Research & Development Honda R&D Technical Review Vol.13 No.2 PDF

Research & Development Honda R&D Technical

  1. Ichiban
    Honda Date of issue:Oct 01, 2001

    Introduction of the Honda ASV-2, an Advanced Cruise-assist Highway System Test Vehicle (Passenger car)

    Summary
    The Advanced Safety Vehicle phase 2 (ASV-2) proposed by the Road Transport Bureau, Ministry of Land, Infrastructure and Transport (formerly the Ministry of Transport) includes driver assistance services composed of 7 services or 8 systems that coordinate between the vehicle and the road infrastructure. The authors participated in proving tests that evaluated the basic functions of these driver assistance services. The following results were obtained:
    • With respect to the “validity of road infrastructure functions,” the services were verified to be effective in response to driver assistance conditions.
    • With respect to “driver acceptance,” we had braking driver assistance tests with haptic warning by brake actuation, and it was verified to be effective in reducing driver’s emergency response time.
    By Hideki KASEYAMA、Hiroshi MASHIMO 、Yoshimi FURUKAWA、Nobuyoshi ASANUMA、Tomoyuki FUKUMARU

    Introduction of the Honda ASV-2 Experimental Vehicle with a Road-vehicle Communication System (Motorcycles)
    Summary
    Joint proving tests of the Advanced Safety Vehicle (ASV) and Advanced Cruise-assist Highway Systems (AHS) were conducted by the Ministry of Land, Infrastructure and Transport (formerly the Ministry of Transport) for Smart Cruise systems. Thirteen domestic vehicle manufacturers participated in the tests on a proving test course set up at the National Institute for Land and Infrastructure Management of the Ministry of Land, Infrastructure and Transport. Seven services and eight test systems were tested. The objective of these systems is to receive information from the road infrastructure via Dedicated Short Range Communication (DSRC) concerning, for example, obstacles in the road ahead and the presence of oncoming vehicles; then, the systems provide warnings and information to motorcycle riders in order to reduce the occurrence of collisions. Honda provided a scooter, with an engine capacity of 250 cm3, loaded with a road-vehicle communication receiver to receive the road information from the Dedicated Short Range Communication system, an information control ECU, and a newly developed Human Machine Interface (HMI) for motorcycles. The tests were conducted to confirm the effectiveness of the road-vehicle communication system from the viewpoint of driver acceptance.
    The proving tests yielded the following findings:
    (1) Information provided from the road infrastructure via DSRC for the purpose of enhancing active safety was confirmed to also be effective for motorcycles.
    (2) An HMI system that combined sound information with visual information was confirmed to be capable of providing information appropriately for each driving assistance service.
    By Kazumitsu KUSHIDA、Kiyotaka SAKAI、Kazuhiro YAMAMOTO、Norihiro KURATA

    Introduction of the Gold Wing GL 1800
    Summary
    The Gold Wing GL 1800 was developed focusing on compatibility with the needs of riders and passengers. As a result, Honda succeeded in revolutionizing the luxury-touring category for motorcycles by combining the superior characteristics of long touring motorcycles with those of the sports type. This was made possible by making the engine more compact and moving it forward. In spite of heightened performance through increasing the engine displacement by 312 cm3, the GL 1800 achieved both reduced weight and improvement of fuel economy. Through adopting numerous new technologies the GL 1800 was able to achieve superior environmental protection in exhaust emissions and was the first U.S.A. production model to apply an aluminum alloy frame.
    By Tetsuya TOSAKA、Koji KANO、Masanori AOKI、Hiroshi ISHIHARA、Hidemi MINAMI

    Development of a Small Tiller: The New Komame F220
    Summary
    The small tiller “Komame” has been used for various agricultural tasks ranging from cultivation of small vegetable gardens to more serious vegetable growing processes for the last 20 years. This tiller has gone through a full model change this year to become the “New Komame F220.” The New Komame’s engine now has a rounded full cover that helps even novice users feel at ease. Reduced emissions from its OHV engine and 5.5dB (A) less noise (obtained by utilizing a resin cam and larger muffler capacity) enable the “New Komame F220” to meet the requirements of both the CARB and EPA emission regulations as well as the EU Noise Directive. The machine weighs 9% less due to the smaller engine and resin parts. Changes to the tilling blades by simulation analysis have provided simple handling together with ample performance. The force required for the recoil starter has been cut by 30% through decreasing engine displacement. The force required to operate the clutch lever has also been reduced by 20% through the use of a different shoe clutch lining material. The new easier to use F220 delivers useful functions and high performance.
    By Masatoshi NAGAOKA、Hideaki KOBAYASHI、Tatsuya TOKUDA、Nobuchika KATAGIRI

