A high capacitance battery such as a lithium-ion battery is fabricated by interlaminating electrodes and separators. Since the strength of the separator is relatively low, many situations exist where damage in the separator sheet induces an initiation of short circuit or air gap between the electrodes. In order to prevent serious incidents by such short circuits and air gaps, it is important to evaluate the electrical contact state of the electrodes through the estimation of the current density between the electrodes. This study has developed a novel estimation method of the current density between the electrodes by the inverse analysis of the magnetic field around the battery, and established the methodology to find the limitation of the proposed method against the noisy magnetic field. In order to numerically investigate the basic behavior and the estimation error of the proposed method, a numerical simulation has been performed by using a single cell model consists of two electrodes and one separator. The correct distribution of the current density between the electrodes was given in advance, and the direct analysis was applied to obtain the simulation data of the magnetic flux density. Then the inverse analysis was applied to the simulation data with artificial disturbances. From the results of the numerical simulation, the followings were summarized: 1) It is confirmed that the possibility of the successful estimation depended on the standard deviation of the artificial disturbance. 2) The reference solution in the inverse analysis affected the selection of the regularization parameter and the estimation error against the standard deviation of the artificial disturbance. 3) The proposed method achieved the successful estimation with 90% probability if the disturbance in the magnetic flux density is less than the 30% as far as this numerical simulation.
Carbon-neutral and biodegradable materials such as wood and poly-L-lactic acid play an important role in reducing environmental loads. Therefore, this study theoretically analyzed the thermoelectroelastic problem for a solid cylinder with D∞ symmetry subjected to a distributed torsional shear stress as a mechanical input and to a nonuniform temperature distribution as a thermal disturbance, in order to gain an elementary understanding of the thermal effects on the electroelastic field in cylindrical bodies with D∞ symmetry. The displacement components are expressed in terms of the elastic displacement potential function, the piezoelastic displacement potential function, and the thermoelastic displacement potential functions, and the electric field components are expressed in terms of the electric potential function. Subsequent to presenting the fundamental equations for thermoelectroelasticity, the governing equations for the above potential functions are derived based on the above fundamental equations. These governing equations are solved by a Fourier transform technique, and the theoretical solutions of the thermoelectroelastic field quantities are obtained. Furthermore, by performing numerical calculations, the distributions of the field quantities are illustrated graphically, and the structures of the thermoelectroelastic field are discussed qualitatively and quantitatively. Moreover, by quantitatively evaluating the ratio of the thermally disturbed electric displacement to the undisturbed electric displacement reflecting the mechanical input, the necessity of the thermoelectroelastic analyses, as treated in this paper, is clearly demonstrated.
Prognosis of fatigue crack growth for mechanical and structural components is vital for aging military aircraft operated near or beyond their original design lives. For modern aircraft, prognostics and health management is supposed to be a designed-in capability; however, prognosis of mechanical and structural damage is yet to fully mature. This paper presents a scheme adopting Bayesian probabilistic modelling, extended Kalman filter (EKF) in particular, to predict fatigue crack growth in a common aircraft structural material: 2024-T3 aluminum alloy. In this scheme, the state model is the widely adopted Paris law in fracture mechanics (used to model the physics of crack growth), and the measurement model is a simple random walk model. The scheme is validated using a set of published crack growth test data, often referred to as the Virkler data, where the state model parameters are derived from one half of the data and the crack length prediction is made on the other half of the data. The EKF framework is further validated using a set of gear tooth crack propagation test data, where the crack length is the unobservable (or hidden) state variable, and the observable variable is a feature extracted from the gear vibration signal. The state model is also derived from the Paris law and the measurement model is developed using the observed relationship between the known crack length, the applied stress, and the energy of the impulsive signature extracted from an optimized sinusoidal model for gear vibration signals. Using the recursive EKF solution, we are able to achieve promising prognostic results in terms of the accuracy of the prediction, and demonstrate the method’s robustness in dealing with uncertainties in the parameters defining the Paris law and the uncertainties in the measurements. Compared to other studies, the proposed method is a much simpler and more robust approach to the prognosis of fatigue crack size in mechanical structures and rotating components.
The surface texture describes the surface topography formed by micro asperities on a surface of a solid member. The Hertz-Mindlin theory is one of contact theories based on the mechanics of elasticity. The main parameters for the theory are the number of the asperity peaks per unit area, the radius of the curvature at the asperity peak and the standard deviation of the asperity peak heights. These parameters are collectively named as the surface texture parameters. Most of the conventional approaches to obtain these parameters are curve fittings applied on the surface texture. However, the 3D measurement with a spatial resolution of a micron is required in the measurement of the surface texture, and the measurable area is limited. This study has developed a novel method to estimate the surface texture parameters by the inverse analysis of the dynamic characteristics of the target. In the proposed method, the natural frequency of the target is obtained by the hammering test and the finite element analysis with the interfacial element based on the Hertz-Mindlin theory. Then the set of the surface texture parameters minimizing the residual between the test result and the analysis result is derived. In order to verify the proposed method, a series of hammering tests was carried out by using specimens with bolted joints. Using the test results, the surface texture parameters were estimated by the proposed method. From the estimation results, it confirmed that the calculation results of the natural frequency in the inverse analysis had good agreement with the results of the hammering test. The estimation accuracy of the proposed method was comparable to that of the 3D surface texture measurement in terms of fitting the quadratic surfaces.
