Precision Material Tester Using the Levitation Mass Method

Transcription

1 Precision Material Tester Using the Levitation Mass Method Yusaku Fujii, Tao Jin and Akihiro Takita Abstract Method for evaluating dynamic response of material against impact force is proposed. A pneumatic linear bearing is used to levitate a mass for generating impact force. A cube-corner prism (CC) is attached on the mass. Doppler shift frequency of laser light beam reflected by the CC is accurately measured by using a laser interferometer. The velocity, position, acceleration and inertial force of the mass are calculated from the shift frequency. A gel block is used in experiment and its impact response is highly accurately measured by means of the proposed method. Keywords Levitation Mass Method, Impact force, Inertial force, Inertial mass, Optical interferometer. F I. INTRODUCTION ORCE, one of the most basic mechanical quantities, is usually measured using force transducers which are usually calibrated by using static method. In other words, the dynamic force generated by actuators or materials can t be accurately measured by transducers. So far, no standard dynamic calibration method for force transducers has been established. Two major problems are existence: (1) the uncertainty in the measured value of the varying force is difficult to estimate. (2) the uncertainty in the time at which the measured varying force is also difficult to evaluate. A method Levitation Mass Method (LMM) has been put forward by the authors for dynamic measurement and calibration. In the LMM, a mass is levitated by a pneumatic linear bearing with sufficiently small friction. The Doppler shift frequency of laser beam measured by using an optical interferometer is used to calculate position, velocity and acceleration of mass. The dynamic force F is calculated as: F= Ma which a is the acceleration. This method has been applied to all the three categories of the dynamic force calibration such as: dynamic calibration method under impact load [1], the dynamic calibration method under oscillation load [2] and the dynamic calibration method under step load [3]. The LMM is also applied to evaluate the viscoelasticity of material under an oscillating load [6] and an impact load [7,8], material friction [9,10], biomechanics [11-12], dynamic performance of a liner motor [13], mass in the International Space Station (ISS) [14-18], dynamic response of an impact hammers [19] and micro-newton level forces [20-23]. The LMM is also used to investigate the frictional characteristics of pneumatic linear bearings [24,25] and the linear ball bearing [26,27,41]. A pendulum mechanism [28] and a frequency measurement technique [29-31] have been developed to improve LMM, and the effect of the inertial mass on dynamic force measurements has been proposed based on LMM [32-34]. The optical interferometer also has been improved [35-37], such us dual beat-frequencies laser Doppler interferometer for removing the velocity limitation [38] and for two-dimensional directional discrimination [39,40]. In this paper, we propose an experiment to test the dynamic response of a gel block against impact force. II. EXPERIMENT SETUP An experimental setup for evaluating the viscoelastic response of materials against impact force is shown in Fig. 1. A pneumatic linear bearing is used to realize linear motion with sufficiently small friction acting on a mass, i.e., the moving part of the bearing. Impact force is generated and applied to the material by collide the mass with base. A cube-corner prism (CC) and some metal block for collision are attached to the moving part; its total mass, M, is approximately kg. The inertial force acting on the mass is accurately measured using an optical interferometer. A gel block as the material for test is attached to the base by its adhesion, and a thin plastic sheet is attached to its other side to prevent the gel block from adhering to the moving part at the time of collision. Fig. 1 Experiment setup. Code: CC=cube corner prism, PBS= polarizing beam splitter, PD=photo dioder. Department of Electronic Engineering, Faculty of Engineering, Gunma University Tenjin-cho, Kiryu, , Japan (fujii@el.gunma-u.ac.jp) 158