    Development of the Lightweight, Compact Sine Wave Inverter-Equipped EU16i Generator
    Summary
    The EU16i sine wave inverter-equipped generator was developed as the most lightweight and compact generator in the 1.6 kVA-rated output class. This generator has both superior portability and output capable of powering household appliances with their large power consumption. It also provides a low noise level, low fuel consumption, low exhaust emissions, and high-quality electrical performance with low waveform distortion and frequency variation. The efficient and lightweight high-speed multi-pole alternator and sine wave inverter system enables the engine to achieve higher speeds with a smaller displacement. With a frame that is fully covered with lightweight resin, this generator achieves a weight approximately one-half that of conventional generators. It also employs an electronic governor with automatic load-dependent speed control, together with an efficient generating system and a two-tiered noise dampening system. These allow this generator to achieve a reduction in noise level of 6 - 8 dB (A) over the practical load range and an improvement in fuel consumption of 20 - 40% compared to conventional generators. The EU16i generator meets the requirements of the EU Noise Directive, Stage II, as well as the CARB Tier II/EPA Phase II exhaust emission regulations. The EU16i is marketed worldwide though it is only marketed as the EU16i domestically. It is sold in North America as the EU2000i and as the EU20i when exported to other regions.
    By Tadafumi HIROSE、Toshifumi KOUCHI、Yukio SUGIMOTO、Motohiro SHIMIZU

    Development of a 1.3L 2-Plug Engine for the 2002 Model ‘Fit\Jazz’
    Summary
    A lightweight and compact, 1.3L 4-cylinder engine was developed as the new-generation i-Series power train. This engine has twin plugs for each cylinder, and achieves rapid combustion by means of high-precision dual-point sequential ignition control that responds to the engine’s operating conditions. In addition, reducing friction and using the newly developed CVT have yielded the low fuel consumption of 23 km/L in the Japanese 10-15 mode. The engine has achieved ‘J-LEV’ certification by reducing exhaust emissions to 50% of the fiscal year 2000 emissions standards.
    By Youichi IWATA、Junji YAMANO、Yukio NAKAYAMA、Makoto SUZUKI

    Application of Stereolithography Apparatus to the Investment Casting of Prototype Parts
    Summary
    Concerning investment casting, “decreased cost,” “reduced lead time” and “quick response to design changes,” are often required in the early stages of a project. Thus, stereolithography apparatus (SLA), a typical rapid prototyping technique, has been applied to the master pattern of investment casting prototype parts for our gas turbine engine. Accompanying this new application were problems peculiar to SLA, for example, adhesion of carbonized resin to the surface of the ceramic mold and SLA layer marks. The adhesion problem has been overcome by optimization of the burning conditions and the problem with the layer marks has been overcome with an improved surface finishing method. As a result, prototype parts, which satisfied the design dimension and configuration requirements, could be produced. At the same time, the cost and lead-time were reduced to 1/15 and 1/8, respectively, of those for the conventional method.
    By Sachio KAJIURA、Sadafumi YOSHINO

    Adaptive Sliding Mode Control for Secondary O2 Feedback (Third Report) —Improvement of Adaptability by Using Prediction and Identification Sliding Mode Control—
    Summary
    Secondary O2 feedback is one effective method for reducing vehicle emissions, and the improvement of this performance yields even greater emissions reductions. This report details a significant advance in the algorithm for the sliding mode controls that were described in our first and second reports, and the application of this newly designed algorithm to secondary O2 feedback. The results show that feedback control performance was significantly improved under all engine loads and catalyst aging conditions. Moreover, the FTP mode emissions were reduced by 32 - 42%, and the emissions stability with respect to catalyst aging conditions was dramatically improved.
    By Yuji YASUI、Yoshihisa IWAKI、Shusuke AKAZAKI、Hiroshi KITAGAWA

