Optical Method for Micro Force Measurement Yusaku FUJII Gunma University
Small Force (1mN to 1N ) It is difficult to generate and evaluate small force, properly. The causes of the Difficulties in measuring small force: (1) No National Measurement Institute supports a direct force realization linked to the International System of Units (SI) below 1 N even for static force. (2) Small force to be generated and/or measured is usually a varying force and any dynamic calibration technique for force sensors has not established. In other words, this fact means that the uncertainty evaluations both for the measured value of the small force and for the time of the measurement are very difficult.
Force Calibration? For generating a force based on its definition, F = M a, The following is required: (1) Acceleration must be well defined. (2) Other external must be negligible.
Static Force Calibration M Mg Reference Force = Gravitational Force
Present Problems There is not any dynamic calibration method for force transducers. The following two major problems arise when varying force is measured using a force transducer. 1 st problem: It is impossible to determine the uncertainty of measured value of the varying force properly. 2 nd problem: It is impossible to determine the distortion of the time axis. The proposed method is free from these problems.
The Levitated-Mass Method Force: F F = M a Rigid object (Mass: M) Optical Interferometer Gravity: M g Small friction
Photograph of the Mechanical Parts Material under test A piece of paper, 7.5 mm in width, 29.0 mm in length Bearing Holder Compressed air piping Moving part (M=21.17 g) CC
Setup for Micro Force Material Test v = λ air (f Doppler )/2 f Doppler = - ( f beat - f rest ) In the experiment, 1 set of collision measurement with 3 collisions is conducted.
Data processing procedure: Calculation of velocity, position, acceleration, force from frequency In the figure, only the 1 st collision out of 3 collisions is shown. During the experiment, only the beat frequency, f beat, and the rest frequency, f rest, are measured. The Doppler shit frequency is measured as the difference between the beat frequency and the rest frequency. Velocity, position, acceleration, force are calculated from frequency afterward.
Measured force against The force acting on the material from the mass is expressed as F according to the law of action and reaction. The moving part moves back and forth between the material under test and the left-hand side-face of the bearing holder. The steep negative peaks represent its collision to the bearing holder. The maximum values of the impact force in the 1st, 2nd and 3rd collision are 1.80 mn, 0.89 mn and 0.23 mn, respectively. The force has some values even during the free sliding motion of the moving part, x > 0. The variation of force during the free sliding motion is thought to mainly come from the dynamic frictional force acting inside the bearing. The component of the gravitational force acting on the moving part of approximately 0.02 mn due to the uncertainty of approximately 0.1 mrad in adjusting the tilting stage to the horizontal might exist.
Measured velocity against position During the free motion of the moving part, the effect of the dynamic frictional force acting on the moving part during the free travel is clearly observed.
Measured force against velocity The lead of the force against velocity, which is caused by the viscosity of the material, is observed. F= 1.798 mn at v= 0.0019ms -1
Measured force against velocity The spring constant is almost constant during the experiment with 3 collisions. The elastic hysteresis, which is caused by the viscosity of the material, is clearly observed. The work done by the moving part is expressed as the integral along the trajectory of motion. The work, W, for the 1 st, 2 nd and 3 rd collision measurements, is calculated to be approximately 0.815 µj, 0.257 µj and 0.023 µj, respectively. The energy dissipation ratio,, for the 1 st, 2 nd and 3 rd collision measurements, is approximately 0.22 (22%), 0.23 (23%) and 0.25 (25%), respectively.
Resolution The resolution of the frequency measurement is 1 Hz and the sampling interval is approximately 14 ms. It corresponds to the resolution of the force measured in the experiment of approximately 0.5 µn. Uncertainty Resolution and Uncertainty At this moment, the uncertainty evaluation of the measured force has not been done. For this, the frictional characteristics of the air bearing are required. To determine them, the method developed for evaluating the frictional characteristics of the larger size air bearing with the moving part of approximately 2 kg can be used.
Advantages Discussions In the proposed method, only the frequency is measured during the oscillation experiment, and all the other quantities, such as velocity, position, acceleration and force, are numerically calculated afterward. The simplicity is the most significant advantage of the proposed method compared with other conventional methods using a force transducer and a position sensor. The set up procedure for a new test is very easy in the proposed method. For Dynamic & Static Micro-Force Calibration The proposed method can be applied to the dynamic calibration of force transducers with very small capacity and the dynamic material tests with very small load. For Material Test using Micro-Force Any object, such as a force transducer, a viscoelastic material or a specimen with complicated structure, can be attached to the base using an appropriate adhesive material or a mechanical holder.
Conclusions A method for generating and measuring the micro- Newton level forces is proposed. The mechanical characteristics of a piece of paper is measured highly accurately using the method. The method will be useful for (1) Material Test using Micro-Force (2) Static & Dynamic Micro-Force Calibration of Force Transducers
Applications Measurement of Arm used in Hard-disk disk Drive Object under test Arm used in a HDD Holder part of the bearing Moving part of the bearing
Applications Measurement of a Hair