sensors Technical Note
Development of a New, High Sensitivity 2000 kg Mechanical Balance Jian Wang Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China; [email protected]; Tel.: +86-10-6452-4609 Academic Editors: Thierry Bosch, Aleksandar D. Raki´c and Santiago Royo Received: 21 February 2017; Accepted: 28 March 2017; Published: 13 April 2017
Abstract: Mass measurement of more than 500 kg on an electronic mass comparator has no better repeatability and linearity of measurement for meeting the calibration requirement of over class F1 weights from pharmacy and power generation plants. For this purpose, a new 2000 kg mechanical balance was developed by the National Institute of Metrology (NIM). The advantages of measurement of more than 500 kg on a new 2000 kg mechanical balance are introduced in the paper. In order to obtain high measurement uncertainty, four vertical forces of two sides of beam are measured and used as reference for adjustment of the beam position. Laser displacement sensors in the indication system are more effective for decreasing reading errors caused by human vision. To improve the repeatability and sensitivity of the equipment, a synchronous lifting control is designed for synchronously lifting the beam ends along the vertical direction. A counterweight selection system is developed to get any combination of weights in a limited space. The sensitivity of the new mechanical balance for 2000 kg is more than 1.7 parts in 10−4 rad/g. The extended uncertainties for the mechanical balance of 500 kg, 1000 kg and 2000 kg are 0.47 g, 1.8 g and 3.5 g respectively. Keywords: sensitivity; mechanical balance; laser displacement sensor; repeatability; synchronous
1. Introduction The calibration requirement of high accuracy for big weights or loads like 500, 600 and 1000 kg is increasing year by year in China. Electronic mass comparators are usually used for calibrating high accuracy weights all over the world. The repeatability and linearity of electronic mass comparators are good for meeting the calibration requirement of over class F1 weights, except for mass comparators with a maximum capacity of more than 500 kg [1–3]. The repeatability and linearity of a mass comparator depends on its lever structure, the position of the applied gravity force and the performance of its load cells. The lever structure in a mass comparator, consisting of a pivot and metal beam, is used to amplify the force of gravity during the mass measurement. The material and deformation of the metal beam are the factors that influence and amplify the accuracy. The precision of the amplification on a small mass comparator is better than that on a large mass comparator. For large electronic mass comparators based on lever structures it is difficult to get better repeatability and linearity in the mass measurement process. A weight placed on different position of the platform could result in a difference between two adjacent measurements. This is more obvious for big weights over 100 kg in mass. For obtaining better measurement result repeatability, the bottom position of the weight on the platform is usually marked. This ensures the weight will be placed on the same position each time during the measurement process. Due to the characteristics of load cells, electronic mass comparators with different maximum capacities may be selected when used for measuring the masses of weights with the same accuracy and different nominal values. It is necessary for the weights mentioned above to use several electronic mass comparators for performing the corresponding measurements. Sensors 2017, 17, 851; doi:10.3390/s17040851
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and different nominal values. It is necessary for the weights mentioned above to use several electronic mass comparators for performing the corresponding measurements. The mechanicalbalance balancewith withone oneindicator indicator based optical principle is commonly The mechanical based onon thethe optical principle is commonly usedused all all over the world. Usually the operator participates in the data acquisition, and automatic data over the world. Usually the operator participates in the data acquisition, and automatic data acquisition acquisition is is not not available. available. This This method method introduces introduces some some reading reading uncertainty. uncertainty.ItItcauses causesan anincrease increasein the measurement uncertainty of a mechanical balance [4,5]. A new method based on laser displacement in the measurement uncertainty of a mechanical balance [4,5]. A new method based on laser sensors is proposed the to problem this paper. in this paper. displacement sensorstoisresolve proposed resolvein the problem Due weight of the measured weight, the counterweights are usually not installed Due to tothe thedifferent different weight of the measured weight, the counterweights are usually not on the mechanical balance. When used, counterweights are selected to be loaded on the side of the installed on the mechanical balance. When used, counterweights are selected to be loaded on the mechanical balance [6].balance This is[6]. notThis convenient to operate it affects measurement accuracy. side of the mechanical is not convenient toand operate and itthe affects the measurement To resolve this a special designa with counterweights on the mechanical accuracy. To problem, resolve this problem, special design withmounted counterweights mounted balance on the is introduced this paper. mechanical in balance is introduced in this paper. The beam of a mechanical mechanical balance balance has has better betterstiffness stiffnessand andless lessdeformation deformationthan thanthat thatofofanan electronic onon thisthis characteristic, we have developed a newa mechanical balance electronic mass masscomparator. comparator.Based Based characteristic, we have developed new mechanical with a maximum capacity of 2000 kg. The sensitivity of the mechanical balance for 2000 kg is more balance with a maximum capacity of 2000 kg. The sensitivity of the mechanical balance for 2000 kg is − 4 −4 more1.7 than 1.7in parts 10 rad/g. The repeatability for kg 2000 kg isthan less0.15 thang.0.15 g. It measure could measure than parts 10 inrad/g. The repeatability for 2000 is less It could weights weights with different values kg kg. to 2000 kg. with different nominal nominal values from 100from kg to100 2000
2. Structure of Mechanical Mechanical Balance Balance The mechanical balance isis composed composed of of beam beamsystem, system,middle middleknife, knife,side sideknives, knives,indicator, indicator, mechanical balance counterweights, selecting system, system, weighing weighing system, system,motors motorsand andcontroller. controller.The Thestructure structureofofthe the counterweights, selecting mechanical balance is shown shown in in Figure Figure 1. 1.
Figure 1. The structure of the mechanical balance. Figure 1. The structure of the mechanical balance.
Figure 2 is a picture of mechanical balance. The height of the mechanical balance is 2.8 m. The Figure is a picture mechanical balance. The height of the mechanical balance is 2.8 m. length of the2balance beam of equals 2 m. The length of the balance beam equals 2 m.
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Figure Figure2. 2.The Thepicture pictureof ofmechanical mechanicalbalance. balance. Figure 2. The picture of mechanical balance.
2.1. 2.1.Knives Knivesof ofMechanical MechanicalBalance Balance 2.1. Knives of Mechanical Balance For For supporting supporting an an approximate approximate 777 ttt load, load, TH10 TH10 high-speed high-speed steel steel is is used used as as the the material material of of the the For supporting an approximate load, TH10 high-speed steel is used as the material of the middle knife and side knives after a special heat treatment process as shown in Figure 3. The special middleknife knifeand andside sideknives knivesafter afteraaspecial specialheat heattreatment treatmentprocess processas asshown shownin inFigure Figure3.3. The The special special middle heat treatment process includes preheating two times at 500–600 ℃ and 800–850 ℃, respectively, heat treatment process includes preheating two times at 500–600 ℃ and 800–850 ℃, respectively, heat treatment process includes preheating two times at 500–600 °C and 800–850 °C, respectively, quenching quenching at at 1200–1250 1200–1250 ℃, ℃, tempering tempering three three times times at at 550–570 550–570 ℃ ℃ and and aaa deep deep cooling cooling cycle cycle down down to to quenching at 1200–1250 °C, tempering three times at 550–570 °C and deep cooling cycle down to –120 ℃ [7]. After machining the knives have maintained high hardness and high toughness under –120°C ℃ [7]. [7]. After After machining machining the the knives knives have have maintained maintained high high hardness hardness and and high high toughness toughness under under –120 heavy load conditions [8]. heavy load conditions [8]. heavy load conditions [8].
Figure Figure 3. Heat treatment process of TH10. Figure3. 3.Heat Heattreatment treatmentprocess processof ofTH10. TH10.