    Development of a Magnetic Coupling Type Water Pump for 4-Stroke 50 cm3 Scooter Engines
    Summary
    In the development of a magnetic coupling type water pump, the coupling pull-out phenomena, which leads to the impeller stopping, has been a concern. As a result of analysis of magnetic coupling behavior, two-types of pull-out were determined: pull-out due to insufficient transmission torque of the magnetic coupling in the high speed rotation range; and, pull-out due to the resonance of the inner and outer magnets. Major factors causing pull-out are the angular velocity input to the drive side, the inertia moment of the driven side, magnetic coupling characteristics, and the damping effect of coolant. Using the results of actual testing and a behavior simulation of a water pump, design specifications for a magnetic coupling were set within conditions that did not allow pull-out to occur. Consequently, the reliability of drive power transmission was assured. As a result, it was possible to decrease the size and weight of the water pump, and, at the same time, decrease engine friction.
    By Tadashi NIINO、Osamu SATOU、Yutaka MIYAKE、Masatoshi FUKAMACHI、Shin NABEYA

    Development of a 4WD System for SUVs
    Summary
    Surveys of sports utility vehicle (SUV) use in the United States, where they are extremely popular, show that they are mostly driven on streets in urban areas. However, most SUVs are based on a truck chassis, and performance under adverse conditions is regarded as more important than on-road controllability and efficiency. Therefore, this system was created using an FF passenger car chassis with functions integrated in the rear final drive unit, clutch units installed on the axle for the left and right rear wheels, electronically controlled torque control, torque limit control, and so on. The result combines the rough road performance required for an SUV with the controllability of a passenger car, and achieves these goals in a system weighing only 97 kg, making it the lightest in its class.
    By Takeshi HORI、Koji KURODA、Yoshikazu KONISHI、Kazunori KOBAYASHI、Kenzo NISHIDA、Kazuhiro NAKANO

    Enhancements in Handling on Slippery Roads with VSA

    Summary
    The performance of Vehicle Stability Assist VSA was tested for reproducibility under various conditions encountered on slippery roads. The results showed that VSA enhances stability and steerability, that driver fatigue was reduced, and collision avoidance performance was enhanced. This thus demonstrated the effectiveness of VSA.
    By Keiyu KIN、Tohru IKEDA、Osamu YANO

    Changes in Drivers’ Heart Rates due to the Influence of Braking
    Summary
    This project focused on changes in drivers’ heart rates while braking, as an approach to understanding driving behavior. Using tests designed to model a variety of braking conditions, it was observed that driver psychological states while braking are displayed in the form of changes in heart rate. In a test where an obstacle darts out from the side of the road, driver heart rates were observed to increase suddenly. On the other hand, a test where the vehicle comes to a halt at a stop line showed the heart rate gradually slowing before the vehicle stopped. It was thus inferred that changes in heart rate take on a distinctive pattern in response to braking behavior. In this light, an index formula was proposed that uses the magnitude of the response in heart rate acceleration during braking to determine whether an instance of braking behavior represented panic braking.
    By Koji TANIDA

    Effects of Steering Torque Control Using a Driving Diagram
    Summary
    This paper proposes a driving diagram, sets out a new steering torque control method derived from the diagram, and explains the effectiveness of this method. The driving diagram uses the actual steering angle δ of the front road wheels and the difference between the front tire slip angle and the rear tire slip angle βfr to express the vehicle behavior resulting from driver operation. The new steering torque control applies steering reaction torque to the driver in order to elicit the actual steering angle of the front road wheel that will bring about the most stable state of the vehicle. In this way, when the vehicle enters a spinning state, the driver can know the direction in which to steer in order to help stabilize the vehicle.
    Along with a discussion of the effectiveness of this driving diagram, the paper also provides the results of driving tests conducted using a vehicle equipped with Electric Power Steering (EPS) with steering torque control. These tests confirmed the effectiveness of this method for the vehicle in both under-steer and over-steer states.
    By Shigeru YAMAWAKI、Yasuo SHIMIZU

    Development of a Real-time Analytical System for Motor Performance Measurement
    Summary
    A method was devised for utilizing vector analysis to quantify inductance during switching, which is a major factor affecting such motor performances as maximum power and efficiency, and the appropriateness of this method was confirmed. The application of this method makes it possible to measure actual motor inductance during switching and to observe the magnetic saturation of the motor. By systematizing this analysis method, and representing measured values as a circle diagram, it is possible to evaluate motor operating conditions in real-time. This makes it possible for optimum motor control parameters, which are conventionally determined by analysis after testing, to be established during testing. This system reduces the overall manpower used in motor testing and data analysis by 30%. By incorporating the motor inductance value that is calculated with this method into the motor’s digital control flow, the torque response is enhanced.
    By Makoto KISHIDA、Hirofumi ATARASHI、Kiyoshi ASAMI、Yoshinari MURAYAMA