Recently, the replacement of chemical resources with natural resources has been strongly desired for the recovery of ecosystems. Considering this, we have been focusing on bamboo fibers as a structural member of vehicles. Because bamboo can be returned to the soil after its use, its environmental impact is much lower than that of recyclable metals and plastics. If the industrial application of bamboo is expanded and the regeneration of bamboo forests is accordingly promoted, its environmental impact can be reduced. In previous studies, we developed a bamboo-fiber-reinforced laminated plate (BFRLP) with improved specific rigidity and specific strength by arbitrarily arranging and laminating bamboo fibers. Using the BFRLPs as a structural material, we also developed an ultra-small one-person electric tricycle called the personal green mobility (PGM) tricycle to help the elderly travel and go shopping in limited areas. A carry-bag-type design was adopted to realize a lightweight PGM tricycle with a simple structure. And, we also developed a new material by joining reinforced corrugated fiberboard (RCF) and BFRLPs and called it a green composite hybrid material (GCHM). The structural members of the new lightweight PGM tricycle are made of bamboo, vegetable fiber materials, and RCF. It can be assembled and repaired at home by the elderly and is capable of traveling at an ultralow speed using six AA-size rechargeable batteries. As a national policy, towns where the elderly can lead a pleasant life should be built. The biodegradable PGM tricycle using vegetable fiber materials is proposed as a new alternative in a society based on the vehicle.
The influence of specimen twisting on Young's modulus of thermal barrier coatings (TBCs) was studied using four-point bending tests based on ISO 19477 and three-dimensional finite element analysis (3D FEM). Twisted substrate specimens were four-point bent using a jig with or without pin rotation to investigate the influence of pin contact conditions. The Young's modulus was calculated by strain gauge and maximum-displacement methods. The results showed that load-strain and load-maximum displacement curves of the twisted substrate specimens showed linear relationships for fixed and rotating pin conditions. The decrease in the Young's modulus with increasing twisting angle was not observed for the strain gauge method but was for the maximum-displacement method. However, the maximum decrease of around 5% for the maximum-displacement method was improved by pin rotation. 3D FEM results showed that the Young's modulus obtained by the FEM quantitatively agreed well with the experimental value. Analyzed strain distribution clarified the insensitivity to specimen twisting for the strain gauge method because of the small difference in the strain at the center of the specimen where the strain gauge was attached. The decrease in the Young's modulus of the twisted specimen for the maximum-displacement method corresponded to the inhomogeneous curvature distribution of the specimen. The influence of the specimen twisting of TBCs on Young's modulus was evaluated by 3D FEM. The same tendency as that for the substrate specimen was observed, but the amount of decrease became large. A decrease around 5 times larger than that for the substrate specimen was observed with a twisting angle of 0.058 by the maximum-displacement method under fixed pin conditions. However, the decrease was improved by pin rotation. The analysis result showed that the strain gauge method had sufficient accuracy to evaluate the Young's modulus of twisted TBC specimens up to a twisting angle of 0.058.
Self-healing fiber-reinforced ceramic (shFRC) is a new functional material. When a microcrack propagates in this material, self-healing occurs owing to high-temperature oxidation. Then, the strength of the material recovers to its robust state since the microcrack is rebounded. However, to effectively demonstrate the self-healing function, a crack bifurcation, i.e., penetration/deflection, must be controlled. Therefore, the optimal composite design, in which the microcrack is induced in the interface along the fiber, is a key factor in developing shFRC. In this study, we investigate crack propagation using Finite Element Analysis (FEA). In FEA, the two-dimensional microscopic structure of shFRC with a three-layer construction is discretized. The three layers of construction are the matrix layer, the fiber bundle layer, and the non-oxide layer, called the self-healing agent. Using FEA, we examine ideal relationships of fracture stress and critical energy release rate between the fiber and interface layer considering the sintering characteristics. Furthermore, the relationship between fracture toughness, Young's modulus, and the relative density of the interlayer to induce a crack deflection at the interface is derived.
The purpose of present study is to investigate the nanoparticle dispersion formation under drying process of micro solution droplet including nanoparticles, and develop the film fabrication method on the basis of the formation result. First, the Ag nanoparticles dispersed solution is prepared, and the solution droplet is dropped and dried on a glass plate while changing the droplet quantity. Then, the effect of droplet quantity on the Ag nanoparticle dispersion formation is investigated. As a result, it was seen that the nanoparticle dispersion formation depended on presence or absence of internal flow in a droplet under drying process. Second, in-house painting device is developed to produce ~100μm droplets on a glass plate. Using the in-house painting device, the nanoparticle dispersion size can be adjusted by changing blowing time. Next, the nanoparticle solution is fabricated using Al2O3 nanoparticles and water. The concentrations are adjusted to 0.05vol.% with water. The blow and dry of the Al2O3 solusion micro droplets are cyclically conducted on a substrate, then Al2O3 film is formed on a substrate. Consequently, final Al2O3 film structure depends on the blowing time. The valley between Al2O3 particle dispersions decreases with increasing in total blowing time for all blowing times. However, the size of valley becomes large with increasing in blowing time.