2.2. 2.2.Indicators Indicatorsof ofMechanical MechanicalBalance Balance 2.2. Indicators of Mechanical Balance The includes two individual indicators. is an The display display device device includes includes two two individual individual indicators. indicators. One an indicator indicator based based on on optical optical The display device One is an indicator based on optical principles. It is composed of a small scale, a high definition camera and a liquid crystal principles. It is composed of a small scale, a high high definition definition camera camera and and aa liquid liquid crystal crystal display display principles. display (LCD). shown in Figure 4.4.AAmetal (LCD).The Thescale scaleand andthe theLCD LCDare areshown shownin inFigure Figure4. metalthin thinrod rodfixed fixedin inthe themiddle middleof ofbeam beamis (LCD). The scale and the LCD are A metal thin rod fixed in the middle of beam isis perpendicular to the beam. The scale of the indicator is mounted on the end of the metal thin rod perpendicularto tothe thebeam. beam.The Thescale scaleofof the indicator is mounted of metal the metal rod perpendicular the indicator is mounted on on the the endend of the thin thin rod and and to the The between the knife-edge and the isis 42 cm. The and parallel parallel the beam. beam. The distance distance between the middle middle knife-edge and the scale scale 42The cm.scale The parallel to thetobeam. The distance between the middle knife-edge and the scale is 42 cm. scale with the of beam and 160 The between divisions scaleswings swings with theswing swing ofthe theand beam andincludes includes 160divisions. divisions. Theinterval interval between divisions swings with the swing of the beam includes 160 divisions. The interval between divisions of the of the scale is equal to 0.25 mm. A high definition camera with 14 million pixels is used for of the scale is equalmm. to 0.25 mm. A highcamera definition with 14 million pixels is used the for scale is equal to 0.25 A high definition withcamera 14 million pixels is used for amplifying amplifying the scale and displaying it on the LCD. During the measurement, the operator reads the amplifying the scale and displaying it on the LCD. During the measurement, the operator reads the scale and displaying it on the LCD. During the measurement, the operator reads the LCD readings. LCD readings. LCDAnother readings.includes two laser displacement sensors, a signal processor and acomputer. Another includes two sensors, aa signal processor and Laser includes two laser laser displacement displacement signal processor and asides a computer. computer. Laser LaserAnother displacement sensors with the resolution sensors, of 3 µm are mounted on both of the beam. displacement sensors with the resolution of 3 m are mounted on both sides of the beam. The displacement sensors with the resolution of 3 m are mounted on both sides of the beam. The distance between the middle knife-edge and each laser displacement sensor is 42 The cm. distance between the knife-edge and laser sensor is 42 The distance between the middle middle knife-edge sensors and each each laser displacement displacement sensor 42 cm. cm. The The installation of two laser displacement is shown as Figure 5. When theisbeam swings, installation of displacement sensors as When beam the installation of two two laser laser displacement sensors isis shown shown as Figure Figureto5.5.equilibrium When the the position beam swings, swings, the the laser displacement sensor-L gets the displacement corresponding on the left laser displacement sensor-L gets the displacement corresponding to equilibrium position on the left laser displacement sensor-L gets the displacement corresponding to equilibrium position on the left side. Meanwhile the laser displacement sensor-R gets the displacement on the right side. The difference side. Meanwhile the laser displacement sensor-R the on right The side. Meanwhile of the laser displacement sensor-Rofgets gets the displacement displacement on the right side. side. of displacements both sides is the displacement the beam. It can eliminate the influence of The the difference of displacements of both sides is the displacement of the beam. It can eliminate difference of displacements of both sides is the displacement of the beam. It can eliminate the the influence of the zero drift of the laser displacement sensor. The difference is processed by the signal influence of the zero drift of the laser displacement sensor. The difference is processed by the signal processor processorand andsent sentto tothe thecomputer. computer.
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zero drift of the laser displacement sensor. The difference is processed by the signal processor and sent to the 2017, computer. Sensors 17, 851 4 of 12 Sensors 2017, 17, 851 Sensors 2017, 17, 851
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(a) (b) (a) (b) (a) (b) Figure 4. (a)The scale and (b) the LCD. Figure 4. (a) The scale and (b) the LCD. Figure 4. (a)The scale and (b) the LCD. Figure 4. (a)The scale and (b) the LCD.
Figure 5. The installation of two laser displacement sensors. Figure 5. The installation of two laser displacement sensors. Figure 5. The installation of two laser displacement sensors.
The indicator based on optical principle is used for adjusting the indicator with two laser The indicator based onWhen optical is the used forisadjusting the with displacement sensors [9,10]. theprinciple pointer on LCD located on theindicator left end of the two scale,laser the The indicator based on optical principle principle is used for for adjusting adjusting the the indicator indicator with with two two laser laser The indicator based on optical is used displacement [9,10]. thetopointer on the LCD is located on the left end of pointer in thesensors computer is When adjusted the minimum position. When pointer onthe thescale, LCDthe is displacement sensors [9,10]. When the pointer onon thethe LCD is located on thethe leftleft endend of the scale, the displacement When the pointer LCD located of scale, pointer on in the computer to computer the minimum position. Whentoon the onBased thethe LCD is located thesensors middle[9,10]. of is theadjusted scale, the pointer is is adjusted thepointer middle. on the pointer in the computer is adjusted to to the minimum position. When the pointer on the LCD is the pointer in the computer is adjusted the minimum position. When the pointer on the LCD is located on the middle of the scale, the computer pointer is adjusted to the middle. Based on the adjustments on these positions, the indicator with two laser displacement sensors can get located on the middle of the scale, the computer pointer is adjusted to the middle. Based on the located on of the scale, computer pointer is adjusted to the middle. Based onas the adjustments onmiddle these automatically. positions, thetheThe indicator with twotwo laser displacement sensors canused get the readings bythe computer indicator with laser displacement sensors a adjustments on onthese thesepositions, positions, the indicator with two displacement laser displacement sensors can readings get the adjustments the indicator with two laser sensors can get the readings by computer automatically. The indicator with two laser displacement sensors used as reading system of the mechanical balance is available for decreasing reading errors caused bya readings by computer automatically. The indicator with two laser displacement used sensors as a by computer automatically. Thethe indicator with two displacement ascaused aused reading reading system of the 6mechanical balance isofavailable for decreasing sensors reading errors by human vision. Figure shows position one laser laser displacement sensor and the software reading system of the mechanical balance is available for decreasing reading errors caused by system of the mechanical balance is available for decreasing reading errors caused by human vision. human vision. Figure 6 shows the position of one laser displacement sensor and the software interface of the indicator. human6 vision. Figure 6 shows of onesensor laser and displacement andofthe software Figure position of onethe laserposition displacement the softwaresensor interface the indicator. interfaceshows of the the indicator. interface of the indicator.
(a) (b) (a) (b) (a)position of one sensor and (b) the software (b) interface. Figure 6. (a) The Figure interface. Figure 6. 6. (a) (a) The The position position of of one one sensor sensor and and (b) (b) the the software software interface. Figure 6. (a) The position of one sensor and (b) the software interface.
2.3. Counter Weight Selecting System 2.3. Counter Weight Selecting System 2.3. Counter System requirement of full range from 100 kg to 2000 kg in a limited Weight Selecting According to the measurement According to the measurement requirement of full range from 100 kgcounterweight to 2000 kg in aselection limited space, a counterweight selection system is designed and produced. The requirement According to the measurement requirement of full range from 100 kg to 2000 kg in a limited space, ashown counterweight selection system is designed and produced. The counterweight selection system in Figure 7 consists of one stainless steel frame with three layer support, nested 1, 2, 2, space, a counterweight selection system is is designed designed and and produced. produced. The counterweight selection system shown in Figure 7 consists of one stainless steel frame with three layer support, nested 2, 2, 5system ratio counterweights the inside to the outside and three sets of selection modules with1,nine shown in Figurefrom 2, 2, 2, 7 consists of one stainless steel frame with three layer support, nested 1, 2, 5 ratio counterweights the inside toThe the outside and three sets with of selection modules withtop nine motors for selecting thefrom counterweights. first selection module four motors on the of 5 ratio counterweights from the inside to the outside and three sets of selection modules with nine motors for selecting the counterweights. The selection module with four motors on among the top10, of the counterweight selection system is used forfirst selecting one weightwith or one set of weights motors for module four motors on on the the top top of the for selecting selectingthe thecounterweights. counterweights.The Thefirst firstselection selection module with four motors of the counterweight selection system is used for selecting one weight or one set of weights among 10, 20, 20 and 50 kgselection options. system The second onefor is similar as the first layer selecting one weight counterweight is used selecting oneone weight orstructure one set set offor weights among 10, 10, 20, the counterweight selection system is used for selecting weight or one of weights among 20,one 20 and kg options. The second one similar first layer structure for selecting oneand weight or set 50 of weights among 100, 200, 200isand 500as kgthe options. There is one 1000 kg weight one 20, 20 and 50 kg options. The second one is similar as the first layer structure for selecting one weight or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of selection modules with one motor in the third layer. or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of selection modules with one motor in the third layer. set of selection modules with one motor in the third layer.
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20 and 50 kg options. The second one is similar as the first layer structure for selecting one weight or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of Sensors 2017, 2017, 17, 851 851 with one motor in the third layer. of 12 12 selection modules Sensors 17, 55 of
Figure 7. 7. Counterweight Counterweight selection selection system. system. Figure Figure 7. Counterweight selection system.
2.4. Synchronous Synchronous Lifting Lifting Control Control 2.4. 2.4. Synchronous Lifting Control To improve improve the the repeatability repeatability and and sensitivity sensitivity of of the the mechanical mechanical balance, balance, aa synchronous synchronous lifting lifting To To improve the repeatability and sensitivity of the mechanical balance, selection a synchronous lifting control is developed for lifting the weighing system and the counterweight system along control is developed for lifting the weighing system and the counterweight selection system along control is developed for lifting the weighing system and the counterweight selection system along the the vertical vertical direction direction synchronously synchronously [11]. [11]. Four Four motors motors under under the the weighing weighing system system and and four four motors motors the vertical direction synchronously [11]. Four motors under the weighing system and four motors under under the the counterweight counterweight selection selection system system are are driven driven synchronously synchronously for for decreasing decreasing the the displacement displacement under the counterweight selection system are driven synchronously for decreasing the displacement errors errors between them. errors between them. between them. 2.5. Monitor Monitor System for for the Balance Balance of of the the Beam Beam 2.5. 2.5. Monitor System System for the the Balance of the Beam After the the weighing system system and the the counterweight selection selection system are are lifted synchronously, synchronously, the the After After the weighing weighing system and and the counterweight counterweight selection system system are lifted lifted synchronously, the beam including the middle knife and side knives is dropped. The middle knife-edge and beam including includingthethe middle andknives side isknives is The dropped. middleand knife-edge and beam middle knifeknife and side dropped. middleThe knife-edge corresponding corresponding bearing bearing block block form form the the pivot pivot to to support support everything. everything. Four Four force force sensors sensors are are mounted mounted corresponding bearing block form the pivot to support everything. Four force sensors are mounted at two sides of the at two two sides sides of of the the beam. beam. The The installation installation positions positions are are shown shown in in Figure Figure 8. 8. When When the the beam beam is is at beam. The installation positions are shown in Figure 8. When the beam is dropping, the vertical forces dropping, the vertical forces of four points on the beam are measured to judge the loading dropping, theonvertical forces of four points beamsynchronization are measured and to judge loading of four points the beam are measured to judgeonthethe loading adjust the the position synchronization and and adjust adjust the the position position of of the the beam. beam. synchronization of the beam.
