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**Levitation Mass Method: A Method for Precision Force Measurement**

Yusaku Fujii

Department of Electronic Engineering, Gunma University,

1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, JAPAN

Keywords:dynamic calibration, impact force, dynamic force, force sensor, force transducer, inertial force, inertial mass, optical interferometer, Levitation Mass Method

Abstract.The present status and the future prospects of a method for precision mass and force measurement, the levitation mass method (LMM), are reviewed. In the LMM, the inertial force of a mass levitated using a pneumatic linear bearing is used as the reference force applied to the objects under test, such as force transducers, materials, or structures. The inertial force of the levitated mass is measured using an optical interferometer. The author has modified it as calibration methods for the three categories of the dynamic force calibrations, that are the dynamic calibration method under impact load, the dynamic calibration method under oscillation load and the dynamic calibration method under step load. The author have applied the LMM for material testing, such as methods for evaluating material viscoelasticity under an oscillating load and under an impact load, a method for evaluating material friction, a method for evaluating biomechanics, a method for evaluating dynamic response of impact hammers, and a method for generating and measuring a micro-Newton level forces.

Introduction

Although force is one of the most basic mechanical quantities and is usually measured using force transducers, the dynamic calibration method for force transducers has not been established yet. The lack of the dynamic force calibration method results in the two major problems concerning material testing. One is that it is difficult to evaluate the uncertainty in the measured value of the varying force. The other is that it is difficult to evaluate the uncertainty in the time at which the varying force is measured.

The author has proposed a method, the “Levitation Mass Method” (LMM) [1-12]. In this method, the inertial force of a mass levitated using a pneumatic linear bearing is used as the reference force applied to the objects being tested, such as force transducers, materials and structures. Figure 1 shows the principle of the LMM. The inertial force of the levitated mass is measured using an optical interferometer. In the LMM, only the motion-induced time-varying beat frequency is measured during the measurement, and all the other quantities, such as velocity, position, acceleration and force, are numerically calculated afterwards. This results in the good synchronization between the obtained quantities. In addition, force is directly calculated according to its definition, that is, the product of mass and acceleration.

In this paper, the present status and the possible applications of the LMM are discussed.

**Dynamic force calibration**

In this section, the applications of the LMM to dynamic calibration of force transducers are reviewed. Figure 1 shows the experimental setup for measuring the electrical and mechanical responses of the force transducer against the impact load [9]. A conventional S-shaped strain-gauge-type force transducer, whose nominal force is 200 N is attached to the base.

By means of the Interferometer-1, the velocity of the mass v1 is measured; then the position **x1, acceleration a1**, and force acing on the mass Fmass are calculated. By means of the Interferometer-1, the velocity of the sensing element of the force transducer v2 is measured; then the position **x2 and acceleration a2** are calculated. Electric response of the transducer is measured using the digital voltmeter (DVM). With the proposed method, the electrical and mechanical responses of force transducers against impact loads can be simultaneously evaluated.

Figure 3 shows theforce measured by the force transducer and force measured by the proposed method. Recently, the author found that the error in dynamic force measurements is almost proportional to the acceleration at the sensing point of the transducer; this can be explained as the effect of the inertial force of a part of the transducer itself[12]. From the relationship between the acceleration of the sensing point a2and the difference between the values measured by the transducer and those measured by the proposed method, **Fdiff =Ftrans - Fmass, the regression line, Freg =Ftrans - Fmass =0.325a2**, is estimated. The inclination of the line, 0.325, can be considered as the estimated effective inertial mass of the transducer, Mestimated.

Figure 4 shows thedifference between the values measured by the transducer and those measured by the proposed method, and the estimated inertial force of the sensor element.The two curves, **Fdiff = Ftrans–Fmass and Freg = 0.325a2**, coincide well with each other.

**Material Tester Without Force Transducer**

In this section, the applications of the LMM to dynamic calibration of force transducers are discussed. The experimental set up for evaluating the mechanical response of materials against small impact force is shown in Figure 5. The material under test is attached to the base. A small aerostatic linear bearing is used to realize linear motion with sufficiently small friction acting on the mass, i.e., the moving part of the bearing. An arm of a hard-disk drive (HDD) is used as the object for test. The experimental set up is almost the same as the experimental set up for dynamic force calibration of force transducers shown in Figure 2. Figure 6 shows the change in force acting on the mass from the arm of the HDD, F =Ma, against position x. The spring constant, or inclination of the curve, is almost constant during the experiment with 4 collisions.