High electrical conductivity and high optical transparency are desired for transparent conductive films (TCFs). The currently used conducting material, indium tin oxide (ITO), is high cost owing to the lack of indium source. In addition, its brittleness has limited its applications in flexible electronic devices. Although the alternative materials, such as carbon nanotube and metallic nanowires, have been extensively studied, there are still some issues needed to be addressed for their practical uses. This research reports a highly stretchable TCF, which is made by transferring a Pt nanocoil (NC) web to a transparent silicone rubber membrane. The fabricated Pt TCF exhibited a high optical transmittance over 90% within visible region. The stretching behaviors of a single-layered freestanding Pt NC web and a Pt TCF were investigated and the fracture mechanism was discussed. As a result, the respective fracture strain of freestanding Pt NC web and Pt TCF was approximately 20% and 15%, both of which were higher than that of ITO film. The decreased fracture strain of Pt TCF was attributed to a possible reason as follows. Compared to the freestanding Pt NC web, the in-plane deformation of Pt NCs in the TCF was restricted by the substrate layer, and hence the Pt TCF fractured more easily than the freestanding Pt NC web.
The prevention of excessive deformation by thermal ratcheting is important in the design of high-temperature components of fast breeder reactors (FBR). In an experimental study that simulated a fast breeder reactor vessel near the coolant surface, it was reported that the long distance travel of temperature distribution causes a new type of thermal ratcheting, even in the absence of primary stress. In this paper, we propose a simple screening criterion to prevent continuous accumulation of plastic strain derived from long distance travel of temperature distribution. The major cause of this ratcheting is the lack of residual stress that brings shakedown behavior at the center of yielding area. Because residual stresses are derived from constraint by the neighboring elastic region, we focused on the distance from the center of yielding area to the elastic region. Accordingly, the proposed criterion restricts the axial length of the full-section yield area, which is the double of the above distance. We validated the proposed criterion based on finite element analyses using an elastic-perfectly plastic material. As a result of the validation analyses, we confirmed that the accumulation of plastic strain saturates before second cycles in the cases satisfying the proposed criterion, regardless of the shape of temperature distribution.
Most cold forming processes are perceived as simple surface treatments without a heating process and are widely used to improve the fatigue strength of various engineering components. The method for measuring the residual stresses caused by such surface treatment is very important when evaluating the fatigue strength of engineering components. The inherent strain method is one of the most effective measures for predicting the internal residual stress distribution. The residual stresses within a body are caused by internal permanent strains known as inherent strain or eigenstrain. In the case of cold formed components, the inherent strains are induced by plastic deformation. If a component is cut, the residual stress distribution changes, but the inherent strains of the original shape before cutting are preserved. The inherent strains are predicted by the inverse analysis of a finite element model using the measurement results of residual stresses on the slice or the cut surface of a body. On the other hand, a two-dimensional X-ray diffraction system based on a cosα method is useful for measuring the residual stresses because of its compactness and higher measurement speed than the conventional sin2Ψ method. In this paper, we propose an efficient approach that combines the inherent strain method and an X-ray stress measurement along with a new measurement procedure for the fillet portion of an axisymmetric shaft with a flange after the cold forming process. This report compares the results estimated using the inherent strain method by the sin2Ψ and cosα methods, and confirms that the differences in the results were very small. Furthermore, three advantages of the cosα method—wider measurable area, shorter measurement time, and shear stress measured at the same time as normal stress—are examined. Consequently, it is verified that the cosα method is effective for the proposed new approach.
Effects of surface roughness of polyether ether ketone (PEEK) on the seizure behaviors of PEEK/steel pairs are studied using a block-on-ring wear tester under oil-lubricated conditions. The blocks are made of unfilled PEEK and a PEEK composite filled with carbon fibers of 30 mass%. The block's surface roughness varies between 0.03 to 4.77 μm Ra. The ring is made of forged steel (SF540A) and its surface roughness is 0.12 μm Ra. The sliding velocity and load are 19 m/s and 883 N respectively. During the test, the ring temperature is measured with an alumel-chromel thermo-couple with a diameter of 0.5 mm, located 1 mm below the frictional surface. Results indicate that the seizure behaviors are strongly dependent on the PEEK material's surface roughness. Seizure occurs in both materials when the surface roughness exceeds a certain value. The critical surface roughness in the PEEK composite is significantly higher than in PEEK. Thus it is concluded that the PEEK composite has an excellent seizure-resistant property at high sliding velocity. Wear scars are observed using a scanning electron microscope. The seizure mechanisms are discussed from the viewpoints of the SEM observation results and the ring temperature.
In this paper, the effects of subjecting a thin-walled cylinder filled with silicone rubber to low-velocity impact on energy absorption were clarified on the basis of the results of drop weight testing and theoretical analysis. Aluminum alloy cylinders filled with silicone rubber with different hardnesses were prepared as specimens for the drop weight testing with an impact velocity of up to 5.5 m/s to measure the impact load-deformation relation. The analysis was conducted with elastic-perfectly plastic solid mechanics. The absorbed energy per unit deformation, namely the average load, was found to increase significantly due to filling the cylinders with rubber since the plastic deformation occurred in the whole cylinder due to radial expansion of the rubber during dynamic compression. The average load of the filled specimen was more than double that of the empty cylinder. Even though the cylinder fractured after the impact energy exceeded the capacity of the cylinder, high strength rubber could be utilized to support the impact load as a fail-safe. Therefore, it was clarified that the rubber inside the thin-walled cylinder contributed to increase the energy absorption and support the impact load as a fail-safe after the cylinder fractured.