2 The force acting on the material from the moving part is equal to its inertial force according to the law of inertia if other forces, such as the frictional force inside the bearing, can be ignored. In this condition, the force acting on the moving part from the material can be identified as: F = M a. The acceleration is calculated from the velocity of the moving part which is measured as Doppler shift frequency of the signal beam of a laser interferometer, f Doppler, which can be expressed as: v = λ air (f Doppler )/2, f Doppler = - ( f beat - f rest ), where λ air is the wavelength of the signal, f beat is the beat frequency, i.e., the frequency difference between the signal beam and the reference beam, f rest is the rest frequency which is the value of f beat when the moving part is at a standstill, and the direction of the coordinate system for the velocity, the acceleration and the force acting on the moving part is towards the right in Fig. 1. A Zeeman-type two-frequency He-Ne laser is used as the light source. The frequency difference between the signal beam and the reference beam, i.e., the beat frequency, f beat, is measured by using a frequency counter (model: R5363; manufactured by Advantest Corp., Japan); it varies around f rest, approximately 2.7 MHz in our experiment, depending on the velocity of movement. This counter continuously measures and records the beat frequency, f beat, times with a sampling interval of T=400/ f beat, and stores the values in memory without dead time. The sampling period of the counter is approximately 0.15 ms at a frequency of 2.8 MHz. Another electric counter (model: TA-1100; manufactured by Yokogawa Electric Corp., Japan) measures the rest frequency, f rest, using the electric signal supplied by a photodiode embedded inside the He-Ne laser. The thickness of pneumatic linear Air-Slide TAAG10A-02 (NTN Co., Ltd., Japan) bearing is approximately 8µm, the stiffness of the air film is more than 70 N/µm, and the straightness of the guideway is better than 0.3µm/100 mm. The frictional characteristics are determined in detail by means of the developed method [9]. The two frequency counters are triggered by means of a sharp trigger signal generated using a digital to analog converter. This signal is initiated by means of a light switch, a combination of a laser-diode and a photodiode. In the experiment, 10 sets of collision measurements are conducted by changing the initial velocity of the moving part of the pneumatic linear bearing, which is manually given to it. Fig. 2 Data processing procedure: Frequency, velocity, acceleration, force and position. III. RESULTS Fig. 2 shows the data processing procedure in our experiment. During the collision experiment the velocity, position, acceleration and inertial force of the mass are calculated from the Doppler shift frequency. Doppler shit frequency is measured as the difference between the beat frequency and the rest frequency. In the experiment, the maximum value of the impact force is approximately N, and the half value width of the impulse is approximately 12 ms. The origin of the timing axis and the origin of the position axis are set to be the time and the position where the reaction force from the material under test is detected, respectively. 159

3 Fig. 3 shows the change in force acting on the mass from the material, F =Ma, against position. The force acting on the material from the mass is expressed as -F according to the law of action and reaction. The inclination of the curve increases according to the increase of the displacement. The elastic hysteresis is caused by the viscosity of the material. The work done by the moving part is expressed as the integration along trajectory of motion, W (= ( F)dx), and is calculated to be approximately J. The absolute value of this work is equal to the area bounded by the curve shown in Fig. 4. This value coincides well with the reduction of the kinetic energy of approximately J calculated using the velocity before and after the collision, v 1 and v 2. The energy dissipation ratio W 1 2 W mv 1 E 1 2 is approximately 0.33 (33%) in our experiment. The lead of force against the position, which is caused by the viscosity of the material, is observed in all the collision measurements. The shape of the curves can be divided into two types, and the change of the types seems to occur around the maximum value of the force of approximately 50 N. Fig. 5 Change in force against velocity. All the 10 measurements IV. UNCERTAINTY EVALUATION Fig. 3 Change in force against position Fig.4 shows the change in force against velocity in all the 10 collision measurements. The lead of force against the velocity is same as shown in Fig. 3, but 10 sets of collision are measured in our experiment. Fig. 4 Change in force against position. All the 10 measurements Fig. 5 shows the change in force against position which is calculated from velocity in all the 10 collision measurements. A. Determination of the inertial force of the moving part 1) Mechanical vibration The root mean square value of the standard deviation of the velocity before and after the collision, σ v_before and σ v_after, are approximately m/s and m/s, respectively. This difference is mainly caused by the mechanical vibration of the optical interferometer. σ v_after is larger than σ v_before, due to the vibration of the optics initiated by the shock of the collision. The vibration of acceleration and force caused by collision are ms -2 and 1.0 N approximately, respectively 2) Electric counter (R5363) The uncertainty of beat frequency is approximately 100Hz from the electric counter R5363 with the sampling interval of 400/f beat. This uncertainty of the beat frequency corresponds to the uncertainty of the velocity of the moving part of approximately m/s. This corresponds to the uncertainty of the acceleration and force of approximately ms -2 and 1.3 N, respectively. 3) Mass The standard uncertainly of electronic scale used to measure the mass of moving part is approximately 0.1 g. According to F=Ma, the relative standard uncertainty in force determination of approximately which can be neglected. 4) Frequency stability The uncertainty of laser beam is 10 Hz. The corresponding uncertainty of velocity and force are approximately m/s and 0.13 N, respectively. B. Determination of the external force The frictional force acting on the inside of pneumatic linear bearing is dominant under the condition that the air film of approximately 8 µm thickness inside the bearing is not broken. 160

