New microforce generating machine using electromagnetic force


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 109 

ACTA IMEKO 
ISSN: 2221-870X 
December 2020, Volume 9, Number 5, 109 - 112 

 
 

NEW MICROFORCE GENERATING MACHINE USING 

ELECTROMAGNETIC FORCE 
 

Junfang Zhu1, Toshiyuki Hayashi1, Atsuhiro Nishino1, Koji Ogushi1 

 
1 National Metrology Institute of Japan (NMIJ), AIST, Tsukuba, Japan, zhu-junfang@aist.go.jp  

 

Abstract: 

This paper reports a new microforce generating 

machine under development at NMIJ, AIST. We 

proposed a new microforce generating method by 

referring to the principle of the Kibble balance 

experiment and planned to apply it to a rotary type 

machine. Microforce in the micronewton and 

millinewton range can precisely be generated using 

this newly developed machine.  

Keywords: microforce, electromagnetic force, 

Kibble balance, rotary type machine, force standard 

1. INTRODUCTION 

Microforce measurements in the micronewton 

and millinewton range have been applied in many 

industries and research fields, and the reliability of 

these measurements becomes essential, for example, 
for the evaluation of material mechanical property 

using an atomic force microscope (AFM). 

Therefore, several national metrology institutes 

(NMIs) have developed various facilities, including 

microforce comparators that use the principle of the 

electromagnetic balance, to establish the 

traceability of microforce [1–3]. The National 

Metrology Institute of Japan (NMIJ), National 

Institute of Advanced Industrial Science and 

Technology (AIST), has developed a 2 N dead-

weight type force standard machine that uses 

gravity force and can extend the Japanese force 

standard down to 10 mN [4]. The above facilities all 

need to be traceable to mass in the sub-gram and 

milligram range. However, there is a limitation due 

to factors such as manufacturing technology and 

calibration of small weights. 

By referring to the principle of Kibble balance 

experiment [5, 6], and an electromagnetic force type 

torque standard machine developed in NMIJ [7], we 

proposed a new microforce generating method 

using electromagnetic force and planned to apply it 

to a rotary type machine.  

2. PRINCIPLE OF PROPOSED METHOD 

As in the Kibble balance experiment, there are 

two modes in measurement: static mode and 

 
Figure 1: Principle of the proposed method 
 

dynamic mode, as shown in Fig. 1. A rotating 

coordinate system was applied.  

In the static mode, when an electric current I 

flows through a rectangular coil with a rotation axis 

shown in the broken red line in a magnetic field of 

a magnetic flux density B, an electromagnetic force 

F is generated as:  

𝐹 = 𝐵𝑙𝐼 or 𝐹 = −𝐵𝑙𝐼 , (1) 

where l is the length of the rectangular coil parallel 

to the rotation axis. These two forces are in opposite 

directions, and their magnitudes are equal. 

Therefore, a torque T is generated around the 

B 

F 

r 

l 

d 

I 

B 
F 

F
m
 

I 

R 

I 
 

F 

F 

T 

F
m
 

B I 

U 

 

 

t 

(a) Static mode 

(b) Dynamic mode 

Rotation axis 

Rotation axis 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 110 

rotation axis of the coil indicated by the broken red 

line as: 

𝑇 = 𝑁𝐵𝐴𝐼 cos𝜃 , (2) 

where N is the number of turns of the rectangular 

coil, A (= ld) is the area of the rectangle coil. If an 

arm with a length r is attached from the center of the 

coil in rotation axis, a force F
m
 can be generalized 

and expressed as:  

F
m

= 𝑇/𝑟 = 𝑁𝐵𝐴𝐼 cos𝜃/𝑟 . (3) 

In the dynamic mode, when the rectangular coil 

is rotated with the rotation axis indicated by the 

broken red line to in the magnetic field at a constant 

angular velocity , an induced electromotive force 
U is generated as: 