The technique of rapid evaluation of fatigue limit using infrared thermography was developed and has been paid attention during the past 30 years. This technique is beneficial because it also makes possible to detect the location of fatigue damage in real products. In the thermographic technique, the fatigue limit is determined based on the temperature evolution with the load amplitude. In this research, two methods for quantifying the temperature evolution from measured temperature variation (mean temperature rise and second harmonic amplitude) as well as two types of infrared camera (quantum and thermal type) are compared with each other in order to assess the applicability of the thermographic technique. Experiments are conducted for double edge notched specimens of type 304 stainless steel. A data processing technique developed by the authors recently is employed in order to determine the fatigue limit appropriately. The results of fatigue limit evaluation are compared with true fatigue limit. In conclusion, it is found that the second harmonic amplitude is not affected by heat conduction and provides sufficiently accurate result. In contrast, the mean temperature rise is affected by heat conduction and should not be applied to objects with high stress concentration. It is also shown that the thermal type camera is not sensitive enough to measure the second harmonic amplitude.
Effect of microstructure on two-body abrasive wear behavior in electrodeposited Ni -4.4 mass% P alloy was investigated to obtain a clue to development of nanocrystalline materials with high wear resistance. The as-electrodeposited nanocrystalline Ni -4.4 mass% P alloy, which was in a supersaturated solid-solution, transformed into a dual phase alloy composed of Ni and Ni3P grains as a result of the precipitation of Ni3P phase by annealing. The Hall-Petch relationship between the hardness and average grain size was maintained in the annealed dual phase alloy specimens with average grain size ranging from 50 nm to 1230 nm. The wear rate of the annealed specimens decreased with decreasing average grain size accompanied by hardening. The wear rate of the annealed specimens containing hard Ni3P grains was lower than that of the as-electrodeposited specimen with the similar hardness. Although the very fine grain size induced smooth wear grooves, the conventional grain size induced rough wear grooves with turning of Ni phase. The hardness dependence of wear resistance in Ni -4.4 mass% P alloy specimens was weaker than that obtained in the case of pure metal specimens with different hardness.
In this study, the nominal tensile strength, Young's modulus and Weibull scale and shape parameter of the nominal tensile strength distribution of the MWCNTs synthesized by a thermal chemical vapor deposition (CVD) method were investigated by conducting uniaxial tensile tests. In addition, the structural defects which induced the failure of the MWCNTs were observed by a transmission electron microscope (TEM). TEM observations revealed that the MWCNTs exhibited several types of structural defects: discontinuous flaws such as holes, kinks and bends and remnant catalysts even though crystalline graphene layers were aligned with the MWCNT axis. The nanotube tested in this study fractured at the structural defects such as discontinuous flaws and kinks and bends, suggesting that the tensile strength of the CVD-grown MWCNTs used in this study was dominated by the above-mentioned structural defects. The tensile-loading experiments demonstrated that the nominal tensile strength, Young's modulus and Weibull scale and shape parameter of the as-grown MWCNTs were 5.2 ± 2.1 GPa, 210 ± 150 GPa, 5.9 GPa and 2.7, respectively. The MWCNTs used in this study showed larger Weibull scale parameter values compared with both the CVD-grown and arc-discharge-grown MWCNTs evaluated an earlier study. This suggested that there was an optimal nanotube structure for increasing nominal tensile strength; not too weak but also not too strong inter-tube coupling to permit an adequate load transfer between the nanotube walls and thus a consequent clean break fracture. We also investigated the effects of the thermal annealing on the mechanical properties of the MWCNTs. The structural changes observed after annealing led to no significant impact on the nominal tensile strength of the MWCNTs, which was mainly due to incomplete removal of the structural defects by thermal annealing.
It is well known that the compressive strength of composite laminates decreases after impact load, even if the impact damage is barely visible in appearance. This compression after impact (CAI) strength is one of the most important design criteria for composite structures. Currently, in order to reduce time-consuming model tests and simultaneously ensure structural reliability, analytical or numerical methods are required which are capable of reproducing the actual failure behavior of composite structures (failure mode and load). In this study, impact damage and CAI strength were continuously evaluated by means of numerical progressive failure analysis using dynamic explicit FEA. Since impact and subsequent CAI are dynamic and a static loading processes, respectively, analyses for removing the dynamic effect in the CAI process were performed in the following three steps: 1) impact, 2) relaxation of vibration and 3) CAI. In these analyses, the LaRC failure criteria which take into account fiber-kinking failure mode were employed as stress-based damage initiation criteria, and damage evolution for each lamina was simulated through energy-based damage mechanics. The damage initiation criteria and evolution law were implemented in analyses using the user-subroutine VUMAT of Abaqus/Explicit. In addition, delamination was represented by cohesive elements in stress-based damage initiation criteria and energy-based damage mechanics. As a result of comparison with tests, both of the projected delamination areas caused by impact loading and CAI strength were satisfactorily predicted within an accuracy of ± 15 %. In the CAI simulation, fiber-kinking damage propagated in the direction of width at the maximum applied load, but delamination did not start to propagate. The fiber kinking failure mode was caused by bending due to local buckling at impact area where delamination existed. Accordingly, both of the in-plane fiber kinking damage (which is critical failure mode in CAI) and the delamination (which strongly affects local buckling and subsequent in-plane fiber kinking) are quite important for the accurate prediction of CAI strength.
