Analysis of mechanical properties for the key force transfer components of 2 MN deadweight force standard machine


ACTA IMEKO | www.imeko.org  December 2020 | Volume 9 | Number 5 | 91 

ACTA IMEKO 
ISSN: 2221-870X 
December 2020, Volume 9, Number 5, 91 - 96 

 
 

ANALYSIS OF MECHANICAL PROPERTIES FOR THE KEY FORCE 

TRANSFER COMPONENTS OF 2 MN DEADWEIGHT FORCE STANDARD 

MACHINE 
 

Wei Tieping1, Guo Jinquan2, Lai Zhengchuang3, Lin Shuo4, Yang Xiaoxiang5 

 
1 School of Mechanical and Automotive Engineering, Fujian University of Technology, Fuzhou, China, 

tpwei@fjut.edu.cn    
2 School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, China, maxguo@163.com  

3 Fujian Province Institute of Metrology, Fuzhou, China, lzcfjjl@126.com  
4 Fujian Province Institute of Metrology, Fuzhou, China, linshuo1001@126.com  

5 School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, China, yangxx@fzu.edu.cn  

 

Abstract:  

The good mechanical properties of deadweight 

force standard machine (DWM) are the basis to 

ensure the accuracy of its measurement. Aiming at 

the development of 2 MN DWM, this paper carries 

out simulation analysis on the key components of 

the force value transfer process. The analysis results 

provide constructive suggestions for the 

development of 2 MN DWM. 

 

Keywords: Uncertainty; 2 MN deadweight 

force standard machine (DWM); finite element 

method; mechanical properties 

1. INTRODUCTION 

With the development of economy and industrial 

technology, people's demand for force measurement 

with high precision and large range becomes more 

and more obvious. At present, a large number of 

researchers and funds have been invested in 

developing the force standard (base) machine as the 

highest standard for force traceability, and a series 

of static machines with different ranges (50 N ~ 

4.45 MN) and measuring accuracy have been 

developed, including 1 MN (Urel = 0.002 %, k = 2) 

in China, 1 MN (Urel = 0.002 %, k = 2) in 

INRIM/Italy, 1 MN (Urel = 0.002 %, k = 2) in 

NPL/India, 1.2 MN (Urel = 0.002 %, k = 2) in 

NPL/UK, 2 MN/1 MN (Urel = 0.002 %, k = 2) in 

PTB/Germany, 4.45 MN in NIST/USA. 

The theoretical value of uncertainty of DWM 

measurement is 1 × 10-5, but the actual value is only 

5 × 10-5 [1]. There are many factors affecting the 

measurement uncertainty of DWM, usually 

including the local acceleration of gravity, weight 

material density, uncertainty of weight mass, the 

density of air quality, the swing of the central boom 

and beam tilt (the uncertainty of DWM and the force 

transducer structures) [2-7]. Also, it includes the 

influence of tidal level effect on gravitation, the 

influence of air conditioning airflow, the influence 

of gravitation between weights, humidity, 

temperature, hardness of the pad, and so on [8]. 

Among these factors, some factors contribute more 

weight to the evaluation of measurement results. 

Some influencing factors contribute little to the 

evaluation of the measurement results, but they also 

have great influence on the measurement stability of 

the static crane. Among them, the strength, stiffness 

and stability of DWM are the most basic and the 

most presupposition factors. 

For structure design of 2 MN DWM in Fujian 

Province Institute of Metrology, its key value 

transfer components including the main body frame 

structure, the weight installation platform lifting 

mechanism, the structure of the inverter and the 

central derrick were simulated based on finite 

element method and the improved mechanical 

property solutions were put forward, which can 

provide constructive suggestions for the successful 

design of 2 MN DWM. 

2. THE OPERATING PRINCIPLE OF 2 MN 
DWM 

The structure diagram of 2 MN DWM is shown 

in Figure 1. The suspension system of DWM is 

made of an inverter and a central derrick. The 

gravity value of the hanging system is 40 kN. There 

are a total of 39 pieces of weights, which are 

independently added by the motors [3]. This 

configuration can be used to load the internal force 

values of (10 kN ~ 1 MN) and (20 kN ~ 2 MN) in 

the range increasing by the multiple of 5 kN.  

Before DWM works, the inverter and the central 

derrick are all placed on the rack. At the same time, 

the weight is placed in the V-shaped block of the 

transmission device through the weight handle.  

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mailto:tpwei@fjut.edu.cn
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While the calibration is in progress, the force 

transducer is placed on the moving beam to ensure 

that the central axis of the force transducer coincides 

with the central axis of the hanging system. The 

beam is driven upward through the roller screw by 

the motor until the hanging system is fully 

supported to reach stability by the force transducer. 