𝑈 = 𝑁𝐵𝐴𝜔 sin𝜔𝑡 . (4) 

When the magnetic flux lines and the rectangular 

coil are parallel in both static and dynamic modes, 

F
m
 and U reach their maximum values F

mmax
 and 

U
max

. By considering the 𝑁𝐵𝐴 is a value associated 

with the machine developed, F
mmax

 can be expressed 

as:  

F
mmax

= 𝑈max𝐼/(𝜔𝑟) . (5) 

Therefore, F
mmax

 is obtained from measuring 

U
max

 and  in the dynamic mode, I in the static mode 

and r. 

3. DESIGN 

Figure 2 shows an overview of the new machine 

in developing. It mainly consists of a servo motor, a 

rotary encoder, a pair of neodymium magnets fixed 

to a yoke, a rectangular coil, a balancing arm, a self-

developed aerostatic bearing, a loading frame, 

counterweights, a laser displacement sensor, and a 

lifting mechanism of the force transducer. A force 

transducer to be calibrated is installed on top of an 

exchangeable X, Y, θ stage. More details of main 

mechanisms are described in the following sections.   

Servo motor 

Rotary encoder 

Aerostatic bearing 

  

Rectangular coil 

Neodymium magnets Laser displacement sensor 

(Head) 

Lifting 

mechanism 

Force Transducer 

Balancing arm 

  

X, Y, θ stage 

Figure 2: Overview of the new machine 

 

Loading Frame 

Counterweights 

  

Figure 3: Arrangement of the magnets and the coil 

Coupling 

Servo motor Rotary encoder 

Drive shaft Rectangular coil 

Balancing arm 

Aerostatic bearing 

  Neodymium magnets 

Connecting Shaft 

Rotation axis 

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3.1. Neodymium magnets and coil 
Figure 3 shows the arrangement of the magnets 

and the coil viewed from the top. The neodymium 

magnets can be rotated with the rotation axis by 

connecting to the servo motor through a drive shaft 

and a coupling. The ring of the rotary encoder is 

mounted coaxially on the driveshaft to monitor the 

angle of the neodymium magnets. The coil is fixed 

to the balancing arm through a connecting shaft 

inserted in the aerostatic bearing. In fact, in the 

dynamic mode, the neodymium magnets are rotated 

by the Servo motor, and the rectangular coil is fixed 

in an equilibrium position to induce the 

electromotive force U. We visually confirm the 

rectangular coil parallel to the neodymium magnets 
before the measuring of the dynamic mode. After 

measuring, a specific angular position of the 

neodymium magnets in U
max

 can be defined. 

Currently, the neodymium magnets have already 

been manufactured, the distribution of the magnetic 

flux density was evaluated by the manufacturer, and 

the average value of the magnetic field where the 

coil passes was estimated to be approximately 350 

mT by the manufacturer's test report. We also have 

determined the area of the rectangular coil A, and 
the number of turns N is adjusted by referring to the 

estimated relationship between the magnitude of 

force generated F
mmax

 and the magnitude of current 

I. 

3.2. Force transmission mechanism  
Figure 4 shows an overview of the force 

transmission mechanism viewed from the front. The 

loading frame is linked to the balancing arm by a 

five-μm-thick metal band to act as an elastic hinge 

and can apply a compressive or tensile force on a 

force transducer. Counterweights are set on the 

other end of the balancing arm and used to cancel 

out the force acting on the loading frame by monitor 

the equilibrium position of the balancing arm using 

a high precision laser displacement sensor. Similar 
to the previous study [4], the aerostatic bearing is 

adopted as a high sensitivity less friction fulcrum. 
The length r indicating distance between fulcrum 

and force action point will be precisely measured 

and traceable to length standard. Since the two ends 

of the balancing arm are processed into round ends 

with a radius of 250 mm centered on the fulcrum, it 

is considered that r does not change even if the 

balancing arm is rotated a certain angle. Therefore, 

in the static mode, the neodymium magnets are 

fixed in the specific angular position, and the 

rectangular coil is free. When an electric current I 

flows through a rectangular coil, the torque T is 

generated, and the force F
mmax

 can be applied to the 

force transducer in compressive calibration, as 

shown in Fig. 4.  