The intermetallic compound ZrCu experiences a transformation from a parent phase into a martensitic phase with rapid cooling. ZrCu possesses considerable promise as a high-temperature shape memory alloy. In the present study, the shape memory effects of ZrCu, which was formed in a Zr-Cu-Al ternary alloy, was investigated. The Zr-Cu binary and Zr-Cu-Al ternary alloys with different alloy compositions were prepared. The crystalline structure, martensitic transformation temperature and macroscopic shape recovery behavior of these alloys were evaluated by means of X-ray diffraction, differential scanning calorimetry and compressive tests; the crystalline structure of the ZrCu in Zr-Cu-Al alloys varies with increasing Al concentration. In addition, it was confirmed that both the Zr-Cu binary and Zr-Cu-Al ternary alloys possess shape memory effects. Furthermore, it was found that the macroscopic shape recovery temperatures of these alloys decrease with increasing Al concentration.
From the standpoint of evaluating Type IV creep damage in the fine-grained heat affected zones (FGHAZ) of welded joints, an analysis method combining continuum damage mechanics (CDM) and a cavity nucleation model is proposed and applied to the creep testing of simulated-FGHAZ notched bars of mod. 9Cr-1Mo steel at 650°C. The Perrin-Hayhurst CDM model is adopted, which considers both softening by precipitate coarsening and damage by creep cavities. For the cavity nucleation model, a proposal by Gonzalez and Cocks is employed, which considers the randomness of grain-boundary-facet orientations in a polycrystalline material and gives a nucleation rate that is a function of the creep strain rate and a tri-axiality factor. The critical value of the damage parameter, corresponding to the initiation of micro cracks due to the coalescence of creep cavities, is expressed in terms of a critical value of the number density of creep cavities as determined from grain-boundary-resistance model simulations by the present authors. Creep rupture experiments have been conducted for circumferentially notched bar specimens with two kinds of notch acuities. The applicability of the combined CDM and cavity nucleation model is demonstrated by comparing the distribution of creep cavities observed experimentally with the simulation results. The final rupture life of the circumferentially notched bar specimens was also predicted to within a factor of two.
Oxidation tests using coupon specimens of alloy 625 and alloy 617, and four-point bending tests for a duration of 100 hrs were carried out in supercritical water (SCW) environment at a pressure of 24 MPa and in superheated steam (SHS) environments at 750°C. The noticeable difference between the oxidation in two environments appeared in the oxidation behavior of primary precipitates like Nb rich MC carbide for alloy 625. In the SCW environment, a large number of pitting was observed. Those were thought to be made by electrochemical reactions, while in SHS most of the carbides were oxidized as Nb oxides with some extent of volume expansion. In the case of alloy 617, the pitting formation was also observed in both environments. It seemed to have a dependence on the oxidation behavior of the primary carbides similar to that of alloy 625. The effect of the applied stress was not apparent under current experimental conditions because permanent deformation was observed in all the specimens and stress relaxation subsequently occurred during the test. In addition, no cracks were observed on both alloys after four-point bending tests. In the outer layer of the oxide film formed in the SCW, the Cr content exhibit to have smaller in both alloys, and the oxide thicknesses were 0.53 to 0.88 times thinner than those in the SHS.
This paper deals with the optimization and the comparison of passive magnetic thrust bearings made up of radial stacks of permanent magnet rings. Various topologies are considered, depending on the polarization direction of the permanent magnet rings and the presence of back-iron. The coulombian approach and the method of image charges are used to determine the load capacity of topologies with back-iron. On this basis each topology is optimized in order to minimize the permanent magnet volume for a fixed load capacity, airgap thickness and remanent flux density. Varying these parameters, scaling laws of the optimum permanent magnet ring dimensions are derived to allow fast sizing and comparison of the topologies. The latter highlights that the topology with Halbach configuration and back-iron is the most performant, but that the topology with axial polarization is almost as good.
This paper demonstrates the design and simulation results of model based controllers for AMB systems, subjected to uncertain and changing dynamic seal forces. Specifically, a turbocharger with a hole-pattern seal mounted across the balance piston is considered. The dynamic forces of the seal, which are dependent on the operational conditions, have a significant effect on the overall system dynamics. Furthermore, these forces are considered uncertain. The nominal and the uncertainty representation of the seal model are established using results from conventional modelling approaches, i.e. Computational Fluid Dynamics (CFD) and Bulkflow, and experimental results. Three controllers are synthesized: I) An H∞ controller based on nominal plant representation, II) A μ controller, designed to be robust against uncertainties in the dynamic seal model and III) a Linear Parameter Varying (LPV) controller, designed to provide a unified performance over a large operational speed range using the operational speed as the scheduling parameter. Significant performance improvement is shown for robust control, incorporating model uncertainty, compared to nominal model based control.
New six pole type hybrid magnetic bearing is introduced. It is intended to apply to high speed turbo-machinery. Traditionally turbo-machinery uses standard electromagnet (EM) type active magnetic bearing (AMB) which requires PWM power amplifiers. Recently turbo manufacturers want to develop their own magnetic bearing. Sometimes they are not accustomed to developed standard EM type magnetic bearings. The proposed magnetic bearing uses bias Permanent Magnet (PM), hence it is easily manufactured. The developed magnetic bearing also has good characteristics due to six directional control pole compared with the standard four directional control one. An experimental setup is fabricated and tested with good results. Finally auto balancing control is applied to the free side of proposed magnetic bearing.