Figure 8. 8. The The force force sensors sensors installation installation positions. positions. Figure The force sensors Figure 8. installation positions.
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3. Operational Principle 3. Operational Principle The weighing system is located at the left of the mechanical balance, and the counterweight The weighing system is located at the aleft of the mechanical balance, and the weight counterweight selection system is on the right side. When measurement is started, the reference and the selection system is on the right side. When a measurement is started, the reference weight and the test test weight are place on the weighing system of the mechanical balance in turn. Meanwhile, weight areto place on the weighing of weight, the mechanical balance in according according the nominal mass of system reference a counterweight orturn. a set Meanwhile, of counterweights are to the nominal mass of reference weight, a counterweight or a9 set of counterweights are selected on selected on the counterweight selection system. Figure shows a general two-dimensional the counterweight selection system.balance Figure showing 9 shows athe general two-dimensional representation of the representation of the mechanical characteristic quantities of the mechanical mechanical balance characteristic of theof mechanical balance.acts Theatpoint S’ is the balance. The point showing S’ is the the beam's pivot. Thequantities gravity force beam mass its center of beam's pivot. The gravity force of beam mass m acts at its center of gravity S. The masses m and m S R gravity S. The masses and hang at points L and R. The broken line connecting LL and R hang The brokenline linethrough connecting L and R forms an angle α with the horizon line formsatanpoints angleLαand withR.the horizon point S’, and is divided perpendicularly through S’ through divided perpendicularly through S’ with the length a into the sections lL and lR . with the point lengthS’,aand intoisthe sections and .
Figure 9. The general two-dimensional representation.
The lever center of gravity withwith a length an angle γ withγa.with These The lever arm armofofthe thebalance's balance's center of gravity a lengthforms lS forms an angle a. torques around point S’ are neutralized under the equilibrium condition [12]. With the gravitational These torques around point S’ are neutralized under the equilibrium condition [12]. With the accelerations accelerations , and gLin three gravitational centers of the masses, the following expression gravitational , gthe R and gS in the three gravitational centers of the masses, the following is valid: expression is valid: (1) cos + sin = cos − sin + sin − mR gR (lL cos α + a sin α) = mL gL (lL cos α − a sin α) + mS gS lS sin(γ − α) (1) = = = , the sensitivity of the mechanical balance is defined It is assumed that It is assumed that g(1) according to Equation asgfollows: L = R = gS = g, the sensitivity of the mechanical balance is defined according to Equation (1) as follows: ∂α cos − sin = (2) sin + cos + + cos − ∂α ∂ lL coscos α − a−sinsin α = (2) α) + mR=( a0,cos α − lR sin + mS lS cos − α) In the case∂m ofL = m 0,L (lL=sin α=+, a cos = 0 and formula (1) αis) changed as(γ follows: = Equation (1) is changed as follows: In the case of a = 0, lL = lR = l, γ = 0 and=α = 0,
The sensitivity of mechanical balance is modified as follows: mL = mR = m
∂α = ∂ The sensitivity of mechanical balance is modified as follows:
(3) (3)
(4)
The sensitivity is independent of load, depending only on the mass of the beam and the position l ∂α of the center of gravity. = 0 means that the mechanical balance is symmetrical. The beam of(4)a = ∂mL m S lS symmetrical balance is horizontal only if the masses of the ends of beam are equal. = 0, = 0 means that the pivots are on one level. The sensitivity is independent of load, depending only on the mass of the beam and the position onofthe principle above, production and assembly of one long of theBased center gravity. γ =mentioned 0 means that thethe mechanical balance is symmetrical. The beam beamwith of a knives and bearing blocks is very important for improving repeatability of a symmetrical balance is horizontal only if the masses of the ends the of beam are equal.and a =sensitivity 0, α = 0 means mechanical balance. coordinate measurements and adjusting technology is used for adjusting that the pivots are onThree one level. the straightness, and flatness between the middle and knifeassembly and sideof knives to bebeam mounted Based on theparallelism principle mentioned above, the production one long with on the beam. The parallelism flatness between middlethe knife-edge and side knives and bearing blocks is and verythe important for improving repeatability and knife-edges sensitivity ofare a less than 20 m. The straightness of each knife-edge is also less than 20 m. mechanical balance. Three coordinate measurements and adjusting technology is used for adjusting
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the straightness, parallelism and flatness between the middle knife and side knives to be mounted on the beam. The parallelism and the flatness between middle knife-edge and side knife-edges are less than 20 µm. The straightness of each knife-edge is also less than 20 µm. 4. Mechanical Balance Experiments 4.1. Mechanical Balance Results Class E2 weights of 5, 10 and 20 g are used as sensitivity weights from no load to full load. Ten pieces of class E2 50 kg weights are used as the reference weight of 500 kg. One hundred pieces of class F1 20 kg weights are used as the reference weights for 1000 kg or 2000 kg. The steps of balance calibration are shown as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
Under no loading conditions, one uses the small counterweights to adjust the balance of the beam. Record the indication of the balance. Add a sensitivity weight of 5 g on the left side. Record the indication of the balance. Remove the sensitivity weight of 5 g. Load the reference weights of 2000 kg on the left side and the 2000 kg counterweight on the right side. Increase or decrease the small counterweights until the beam is balanced. Record the indication of the balance. Add a sensitivity weight of 20 g on the left side. Record the indication of the balance. Remove the sensitivity weight of 20 g. Unload the reference weights of 2000 kg on both sides. Use the small counterweights to adjust the balance of the beam. Record the indication of the balance. Add a sensitivity weight of 5 g on the right side. Record the indication of the balance. Remove the sensitivity weight of 5 g. Repeat (6) and (7). Record the indication of the balance. Add a sensitivity weight of 20 g on the right side. Record the indication of the balance.
The sensitivities of no load and full load are shown as Table 1. The full load sensitivity is more than 1.7 part in 10−4 rad/g. The standard deviations of no load and full load are shown in Tables 2 and 3, respectively. Table 1. Sensitivity measurements of the mechanical balance. Left Side
Right Side
Results (Division)
Sensitivity (10−4 rad/g)
No load Sensitivity weight 5 g
No load No load
15.381 32.072
7.3
Full load Sensitivity weight 20 g
Full load Full load
18.694 34.130
1.7
No load No load
No load Sensitivity weight 5 g
15.803 −4.177
7.3
Full load Full load
Full load Sensitivity weight 20 g
18.838 3.298
1.7
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Table 2. Standard deviation of no load. Results (Division)
Sensitivity (10−4 rad/g)
Standard Deviation (g)
15.394 15.515 15.637 15.714 15.452 15.546
7.3 7.3 7.3 7.3 7.3 7.3
0.04
Table 3. Standard deviation of full load. Results (Division)
Sensitivity (10−4 rad/g)
Standard Deviation (g)
18.765 18.783 18.888 19.026 18.896 18.954
1.7 1.7 1.7 1.7 1.7 1.7
0.13
After the indicator based on laser displacement sensors is adjusted, the reading comparisons between indicators based on optical principles and laser displacement sensors at 500 kg are shown as Table 4 and Figure 10. The comparison steps between indicators are as follows: (1) (2) (3) (4) (5)
Place the 500 kg weight on the weighing pan (left side of the mechanical balance) and select a 500 kg counterweight on the right side of the mechanical balance. Read the first divisions from the two indicators, respectively, after reaching balance. Place a sensitivity weight of 5 g on the top of the counterweights or the weighing pan. Read the second divisions, respectively. Divide 5 g into the difference between the first divisions and the second divisions. The mass against one division that represents the sensitivity of the mechanical balance at 500 kg could be known.
