& 0& 1& 0& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_6+4{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{12})/10\\ 0& 0& 0& 0& 1& ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+4{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{12})/10\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{12})/2\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_6-3{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{12})/10\end{array}\right]$

For obtaining the numerical value of more high precision, the meansigma methods generally taking two groups of numerical value is final result, i.e. takes the flat of two matrixes Average is final result matrix, it may be assumed that

$\begin{array}{c}X=(P+Q)/2\\ =\end{array}$

$\left[\begin{array}{cccccc}1& 0& 0& 0& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4)/4\\ 0& 1& 0& 0& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10})/10\\ 0& 0& 1& 0& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12})/10\\ 0& 0& 0& 1& 0& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6+4{\mathrm{\Δm}}_7+4{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{11}+5{\mathrm{\Δm}}_{12})/20\\ 0& 0& 0& 0& 1& (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4+4{\mathrm{\Δm}}_5-4{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{11}+5{\mathrm{\Δm}}_{12})/20\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_9+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{11}-2{\mathrm{\Δm}}_{12})/4\\ 0& 0& 0& 0& 0& (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-3{\mathrm{\Δm}}_7-3{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_9+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{11}--2{\mathrm{\Δm}}_{12})/20\end{array}\right]$

The most i.e. obtain the mathematical model of tested counterbalance mass correction value:

x₁=mc₅=(2mc_A+△m₁+△m₂-△m₃-△m₄)/4

x₂=mc₂=(2mc_A+△m₁+△m₂+△m₃+△m₄-△m₅-△m₆-△m₇-△m₈-△m₉-△m₁₀)/10

x₃=mc_2*=(2mc_A+△m₁+△m₂+△m₃+△m₄+△m₅+△m₆+△m₇+△m₈-△m₁₁-△m₁₂)/10

x₄=mc₁=(2mc_A+△m₁+△m₂+△m₃+△m₄-△m₅-△m₆+4△m₇+4△m₇-△m₉-△m₁₀+5△m₁₁ +5△m₁₂)/20

x₅=mc_1*=(2mc_A+△m₁+△m₂+△m₃+△m₄+4△m₅-4△m₆-△m₇-△m₈-△m₉-△m₁₀+5△m₁₁ +5△m₁₂)/20

As calculated tested counterweight value listed in next counterweight metering, above-mentioned mathematical model can be done at simplification Reason, it may be assumed that

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

Below tested counterweight value is obtained exactly.

Determine the uncertainty of measurement result；

The analysis on Uncertainty of the result of this measuring method

By above method, following a pair four linear mathematical models are drawn.

x₁=mc₅=(2mc_A+Δm₁+Δm₂-Δm₃-Δm₄)/4

x₂=mc₂=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄-Δm₅-Δm₆-Δm₇-Δm₈-Δm₉-Δm₁₀)/10

x₃=mc_2*=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄+Δm₅+Δm₆+Δm₇+Δm₈-Δm₁₁-Δm₁₂)/10

x₄=mc₁=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄-Δm₅-Δm₆+4Δm₇+4Δm₇-Δm₉-Δm₁₀+5Δm₁₁ +5Δm₁₂)/20

x₅=mc_C=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄+4Δm₅-4Δm₆-Δm₇-Δm₈-Δm₉-Δm₁₀+5Δm₁₁ +5Δm₁₂)/20

Quality difference DELTA m is:

${\mathrm{\Δm}}_i=\frac{I_{iB}-I_{iA}+I_{(i+1)B}-I_{(i+1)A}}{2}$

It is to complete on same weighing apparatus owing to weighing, so the uncertainty that quality difference introduces is identical, Its expanded uncertainty is for weighing instrument interval half-breadth, and obedience is uniformly distributed, it may be assumed that

$u\left(\mathrm{\Δ}m\right)=u\left({\mathrm{\Δm}}_i\right)=u\left(I_{A1}\right)=u\left(I_{A2}\right)=u\left(I_{B1}\right)=u\left(I_{B2}\right)=\frac{d}{2\sqrt{3}}$

Then:

$\begin{array}{c}u\left({\mathrm{mc}}_5\right)=\sqrt{{\left(\frac{u\left({\mathrm{mc}}_A\right)}{2}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_1}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_2}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_3}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_4}{4}\right)}^2}\\ =\sqrt{{\left(\frac{u\left({\mathrm{mc}}_A\right)}{2}\right)}^2+{\left(\frac{u(\mathrm{\Δ}m}{4}\right)}^2}=\frac{1}{2}\sqrt{u^2\left({\mathrm{mc}}_A\right)+u^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_2\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)\\ +u^2\left({\mathrm{\Δm}}_6\right)+u^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_8\right)+u^2\left({\mathrm{\Δm}}_9\right)+u^2\left({\mathrm{\Δm}}_{10}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{1}{10}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_{2*}\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)\\ +u^2\left({\mathrm{\Δm}}_6\right)+u^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_8\right)+u^2\left({\mathrm{\Δm}}_{11}\right)+u^2\left({\mathrm{\Δm}}_{12}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{1}{10}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_1\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{20}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{20}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)+u^2\left({\mathrm{\Δm}}_6\right)\\ +4^2{u}^2\left({\mathrm{\Δm}}_7\right)+4^2{u}^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_9\right)+u^2\left({\mathrm{\Δm}}_{10}\right)+5^2{u}^2\left({\mathrm{\Δm}}_{11}\right)+5^2{u}^2\left({\mathrm{\Δm}}_{12}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{90}{{20}^2}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

Comparison with JJG99-2006 " counterweight " vertification regulation test method

JJG99-2006 " counterweight " code combination method measurement result uncertainty

Known code regulation combined method correction value computing formula is as follows:

${\mathrm{mc}}_5=\frac{{\mathrm{mc}}_A+{\mathrm{\Δm}}_1-{\mathrm{\Δm}}_2}{2}$

${\mathrm{mc}}_2=\frac{{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-3{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5}{5}$

${\mathrm{mc}}_{2\·}=\frac{{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+2{\mathrm{\Δm}}_3-3{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5}{5}$

${\mathrm{mc}}_1=\frac{{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+7{\mathrm{\Δm}}_3-3{\mathrm{\Δm}}_4-4{\mathrm{\Δm}}_5}{10}$

Calculating uncertainty:

$u\left({\mathrm{mc}}_5\right)=\sqrt{{\left(\frac{u\left({\mathrm{mc}}_A\right)}{2}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_1}{2}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_2}{2}\right)}^2}=\frac{1}{2}\sqrt{u^2\left({\mathrm{mc}}_A\right)+2u^2\left({\mathrm{\Δm}}_1\right)}$

$\begin{array}{c}u\left({\mathrm{mc}}_2\right)=\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{5}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+3^2{u}^2\left({\mathrm{\Δm}}_3\right)+2^2{u}^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{16}{25}{u}^2\left(\mathrm{\Δ}m\right){)}^2}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_{2*}\right)=\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{5}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+2^2{u}^2\left({\mathrm{\Δm}}_3\right)+3^2{u}^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{16}{25}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_1\right)=\sqrt{{\left(\frac{1}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+7^2{u}^2\left({\mathrm{\Δm}}_3\right)+3^2{u}^2\left({\mathrm{\Δm}}_4\right)+4^2{u}^2\left({\mathrm{\Δm}}_5\right)}\\ =\sqrt{{\left(\frac{1}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{76}{{10}^2}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

The measurement result uncertainty of JJG99-2006 " counterweight " code direct comparison method

Known code regulation direct comparison method correction value computing formula is as follows:

mc_t=mc_A+△m

$u\left({\mathrm{mc}}_t\right)=\sqrt{u^2\left({\mathrm{mc}}_A\right)+u^2\left(\mathrm{\Δ}m\right)}$

Comparison with JJG99-2006 " counterweight " code test method measuring result uncertainty

See table:

With weight nominal value (× 10^k) do abscissa, with by weighing the partial uncertainty that causes of instrument as vertical coordinate, To the comparative result shown in Fig. 1.

As can be known from Fig. 1, the combined method two that the result uncertainty utilizing this method to measure provides less than JJG99-2006 / mono-；The relative method 1/4th provided less than JJG99-2006.

The verification function of a pair four combined methods of the present invention, the measurement model provided according to this method, available every series The numerical value of the check standard counterweight of counterweight group, calculates the most according to the following equation:

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

Due in this series counterweight 5,2,2*, 1 be all tested counterweight, and 1* is the check standard of known quality value, therefore After a series is finished, calculated 1* mass value can compare with its mass value, thus obtains this series data Correctness.

In this specification, each embodiment uses the mode gone forward one by one to describe, and what each embodiment stressed is and other The difference of embodiment, identical similar portion reference mutually between each embodiment.

Described above to the disclosed embodiments, makes professional and technical personnel in the field be capable of or uses the present invention. Multiple amendment to these embodiments will be apparent from for those skilled in the art, as defined herein General Principle can realize without departing from the spirit or scope of the present invention in other embodiments.Therefore, the present invention It is not intended to be limited to the embodiments shown herein, and is to fit to and principles disclosed herein and features of novelty phase one The widest scope caused.