The adoption of magnetic levitation is experiencing a steady growth in the vacuum industry and, in particular, in turbomolecular pumps. Nowadays, the most common solutions for pumps of small and medium pumping capacity are based on hybrid architectures where passive magnetic bearings are combined to ceramic ball bearings. By converse, fully active magnetic suspensions with cylindrical configuration represent the standard for medium to high pumping rate machines. Although simple, the cylindrical configuration is prone to drawbacks related in particular to the strains growing in the disc of the axial actuator that motivate the investigation of alternative architectures. As shown in previous literature, the use of conical configuration, besides compacting driving electronics, seems to be promising considering that the control of the radial and axial degree of freedom is performed simultaneously by the same devices acting in two actuation planes.This paper describes the development and the experimental characterization of a turbomolecular pump supported by conical active magnetic bearings. The control design is based on a SISO decentralized technique with position and control embedded loops. A rotor centering technique based on the characterization of the current loops is exposed. The external position loop is tuned by measuring relevant transfer functions to refine the controller and allow a safe critical speed crossing. The power actuation of the eight electromagnets is performed with a three-phase configuration drive technique instead of standard H-bridges to minimize the number of power switches. Experimental results along with numerical computations obtained with simulation models are reported as proof of the validity of the modeling approach and of the conical architecture effectiveness.
In permanent magnet motors, the presence of rotor eccentricities can alter the airgap field distribution. This results in parasitic radial detent forces that can be reduced by connecting the stator phases in parallel. As a consequence, currents are passively induced in the windings when the rotor spins in an off-centered position, yielding balancing electrodynamic forces. Specific models were developed to predict these forces, but their complexity can be prohibitive. Therefore, this paper proposes to study the effect of the rotor off-centering in permanent magnet motors using a simpler model developed for electrodynamic bearings. This model consists in a linear differential equation with only four parameters that depend neither on the spin speed nor on the rotor position. As an illustration, the paper applies this model to the study of a high-speed, slotted permanent magnet motor. To support this, the main hypotheses of the model are validated in this particular case. Then, the centering electrodynamic forces in a staticeccentricity configuration are predicted using the model and compared to finite element simulation results. Finally, a preliminary study showing the impact of the width and permeability of the stator teeth on the centering force is performed.
Bearingless machines are used for a variety of applications with demand for low mechanical loss, low wear and low contamination. These machines use contact-free magnetic suspension to levitate the rotor. The control of the machine requires precise radial and angular position information in order to ensure stable levitation. This information is usually obtained with two types of sensors: radial displacement sensors and angle sensors. Alternatively, an angle-sensorless control scheme can be used, reducing the complexity and the cost of the machine. While such a control is well known for conventional machines it is challenging to adapt it for bearingless machines. The reason is that most methods fail to provide the angle information at zero and at low speed but bearingless machines require knowledge about the rotor angle at all speeds in order to function. The theoretical mode of operation of a model based angle observer for zero and low speed operation of a bearingless machine was shown in previous publications. The observer obtains the rotor angle estimation error by analyzing the performance of the radial bearing and comparing it to the performance of a model with zero angle error. This observer can be used for operation at standstill and over the whole speed range. This paper provides a more detailed description of the non-idealities of the zero and low speed observer and presents results of machine operation without angle sensors. The generation of torque and force inside the machine is analyzed in more detail. Furthermore, it is shown how to combine the novel observer with a conventional, back electromotive force based, high speed angle observer. The experimentally verified results of this paper indicate that the novel observer can be used up to speeds at which back electromotive force estimation is possible. This allows the efficient, angle-sensorless operation of the machine over the whole speed range.
Backup bearings (BB) limit the translational movement of rotors during malfunction, overload or power loss in the active magnetic bearings (AMB) in order to enable safe spin down and reduce secondary damage. Especially for high speed applications like flywheels with high rotor inertia, the requirements towards the load capacity and service life of the BB is comparably high. For a special type of flywheel with exceptionally high speeds in the BB interface, a planetary BB system is presented. The planetary BB consists of multiple bearing units placed circumferentially around the stator. Its elastic properties are described as well as a contact damping model. For cost efficient BB investigation, a scaled test rig is introduced and a parametric study of different delevitation simulations is done. Several quantification methods to evaluate severity, bearing loads and lifetime utilization during rotor delevitations are presented and applied to the simulations. Using a dry friction model a service life estimation of MoS2 ball bearing lubrication is made. The applicability of the planetary BB to vertical high speed rotors is confirmed by the simulation data and bearing element selection is affirmed. The results of the quantification methodologies show specific correlation to initial conditions and parameters like unbalance and in particular friction coefficient. Further the influence of the rotor weight and size to the bearing loads is investigated.
A topology composed of a hollow-shaft rotor on rolling element bearings coupled with internal-stator magnetic bearings mounted on independently supported flexible shafts is considered for the purposes of vibration reduction. Details of a bespoke test rig constructed to assess this topology are presented. The rig makes use of custom-designed internal-stator magnetic bearings fabricated from Soft Magnetic Composite material. Results from standard numerical analysis of the rig are given to demonstrate the expected behaviour of the system, with a particular focus on its potential to reduce synchronous vibration seen in the rotor while passing critical speeds. These behaviours are then confirmed via a series of experimental tests. These results show that the proposed topology can be used effectively to alter the system vibration behaviour.