    Development of a Finite Element Model for the Pedestrian Lower Limb – Development and Validation of Bone Models –
    Summary
    A finite element model for a human lower limb in a standing position has been developed that connects long bone models of a lower limb at the knee with ligament models. The knee joint model incorporates both the articular cartilage and the meniscus, which are deemed to be important elements in the accurate prediction of ligament loading. The model has been validated against published lateral lower limb impact tests, and the results showed that the model can accurately reproduce the shearing displacement and bending angle of the knee joint. In addition, comparison of the model with test data on damage to four main knee ligaments showed that the model was able to simulate the ligamentous damage that had been observed in more than half of the test cases.
    By Yuji KIKUCHI、Yukou TAKAHASHI、Atsuhiro KONOSU、Hirotoshi ISHIKAWA

    Development of a Finite Element Model for the Pedestrian Lower Limb – Development and Validation of a Knee Joint Model –

    Summary
    A finite element model for a human lower limb in a standing position has been developed that connects long bone models of a lower limb at the knee with ligament models. The knee joint model incorporates both the articular cartilage and the meniscus, which are deemed to be important elements in the accurate prediction of ligament loading. The model has been validated against published lateral lower limb impact tests, and the results showed that the model can accurately reproduce the shearing displacement and bending angle of the knee joint. In addition, comparison of the model with test data on damage to four main knee ligaments showed that the model was able to simulate the ligamentous damage that had been observed in more than half of the test cases.
    Reference
    B yYuji KIKUCHI、Yukou TAKAHASHI、Atsuhiro KONOSU、Hirotoshi ISHIKAWA

    Development of a Finite Element Model for the Pedestrian Lower Limb – Model validation for car-pedestrian impact –
    Summary
    A finite element model for a human lower limb in a standing position has been validated against published experiments simulating impact between a pedestrian lower limb and a car front. The results showed that the model can reproduce the peak linear acceleration during the impact at both the impact level and the knee joint. The comparison of injuries to leg bones and knee ligaments between the experiment and the computer simulation showed that the model can predict different injury patterns observed under different impact conditions. Further, in addition to reproducing the response of the lower limb, the upper half of the human body was modeled with rigid segments connected by joint elements in order to simulate the kinematics of the upper body. The neck model has been validated against published experiments that used human volunteers. While validating the full body model against published full-scale car-pedestrian impact tests, it was found that the full body model can simulate both injuries to the lower limbs and the kinematics of the human body.
    By Yuji KIKUCHI、Yukou TAKAHASHI、Atsuhiro KONOSU、Hirotoshi ISHIKAWA

    Research on Aluminum Structures for Crash Energy Absorption

    Summary
    This research describes aluminum crash boxes for the purpose of absorbing crash energy. In this research, the load conditions of the boxes were calculated and the mechanisms of energy absorption were analyzed by experiment. This analysis achieved a crash box with a highly effective section shape. The research also achieved the additional goal of increasing the accuracy of crash simulation for evaluation of energy absorption by this crash box.
    By Yuta URUSHIYAMA、Toru KAWANO、Takayuki YAMADA、Shunji SUZUKI

    Research into the Reduction of Stick-Slip Noise in Exhaust System Joints

    Summary
    Ball joints, one type of joint applied as an automobile exhaust system joint, will often generate an abnormal noise upon oscillation. The noise generating mechanism of this phenomenon is explained using element analysis and friction characteristic analysis of the materials making up the surfaces of the joints. It was found that the roundness of the flare flange of ball joints which generate noise is imprecise. This causes the flange to come in partial contact with the spherical gasket eventually resulting in abnormal wear of the guard net in the gasket. The particles resulting from this wear accumulate on the gasket surface, where the stick-slip phenomenon then causes the noise. A study was also conducted to determine input frequency for oscillation angle and temperature of the ball joint during the use of an actual vehicle. The fabrication of a simple excitation device that could apply those input conditions made it possible to conduct a bench evaluation of the noise. This bench test method was used to conduct parameter studies of design variables that significantly affect the generation of the noise. The bench test was also used to determine the range of settings for set spring load and the flare roundness wherein the noise will not be generated.
    By Masashi IWAI、Takeshi FURUKIDO、Etsuo TAKAKU、Masanobu MIKI、Mototaka MAEDA、Yasunori MURAKAMI