At this point, the hanging system is in a free state.  

After that, the transfer device will transmit the 

required weight downward until it is completely 

pressed on the weight tray. Then, the force value of 

the weight will be transmitted to the force 

transducer through the hanging system. At this point, 

the hanging system is in the loading state. 

After the verification, the servo motor reverses 

direction and the transfer device drives the weight 

to move upward until the weight is completely off 

the weight tray. Then, the moving beam moves 

downward until DWM returns to the initial state. 

 

Figure 1: Structural diagram of 2 MN DWM 

3. SIMULATION ANALYSIS FOR THE 
KEY FORCE TRANSFER COMPONENTS 

Based on the above analysis of the working 

principle of 2 MN DWM, it can be known that the 

main frame structure, the central derrick, the 

inverter structure and the lifting mechanism of the 

weight installation platform are all the key load-

bearing components. The mechanical properties of 

these parts directly influence the transfer effect of 

the value in the standard machine, which determines 

the measurement performance of the standard 

machine. The following sections will conduct finite 

element modelling and simulation of the key 

components of the design one by one. The analysis 

results will provide constructive suggestions for the 

development of 2 MN DWM. 

3.1.  The Main Frame Structures 
The main frame of the 2 MN DWM is used for 

placing weights, providing static support for 

weights and fixing the motor that drives weights to 

move up and down. The main frame structure is 

made of the upper and lower supports, the nine 

columns in the middle and every three columns 

form a group. Five fixed bars distributed uniformly 

at the top and bottom are used to connect the 

columns to improve the stability of the structure, as 

shown in Figure 2. The height of the main frame 

reaches 10 m, and the weight placement mechanism 

fixed on it has a maximum load bearing weight 

gravity of 2 MN. Therefore, its strength and 

stiffness should be analysed emphatically. In 

addition, the security of the connection between the 

weight placement mechanism and the main frame is 

also a key consideration. Considering the feasibility 

of the numerical simulation and the reliability of the 

analysis results, the simulation analysis can be 

divided into two parts: (1) the overall analysis: the 

strength and stiffness of the main structure are 

analysed, and the connection between the weight 

placement mechanism and the main frame is not 

considered; (2) the local analysis: the connection 

between the placement mechanism of weights and 

the main frame is considered, and the deformation 

of the main frame structure is not considered. 

 

Figure 2: Schematic diagram of the main frame structure 

(1) Simplification of mechanical model 
As shown in Figure 3, the supporting structure 

for placing weights is simplified to a T-shaped 

bracket for the overall analysis. It is assumed to be 

a rigid body, which is regarded as a whole with the 

main frame. The load of 2 MN acts on the T-shaped 

bracket according to the distribution position of 

weights. As shown in Figure 4, the force value 

transfer mechanism of the connection between the 

weight placement mechanism and the main frame 

structure is comprehensively considered for the 

local analysis. On the premise of not affecting the 

calculation results, the deformation of the 

connecting column with the weight placement 

mechanism is ignored. Therefore, only a section of 

the column structure is intercepted for modelling. 

The connection between the belt and the column is 

a fixed connection. 

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ACTA IMEKO | www.imeko.org  December 2020 | Volume 9 | Number 5 | 93 

 

Figure 3: Simplified schematic diagram of the overall 

analysis structure 

 

Figure 4: Simplified schematic diagram of the local 

analysis structure 

(2) Result analysis 
As shown in Figure 5, the maximum von Mises 

stress value of the overall analysis structure is 

3.99 MPa at the connection position between the 

lower support and the column. The maximum total 

displacement value is 0.043 mm at the middle 

position of the column. Therefore, there are 

sufficient strength and stiffness for the overall frame 

structure to meet the measurement accuracy of 

DWM. As shown in Figure 6, the maximum von 

Mises stress value of the local analysis structure is 

96.61 MPa at the edge of the hole where the 

uppermost screw contacts the rack, which is under 

the action of the maximum weight block (15-ton 

weight). The maximum total displacement value is 

0.076 mm at the outer edge of the V-shaped block. 

 

Figure 5: Stress cloud diagram of the overall frame 

structure 

 

Figure 6: Stress cloud diagram of weight placement 

mechanism 

The maximum von Mises stress value of the 

weight placement mechanism and its connection 

screws are far less than the yield limits of the 

corresponding materials, which indicates that the 

structure is able to meet sufficient strength and 

stiffness for the accurate measurement of DWM. In 

addition, the modal analysis of the first six orders of 

the main frame shows that the frequency of the first 

three orders is about 10 Hz, and the frequency of the 

second three orders is about 25 Hz, which is 

relatively small. Therefore, it is suggested to avoid 

these basic frequencies in practice to prevent 

resonance of the structure. 