3.3. Force transducer lifting mechanism 
Again, the previous study showed the contact 

point between the loading frame and the force 

transducer under calibration has to be maintained 

during calibration irrespective of the height and 

stiffness of the transducer [4]. Figure 5 shows the 

force transducer lifting mechanism newly 

developed with improvements by referring to the 

arrangement of the previous study [4]. This 

mechanism consists of a stepper motor, a coupling, 

a precision ball screw, four pairs of linear shafts and 

Figure 4: Force transmission mechanism 

Balancing arm 

Counterweights 
  

Metal band 
Metal band 

Loading frame 

r 

Loading jig 

Fmmax 
T 

Laser displacement 

sensor (Head) 

Round end 

Round end 

Installation table 

Force Transducer 

X, Y, θ stage 

Stepper motor 

Coupling 

Ball screw 

Linear shaft 

Linear bush 

Figure 5: Force transducers lifting mechanism 
  

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 112 

linear bushes, an installation table, and some 

connection parts. The force transducer to be 

calibrated is installed on top of an X, Y, θ stage 

mounted on the installation table, and it is driven 

vertically by a stepper motor via a precision ball 

screw with a resolution of 1 μm. We can manually 

adjust the horizontal position and the rotation angle 

of the vertical axis of the force transducer in the X, 

Y, and θ stages. However, in many cases of 

microforce transducers, the displacements of their 

elastic body in the rated capacity is small in several 

micrometer order; a lifting mechanism with the 

resolution in nanometer (nm) order is necessary in 

the future. 

4. SUMMARY 

We proposed a new method for generating 

microforces by referring to the principle of Kibble 

balance experiment. Based on the technique, we are 

developing a newly rotary type machine. We plan to 

verify our proposed method after the machine 

completed. In the future, we expect to realize a 

microforce standard using the new microforce 

generating machine in NMIJ. 

5. ACKNOWLEDGMENTS 

This work was supported by JSPS KAKENHI 

grant number jp18k45678. 

6. REFERENCES 

[1] C. Schlegel, O. Slanina, G. Haucke, R. Kumme, 
“Construction of a Standard Force Machine for the 

Range of 100 μN-200 mN”, Measurement vol. 45, 

pp. 2388–2392, 2012. 

[2] J. H. Kim, Y. K. Park, M. S. Kim, J. H. Choi, and 
D. I. Kang, “Development of Force Standard 

Machine in the Milli-Newton Range Based on 

Electromagnetically Compensated Balance”, 

Proceedings of Asia-Pacific Symposium on 

Measurement of Mass, Force and Torque (APMF 

2015), pp. 4–7, Oct. 27–30, 2015, Seoul, South 

Korea, 2015. 

[3] G. Hu, J. Jiang, Z. Zhang, Y. Zhang, U. Brand, and 
M. S. Kim, “Investigation of a small force standard 

with the mass based method”, ACTA IMEKO, vol. 

6, No. 2, pp.13–20, 2017. 

[4] J. Zhu, T. Hayashi, A. Nishino, and K. Ogushi, 
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standard machine”, Measurement, vol. 154, 107463 

(6 pp), 2020. 

[5] B. P. Kibble, “A measurement of the gyromagnetic 
ratio of the proton by the strong field method”, 

Atomic masses and fundamental constants 5, pp. 

545-551 1976. 

[6] B. P. Kibble, I. A. Robinson, and J. H. Belliss, “A 
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Balance”, Metrologia, vol. 27.4, pp. 173-192, 1990.  

[7] A. Nishino, K. Ueda, and K. Fujii, “Design of a new 
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