    A New Analysis Approach for Motorcycle Brake Squeal Noise and Its Adaptation

    Summary
    Concerning the potential for low frequency brake squeal noises from motorcycles, the issue of the noise caused by the structural instability of the system was addressed with mode-coupling mechanism analysis utilizing complex eigenvalue analysis. The equation of motion of the brake system was simplified by converting it from the physical domain to the modal domain. The parameters required for the stability analysis were obtained from the normal mode solution of the system model. Moreover, it was possible to decrease the time required for repeat calculations with different friction coefficients and to complete instability-cause analysis in a mode by 70% or more by using a numerical-analysis solver. A highly accurate analysis model was established and applied in the new approach to specify the modes affecting squeal noises and to study countermeasures. From the test results for the subsequently modified brake system, it was verified that the new method is effective for quickly predicting and making countermeasures for brake squeal noises in the design stage.
    By Masashi KAJITA、Kiyoshi KOBAYASHI、Hiroyuki NAKATA

    Connector Modeling in Vibration Prediction for Motorcycles

    Summary
    Conventionally, when predicting motorcycle vibration using the data from drawings, connector characteristics for the components were uncertain. Therefore, using test pieces, we tested bolt fastening connector characteristics in order to investigate a potential analysis method. Further, a detailed FEM model was created, and the contact domain of connectors was calculated using the nonlinear-GAP static analysis of MSC/NASTRAN. Normal mode analysis was performed by converting the domain into a high rigidity spring element, and it was verified that the resonance frequencies for each mode were generally the same. By applying this method to an actual motorcycle and by also applying NASTRAN’s RESVEC calculation to connectors of a component, the FEM model was improved.
    By Hiroyuki KUWAHARA、Youji FUKUI

    Constructing n-sided G1 Patches with the Energy Integral Minimization
    Summary
    A technique to create n-sided patches from n closed boundary curves with G1 continuity to the bounding surfaces has been developed. By using the data points on the boundary curves and the normal vectors of the bounding surfaces as the constraints, least squares patches are constructed with G1 continuity based on squares error minimization. Furthermore, the energy integral of the B-spline basis functions is calculated and the least squares patches are smoothed with energy integral minimization. Two coefficients,  (stretching term) and  (bending term), are introduced as the elements used to adjust the smoothing. Consequently, the quality of the n-sided patches is improved. By using this technique the quality of the n-sided patches required for high quality styling design is improved and the time used to keep G1 continuity to the bounding surfaces is reduced.
    By Hongjun XIE、Kentaro MATSUMOTO

    Establishment of a Method for Predicting Powertrain Vibration at Engine Mounting Points under Running Conditions

    Summary
    It is well known that powertrain vibration characteristics are a critical factor influencing booming and other cabin noises. As vibration at the engine mounting points is one of the most influential of all the vibrations a precise analytical method for the prediction of vibration at the engine mounting points under running conditions was developed. This method uses simulation models that take into consideration the nonlinear characteristics of both main bearing’s oil film and the engine mounts. This makes it possible to predict the vibration level at engine mounting points while preserving a practical level of accuracy. Application of this design method during the initial stages of basic powerplant structural investigations for powertrain design will enable the efficient evaluation of powertrain vibration characteristics.
    By Naoki KAMIMURA、Yasuhiko SEKI、Yukitaka TAKAHASHI、Toshifumi SUZUKI

    Development of a Virtual Road Simulator for Motorcycles
    Summary
    Virtual road simulator technology for motorcycles was established as a method to help predict motorcycle fatigue strength due to loading during running. This technology helped enable the prediction of dynamic behaviors and stresses during the road simulator durability test. The technology consists of the Finite Element Method, Multi Body Simulation, Road Simulator control, and fatigue analysis. The study helped enable the reproduction of the behavior of motorcycles using a simplified model of motorcycles and test rigs, including component Finite Element models. As a result, prediction of fatigue life, damage distribution, and stress waveforms of the high-stress regions in a Road Simulator durability test was achieved.
    By Shokichi HARASHIMA、Hideki YAMAGUCHI、Kenji NAKANISHI、Makoto HASEGAWA