It is now common practice to supplement a magnetic bearing with a touchdown bearing to protect the rotor and stator components. Rotor/touchdown bearing contact may arise from rotor drop, caused by power loss or emergency shutdown. This paper considers the control options that are viable when the magnetic bearing is still functional should contact arise from intermittent faults or overload conditions. The problem is that bi-stable rotor responses are possible, with and without contact. If rotor contact should become persistent, the desirable course of action is to destabilize the rotor response and induce a return to contact-free levitation. In order to achieve this, it is appropriate to gain an understanding of the rotor dynamic behavior. This is determined from analytical and simulated results to reveal suitable control actions. These may be applied through the magnetic bearing control system, or by activating the touchdown bearing through a separate control loop. The issue is that standard control action for a contact-free rotor state will not be appropriate for a rotor in persistent contact since the basic plants to be controlled are significantly different. The required control action should be activated only when contact is detected. The results demonstrate that appropriately phased synchronous forcing could destabilize synchronous forward rub responses. Alternatively, small whirl motions of a touchdown bearing could also be beneficial without disturbing the main magnetic bearing control loop.
For flux-switching PM (FSPM) motors, permanent magnets (PMs) are placed in the stator and not in the rotor structure as in the majority of PM motor designs. Recently, FSPM bearingless motors have been developed for special applications. The FSPM concept can be adapted to linear motors. For linear motors, magnets or windings located on the mover significantly decrease the complexity and cost for longer tracks. Following the ideas from the rotating bearingless motors, this work focuses on combining the motoring and levitation functionalities in a linear machine. Still, to separate the controls of air gap and torque (thrust), two sets of windings or multiphase windings are required for both rotating FSPM and linear PM machines. A linear FSPM-levitated motor solution, which integrates the magnets, winding structure, and all the driving and control electronics on the mover is desired in many applications. However, because of electromagnetic unbalances, the machine design is intertwined with the control limitations and requirements. We propose a modeling methodology for accurate derivation of the machine dynamic and static force parameters as a function of air gap, control currents, and track position in an extended operating range. Model-based control simulations based on accurate plant models determine the achievable machine performance and levitation limitations. The design and modeling methodology is universal and can be applied to various PM bearingless motors and magnetic levitation systems. In the case study of a linear FSPM-levitated motor (mover), air gap control is possible in a manner equivalent to classical active magnetic bearings, where it is linearized and independent of the thrust control.
Mechanical circulatory support (MCS) therapy plays a significant role in an alternative therapy of heart transplants for pediatric heart disease patients. However, continuous flow rotary MCS devices for pediatric patients are still undergoing development, and have not been clinically available technology. Technical difficulties, such as high durability, better blood compatibility and miniature device size, prevent the pediatric MCS devices development. In this study, a double stator axial gap maglev motor for pediatric MCS device has been developed. The maglev motor has two identical motor stators, and a levitated rotor impeller which is aligned between the stators. The levitated rotor impeller is fully suspended with 5-degrees of freedom (5-DOF) active control. A double stator mechanism enhances motor torque production. A miniaturized maglev motor was designed and developed based on FEM magnetic field analysis for use in implantable ventricular assist devices (VADs). The diameter and height of the developed maglev motor are 22 mm and 33 mm. This paper is an initial report on the magnetic levitation and rotation performance of the miniaturized maglev motor. The levitated rotor impeller was magnetically levitated and rotated with the 5-DOF active control. The oscillation amplitudes (x, y and z) and inclination angles (θx and θy) of the levitated rotor impeller were then evaluated in both air and water. The developed maglev motor achieved non-contact rotation up to 1600 rpm in air and 4500 rpm in water, respectively. The oscillation amplitudes and inclination angles were sufficiently suppressed in water due to fluid damping. After these experiments, a magnetic circuit of the maglev motor was modified in order to achieve further stable levitation. The developed maglev motor then indicated potential to achieve the practical use of maglev rotatory pediatric VAD.
The electrodynamics of magnetic thrust bearings are characterized by an above-average dependency on the bearing materials. Axially directed fields render laminated stators and rotors ineffective. High induced voltages inside the magnetic core evoke eddy currents and opposing fields, which are compensated by an additional magnetizing current causing a significant delay between the measurable coil current and the force-related magnetic flux. The control dynamics are hampered and even though this effect can be reduced by the use of Soft Magnetic Composites (SMC) for non-rotating parts, the thrust disk is usually made out of steel due to its superior tensile strength and saturation flux density. The analytical modeling of mixed-material magnetic thrust bearings reveals new challenges arising from asymmetries and low permeable magnetic core sections, both of which are addressed in this article. In case the air gap is bounded by core sections made of different materials the established analytical models are not applicable and require the presented asymmetrical air gap wave propagation constant. Furthermore the consideration of the stator corner reluctances for SMC cores compensates the stationary error of 6% of the total effective reluctance present in previous works.