The values of the first column in the Table 4 are the readings based on the optical principle, and the values of the second column are the sensitivities corresponding to the readings. The values of the third column in the Table 4 are the readings based on two laser displacement sensors. The values of the last column are the sensitivities corresponding to the readings based on two laser displacement sensors. The maximum difference between readings based on optical principle and two laser displacement sensors is from the eighth row. It is 0.336 divisions. The mass corresponding to the divisions is 0.2 g, i.e., very small and it can be ignored. The results show the readings between two indicators coincide. Table 4. Reading comparisons between indicators based on optical principle and laser displacement sensors at 500 kg. Optical Principle Results (Division) 17.925 18.450 18.225 18.050 18.275 18.250 18.250 18.300 18.075 18.200
Laser Displacement Sensors
Sensitivity
(10−4
3.75 3.69 3.64 3.54 3.61 3.63 3.64 3.62 3.76 3.65
rad/g)
Results (Division)
Sensitivity (10−4 rad/g)
17.710 18.193 17.943 17.978 18.097 18.116 17.953 17.964 17.856 18.046
3.73 3.60 3.55 3.50 3.54 3.57 3.55 3.54 3.74 3.58
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The results regarding the measurement of beam stability at 2000 kg are shown in Figure 11. The The results regarding the measurement of beam stability at 2000 kg are shown in Figure 11. Thevalue resultsisregarding the measurement of beam stability at 2000 are shown in Figure The maximum 7.201 divisions, and the minimum value is kg 7.329 divisions. The11.difference The maximum value is 7.201 divisions, and the minimum value is 7.329 divisions. The difference maximum value is 7.201 divisions, and the minimum value is 7.329 divisions. The difference between the maximum andand minimum values divisions. between the maximum minimum valuesisisonly only 0.118 0.118 divisions. between the maximum and minimum values is only 0.118 divisions. 7.4
7.4
7.35
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7.3 7.3 Reading Reading 7.25 7.25 (divisions) (divisions) 7.2 7.2 7.15 7.15 7.1
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Number of measurement
Figure 11.11. Measurement ofof beam stability. Figure Measurement beam stability.
Figure 11. Measurement of beam stability. Figure 12 shows the results of 500, 1000 and 2000 kg. The sensitivity for 500 kg is more than Figure 12−4shows the results of 500, 1000 and 2000 kg. The sensitivity for 500 kg is more than 3.6 parts12 in shows 10 rad/g, the sensitivity 1000 kg2000 is more 2.7 parts infor 10−4500 rad/g, and the than Figure the results of 500,for 1000 and kg. than The sensitivity kg is more 3.6 parts in 10−4 rad/g, the sensitivity for 1000−4 kg is more than 2.7 parts in 10−4 rad/g, and the −4 −4 for 2000 kg is more than 1.7 parts in 10 kg rad/g. Figurethan 13 showsparts the relationship between 3.6 sensitivity parts in 10 sensitivity for 1000 is more in 10 rad/g, and the sensitivity for rad/g, 2000 kgthe is more than 1.7 parts in 10−4 rad/g. Figure 13 2.7 shows the relationship between the sensitivity and the load. As the load changes, the sensitivity becomes worse. −4 sensitivity for 2000and kg the is more 1.7 parts in 10 the rad/g. Figure 13 shows the relationship between the sensitivity load. than As the load changes, sensitivity becomes worse.
the sensitivity and the load. As the load changes, the sensitivity becomes worse.
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18 18 16 16 14 14 12 12 Reading 10 (divisions) Reading 108 (divisions) 8 6 64
500 kg 500 kgkg 1000 1000 2000kg kg 2000 kg
42 20 1 1
0
2 2
3 4 5 6 7 8 3 Number 4 5 measurement 6 7 8 of
9 9
10 10
Number of measurement
Sensitivity(rad/g) Sensitivity(rad/g)
Figure 12.12. The results 1000kg kgand and2000 2000 Figure The resultsfor for500 500 kg, kg, 1000 kg.kg. Figure 12. The results for 500 kg, 1000 kg and 2000 kg.
0.0008 0.0008 0.0006 0.0006 0.0004 0.0004 0.0002 0.0002 0 0 0 0
500 1000 500Load(kg) 1000
2000 2000
Load(kg) Figure 13. The relationship between the sensitivity and the load.
Figure 13. The relationship between the sensitivity and the load. Figure 13. The relationship between the sensitivity and the load. 4.2. Uncertainties of Mechanical Balance
4.2. Uncertainties of Mechanical Balance According to the operational principle of the mechanical balance, the expression of indication 4.2. Uncertainties of Mechanical Balance According to thetooperational principle mechanical balance, the expression of indication error with respect the mechanical balanceof is the as follows: to the operational principle mechanical balance, the expression of indication errorAccording with respect to the mechanical balanceof is the as follows: E = I −L (5) error with respect to the mechanical balance is as follows: (5) = − where E is the error between the indication of the balance and the applied load, I is the (5) = mechanical − where E is the error between the indication of the mechanical balance and the applied load, I is the indication of mechanical balance regarding applied load and L is the applied load [13–15]. where E isThe theuncertainty error between indication of the mechanical and the applied load, I is the indication of mechanical regarding applied load and Lbalance is the applied load [13–15]. ofbalance the the mechanical balance is as follows: indication of mechanical balance regarding applied and L is the applied load [13–15]. The uncertainty of the mechanical balance is asload follows: 2 d2 The uncertainty of the mechanical balance is asd follows: u2 ( E ) = s2 ( I ) + 0 + L + u2 ( L ) (6) (6) = + 12 + 12 + 12 12 + + +of the mechanical balance corresponding (6) where u( E) is the uncertainty of error, s(= I ) is the repeatability 12 the12repeatability where is the uncertainty of error, is of the mechanical balance to the applied load, d0 is the no load sensitivity, dL is the applied load sensitivity, u( L) is the uncertainty where is the uncertainty of error, is the repeatability of mechanical balance is the no load sensitivity, is thethe applied load sensitivity, corresponding to the applied load, deriving from the reference weight including the air buoyancy correction. The uncertainties of 500, is the no loadweight sensitivity, is the air applied load sensitivity, corresponding to the applied load, is the deriving from5.the reference including buoyancy correction. 1000 anduncertainty 2000 kg are shown in Table is the uncertainty reference the air buoyancy correction. The uncertainties of 500,deriving 1000 andfrom 2000the kg are shownweight in Tableincluding 5. The uncertainties of 500, 1000 and 2000 kg are shown in Table 5. Table 5. The extended uncertainties of 500, 1000 and 2000 kg. Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Load (kg) Load (kg)
500 1000 500 2000
Standard Uncertainty Standardof the Weighing Process Uncertainty of the(g)
Standard Uncertainty Due to Standard the Sensitivity Uncertainty Due(g) to
Standard Uncertainty of the Reference Weight with Standard Uncertainty of Air the BuoyancyWeight Correction Reference with (g) Air
Combined Standard Combined Uncertainty Standard (g)
Extended Uncertainty Extended (k = 2, g) Uncertainty
0.072 Weighing Process (g)
0.176 (g) the Sensitivity
Buoyancy0.134 Correction (g)
0.232 (g) Uncertainty
(k 0.47 = 2, g)
0.028 0.072 0.117
0.236 0.176 0.469
0.833 0.134 1.667
0.867 0.232 1.736
1.8 0.47 3.5
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Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Load (kg)
Standard Uncertainty of the Weighing Process (g)
Standard Uncertainty Due to the Sensitivity (g)
Standard Uncertainty of the Reference Weight with Air Buoyancy Correction (g)
Combined Standard Uncertainty (g)
Extended Uncertainty (k = 2, g)
500 1000 2000
0.072 0.028 0.117
0.176 0.236 0.469
0.134 0.833 1.667
0.232 0.867 1.736
0.47 1.8 3.5
5. Conclusions The establishment of a new 2000 kg mechanical balance is important for traceability of class F1 weights from 500 kg to 2000 kg used in industrial processes. To develop a mechanical balance with high accuracy and a wide measurement range for measurement of class F1 weights over 500 kg, a new heat treatment method of metal material, three coordinate measurement and adjustment technology, dynamic monitoring with regards to the balance of the beam and synchronous lifting control are used to improve the repeatability and sensitivity of the mechanical balance. For the realization of any combinations of counterweights in a limited space, a new counter-weight selection system is designed and its construction accomplished. The sensitivity of the new 2000 kg mechanical balance is more than 1.7 parts in 10−4 rad/g. The extended uncertainties of 500, 1000 and 2000 kg for the mechanical balance are 0.47 g, 1.8 g and 3.5 g, respectively. The results show the performance of the new mechanical balance is better than that of electronic mass comparators used in commerce. Acknowledgments: This work was supported in part by the National Science and Technology Support Program under Grant 2011BAK15B06, in part by the Special-Funded Program through the National Key Scientific Instruments and Equipment Development under Grant 2012YQ090208, and in part by National Key Research and Development Program for National Quality Infrastructure under Grant 2016YFF0200103. Conflicts of Interest: We declare that we have no conflict of interest.
