CHAPTER 1

Principle of the Levitation Mass Method

How it works

Levitate: a rigid object (mass M) is supported by an air bearing so that it can move in one direction with almost no friction. Gravity Mg is borne by the bearing.
Apply a force: the mass collides with, or oscillates against, the object under test (a force transducer, a material, a structure).
Measure the motion: a laser beam reflected by a cube-corner prism on the mass gives a Doppler-shift frequency, measured with an optical interferometer.
Calculate: velocity v is proportional to the Doppler-shift frequency (v = λ_air × f_Doppler / 2, with f_Doppler = f_beat − f_rest). Acceleration a and position x are calculated from velocity, and the force acting on the mass is F = Ma.

Figure: Data processing: frequency → velocity → acceleration and position → force

Figure: Example result. Velocity, acceleration, force and position are derived in turn from frequency (uncertainty about 0.5%)

Strength	What it means
Based on the definition	Force is obtained directly from its definition as mass times acceleration. Mass can be measured precisely, and acceleration is traceable to the wavelength of light
Synchronised time axis	Only frequency is recorded during measurement; everything else is calculated afterwards, so velocity, position, acceleration and force share exactly the same time axis
No force transducer needed	The reference force does not rely on a force transducer, so force transducers themselves can be calibrated

Area	Targets	Chapter
Dynamic calibration of force transducers	Impact, oscillation and step forces; mechanical response	Ch. 4, Ch. 5
Material tester without force transducers	Micro-force, viscoelasticity, friction, biomechanics	Ch. 7, Ch. 8
Space balance	Mass measurement under weightless conditions	Ch. 3

The Levitation Mass Method: precision force measurement by the definition of force | Yusaku Fujii (Gunma University)