Claims (1)

1. a counterweight value component combination checking method, it is characterised in that

Select the standard test weight of following nominal value and tested counterweight:

---standard test weight A:1 × 10ⁿ(n=1,2,3 or-1 ,-2 ,-3), unit g；

---tested counterweight B:(5,2,2*, 1) × 10^n-1, unit g；

---check standard counterweight C:1* × 10^n-1, unit g；

Wherein, verification step includes:

1) standard test weight A (1 × 10ⁿ) and tested counterweight B [(5+2+2*+1) × 10^n-1] combination compare on relatively instrument, Difference DELTA m1；

2) standard test weight A (1 × 10ⁿ) and tested counterweight B [(5+2+2*) × 10^n-1]+C(1*×10^n-1) combination at relatively instrument Upper comparison, obtains difference DELTA m2；

3) tested counterweight B (5 × 10^n-1) and tested counterweight B [(2+2*+1) × 10^n-1] combination compare on relatively instrument, Difference DELTA m3；

4) tested counterweight B (5 × 10^n-1) and tested counterweight B [(2+2*) × 10^n-1]+C(1*×10^n-1) combination at relatively instrument Upper comparison, obtains difference DELTA m4；

5) tested counterweight B (2+1) × 10^n-1Combination and tested counterweight B (2* × 10^n-1)+C(1*×10^n-1) combination comparing Compare on instrument, obtain difference DELTA m5；

6) repeat, tested counterweight B [(2+1) × 10^n-1] combination and tested counterweight B (2* × 10^n-1)+C(1*×10^n-1) group It is combined in compare and compares on instrument, obtain difference DELTA m6；

7) tested counterweight B (2 × 10^n-1)+C(1*×10^n-1) combination and tested counterweight B [(2*+1) × 10^n-1] combine and comparing Compare on instrument, obtain difference DELTA m7；

8) repeat, tested counterweight B (2 × 10^n-1)+C(1*×10^n-1) combination and tested counterweight B (2*+1) × 10^n-1Combination Relatively instrument compares, obtains difference DELTA m8；

9) tested counterweight B (2 × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination on relatively instrument compare Relatively, difference DELTA m9 is obtained；

10) tested counterweight B (2 × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination on relatively instrument compare Relatively, difference DELTA m10 is obtained；

11) tested counterweight B (2* × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination on relatively instrument Relatively, difference DELTA m11 is obtained；

12) tested counterweight B (2* × 10^n-1) and tested counterweight C (1* × 10^n-1)+B(1×10^n-1) combination on relatively instrument Relatively, difference DELTA m12 is obtained；

Obtain following measurement pattern:

Standard test weight A Relatively 5+2+2*+1 Standard test weight A Relatively 5+2+2*+C 5 Relatively 2+2*+1 5 Relatively 2+2*+C 2+1 Relatively 2*+C 2+1 Relatively 2*+C 2+C Relatively 2*+1 2+C Relatively 2*+1 2 Relatively 1+C 2 Relatively 1+C 2* Relatively 1+C 2* Relatively 1+C

If: m_AFor standard test weight A mass value, standard test weight A is known standard value；

x₁-tested counterweight (5) mass value；

x₂One tested counterweight (2) mass value；

x₃One tested counterweight (2*) mass value；

x₄-tested counterweight (1) mass value；

x₅-check standard counterweight C mass value；

Can draw two groups of linear equation:

By resolving above-mentioned two equation, available x₁、x₂、x₃、x₄、x₅Numerical value, i.e. obtain tested counterweight 5,2,2*, the reality of 1 Value；

The most first list the augmented matrix of equation:

The augmented matrix P of equation one:

$P=\left[\begin{array}{cccccc}1& 1& 1& 1& 0& {\mathrm{\Δm}}_1+{\mathrm{mc}}_A\\ -1& 1& 1& 1& 0& {\mathrm{\Δm}}_3\\ 1& -1& -1& 0& 1& {\mathrm{\Δm}}_4\\ 0& 1& -1& 1& 1& {\mathrm{\Δm}}_5\\ 0& 1& -1& -1& -1& {\mathrm{\Δm}}_7\\ 0& 1& 0& -1& 1& {\mathrm{\Δm}}_9\\ 0& 0& 1& -1& 1& {\mathrm{\Δm}}_{11}\end{array}\right]$

The augmented matrix Q of equation two:

$Q=\left[\begin{array}{cccccc}1& 1& 1& 0& 1& {\mathrm{\Δm}}_2+{\mathrm{mc}}_A\\ -1& 1& 1& 1& 0& {\mathrm{\Δm}}_3\\ 1& -1& -1& 0& 1& {\mathrm{\Δm}}_4\\ 0& 1& -1& 1& 1& {\mathrm{\Δm}}_6\\ 0& 1& -1& -1& -1& {\mathrm{\Δm}}_8\\ 0& 1& 0& -1& 1& {\mathrm{\Δm}}_{10}\\ 0& 0& 1& -1& 1& {\mathrm{\Δm}}_{12}\end{array}\right]$

Augmented matrix P and Q is resolved, utilizes Gaussian elimination method to produce one " row echelon form "；The acquisition of echelon matrix Mean that unknown number tries to achieve solution, the most just obtain the value of tested counterweight；

By the parsing to matrix P and Q, draw following echelon matrix:

$P=\left[\begin{array}{cc}\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\end{array}& \begin{array}{c}({\mathrm{mc}}_A+{\mathrm{\Δm}}_1-{\mathrm{\Δm}}_3)/2\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9)/5\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_{11})/5\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5+4{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9+5{\mathrm{\Δm}}_{11})/10\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_4+4{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9+5{\mathrm{\Δm}}_{11})/10\\ (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_7+2{\mathrm{\Δm}}_9-2{\mathrm{\Δm}}_{11})/2\\ (-{\mathrm{\Δm}}_5-3{\mathrm{\Δm}}_7+2{\mathrm{\Δm}}_9-2{\mathrm{\Δm}}_{12})/10\end{array}\end{array}\right]$

$Q=\left[\begin{array}{cc}\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\end{array}& \begin{array}{c}({\mathrm{mc}}_A+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_4)/2\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10})/5\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{12})/5\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_6+4{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{12})/10\\ ({\mathrm{mc}}_A+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+4{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{12})/10\\ (-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{12})/2\\ (-{\mathrm{\Δm}}_6-3{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{12})/10\end{array}\end{array}\right]$

For obtaining the numerical value of more high precision, the meansigma methods generally taking two groups of numerical value is final result, i.e. takes the meansigma methods of two matrixes For final result matrix, it may be assumed that

$\begin{array}{c}X=(P+Q)/2\\ =\end{array}$

$\left[\begin{array}{cc}\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\end{array}& \begin{array}{c}(2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4)/4\\ (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10})/10\\ (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12})/10\\ (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6+4{\mathrm{\Δm}}_7+4{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{11}+5{\mathrm{\Δm}}_{12})/20\\ (2{\mathrm{mc}}_A+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2+{\mathrm{\Δm}}_3+{\mathrm{\Δm}}_4+4{\mathrm{\Δm}}_5-4{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}+5{\mathrm{\Δm}}_{11}+5{\mathrm{\Δm}}_{12})/20\\ (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_9+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{11}-2{\mathrm{\Δm}}_{12})/4\\ (-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-3{\mathrm{\Δm}}_7-3{\mathrm{\Δm}}_8+2{\mathrm{\Δm}}_9+2{\mathrm{\Δm}}_{10}-2{\mathrm{\Δm}}_{11}--2{\mathrm{\Δm}}_{12})/20\end{array}\end{array}\right]$

The most i.e. obtain tested counterbalance mass correction value:

x₁=mc₅=(2mc_A+Δm₁+Δm₂-Δm₃-Δm₄)/4

x₂=mc₂=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄-Δm₅-Δm₆-Δm₇-Δm₈-Δm₉-Δm₁₀)/10

x₃=mc_2*=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄+Δm₅+Δm₆+Δm₇+Δm₈-Δm₁₁-Δm₁₂)/10

x₄=mc₁=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄-Δm₅-Δm₆+4Δm₇+4Δm₇-Δm₉-Δm₁₀+5Δm₁₁+5Δ m₁₂)/20

x₅=mc_c=(2mc_A+Δm₁+Δm₂+Δm₃+Δm₄+4Δm₅-4Δm₆-Δm₇-Δm₈-Δm₉-Δm₁₀+5Δm₁₁+5Δ m₁₂Simplification process, as calculated tested counterweight value is listed in next counterweight metering, can be done by above-mentioned in)/20, it may be assumed that

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4};$

By

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

The numerical value of the check standard counterweight of available every series counterweight group；

Due in this series counterweight 5,2,2*, 1 be all tested counterweight B, and check standard counterweight C is the verification mark of known quality value Standard, therefore after a series is finished, calculated C mass value can compare with its mass value, thus obtain this and be The correctness of column data；