4 The frictional characteristics of the air bearing are determined using the developed method [9]. The dynamic frictional force acting on the moving part is calculated to be approximately 0.02 N at a velocity of approximately 0.2 m/s. Therefore, the standard uncertainty of the force acting on the material is estimated to be 1.6 N which is (0.8%) of the maximum applied force in the experiments. V. DISCUSSION In the proposed method, all the quantities, i.e. velocity, position, acceleration and force are numerically calculated from Doppler shift frequency during the oscillation experiment. In addition, force is directly calculated according to its definition F=Ma. This simple method is the most significant compared with other conventional methods by using force transducers and position sensors [3,4]. It s very easy to set an experiment for testing any object such as a viscoelastic material or specimen with complicated structure which can be attached to the base using an appropriate adhesive material or a mechanical holder. Then its dynamic response against impact force is evaluated highly accurately by means of measuring the Doppler shift. Since materials are variable against temperature, therefore a constant temperature box is usefully for precision measurement. In this case, the extension block should be made long and stiff enough such as a ceramics, then, the rest of the apparatus including the pneumatic linear bearing can be placed outside the constant temperature box. VI. CONCLUSIONS A method for evaluating dynamic response of general materials against impact force is proposed. In the method, a mass levitated with sufficiently small friction using a pneumatic linear bearing is made to collide with a material under test. During the collision measurement, only the Doppler shift frequency of the laser light beam reflecting on the mass is measured highly accurately using an optical interferometer. The velocity, the position, the acceleration and the inertial force of the mass are calculated from the frequency afterward. The impact response of the under test material gel block is highly accurately determined by means of the proposed method. The performances of this method are discussed. The uncertainties in our experiment are evaluated. The advantages and future prospects of the proposed method are discussed. ACKNOWLEDGMENT This work is supported in party by a research-aid fund of the Asahi Glass Foundation, a research-aid fund of the NSK Foundation for the Advancement of Mechatronics, and Grant-in-Aid for Scientific Research (B) (KAKENHI ). REFERENCES [1] Y. Fujii, Measurement of steep impulse response of a force transducer, Meas. Sci. Technol., Vol. 14, No.1 pp , [2] Y. 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5 [31] Y. Fujii and J. P. Hessling, A frequency estimation method for use in the Levitation Mass Method, Exp. Techniques, Vol.33, No.5, pp.64-69, [32] Y. Fujii, Method for correcting the effect of the inertial mass on dynamic force measurements, Meas. Sci. Technol., Vol.18, No.5, pp.n13-n20, [33] Y. Fujii and K. Maru, Self-correction method for dynamic measurement error of force sensors, Exp. Techniques, Vol.35, No.3, pp.15-20, [34] K. Maru and Y. Fujii, Wavelength-insensitive laser Doppler velocimeter using beam position shift induced by Mach-Zehnder interferometers, Optics Express, Vol.17, No.20, pp , [35] K. Maru and Y. Fujii, Reduction of chromatic dispersion due to coupling for synchronized-router-based flat-passband filter using multiple-input arrayed waveguide grating, Optics Express, Vol. 17, No. 24, pp , Nov [36] K. Maru and Y. Fujii, Integrated wavelength-insensitive differential laser Doppler velocimeter using planar lightwave circuit, Journal of Lightwave Technology, Vol. 27, No. 22, pp , Nov [37] K. Maru, K. Kobayashi, and Y. Fujii, Multi-point differential laser Doppler velocimeter using arrayed waveguide gratings with small wavelength sensitivity, Optics Express, Vol. 18, No. 1, pp , Jan [38] A. Takita, H. Ebara and Y. Fujii, Dual beat-frequencies laser Doppler interferometer, Rev. Sci. Instrum., Vol.82, pp , [39] K. Maru and Y. Fujii, Laser Doppler velocimetry for two-dimensional directional discrimination by monitoring scattered beams in different directions, IEEE Sens. J., Vol.11, No.2, pp , [40] K. Maru, L. Y. Hu, R. S. Lu, Y. Fujii and P. P. Yupapin, Two-dimensional laser Doppler velocimeter using polarized beams and 90ºphase shift for discrimination of velocity direction, Optik, Vol.122, No.11, pp , [41] Y. Fujii, K. Maru, T. Jin, P.Yupapin and S. Mitatha, A method for evaluating dynamical friction in linear ball bearings, Sensors, Vol. 10, No. 11, pp , Yusaku Fujii was born in Tokyo, japan, in He received the B. E., M.E., and Ph.D. degrees from Tokyo University, Tokyo, Japan, in 1989, 1991 and 2001, respectively. In 1991, he joined Kawasaki Steel Corporation. In 1995, he moved to the National Research Laboratory of Metrology, Tsuskuba, Japan, where he studied the replacement of the kilogram using superconducting magnetic levitation. In 2002, he moved to Gunma University, Kiryu, Japan, where he was invented and studied the levitation mass method as precision force measurement method. 162