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Isaac Skog, Peter Händel
CALIBRATION OF A MEMS INERTIAL MEASUREMENT UNIT

An approach for calibrating a low-cost IMU is studied, requiring no mechanical platform for the accelerometer calibration and only a simple rotating table for the gyro calibration. The proposed calibration methods utilize the fact that ideally the norm of the measured output of the accelerometer and gyro cluster are equal to the magnitude of applied force and rotational velocity, respectively. This fact, together with model of the sensors is used to construct a cost function, which is minimized with respect to the unknown model parameters using Newton’s method. The performance of the calibration algorithm is compared with the Cram´er-Rao bound for the case when a mechanical platform is used to rotate the IMU into different precisely controlled orientations. Simulation results shows that the mean square error of the estimated sensor model parameters reaches the Cram´er-Rao bound within 8 dB, and thus the proposed method may be acceptable for a wide range of low-cost applications.

Gordon A. Shaw, Jon R. Pratt, John A. Kramar
CALIBRATION OF MICROFABRICATED CANTILEVERS FOR SI-TRACEABLE SMALL FORCE MEASUREMENT

A procedure is described by which the spring constant of a microfabricated cantilever beam can be calibrated for the measurement of small forces in an atomic force microscope (AFM) or other device. The procedure utilizes dynamic force instrumented indentation to determine the mechanical properties of the beam by applying a well-characterized oscillating force and measuring resulting displacement of the system. An uncertainty analysis is carried out, and by intercomparison with the U.S. National Institute of Standards and Technology (NIST) Electrostatic Force Balance (EFB). The spring constants determined using the indentation method agree within 2% of the values determined using the EFB for spring constants as low as 2 N/m.

Yusaku Fujii
DYNAMIC CALIBRATION METHODS FOR FORCE TRANSDUCERS

Three Methods for evaluating the dynamic response of force transducers against varying force are described in this paper. In all methods, the inertial force of a mass is used as the known dynamic force, and this reference force is applied to a force transducer under test. The inertial force is measured highly accurately as the product of the mass and the acceleration. An aerostatic linear bearing is used to obtain linear motion with sufficiently small friction acting on the mass (i.e., the moving part of the bearing). Three experimental setups were built for the dynamic calibration against an impact force, an oscillation force and a step force. Ways of establishing dynamic calibration methods are also discussed.

Toshiyuki Hayashi, Yoshihisa Katase, Kazunaga Ueda, Tsuyoshi Hoshino, Hiroshi Suzawa, Masaaki Kobayashi
DEVELOPMENT AND EVALUATION OF TUNING FORK TYPE FORCE TRANSDUCERS

Tuning fork type load cells are expected to have better long-term stability than conventional strain gauge type load cells. A new 50 N rated capacity load cell has been developed herein adopting a Double-Ended Tuning Fork (DETF) sensing unit. The performance of two such load cells was evaluated using the 500 N force standard machine at the National Metrology Institute of Japan (NMIJ). The DETF load cells were found to have low creep, low hysteresis and superior long-term stability.

Zhu Zijian
GREY THEORY BASED ON LOAD CELL FAILURE PREDICTION IN A WEIGHING SYSTEM

The reliability of the weighing system is becoming more and more important these years. This paper deals with a new approach to load cell soft failure prediction by the application of Grey theory. Grey theory is a theory which studies poor information and sets up a math model to simulate and predict a system behavior. Collecting the historical data of zero and sensitivity drift to set up a grey model GM (1.1) and with this model, the system can not only simulate the zero and sensitivity drifts but also calculates their possible value in the near future. Therefore, a previous action could be taken before zero and sensitivity running out of the acceptable range. This method is hoped to be able to improve the reliability of a system and have a potential future in the field of measurement.

Yoshihiro Fujioka, Jianxin Sun, Toshiro Ono
ACCURATE WEIGHING SYSTEM USED UNDER THE VIBRATION-LIKE MOVING CONDITIONS

This paper describes a weighing system used under the conditions in which various movements exist. These various movements are heaving motion, rolling motion, pitching motion, etc. In this paper, these various movements are collectively called as “vibration-like movement”. The term of “vibration-like moving conditions” means the conditions in which vibration-like movements exist. In the previous paper, the new weighing method was proposed. This method basically requires 4 loadcells which observe the vibration-like moving conditions. These loadcells are called as “dummy loadcell”. Installing 3 dummy loadcells properly and estimating two angular velocities, this weighing method is feasible to measure the mass value of a weighed object by means of 3 dummy loadcells. In this paper, the estimating method of these velocities is explained in detail. We manufactured the weighing system which consists of a weighing loadcell and 3 dummy loadcells on trial. Several numerical simulations and experiments by using this weighing system were conducted. It is confirmed that the estimation of the angular velocities is feasible and the accurate weighing under the vibration-like moving conditions is also feasible.

Luis O. Becerra, Eduardo González, Félix Pezet, José Revuelta M, José Revuelta R, Sylvia Maeda
COMPARISON OF METHODS FOR THE WEIGHING TEST IN CALIBRATION OF HIGH CAPACITY NON-AUTOMATIC WEIGHING INSTRUMENTS

This paper presents the results obtained from the comparison of different techniques for the weighing tests for the calibration of high capacity weighing instruments, in order to evaluate their use as a function of the amount of available weights and the required uncertainty of the instrument in their normal use.

Takanori Yamazaki, Akihiro Watanabe, Hideo Ohnishi, Masaaki Kobayashi, Shigeru Kurosu
DEVELOPMENT OF MASS AND LENGTH MEASUREMENT SYSTEM ON CONVEYOR BELT

Our aim is to establish a measurement system that enables highly accurate measuring mass and length of moving products with a relatively high speed on a conveyor belt. In this paper, effectiveness of the proposed measurement system is demonstrated by an analysis of a digital image taken by a digital camera. In our experimental results, it can be found in the following: First, our discrimination method of colors is that there is no need to count the number of pixels for all three primary colors, but the only one component indicated the highest value of graduation should be counted. Second, the length measurements are performed using these six kinds of the reference unit pixels for the products having lengths within a range from 200 to 1200 mm. It is quite obvious that even through any reference lengths used, the required accuracies less than ±5 mm cannot be achieved without calibration method.

Gerhard Schulder, Ulrich Kolwinski, Daniel Schwind
A NEW DESIGN OF A 5,4 MN BUILD-UP SYSTEM

The main purpose of the build-up system is the use in verification measurements of force standard machines up to 5MN or even higher capacity. The special design of the described build-up system allows the use of nine force transfer standards either individually, in groups of three transducers or all transducers together in three groups of three. A 9-channel digital measuring amplifier (GTM VNDigitizer 3.0) enables the user to get the readout of all transducers simultaneously.

Sinan Fank, Rolf Kumme, Bülent Aydemir, Ercan Pelit, Bernd Glöckner, Guenther Haucke
INTERCOMPARISON OF 3 MN HYDRAULIC TYPE BUILD-UP AND 1.1 MN LEVER AMPLIFICATION FORCE STANDARD MACHINE BETWEEN UME AND PTB

The 1.1 MN lever amplification dead weight force standard machine (FSM) and a new 3 MN hydraulic type build up FSM were installed at UME in 1995 and 2002 respectively. Both machines were regularly intercompared to each other and to PTB to maintain the performances. After making a new cooperation contract, a new intercomparison measurment were organised to see the existing performances of the both machines. The measurement results show that relative measurement uncertainty of the machines are better than 1·10-4 for 1.1 MN machine and better than 4·10-4 for 3 MN build-up machine of UME.

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