3.2.  The Central Derrick 
(1) Simplification of mechanical model 

On the one hand, the structure size of the central 

derrick will affect the project installation. On the 

other hand, there are many ways to combine weights 

at the check points. In addition, the strength and 

stiffness of the central derrick directly affect the 

measurement performance of DWM. Therefore, it is 

of great importance to design the reasonable 

structure size for the central derrick. Here, the 

simulation results of the derrick with the dimensions 

of equal section and stepped structure are compared, 

which can provide theoretical basis for the structural 

design of the central derrick. As shown in Figure 7, 

the central derrick structure designed is composed 

of two round rods with equal sections in Figure 7 

(top), while the central derrick structure designed is 

composed of five round rods with variable sections 

in Figure 7 (bottom). Both are made of 2Cr13. All 

levels of derrick are connected by threads and 

connecting rods. Each stage of derrick is installed 

with an equal size ring. In addition, the main 

function of the ring is to support the weight tray and 

transfer weight gravity to the hanger. 

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Figure 7: Structure design scheme of the central derrick, 

top: two round rods with equal sections, bottom: five 

round rods with variable sections 

(2) Result analysis 

The analysis results of the two design schemes 

are shown in Figure 8 and Figure 9. Compared with 

the equal-section central derrick, the von Mises 

stress value of the variable-section central derrick 

decreases by 29.99 %. The von Mises stress value is 

far smaller than the yield limit of the material and 

the structure obtains better strength. In addition, the 

total displacement value for the variable-section 

central derrick is reduced by 31.45 %, and the 

structure has better stiffness. Therefore, the 

variable-section central derrick is more in line with 

the actual high precision measurement requirements 

of DWM. 

In addition, the weight should be lowered to the 

weight tray slowly during loading and returned to 

the lifting platform immediately after verification, 

which can reduce the creep effect of force 

fluctuation on the central derrick. At the same time, 

it is easier for the multiple levels of variable-section 

derrick to install. Therefore, the structural design of 

multi-level central derrick with variable cross-

section is more in line with the actual situation. 

 

Figure 8: Stress cloud diagram of hanging structure with 

equal diameter central derrick 

 

Figure 9: Stress cloud diagram of the hanging structure 

in the classification central derrick 

3.3.  The Inverter Structure 
(1) Mechanical model 

The inverter is the key load-bearing component, 

and its initial design structure and the structure after 

topology optimization are shown in Figure 10. It is 

very important to ensure that the structure of the 

inverter is subjected to uniform and stable load in 

the verification process. The structure consists of an 

upper beam, three support rods and a lower beam. 

Furthermore, the support rods are fixed to the top 

frame of the force standard device. 

In the tensile state, the lower beam of the inverter 

can bear the force up to 2 MN, which is transmitted 

to the fixed platform through the support rods. Then, 

the tension sensor between the upper beam and the 

fixed platform is subjected to the weight gravity. In 

the pressure state, the lower beam of the inverter is 

subjected to the force up to 2 MN, which is 

transmitted to the upper beam through the support 

rods. Then, the compression sensor located between 

the upper beam and the fixed platform is begin to be 

verified. Here, the structure of the initial design is 

simulated and analysed, and the size of the initial 

structure is topologically optimized to obtain the 

optimized structure. Meanwhile, the analysis results 

of the two are compared. 

                                         

Figure 10: The inverter structure, left: initial design, right: 

after topological optimization 

(2) Result analysis 

Figure 11 and Figure 12 are the overall 

displacement cloud maps of the two structures 

before and after optimization, respectively. 

It can be seen from the figures that the maximum 

von Mises stress value of the inverter structure at the 

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ACTA IMEKO | www.imeko.org  December 2020 | Volume 9 | Number 5 | 95 

contact point between the lower beam and the 

bearing decreases from 472 MPa to 176 MPa, 

which is far less than the yield limit of the material 

and could meet the strength requirement. The 

maximum overall displacement value of the inverter 

structure at the contact point between the lower 

beam and the hanger decreases from 2.6 mm to 

1.6 mm. In addition, the modal analysis of the first 

six orders of the main frame is carried out, and it is 

found that the frequency of the first three orders 

after optimization is around 10 Hz, which is one 

order larger than that the structure before 

optimization. While the frequencies of the second 

three orders before and after optimization are 

around 100 Hz with little change. 

As can be seen from the above, the maximum 

von Mises stress value of the lower beam of the 

optimized inverter is obviously reduced. 

Furthermore, the stress distribution range of the 

optimized structure is smaller and the overall force 

is more uniform. Therefore, the optimized inverter 

is able to obtain a more stable working state. 