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Kochsiek, M.; Gläser, M. (Eds.) Comprehensive Mass Metrology; Wiley: Berlin, Germany, 2000. Joint Committee for Guides in Metrology. Evaluation of Measurement Data, Supplement 1 to the ”Guide to the Expression of Uncertainty in Measurement”—Propagation of Distributions Using a Monte Carlo Method Draft; Joint Committee for Guides in Metrology: Sèvres, Frane, 2007; pp. 17–20. Wang, J.; Fuchs, P.; Russi, S.; Ren, X.; Cai, C.; Yang, N. Uncertainty evaluation for a system of weighing equations for the determination of microgram weights. IEEE Trans. Instrum. Meas. 2015, 64, 2272–2279. [CrossRef] JCGM. Uncertainty of Measurement—Part 3: Guide to the Expression of Uncertainty in Measurement (GUM:1995) Supplement 1: Propagation of Distributions Using a Monte Carlo Method; Document Rec. ISO/IEC GUIDE 98–3/Suppl.1; BIPM: Paris, France, 2008; pp. 4–7. © 2017 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Development of a New, High Sensitivity 2000 kg Mechanical Balance Jian Wang Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China; [email protected]; Tel.: +86-10-6452-4609 Academic Editors: Thierry Bosch, Aleksandar D. Raki´c and Santiago Royo Received: 21 February 2017; Accepted: 28 March 2017; Published: 13 April 2017
Abstract: Mass measurement of more than 500 kg on an electronic mass comparator has no better repeatability and linearity of measurement for meeting the calibration requirement of over class F1 weights from pharmacy and power generation plants. For this purpose, a new 2000 kg mechanical balance was developed by the National Institute of Metrology (NIM). The advantages of measurement of more than 500 kg on a new 2000 kg mechanical balance are introduced in the paper. In order to obtain high measurement uncertainty, four vertical forces of two sides of beam are measured and used as reference for adjustment of the beam position. Laser displacement sensors in the indication system are more effective for decreasing reading errors caused by human vision. To improve the repeatability and sensitivity of the equipment, a synchronous lifting control is designed for synchronously lifting the beam ends along the vertical direction. A counterweight selection system is developed to get any combination of weights in a limited space. The sensitivity of the new mechanical balance for 2000 kg is more than 1.7 parts in 10−4 rad/g. The extended uncertainties for the mechanical balance of 500 kg, 1000 kg and 2000 kg are 0.47 g, 1.8 g and 3.5 g respectively. Keywords: sensitivity; mechanical balance; laser displacement sensor; repeatability; synchronous
1. Introduction The calibration requirement of high accuracy for big weights or loads like 500, 600 and 1000 kg is increasing year by year in China. Electronic mass comparators are usually used for calibrating high accuracy weights all over the world. The repeatability and linearity of electronic mass comparators are good for meeting the calibration requirement of over class F1 weights, except for mass comparators with a maximum capacity of more than 500 kg [1–3]. The repeatability and linearity of a mass comparator depends on its lever structure, the position of the applied gravity force and the performance of its load cells. The lever structure in a mass comparator, consisting of a pivot and metal beam, is used to amplify the force of gravity during the mass measurement. The material and deformation of the metal beam are the factors that influence and amplify the accuracy. The precision of the amplification on a small mass comparator is better than that on a large mass comparator. For large electronic mass comparators based on lever structures it is difficult to get better repeatability and linearity in the mass measurement process. A weight placed on different position of the platform could result in a difference between two adjacent measurements. This is more obvious for big weights over 100 kg in mass. For obtaining better measurement result repeatability, the bottom position of the weight on the platform is usually marked. This ensures the weight will be placed on the same position each time during the measurement process. Due to the characteristics of load cells, electronic mass comparators with different maximum capacities may be selected when used for measuring the masses of weights with the same accuracy and different nominal values. It is necessary for the weights mentioned above to use several electronic mass comparators for performing the corresponding measurements. Sensors 2017, 17, 851; doi:10.3390/s17040851
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and different nominal values. It is necessary for the weights mentioned above to use several electronic mass comparators for performing the corresponding measurements. The mechanicalbalance balancewith withone oneindicator indicator based optical principle is commonly The mechanical based onon thethe optical principle is commonly usedused all all over the world. Usually the operator participates in the data acquisition, and automatic data over the world. Usually the operator participates in the data acquisition, and automatic data acquisition acquisition is is not not available. available. This This method method introduces introduces some some reading reading uncertainty. uncertainty.ItItcauses causesan anincrease increasein the measurement uncertainty of a mechanical balance [4,5]. A new method based on laser displacement in the measurement uncertainty of a mechanical balance [4,5]. A new method based on laser sensors is proposed the to problem this paper. in this paper. displacement sensorstoisresolve proposed resolvein the problem Due weight of the measured weight, the counterweights are usually not installed Due to tothe thedifferent different weight of the measured weight, the counterweights are usually not on the mechanical balance. When used, counterweights are selected to be loaded on the side of the installed on the mechanical balance. When used, counterweights are selected to be loaded on the mechanical balance [6].balance This is[6]. notThis convenient to operate it affects measurement accuracy. side of the mechanical is not convenient toand operate and itthe affects the measurement To resolve this a special designa with counterweights on the mechanical accuracy. To problem, resolve this problem, special design withmounted counterweights mounted balance on the is introduced this paper. mechanical in balance is introduced in this paper. The beam of a mechanical mechanical balance balance has has better betterstiffness stiffnessand andless lessdeformation deformationthan thanthat thatofofanan electronic onon thisthis characteristic, we have developed a newa mechanical balance electronic mass masscomparator. comparator.Based Based characteristic, we have developed new mechanical with a maximum capacity of 2000 kg. The sensitivity of the mechanical balance for 2000 kg is more balance with a maximum capacity of 2000 kg. The sensitivity of the mechanical balance for 2000 kg is − 4 −4 more1.7 than 1.7in parts 10 rad/g. The repeatability for kg 2000 kg isthan less0.15 thang.0.15 g. It measure could measure than parts 10 inrad/g. The repeatability for 2000 is less It could weights weights with different values kg kg. to 2000 kg. with different nominal nominal values from 100from kg to100 2000
2. Structure of Mechanical Mechanical Balance Balance The mechanical balance isis composed composed of of beam beamsystem, system,middle middleknife, knife,side sideknives, knives,indicator, indicator, mechanical balance counterweights, selecting system, system, weighing weighing system, system,motors motorsand andcontroller. controller.The Thestructure structureofofthe the counterweights, selecting mechanical balance is shown shown in in Figure Figure 1. 1.
Figure 1. The structure of the mechanical balance. Figure 1. The structure of the mechanical balance.
Figure 2 is a picture of mechanical balance. The height of the mechanical balance is 2.8 m. The Figure is a picture mechanical balance. The height of the mechanical balance is 2.8 m. length of the2balance beam of equals 2 m. The length of the balance beam equals 2 m.
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Figure Figure2. 2.The Thepicture pictureof ofmechanical mechanicalbalance. balance. Figure 2. The picture of mechanical balance.
2.1. 2.1.Knives Knivesof ofMechanical MechanicalBalance Balance 2.1. Knives of Mechanical Balance For For supporting supporting an an approximate approximate 777 ttt load, load, TH10 TH10 high-speed high-speed steel steel is is used used as as the the material material of of the the For supporting an approximate load, TH10 high-speed steel is used as the material of the middle knife and side knives after a special heat treatment process as shown in Figure 3. The special middleknife knifeand andside sideknives knivesafter afteraaspecial specialheat heattreatment treatmentprocess processas asshown shownin inFigure Figure3.3. The The special special middle heat treatment process includes preheating two times at 500–600 ℃ and 800–850 ℃, respectively, heat treatment process includes preheating two times at 500–600 ℃ and 800–850 ℃, respectively, heat treatment process includes preheating two times at 500–600 °C and 800–850 °C, respectively, quenching quenching at at 1200–1250 1200–1250 ℃, ℃, tempering tempering three three times times at at 550–570 550–570 ℃ ℃ and and aaa deep deep cooling cooling cycle cycle down down to to quenching at 1200–1250 °C, tempering three times at 550–570 °C and deep cooling cycle down to –120 ℃ [7]. After machining the knives have maintained high hardness and high toughness under –120°C ℃ [7]. [7]. After After machining machining the the knives knives have have maintained maintained high high hardness hardness and and high high toughness toughness under under –120 heavy load conditions [8]. heavy load conditions [8]. heavy load conditions [8].
Figure Figure 3. Heat treatment process of TH10. Figure3. 3.Heat Heattreatment treatmentprocess processof ofTH10. TH10.