Determine the uncertainty of measurement result again；

If: m_AFor standard test weight A mass value, standard test weight A is known standard value；

x₁Tested counterweight (5) mass value；

x₂Tested counterweight (2) mass value；

x₃Tested counterweight (2*) mass value；

x₄Tested counterweight (1) mass value；

x₅Check standard counterweight C mass value；

By a pair four linear mathematical models:

${\mathrm{mc}}_5=\frac{2{\mathrm{mc}}_{10}+{\mathrm{\Δm}}_1+{\mathrm{\Δm}}_2-{\mathrm{\Δm}}_3-{\mathrm{\Δm}}_4}{4}$

${\mathrm{mc}}_2=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4-{\mathrm{\Δm}}_5-{\mathrm{\Δm}}_6-{\mathrm{\Δm}}_7-{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_9-{\mathrm{\Δm}}_{10}}{10}$

${\mathrm{mc}}_{2*}=\frac{4{\mathrm{mc}}_5+2{\mathrm{\Δm}}_3+2{\mathrm{\Δm}}_4+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{7+}{\mathrm{\Δm}}_8-{\mathrm{\Δm}}_{11}-{\mathrm{\Δm}}_{12}}{10}$

${\mathrm{mc}}_1=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_7+{\mathrm{\Δm}}_8+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

${\mathrm{mc}}_C=\frac{2{\mathrm{mc}}_2+{\mathrm{\Δm}}_5+{\mathrm{\Δm}}_6+{\mathrm{\Δm}}_{11}+{\mathrm{\Δm}}_{12}}{4}$

Determine that quality difference △ m is:

${\mathrm{\Δm}}_i=\frac{I_{iB}-I_{iA}+I_{(i+1)B}-I_{(i+1)A}}{2}$

Being to complete on same weighing apparatus owing to weighing, so the uncertainty that quality difference introduces is identical, it expands Exhibition uncertainty is for weighing instrument interval half-breadth, and obedience is uniformly distributed, it may be assumed that

$u\left(\mathrm{\Δ}m\right)=u\left({\mathrm{\Δm}}_i\right)=u\left(I_{A1}\right)=u\left(I_{A2}\right)=u\left(I_{B1}\right)=u\left(I_{B2}\right)=\frac{d}{2\sqrt{3}}$

Then:

$\begin{array}{c}u\left({\mathrm{mc}}_5\right)=\sqrt{{\left(\frac{u\left({\mathrm{mc}}_A\right)}{2}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_1}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_2}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_3}{4}\right)}^2+{\left(\frac{u({\mathrm{\Δm}}_4}{4}\right)}^2}\\ =\sqrt{{\left(\frac{u\left({\mathrm{\Δc}}_A\right)}{2}\right)}^2+{\left(\frac{u(\mathrm{\Δ}m}{2}\right)}^2}=\frac{1}{2}\sqrt{u^2\left({\mathrm{mc}}_A\right)+u^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_2\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)\\ +u^2\left({\mathrm{\Δm}}_6\right)+u^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_8\right)+u^2\left({\mathrm{\Δm}}_9\right)+u^2\left({\mathrm{\Δm}}_{10}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{1}{10}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_{2*}\right)=\sqrt{\begin{array}{c}{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{10}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)\\ +u^2\left({\mathrm{\Δm}}_6\right)+u^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_8\right)+u^2\left({\mathrm{\Δm}}_{11}\right)+u^2\left({\mathrm{\Δm}}_{12}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{5}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{1}{10}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}$

$\begin{array}{c}u\left({\mathrm{mc}}_1\right)=\sqrt{\begin{array}{c}{\left(\frac{2}{20}u\right({\mathrm{mc}}_A\left)\right)}^2+{\left(\frac{1}{20}\right)}^2\left(u^2\right({\mathrm{\Δm}}_1)+u^2\left({\mathrm{\Δm}}_2\right)+u^2\left({\mathrm{\Δm}}_3\right)+u^2\left({\mathrm{\Δm}}_4\right)+u^2\left({\mathrm{\Δm}}_5\right)+u^2\left({\mathrm{\Δm}}_6\right)\\ +4^2{u}^2\left({\mathrm{\Δm}}_7\right)+4^2{u}^2\left({\mathrm{\Δm}}_7\right)+u^2\left({\mathrm{\Δm}}_9\right)+u^2\left({\mathrm{\Δm}}_{10}\right)+5^2{u}^2\left({\mathrm{\Δm}}_{11}\right)+5^2{u}^2\left({\mathrm{\Δm}}_{12}\right)\end{array}}\\ =\sqrt{{\left(\frac{1}{10}u\right({\mathrm{mc}}_A\left)\right)}^2+\frac{90}{{20}^2}{u}^2\left(\mathrm{\Δ}m\right)}\end{array}.$