[Topic-5] 浮上質量法 / The Levitation Mass Method (LMM)

浮上質量法（Levitation Mass Method, LMM）は，私（藤井）によって発案・開発された，ユニークで世界的に類を見ない手法です．この方法は，浮上支持された慣性質量（浮上質量）に作用する慣性力を，光波干渉計を用いて高精度に測定する，「変動する力」の発生・計測技術です．LMMは，力学量の高精度な計測を可能とする革新的な技術であり，力センサ動的校正・評価から材料試験・生体計測まで，「変動する力の高精度測定」の要求に答える形で，多岐にわたる応用が期待されます．

The Levitation Mass Method (LMM), conceived and developed by me (Fujii), is a unique and unparalleled technique globally. This method utilizes an inertial mass supported by levitation (levitated mass) to precisely measure inertial forces acting on it through the use of an optical interferometer. It is a groundbreaking technology for generating and measuring "variable forces" with high precision. LMM enables highly accurate measurement of mechanical quantities and holds great potential for diverse applications. From dynamic calibration and evaluation of force sensors to material testing and biological measurements, it is expected to meet the demand for "high-precision measurement of variable forces" across a wide range of fields.

 



特長（Features）:


応用分野（Application Fields）:

 

 

研究実績（Research Achievements）:


力センサの動的校正法に関しては，主要国の標準研究所などで半世紀に渡り研究されて来ているが，確立される目途は立っていない．動的校正法確立の順番として，以下が妥当であると考える．
第１段階：力センサが固定された状態を対象とする．
第２段階：力センサの台座が加速度運動している状態を対象とする．
 多くの研究開発が第２段階からスタート (=力センサごと加振器で加振) しているが，現実の様々な使用条件における台座の加速度運動・振動状態を，網羅・統合することは難しい．このことが，標準研究所での研究開発が四半世紀間も迷走し，動的校正法が確立できない原因と考えている．まず，第一段階の動的校正法を確立の後，第二段階に進むのが妥当と考える．

Research on dynamic calibration methods for force sensors has been ongoing for over half a century in major national standards laboratories, yet no established method has been achieved. The following sequential approach is considered appropriate for establishing a dynamic calibration method:
Stage 1: Focus on cases where the force sensor is stationary.
Stage 2: Focus on cases where the base of the force sensor is undergoing accelerated motion.
 Many research and development efforts have started directly from Stage 2 (i.e., vibrating the force sensor along with a shaker). However, it is extremely challenging to comprehensively and systematically address the various acceleration and vibration conditions of the base under real-world use cases. This difficulty is believed to be a key reason why research and development in standard laboratories has stagnated for decades, preventing the establishment of a dynamic calibration method. It is therefore reasonable to first establish a dynamic calibration method for Stage 1 before proceeding to Stage 2.

2025年においては，予算の有無に関わらず，浮上質量法の理論面での検討を進め，論文発表を行います．


In 2025, regardless of budget constraints, I will advance theoretical investigations of the Levitation Mass Method and publish the findings in academic papers.

また，力センサの動的校正法への道筋を示すことを目的とした，申請中予算（科研費・萌芽）が採択された場合，以下を実施する予定です．「土台が固定された条件」において，歪ゲージ式力センサなどを対象として，「変動する力」(①衝撃力, ②振動力, ③ステップ力) に対して，浮上質量法 (The Levitation Mass Method) を用いて動的校正を実施します．例えば，浮上質量法による①衝撃力応答評価においては，空気軸受で浮上支持した質量を，固定した力センサに対して衝突させ，質量とその加速度（光波干渉計で計測）の積として力センサに作用した衝撃力を計測します．これらをパイロットケースとして，「土台が固定された条件下」における動的校正法確立に向けた提言を行います．次に，土台が単振動する条件下で実験を行い，土台振動の影響を評価する．この結果に基づいて，「土台が加速度運動する条件下」での動的誤差推定の困難性を検証すると共に，その困難性を克服する方法を提言します．

If the currently pending budget application (KAKENHI - Exploratory Research) is approved, the following activities will be conducted with the goal of paving the way for a dynamic calibration method for force sensors: Under “fixed base conditions”, dynamic calibration will be performed on strain gauge-based force sensors and other types of sensors using the Levitation Mass Method (LMM) for "variable forces," including: [a] Impact forces, [b] Vibrational forces, [c] Step forces
 For example, in the evaluation of impact force response using LMM, a mass supported by air bearings will be allowed to collide with a fixed force sensor. The impact force acting on the force sensor will be measured as the product of the mass and its acceleration, determined using an optical interferometer. These experiments will serve as pilot cases for proposing a framework for dynamic calibration methods under “fixed base conditions”.
 Next, experiments will be conducted under conditions where the base undergoes simple harmonic motion to evaluate the effects of base vibration. Based on these results, the challenges of estimating dynamic errors under “accelerating base conditions” will be examined. Additionally, methods to overcome these challenges will be proposed.

浮上質量法について，ここ10年間ほど私は直接的に論文執筆を行っておりませんでした．これからは，これまで得られた知見の実用化を目指します．2025年は，まず，「力センサ動的校正の道筋」などに関する提言的な論文 [6][7] に論理的な深堀を加え，改めて論文投稿を行いたいと考えています．

For the past decade, I have not directly authored papers on the Levitation Mass Method. Moving forward, my focus will shift toward the practical application of the knowledge accumulated thus far. In 2025, I plan to revisit and delve deeper into the logical foundations of proposal-based papers, such as those on “the pathway to dynamic calibration of force sensors” [6][7]. With these enhancements, I aim to submit improved papers for publication.

[6] Y. Fujii, “Toward dynamic force calibration”, Measurement, Vol.42, No.7, pp.1039-1044, 2009.
   https://doi.org/10.1016/j.measurement.2009.03.006
[7] Y. Fujii, “Toward establishing dynamic calibration method for force transducers”, IEEE Trans. Instrum. Meas., Vol.58, No.7, pp.2358-2364, 2009.
   https://ieeexplore.ieee.org/document/4787137/