2.2. 2.2.Indicators Indicatorsof ofMechanical MechanicalBalance Balance 2.2. Indicators of Mechanical Balance The includes two individual indicators. is an The display display device device includes includes two two individual individual indicators. indicators. One an indicator indicator based based on on optical optical The display device One is an indicator based on optical principles. It is composed of a small scale, a high definition camera and a liquid crystal principles. It is composed of a small scale, a high high definition definition camera camera and and aa liquid liquid crystal crystal display display principles. display (LCD). shown in Figure 4.4.AAmetal (LCD).The Thescale scaleand andthe theLCD LCDare areshown shownin inFigure Figure4. metalthin thinrod rodfixed fixedin inthe themiddle middleof ofbeam beamis (LCD). The scale and the LCD are A metal thin rod fixed in the middle of beam isis perpendicular to the beam. The scale of the indicator is mounted on the end of the metal thin rod perpendicularto tothe thebeam. beam.The Thescale scaleofof the indicator is mounted of metal the metal rod perpendicular the indicator is mounted on on the the endend of the thin thin rod and and to the The between the knife-edge and the isis 42 cm. The and parallel parallel the beam. beam. The distance distance between the middle middle knife-edge and the scale scale 42The cm.scale The parallel to thetobeam. The distance between the middle knife-edge and the scale is 42 cm. scale with the of beam and 160 The between divisions scaleswings swings with theswing swing ofthe theand beam andincludes includes 160divisions. divisions. Theinterval interval between divisions swings with the swing of the beam includes 160 divisions. The interval between divisions of the of the scale is equal to 0.25 mm. A high definition camera with 14 million pixels is used for of the scale is equalmm. to 0.25 mm. A highcamera definition with 14 million pixels is used the for scale is equal to 0.25 A high definition withcamera 14 million pixels is used for amplifying amplifying the scale and displaying it on the LCD. During the measurement, the operator reads the amplifying the scale and displaying it on the LCD. During the measurement, the operator reads the scale and displaying it on the LCD. During the measurement, the operator reads the LCD readings. LCD readings. LCDAnother readings.includes two laser displacement sensors, a signal processor and acomputer. Another includes two sensors, aa signal processor and Laser includes two laser laser displacement displacement signal processor and asides a computer. computer. Laser LaserAnother displacement sensors with the resolution sensors, of 3 µm are mounted on both of the beam. displacement sensors with the resolution of 3 m are mounted on both sides of the beam. The displacement sensors with the resolution of 3 m are mounted on both sides of the beam. The distance between the middle knife-edge and each laser displacement sensor is 42 The cm. distance between the knife-edge and laser sensor is 42 The distance between the middle middle knife-edge sensors and each each laser displacement displacement sensor 42 cm. cm. The The installation of two laser displacement is shown as Figure 5. When theisbeam swings, installation of displacement sensors as When beam the installation of two two laser laser displacement sensors isis shown shown as Figure Figureto5.5.equilibrium When the the position beam swings, swings, the the laser displacement sensor-L gets the displacement corresponding on the left laser displacement sensor-L gets the displacement corresponding to equilibrium position on the left laser displacement sensor-L gets the displacement corresponding to equilibrium position on the left side. Meanwhile the laser displacement sensor-R gets the displacement on the right side. The difference side. Meanwhile the laser displacement sensor-R the on right The side. Meanwhile of the laser displacement sensor-Rofgets gets the displacement displacement on the right side. side. of displacements both sides is the displacement the beam. It can eliminate the influence of The the difference of displacements of both sides is the displacement of the beam. It can eliminate difference of displacements of both sides is the displacement of the beam. It can eliminate the the influence of the zero drift of the laser displacement sensor. The difference is processed by the signal influence of the zero drift of the laser displacement sensor. The difference is processed by the signal processor processorand andsent sentto tothe thecomputer. computer.
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zero drift of the laser displacement sensor. The difference is processed by the signal processor and sent to the 2017, computer. Sensors 17, 851 4 of 12 Sensors 2017, 17, 851 Sensors 2017, 17, 851
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(a) (b) (a) (b) (a) (b) Figure 4. (a)The scale and (b) the LCD. Figure 4. (a) The scale and (b) the LCD. Figure 4. (a)The scale and (b) the LCD. Figure 4. (a)The scale and (b) the LCD.
Figure 5. The installation of two laser displacement sensors. Figure 5. The installation of two laser displacement sensors. Figure 5. The installation of two laser displacement sensors.
The indicator based on optical principle is used for adjusting the indicator with two laser The indicator based onWhen optical is the used forisadjusting the with displacement sensors [9,10]. theprinciple pointer on LCD located on theindicator left end of the two scale,laser the The indicator based on optical principle principle is used for for adjusting adjusting the the indicator indicator with with two two laser laser The indicator based on optical is used displacement [9,10]. thetopointer on the LCD is located on the left end of pointer in thesensors computer is When adjusted the minimum position. When pointer onthe thescale, LCDthe is displacement sensors [9,10]. When the pointer onon thethe LCD is located on thethe leftleft endend of the scale, the displacement When the pointer LCD located of scale, pointer on in the computer to computer the minimum position. Whentoon the onBased thethe LCD is located thesensors middle[9,10]. of is theadjusted scale, the pointer is is adjusted thepointer middle. on the pointer in the computer is adjusted to to the minimum position. When the pointer on the LCD is the pointer in the computer is adjusted the minimum position. When the pointer on the LCD is located on the middle of the scale, the computer pointer is adjusted to the middle. Based on the adjustments on these positions, the indicator with two laser displacement sensors can get located on the middle of the scale, the computer pointer is adjusted to the middle. Based on the located on of the scale, computer pointer is adjusted to the middle. Based onas the adjustments onmiddle these automatically. positions, thetheThe indicator with twotwo laser displacement sensors canused get the readings bythe computer indicator with laser displacement sensors a adjustments on onthese thesepositions, positions, the indicator with two displacement laser displacement sensors can readings get the adjustments the indicator with two laser sensors can get the readings by computer automatically. The indicator with two laser displacement sensors used as reading system of the mechanical balance is available for decreasing reading errors caused bya readings by computer automatically. The indicator with two laser displacement used sensors as a by computer automatically. Thethe indicator with two displacement ascaused aused reading reading system of the 6mechanical balance isofavailable for decreasing sensors reading errors by human vision. Figure shows position one laser laser displacement sensor and the software reading system of the mechanical balance is available for decreasing reading errors caused by system of the mechanical balance is available for decreasing reading errors caused by human vision. human vision. Figure 6 shows the position of one laser displacement sensor and the software interface of the indicator. human6 vision. Figure 6 shows of onesensor laser and displacement andofthe software Figure position of onethe laserposition displacement the softwaresensor interface the indicator. interfaceshows of the the indicator. interface of the indicator.
(a) (b) (a) (b) (a)position of one sensor and (b) the software (b) interface. Figure 6. (a) The Figure interface. Figure 6. 6. (a) (a) The The position position of of one one sensor sensor and and (b) (b) the the software software interface. Figure 6. (a) The position of one sensor and (b) the software interface.
2.3. Counter Weight Selecting System 2.3. Counter Weight Selecting System 2.3. Counter System requirement of full range from 100 kg to 2000 kg in a limited Weight Selecting According to the measurement According to the measurement requirement of full range from 100 kgcounterweight to 2000 kg in aselection limited space, a counterweight selection system is designed and produced. The requirement According to the measurement requirement of full range from 100 kg to 2000 kg in a limited space, ashown counterweight selection system is designed and produced. The counterweight selection system in Figure 7 consists of one stainless steel frame with three layer support, nested 1, 2, 2, space, a counterweight selection system is is designed designed and and produced. produced. The counterweight selection system shown in Figure 7 consists of one stainless steel frame with three layer support, nested 2, 2, 5system ratio counterweights the inside to the outside and three sets of selection modules with1,nine shown in Figurefrom 2, 2, 2, 7 consists of one stainless steel frame with three layer support, nested 1, 2, 5 ratio counterweights the inside toThe the outside and three sets with of selection modules withtop nine motors for selecting thefrom counterweights. first selection module four motors on the of 5 ratio counterweights from the inside to the outside and three sets of selection modules with nine motors for selecting the counterweights. The selection module with four motors on among the top10, of the counterweight selection system is used forfirst selecting one weightwith or one set of weights motors for module four motors on on the the top top of the for selecting selectingthe thecounterweights. counterweights.The Thefirst firstselection selection module with four motors of the counterweight selection system is used for selecting one weight or one set of weights among 10, 20, 20 and 50 kgselection options. system The second onefor is similar as the first layer selecting one weight counterweight is used selecting oneone weight orstructure one set set offor weights among 10, 10, 20, the counterweight selection system is used for selecting weight or one of weights among 20,one 20 and kg options. The second one similar first layer structure for selecting oneand weight or set 50 of weights among 100, 200, 200isand 500as kgthe options. There is one 1000 kg weight one 20, 20 and 50 kg options. The second one is similar as the first layer structure for selecting one weight or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of selection modules with one motor in the third layer. or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of selection modules with one motor in the third layer. set of selection modules with one motor in the third layer.
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20 and 50 kg options. The second one is similar as the first layer structure for selecting one weight or one set of weights among 100, 200, 200 and 500 kg options. There is one 1000 kg weight and one set of Sensors 2017, 2017, 17, 851 851 with one motor in the third layer. of 12 12 selection modules Sensors 17, 55 of
Figure 7. 7. Counterweight Counterweight selection selection system. system. Figure Figure 7. Counterweight selection system.