**Possible Collaborations withOthers**

The author expects that the LMM is the key to improve and expand the technology of precision mass and force measurement in the near future by means of the collaborations and efforts of many researchers from various fields.

To improve the efficiency of the LMM and to expand the applications of the LMM, other technologies in the other fields as follows,

(1)Collaboration with the dynamic metrology [13,14]

It will be effective to evaluate the uncertainty of the LMM and improve the uncertainty of the LMM that the recent technology of the dynamic metrology is introduced.

(2)Collaboration with the numerical simulation for HDD technology [15-18]

The LMM could be a good solution to evaluate the dynamic properties of the small mechanical parts, such as HDD. The precision experimental data will contribute to improve the numerical simulation code.

(3)Collaboration with the finite element method for modal analysis [19-21]

To evaluate the uncertainty of the LMM, the modal analysis of the mechanical parts of the experimental setup is desirable. At the same time, the data measured using the LMM will contribute to improve the finite element method for modal analysis.

(4)Collaboration with the biomechanics [22,23]

The LMM is effective to measure the dynamic response of human body.

(5)Collaboration with the precision control technology [24]

Control technology is essential to make an automatic instruments based on the LMM, such as the automatic dynamic force calibration instruments and the automatic material testers.

(6)Collaboration with the space medicine [25-27]

To develop an instrument for measuring the body-mass of astronauts under microgravity conditions, the LMM will be very effective.

(7)Collaboration with the coordinate measuring machine (CMM) technology

The LMM is effective to measure the force and position of the sensing-prove of CMM accurately.

Acknowledgment

This work was supported by Grant-in-Aid for Scientific Research (B) 19360185 (KAKENHI 19360185).

References

[1]Y. Fujii, "Optical method for accurate force measurement: dynamic response evaluation of an impact hammer", Opt. Eng., Vol. 45, 023002-1-7, 2006.

[2] Y. Fujii, "Method for Measuring Transient Friction Coefficients for Rubber Wiper Blades on Glass Surface", Tribol. Int. , (in press).

[3]Y. Fujii, "Pendulum for precision force measurement", Rev. Sci. Instrum., Vol. 77, 035111-1-5, 2006.

[4]Y. Fujii and J. Valera, "Impact force measurement using an inertial mass and a digitizer", Meas. Sci. Technol., Vol.17, pp. 863-868, 2006.

[5]Y. Fujii, "Method for generating and measuring the micro-Newton level forces", Mech. Syst. Signal Pr., Vol.20, pp.1362-1371, 2006.

[6] Y. Fujii, "Method of generating and measuring static small force using down-slope component of gravity", Rev. Sci. Instrum., (in press).

[7]Y. Fujii, "Method of evaluating the dynamic response of materials to forced oscillation", Meas. Sci. Technol., Vol.17, pp. 1935-1940, 2006.

[8]Y. Fujii, "Frictional characteristics of an aerostatic linear bearing", Tribol. Int., Vol.39, pp.888-896, 2006.

[9]Y. Fujii, "Measurement of the electrical and mechanical responses of a force transducer against impact forces", Rev. Sci. Instrum., Vol.77, 085108-1-5, 2006.

[10]Y. Fujii, "Possible applications of the Levitation Mass Method to precision mechanical measurements", J. Chinese S. Mech. Eng., Vol.27, pp.519-523, 2006.

[11]Y. Fujii, "Microforce materials tester based on the levitation mass method", Meas. Sci. Technol., Vol.18, No.6, pp.1678-1682, 2007.

[12]Y. Fujii, "Method for correcting the effect of the inertial mass on dynamic force measurements", Meas. Sci. Technol., Vol.18, pp.N13-N20, 2007.

[12]Y. Fujii, "Impact response measurement of an accelerometer", Mech. Syst. Signal Pr., Vol.21, pp.2072-2079, 2007.

[13]J. P. Hessling, “Dynamic metrology – a new paradigm for dynamic evaluation of measurement systems”, Proc. ISMTII 2007 (Sendai, Japan, Sep. 2007) (to be published).

[14]J. P. Hessling, “A novel method of estimating dynamic measurement errors”, Meas. Sci. Technol., Vol.17, pp2740-2750, 2006.

[15]C. N. Della, D.W. Shu, B.Gu and Y. Fujii, “Collision response measurement of an actuator arm of a hard disk drive by numerical analysis and experiments”, Proc. ISMTII 2007 (Sendai, Japan, Sep. 2007) (to be published).