  

Figure 11: Analysis results of the initial design structure 

of the inverter, left: initial design, right: after topological 

optimization 

  

Figure 12: Analysis results of the optimization structure 

of the inverter, left: stress cloud diagram, right: 

displacement cloud diagram 

3.4.  Lifting Mechanism of Weight Placing 
Platform 

The lifting mechanism of the weight placing 

platform is mainly used in the loading and 

unloading of DWM. Also, it is used for auxiliary 

lifting in the maintenance and repair, which is 

convenient for vertical transportation of personnel 

and rack appliances. As shown in Figure 13 (left), 

the screw rod and the screw nut constitute a screw 

pair, and the motor drives the screw rod to rotate and 

drives the lift platform connected with the screw nut 

to rise and fall. The maximum placement weight of 

2 MN DWM is 15 t supported by three screw rods 

in a 120° distribution. Considering the high lifting 

height of the placing platform, the slender support 

bar and the high safety requirement, the mechanical 

analysis of the structure safety must be carried out. 

       

Figure 13: Schematic diagram of lifting platform 

mechanism for placing weight, left: without guide bars, 

right: with guide bars 

(1) Mechanical model 

The simplified model mainly considers the 

deformation, strength and buckling of the whole 

lifting mechanism of the platform, so the connection 

problem of the detail structure such as the strength 

of screw thread is not considered. Without affecting 

the simulation results, the platform lifting 

mechanism is simplified as following: 1) screw non-

work state cannot rotate, and lift platform by self-

locking stays at a certain height. The top of the 

screw constraint torus only limits horizontal 

displacement, and six degrees of freedom of the 

bottom of the torus are all fixed ignoring the screw 

thread; 2) the railing of the outer ring of the lift 

platform is not considered, and the railing of the 

platform is much smaller than its own weight. 

Therefore, only the weight of the lifting platform 

itself is considered; 3) the disassembled plate meets 

the strength requirement, and it can be considered 

as a rigid plate for the simulation model as shown in 

Figure 14. 

   

Figure 14 Simplified schematic diagram of mechanism 

model of lifting platform for weight, left: without guide 

bars, right: with guide bars 

(2) Result analysis 

As shown in Figure 15 (left), the maximum von 

Mises stress value of the mechanism without guide 

bars is 72.89 MPa located at the triangular floor 

plate under the disassembly end supported by the 

platform lifting mechanism. The maximum total 

displacement value is 1.55 mm located in the 

middle and outer edge of the decorative pattern 

board. As shown in Figure 15 (right), the maximum 

von Mises stress value of the mechanism with guide 

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ACTA IMEKO | www.imeko.org  December 2020 | Volume 9 | Number 5 | 96 

bars is 66.6 MPa at the same location as the 

mechanism without guide bar. The maximum total 

displacement value is 1.35 mm at the same location 

as the mechanism without guide bars. 

  

Figure 15 Finite element analysis results of platform 

lifting mechanism, left: without guide bars, right: with 

guide bars 

According to the mechanical design manual, the 

allowable deflection of the shaft is 0.0003 l = 

2.16 mm, l is the length of the bar. As we known in 

the Figure 15, the maximum total displacement 

value of the lead rod is 1.01 mm without guide bars 

and 1.11 mm with the guide bars. Therefore, it can 

be seen that the screw rods of the two kinds of 

structure meet the deflection requirements. At the 

same time, according to the Euler formula of critical 

load, the screw rod is determined to be a large 

flexibility rod. Furthermore, it is found that the first 

critical load is much larger than the actual maximum 

applied load according to the stability calculation. 

Therefore, the mechanism meets the stability 

requirement. 

In addition, the lifting mechanism of the weight 

placing platform in the middle position is also in the 

extreme working condition, so the corresponding 

calculation and analysis should be carried out. The 

results show that the strength, stiffness and stability 

of the structure meet the requirements. Here, 

because of limited space of the paper, it is not 

elaborated. 

 

Figure 16: 2 MN DWM of Fujian Province Institute of 

Metrology in China 

4. 2 MN DWM DEVELOPMENT RESULT 

The research results of this paper have provided 

a useful theoretical reference and basis for the 

successful development of 2 MN DWM by Fujian 

Province Institute of Metrology. As the largest 

DWM in China, its uncertainty is better than 

0.002 %. At the same time, its performance is 

comparable to that of 2 MN DWM in German PTB. 

Compared with the British NPL 1.2 MN DWM, its 

consistency is better than 0.002 %. 

5. CONCLUSION 

Based on the finite element method, the key 

structure components in the force value 

transmission process of 2 MN DWM designed by 

Fujian Province Institute of Metrology have been 

simulated. The constructive suggestions are 

provided for its development. Furthermore, the 

measurement characteristics of the 2 MN DWM 

will be further studied in the future. 

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