2.4. Synchronous Synchronous Lifting Lifting Control Control 2.4. 2.4. Synchronous Lifting Control To improve improve the the repeatability repeatability and and sensitivity sensitivity of of the the mechanical mechanical balance, balance, aa synchronous synchronous lifting lifting To To improve the repeatability and sensitivity of the mechanical balance, selection a synchronous lifting control is developed for lifting the weighing system and the counterweight system along control is developed for lifting the weighing system and the counterweight selection system along control is developed for lifting the weighing system and the counterweight selection system along the the vertical vertical direction direction synchronously synchronously [11]. [11]. Four Four motors motors under under the the weighing weighing system system and and four four motors motors the vertical direction synchronously [11]. Four motors under the weighing system and four motors under under the the counterweight counterweight selection selection system system are are driven driven synchronously synchronously for for decreasing decreasing the the displacement displacement under the counterweight selection system are driven synchronously for decreasing the displacement errors errors between them. errors between them. between them. 2.5. Monitor Monitor System for for the Balance Balance of of the the Beam Beam 2.5. 2.5. Monitor System System for the the Balance of the Beam After the the weighing system system and the the counterweight selection selection system are are lifted synchronously, synchronously, the the After After the weighing weighing system and and the counterweight counterweight selection system system are lifted lifted synchronously, the beam including the middle knife and side knives is dropped. The middle knife-edge and beam including includingthethe middle andknives side isknives is The dropped. middleand knife-edge and beam middle knifeknife and side dropped. middleThe knife-edge corresponding corresponding bearing bearing block block form form the the pivot pivot to to support support everything. everything. Four Four force force sensors sensors are are mounted mounted corresponding bearing block form the pivot to support everything. Four force sensors are mounted at two sides of the at two two sides sides of of the the beam. beam. The The installation installation positions positions are are shown shown in in Figure Figure 8. 8. When When the the beam beam is is at beam. The installation positions are shown in Figure 8. When the beam is dropping, the vertical forces dropping, the vertical forces of four points on the beam are measured to judge the loading dropping, theonvertical forces of four points beamsynchronization are measured and to judge loading of four points the beam are measured to judgeonthethe loading adjust the the position synchronization and and adjust adjust the the position position of of the the beam. beam. synchronization of the beam.
Figure 8. 8. The The force force sensors sensors installation installation positions. positions. Figure The force sensors Figure 8. installation positions.
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3. Operational Principle 3. Operational Principle The weighing system is located at the left of the mechanical balance, and the counterweight The weighing system is located at the aleft of the mechanical balance, and the weight counterweight selection system is on the right side. When measurement is started, the reference and the selection system is on the right side. When a measurement is started, the reference weight and the test test weight are place on the weighing system of the mechanical balance in turn. Meanwhile, weight areto place on the weighing of weight, the mechanical balance in according according the nominal mass of system reference a counterweight orturn. a set Meanwhile, of counterweights are to the nominal mass of reference weight, a counterweight or a9 set of counterweights are selected on selected on the counterweight selection system. Figure shows a general two-dimensional the counterweight selection system.balance Figure showing 9 shows athe general two-dimensional representation of the representation of the mechanical characteristic quantities of the mechanical mechanical balance characteristic of theof mechanical balance.acts Theatpoint S’ is the balance. The point showing S’ is the the beam's pivot. Thequantities gravity force beam mass its center of beam's pivot. The gravity force of beam mass m acts at its center of gravity S. The masses m and m S R gravity S. The masses and hang at points L and R. The broken line connecting LL and R hang The brokenline linethrough connecting L and R forms an angle α with the horizon line formsatanpoints angleLαand withR.the horizon point S’, and is divided perpendicularly through S’ through divided perpendicularly through S’ with the length a into the sections lL and lR . with the point lengthS’,aand intoisthe sections and .
Figure 9. The general two-dimensional representation.
The lever center of gravity withwith a length an angle γ withγa.with These The lever arm armofofthe thebalance's balance's center of gravity a lengthforms lS forms an angle a. torques around point S’ are neutralized under the equilibrium condition [12]. With the gravitational These torques around point S’ are neutralized under the equilibrium condition [12]. With the accelerations accelerations , and gLin three gravitational centers of the masses, the following expression gravitational , gthe R and gS in the three gravitational centers of the masses, the following is valid: expression is valid: (1) cos + sin = cos − sin + sin − mR gR (lL cos α + a sin α) = mL gL (lL cos α − a sin α) + mS gS lS sin(γ − α) (1) = = = , the sensitivity of the mechanical balance is defined It is assumed that It is assumed that g(1) according to Equation asgfollows: L = R = gS = g, the sensitivity of the mechanical balance is defined according to Equation (1) as follows: ∂α cos − sin = (2) sin + cos + + cos − ∂α ∂ lL coscos α − a−sinsin α = (2) α) + mR=( a0,cos α − lR sin + mS lS cos − α) In the case∂m ofL = m 0,L (lL=sin α=+, a cos = 0 and formula (1) αis) changed as(γ follows: = Equation (1) is changed as follows: In the case of a = 0, lL = lR = l, γ = 0 and=α = 0,
The sensitivity of mechanical balance is modified as follows: mL = mR = m
∂α = ∂ The sensitivity of mechanical balance is modified as follows:
(3) (3)
(4)
The sensitivity is independent of load, depending only on the mass of the beam and the position l ∂α of the center of gravity. = 0 means that the mechanical balance is symmetrical. The beam of(4)a = ∂mL m S lS symmetrical balance is horizontal only if the masses of the ends of beam are equal. = 0, = 0 means that the pivots are on one level. The sensitivity is independent of load, depending only on the mass of the beam and the position onofthe principle above, production and assembly of one long of theBased center gravity. γ =mentioned 0 means that thethe mechanical balance is symmetrical. The beam beamwith of a knives and bearing blocks is very important for improving repeatability of a symmetrical balance is horizontal only if the masses of the ends the of beam are equal.and a =sensitivity 0, α = 0 means mechanical balance. coordinate measurements and adjusting technology is used for adjusting that the pivots are onThree one level. the straightness, and flatness between the middle and knifeassembly and sideof knives to bebeam mounted Based on theparallelism principle mentioned above, the production one long with on the beam. The parallelism flatness between middlethe knife-edge and side knives and bearing blocks is and verythe important for improving repeatability and knife-edges sensitivity ofare a less than 20 m. The straightness of each knife-edge is also less than 20 m. mechanical balance. Three coordinate measurements and adjusting technology is used for adjusting
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the straightness, parallelism and flatness between the middle knife and side knives to be mounted on the beam. The parallelism and the flatness between middle knife-edge and side knife-edges are less than 20 µm. The straightness of each knife-edge is also less than 20 µm. 4. Mechanical Balance Experiments 4.1. Mechanical Balance Results Class E2 weights of 5, 10 and 20 g are used as sensitivity weights from no load to full load. Ten pieces of class E2 50 kg weights are used as the reference weight of 500 kg. One hundred pieces of class F1 20 kg weights are used as the reference weights for 1000 kg or 2000 kg. The steps of balance calibration are shown as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
Under no loading conditions, one uses the small counterweights to adjust the balance of the beam. Record the indication of the balance. Add a sensitivity weight of 5 g on the left side. Record the indication of the balance. Remove the sensitivity weight of 5 g. Load the reference weights of 2000 kg on the left side and the 2000 kg counterweight on the right side. Increase or decrease the small counterweights until the beam is balanced. Record the indication of the balance. Add a sensitivity weight of 20 g on the left side. Record the indication of the balance. Remove the sensitivity weight of 20 g. Unload the reference weights of 2000 kg on both sides. Use the small counterweights to adjust the balance of the beam. Record the indication of the balance. Add a sensitivity weight of 5 g on the right side. Record the indication of the balance. Remove the sensitivity weight of 5 g. Repeat (6) and (7). Record the indication of the balance. Add a sensitivity weight of 20 g on the right side. Record the indication of the balance.
The sensitivities of no load and full load are shown as Table 1. The full load sensitivity is more than 1.7 part in 10−4 rad/g. The standard deviations of no load and full load are shown in Tables 2 and 3, respectively. Table 1. Sensitivity measurements of the mechanical balance. Left Side
Right Side
Results (Division)
Sensitivity (10−4 rad/g)
No load Sensitivity weight 5 g
No load No load
15.381 32.072
7.3
Full load Sensitivity weight 20 g
Full load Full load
18.694 34.130
1.7
No load No load
No load Sensitivity weight 5 g
15.803 −4.177
7.3
Full load Full load
Full load Sensitivity weight 20 g
18.838 3.298
1.7
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Table 2. Standard deviation of no load. Results (Division)
Sensitivity (10−4 rad/g)
Standard Deviation (g)
15.394 15.515 15.637 15.714 15.452 15.546
7.3 7.3 7.3 7.3 7.3 7.3
0.04
Table 3. Standard deviation of full load. Results (Division)
Sensitivity (10−4 rad/g)
Standard Deviation (g)
18.765 18.783 18.888 19.026 18.896 18.954
1.7 1.7 1.7 1.7 1.7 1.7
0.13
After the indicator based on laser displacement sensors is adjusted, the reading comparisons between indicators based on optical principles and laser displacement sensors at 500 kg are shown as Table 4 and Figure 10. The comparison steps between indicators are as follows: (1) (2) (3) (4) (5)
Place the 500 kg weight on the weighing pan (left side of the mechanical balance) and select a 500 kg counterweight on the right side of the mechanical balance. Read the first divisions from the two indicators, respectively, after reaching balance. Place a sensitivity weight of 5 g on the top of the counterweights or the weighing pan. Read the second divisions, respectively. Divide 5 g into the difference between the first divisions and the second divisions. The mass against one division that represents the sensitivity of the mechanical balance at 500 kg could be known.