[16]M.R. Parlapalli, B. Gu, D.W. Shu and Y. Fujii, “Dynamic response measurement of an actuator arm of a hard disk drive by numerical analysis and experiments”, Proc. ISMTII 2007 (Sendai, Japan, Sep. 2007) (to be published).

[17]D.W. Shu, B.J. Shi, H. Meng, F.F. Yap, D.Z. Jiang, Q.Y. Ng, R. Zambri and J.H.T. Lau, “Shock analysis of a head actuator assembly subjected to half-sine acceleration pulses”, Int. J. of Impact Engng., Vol.34, pp.253-263, 2007.

[18]Y. Fujii and D.W. Shu, "Impact force measurement of an actuator arm of a hard disk drive", Int. J. Impact Eng., (in press).

[19]T. Yamaguchi and Y. Fujii, “Dynamic analysis by FEM for a measurement system to observe viscoelasticity using Levitation Mass Method”, Proc. ISMTII 2007 (Sendai, Japan, Sep. 2007) (to be published).

[20]T. Yamaguchi, Y. Fujii, K. Nagai and S. Maruyama, "FEA for vibrated structures with non-linear concentrated spring having hysteresis", Mech. Syst. Signal Pr., Vol.20, pp.1905-1922, 2006.

[21]Y. Fujii, T. Yamaguchi and J. Valera, "Impact response measurement of a human arm", Exp. Techniques, Vol.30, pp.64-68, 2006.

[22]Y. Fujii and T. Yamaguchi, "Method of evaluating the force controllability of human finger", IEEE Trans. Instrum. Meas., Vol.55, pp.1235-1241, 2006.

[23]Y. Fujii and T. Yamaguchi, "Dynamic characteristics measurements of a car wiper blade", JSME Int. J. C, Vol.49, pp.799-803, 2006.

[24]S. Hashimoto and Y. Fujii, “Material tester using a controlled oscillator and an inertial mass”, Proc. ISMTII 2007 (Sendai, Japan, Sep. 2007) (to be published).

[25]K. Shimada and Y. Fujii, “Reconsideration of body mass measurement on the International Space Station and beyond”, Proc. ISMTII 2007 (Sendai, Japan, Sep. 2007) (to be published).

[26]Y. Fujii and K. Shimada, "Instrument for measuring the mass of an astronaut", Meas. Sci. Technol., Vol.17, pp.2705-2710, 2006.

[27] Y. Fujii and K. Shimada, "The space scale: An Instrument for astronaut mass measurement", T. Jpn. Soc. Aeronaut. S. (in press).

**Biography of Prof. Yusaku FUJII:**

Yusaku FUJII was born in Tokyo, Japan, in 1965. He received the B.E., M.E. and Ph.D. degrees from Tokyo University, Tokyo, Japan, in 1989, 1991 and 2001, respectively. He is a Japanese citizen.

**<Present appointment>**

Professorof Electronic Engineering

Faculty of Engineering, Gunma University

1-5-1 Tenjincho, Kiryu 376-8515, Japan

**<Academic qualifications>**

28 March 1989, B.E. (Bachelor of Engineering) conferred by the University of Tokyo.

29 March 1991, M.E. (Master of Engineering) conferred by the University of Tokyo.

15 March 2001, Dr. Eng (Doctor of Engineering) conferred by the University of Tokyo.

**<Work Experience>**

1991-1995: Kawasaki Steel Corp., Japan

Mechanics in hot rolling process

1995-2001: National Research Laboratory of Metrology (NRLM), AIST, Japan

Superconducting magnetic levitation for connecting mechanical and electrical quantities

2001-2002: AIST (National Institute of Advanced Industrial Science and Technology)

2002-: Gunma University

**<Major Research Field>**

Prof.Yusaku Fujii has studied the wide fields, such as the instrumentation engineering, the mechanical engineering, the applied physics and the absolute determination of the fundamental constants.His major research subjects are as follows,

Instrumentation engineering

Mechanical quantities measurement

Optical measurement

The Levitation Mass Method (invention and development)

Dynamic calibration methods for force transducers using The Levitation Mass Method

Material testing methods using The Levitation Mass Method (strength, bending, impact, oscillation, viscoelasticity, friction, etc.)

Micro-Newton Level forces using The Levitation Mass Method (generation and measurement)

Method for measuring mass under micro-gravity condition (The Space Balance, invention and development)

Fundamental constants

Low temperature experiment

Fluid dynamics

Plasticity dynamics

Numerical calculation

The e-JIKEI Network (invension and development)

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