    Development of a Procedure for Interior Noise Estimation by Virtual Vehicle Analysis
    Summary
    This paper summarizes the development of a predictive vibro-acoustic full vehicle model of a mid-size sedan and focuses on the engineering analysis procedures used to evaluate the design performance related to engine-induced noise and vibration during the drawing stage of development. The vehicle model is comprised of a mixture of test-based and finite element component models. FRF-based substructuring is used to join these models. The virtual car model is loaded with engine forces resulting from indirect force identification. This force-set includes combustion, inertia, piston slap and crank bearing forces for engine harmonics from the 0.5 to 10th order. Analysis of this model yields predictions of vibration levels for every component and every interface between components, and of interior noise. The objective is to provide the vehicle NVH engineer with the capability to identify major causes for peak noise levels, to set targets and to develop action plans for every component design team. Having such information at any design stage will effectively reduce both the design cycle duration and the number of physical prototypes.
    By Naoki KAMIMURA、Masahiro TERADA、Tatsuhide SAKAI、Shuichi ONO

    Construction of an Acoustic FE Model for the Purpose of Engine Noise Reduction
    Summary
    A study was conducted in the construction of an acoustic finite element model with the velocity of vibration of the trimmed body as a boundary condition. An experimental model using velocity as the boundary condition was created by measuring the vibrational acceleration of each panel of a trimmed body by excitation measurement. The trim panel impedance was also set as a boundary condition for the acoustic FE model. It was decided that the setting values for the acoustic FE model, which provides a simple representation of multilayered trim panels, should be made approximately equivalent to actual measurement values. This hybridization of a structural experimental model and an acoustic FE model made it possible to represent the acoustic characteristics of the trimmed body up to 350Hz. It also enabled analysis of methods for efficiently minimizing the vibration level of vehicle body panel parts that contribute significantly to engine noise and for reducing the vibro-acoustic transfer function from the engine mount to passenger ear locations.
    By Nobuaki HASHIMOTO、Tatsuhide SAKAI、Kazufumi KAWABATA

    Establishment of an Aero-Dynamic Simulation System for Motorcycles and Its Application
    Summary
    A numerical simulation system for motorcycles was constructed aiming at predicting aerodynamic-characteristics of the bodies at the early stage of development. In order to shorten the time for constructing a complete model of a motorcycle, which have fairly complicated shapes, and to generate meshes on the model as quickly as possible, an orthogonal mesh with porosity for each cell was adopted. An evaluation of this system regarding accuracy and time needed for analysis was carried out by applying the system to some motorcycles actually under development. As a result, we found that a sufficient level of accuracy was obtained in predicting aero resistance forces and wind protection performances.
    By Mutsumi IWASA、Hiroyuki AOKI、Takefumi OKUBO、Takashi WATANABE

    A Method for Evaluation of Low-frequency Noise and Vibration in Powertrain Mount Layouts using Degree of Coupling and Physical Matrices
    Summary
    Ride comfort and idling performance are conflicting low-frequency noise and vibration issues in vehicle development. A convenient index for evaluation of these two phenomena at the design stage was formulated by defining the degree of coupling in a simple numerical expression representing the characteristic matrix based on a physical coordinate system. The degree of coupling was used for performance evaluations of idling and ride comfort in CAE impulse forced response simulation and in an actual vehicle, with good correlation. It was ascertained that this method could be used effectively as a design tool for performance evaluations of powertrain mount layouts in designing total vehicle performance.
    By Masafumi KYUSE、Tatsuhide SAKAI、Satoshi WATANABE

    Strength Evaluation Method for Nd-Fe-B Rare Earth Sintered Magnets
    Summary
    Application of the Weibull theory to an Nd-Fe-B rare earth sintered magnet was studied for use in evaluating the specific strength characteristics arising from the structure of this magnet. The validity of the Weibull theory was verified by the correlation with the Weibull distribution and by the existence of the size effect, whereby strength decreases with increases in size. The correlation with the Weibull distribution was verified by the close correlation shown by the resistance strength Weibull plot approximation line. While the existence of the size effect was verified due to the existence of the fixed relationship between effective volume, determined by the stress distribution, and fracture stress. Consequently, it was judged that the Weibull theory is valid for evaluation of the strength of this magnet. The strength of the magnet when incorporated into the rotor of a motor was also verified, thereby demonstrating the applicability of this theory to this type of magnet.
    By Teruyoshi KITA、Takaaki NAGI

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