The values of the first column in the Table 4 are the readings based on the optical principle, and the values of the second column are the sensitivities corresponding to the readings. The values of the third column in the Table 4 are the readings based on two laser displacement sensors. The values of the last column are the sensitivities corresponding to the readings based on two laser displacement sensors. The maximum difference between readings based on optical principle and two laser displacement sensors is from the eighth row. It is 0.336 divisions. The mass corresponding to the divisions is 0.2 g, i.e., very small and it can be ignored. The results show the readings between two indicators coincide. Table 4. Reading comparisons between indicators based on optical principle and laser displacement sensors at 500 kg. Optical Principle Results (Division) 17.925 18.450 18.225 18.050 18.275 18.250 18.250 18.300 18.075 18.200
Laser Displacement Sensors
Sensitivity
(10−4
3.75 3.69 3.64 3.54 3.61 3.63 3.64 3.62 3.76 3.65
rad/g)
Results (Division)
Sensitivity (10−4 rad/g)
17.710 18.193 17.943 17.978 18.097 18.116 17.953 17.964 17.856 18.046
3.73 3.60 3.55 3.50 3.54 3.57 3.55 3.54 3.74 3.58
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Optical Principle
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Reading（divisions）
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18.2
Optical Principle Laser
17.8 18
Displacement Sensors Laser Displacement Sensors
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1
2 1
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3Number 4 of 5 Measurement 6 7 8
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Number of Measurement Figure 10. Reading results of two indicators. Figure 10. Reading results of two indicators. Figure 10. Reading results of two indicators.
The results regarding the measurement of beam stability at 2000 kg are shown in Figure 11. The The results regarding the measurement of beam stability at 2000 kg are shown in Figure 11. Thevalue resultsisregarding the measurement of beam stability at 2000 are shown in Figure The maximum 7.201 divisions, and the minimum value is kg 7.329 divisions. The11.difference The maximum value is 7.201 divisions, and the minimum value is 7.329 divisions. The difference maximum value is 7.201 divisions, and the minimum value is 7.329 divisions. The difference between the maximum andand minimum values divisions. between the maximum minimum valuesisisonly only 0.118 0.118 divisions. between the maximum and minimum values is only 0.118 divisions. 7.4
7.4
7.35
7.35
7.3 7.3 Reading Reading 7.25 7.25 (divisions) (divisions) 7.2 7.2 7.15 7.15 7.1
7.1
1
1
2
2
3
3
4
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5
5
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Number of measurement
8
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Number of measurement
Figure 11.11. Measurement ofof beam stability. Figure Measurement beam stability.
Figure 11. Measurement of beam stability. Figure 12 shows the results of 500, 1000 and 2000 kg. The sensitivity for 500 kg is more than Figure 12−4shows the results of 500, 1000 and 2000 kg. The sensitivity for 500 kg is more than 3.6 parts12 in shows 10 rad/g, the sensitivity 1000 kg2000 is more 2.7 parts infor 10−4500 rad/g, and the than Figure the results of 500,for 1000 and kg. than The sensitivity kg is more 3.6 parts in 10−4 rad/g, the sensitivity for 1000−4 kg is more than 2.7 parts in 10−4 rad/g, and the −4 −4 for 2000 kg is more than 1.7 parts in 10 kg rad/g. Figurethan 13 showsparts the relationship between 3.6 sensitivity parts in 10 sensitivity for 1000 is more in 10 rad/g, and the sensitivity for rad/g, 2000 kgthe is more than 1.7 parts in 10−4 rad/g. Figure 13 2.7 shows the relationship between the sensitivity and the load. As the load changes, the sensitivity becomes worse. −4 sensitivity for 2000and kg the is more 1.7 parts in 10 the rad/g. Figure 13 shows the relationship between the sensitivity load. than As the load changes, sensitivity becomes worse.
the sensitivity and the load. As the load changes, the sensitivity becomes worse.
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500 kg 500 kgkg 1000 1000 2000kg kg 2000 kg
42 20 1 1
0
2 2
3 4 5 6 7 8 3 Number 4 5 measurement 6 7 8 of
9 9
10 10
Number of measurement
Sensitivity(rad/g) Sensitivity(rad/g)
Figure 12.12. The results 1000kg kgand and2000 2000 Figure The resultsfor for500 500 kg, kg, 1000 kg.kg. Figure 12. The results for 500 kg, 1000 kg and 2000 kg.
0.0008 0.0008 0.0006 0.0006 0.0004 0.0004 0.0002 0.0002 0 0 0 0
500 1000 500Load(kg) 1000
2000 2000
Load(kg) Figure 13. The relationship between the sensitivity and the load.
Figure 13. The relationship between the sensitivity and the load. Figure 13. The relationship between the sensitivity and the load. 4.2. Uncertainties of Mechanical Balance
4.2. Uncertainties of Mechanical Balance According to the operational principle of the mechanical balance, the expression of indication 4.2. Uncertainties of Mechanical Balance According to thetooperational principle mechanical balance, the expression of indication error with respect the mechanical balanceof is the as follows: to the operational principle mechanical balance, the expression of indication errorAccording with respect to the mechanical balanceof is the as follows: E = I −L (5) error with respect to the mechanical balance is as follows: (5) = − where E is the error between the indication of the balance and the applied load, I is the (5) = mechanical − where E is the error between the indication of the mechanical balance and the applied load, I is the indication of mechanical balance regarding applied load and L is the applied load [13–15]. where E isThe theuncertainty error between indication of the mechanical and the applied load, I is the indication of mechanical regarding applied load and Lbalance is the applied load [13–15]. ofbalance the the mechanical balance is as follows: indication of mechanical balance regarding applied and L is the applied load [13–15]. The uncertainty of the mechanical balance is asload follows: 2 d2 The uncertainty of the mechanical balance is asd follows: u2 ( E ) = s2 ( I ) + 0 + L + u2 ( L ) (6) (6) = + 12 + 12 + 12 12 + + +of the mechanical balance corresponding (6) where u( E) is the uncertainty of error, s(= I ) is the repeatability 12 the12repeatability where is the uncertainty of error, is of the mechanical balance to the applied load, d0 is the no load sensitivity, dL is the applied load sensitivity, u( L) is the uncertainty where is the uncertainty of error, is the repeatability of mechanical balance is the no load sensitivity, is thethe applied load sensitivity, corresponding to the applied load, deriving from the reference weight including the air buoyancy correction. The uncertainties of 500, is the no loadweight sensitivity, is the air applied load sensitivity, corresponding to the applied load, is the deriving from5.the reference including buoyancy correction. 1000 anduncertainty 2000 kg are shown in Table is the uncertainty reference the air buoyancy correction. The uncertainties of 500,deriving 1000 andfrom 2000the kg are shownweight in Tableincluding 5. The uncertainties of 500, 1000 and 2000 kg are shown in Table 5. Table 5. The extended uncertainties of 500, 1000 and 2000 kg. Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Load (kg) Load (kg)
500 1000 500 2000
Standard Uncertainty Standardof the Weighing Process Uncertainty of the(g)
Standard Uncertainty Due to Standard the Sensitivity Uncertainty Due(g) to
Standard Uncertainty of the Reference Weight with Standard Uncertainty of Air the BuoyancyWeight Correction Reference with (g) Air
Combined Standard Combined Uncertainty Standard (g)
Extended Uncertainty Extended (k = 2, g) Uncertainty
0.072 Weighing Process (g)
0.176 (g) the Sensitivity
Buoyancy0.134 Correction (g)
0.232 (g) Uncertainty
(k 0.47 = 2, g)
0.028 0.072 0.117
0.236 0.176 0.469
0.833 0.134 1.667
0.867 0.232 1.736
1.8 0.47 3.5
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Table 5. The extended uncertainties of 500, 1000 and 2000 kg.
Load (kg)
Standard Uncertainty of the Weighing Process (g)
Standard Uncertainty Due to the Sensitivity (g)
Standard Uncertainty of the Reference Weight with Air Buoyancy Correction (g)
Combined Standard Uncertainty (g)
Extended Uncertainty (k = 2, g)
500 1000 2000
0.072 0.028 0.117
0.176 0.236 0.469
0.134 0.833 1.667
0.232 0.867 1.736
0.47 1.8 3.5
5. Conclusions The establishment of a new 2000 kg mechanical balance is important for traceability of class F1 weights from 500 kg to 2000 kg used in industrial processes. To develop a mechanical balance with high accuracy and a wide measurement range for measurement of class F1 weights over 500 kg, a new heat treatment method of metal material, three coordinate measurement and adjustment technology, dynamic monitoring with regards to the balance of the beam and synchronous lifting control are used to improve the repeatability and sensitivity of the mechanical balance. For the realization of any combinations of counterweights in a limited space, a new counter-weight selection system is designed and its construction accomplished. The sensitivity of the new 2000 kg mechanical balance is more than 1.7 parts in 10−4 rad/g. The extended uncertainties of 500, 1000 and 2000 kg for the mechanical balance are 0.47 g, 1.8 g and 3.5 g, respectively. The results show the performance of the new mechanical balance is better than that of electronic mass comparators used in commerce. Acknowledgments: This work was supported in part by the National Science and Technology Support Program under Grant 2011BAK15B06, in part by the Special-Funded Program through the National Key Scientific Instruments and Equipment Development under Grant 2012YQ090208, and in part by National Key Research and Development Program for National Quality Infrastructure under Grant 2016YFF0200103. Conflicts of Interest: We declare that we have no conflict of interest.
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