A small magnetic levitated centrifugal blood pump using a radial type self-bearing motor has been developed for use as an implantable artificial heart. In order to realize an implantable blood pump for a small adult patient, miniaturization and high efficiency of the device are necessary. In this study, a radial type self-bearing motor which is small-diameter and thin was developed, and the axial position change of the rotor-impeller by the rotational magnetic field was proposed. Magnetic suspension characteristics and motor performance were compared the center axial position of the rotor with the displaced axial position of the rotor. Additionally, a magnetic levitated centrifugal blood pump using the self-bearing motor was developed, and pump performance and levitation performance were measured. The magnetic suspension performance in the radial direction was enough ability to control the radial position of the rotor. The magnetic suspension force in the radial direction decreased by displacing the axial position of the rotor. The passive stability performance in the axial direction was enough ability to suspend the rotor. The restoring force was possible to be varied by the rotation magnetic field. The motor performance decreased by shifting the phase angle of the rotational magnetic field from 90 degrees and displacing the axial position of the rotor. At the operating condition with a flow rate of 5 L/min against a pressure of 100 mm Hg, the oscillation amplitude in x, y, z direction were 0.014 mm, 0.014 mm and 0.039 mm, respectively. And, the total power consumption was 7.1 W. The developed magnetic levitated centrifugal blood pump has demonstrated sufficient levitation performance and low total power consumption. The average displacement in z direction of the rotor-impeller was possible to change by changing the phase angle of the rotational magnetic field. By decreasing the phase angle from 90 degrees in range of from 60 degrees to 90 degrees, it is possible to improve the levitation performance with just a little increases the total power consumption.
This paper deals with optimal controller design for active magnetic bearing (AMB) systems for which nonlinear rotordynamic behavior is evident, and so vibration predicted by operating point linearization differs from that which occurs in actuality. Nonlinear H-infinity control theory is applied with a rotordynamic model involving nonlinear stiffness and/or damping terms. The associated Hamilton-Jacobi-Isaacs (HJI) equation is formulated and solved to obtain a state feedback control law achieving specified vibration attenuation performance in terms of the peak L2 gain of the nonlinear system. The method is applied in case study to a flexible rotor/AMB system that exhibits nonlinear stiffness properties owing to rotor interaction with a clearance bearing. Simulations are performed to quantify RMS vibration due to harmonic disturbances and the results compared with the norm-bound values embedded in the HJI equations. A feedback controller design method is then presented that is similar in approach to the standard loop-shaping/mixed-sensitivity methods used for linear systems, and involves augmenting the system model with weighting transfer functions. Experiments are undertaken to compare controller performance for designs based on nonlinear and linearized models. The results highlight the shortcomings of applying linear optimal control methods with rotor systems exhibiting nonlinear stiffness properties as large amplitude vibration and loss of rotordynamic stability can occur. Application of the described nonlinear H-infinity control method is shown to overcome these problems, albeit at the expense of vibration attenuation performance for operation in linear regimes.
This paper discusses an active magnetic bearing (AMB) able to work in liquid nitrogen, which is composed of a stator with four electromagnets (EMs), a rotor, displacement sensors, a permanent magnet (PM) motor, etc. In this paper, two types of AMBs are discussed. One AMB is made to study basic characteristics of the AMB in liquid nitrogen. The other one is made to study basic characteristics of a pump able to work in liquid nitrogen. The rotor is levitated in the center of the stator with a pivot bearing at the rotor bottom. The pump performances using the AMB are studied by measuring the displacement of spinning rotor at extremely low temperature 77 K.
Some active magnetic bearing (AMB) applications require that the mean, or static force exerted by the AMB is zero. Examples include hybrid fluid film - AMB bearing pairings, rotor midspan dampers, and statically indeterminant systems with stiff rotors and more than two radial AMBs. When the position of the rotor relative to magnetic center is not known precisely, this zero force requirement can be hard to meet. A low frequency periodic biasing scheme is developed which enables a controller to detect non-zero static force by sensing rotor motion at the bias carrier frequency. A theoretical basis establishes feasibility but also the potential for coupling between control signals and the periodic bias. Simulation demonstrates that an ad-hoc bias adaptation scheme can successfully drive the static component to zero while permitting otherwise conventional control. Experimental results on a small, single DOF test rig further demonstrate the ability to drive the AMB static force to zero while adding damping to the system. Identification of the system stability boundary provides insight on the structural requirements (mechanical stiffness versus magnetic negative stiffness) and the limitations on the control gain for the biasing scheme to work
In this study, a simple and smooth voltage controller for a three-pole active magnetic bearing (AMB) system is proposed. It is designed with the backstepping procedure. The first step assumes the currents as the control inputs and designs the smooth current controller that has been proposed in the literature. The second step considers that the currents are not actual inputs, but part of the states. Then, the actual control inputs (voltages) are designed using simple proportional and integral (PI) control to make the error states from the first step to be zero asymptotically. Based on the voltage-controlled AMB system, an observer is designed for the rotor displacement estimation. The observer is based on the input voltages and coil currents that drive the magnetic poles. Such an observer can be utilized in the sensorless control of the AMB system. Due to the strong nonlinearity in the dynamics of 3-pole AMB system, the theory of nonlinear high-gain observer is adopted to design the observer. First, it is shown that the strong nonlinear 3-pole AMB system is observable under the zero input condition, which guarantees the existence of a high-gain observer. Then, the system is transformed into a regular form for the design of observer. Finally, a nonlinear observer is designed following the theory of high-gain observer. The proposed smooth voltage controller and nonlinear observer are verified numerically and experimentally. The results show the effectiveness of the smooth voltage controller and the feasibility of the nonlinear high-gain observer.
For the safe operation of devices comprised of bodies with D∞ symmetry, the electroelastic field in a solid cylinder subjected to a non-axisymmetric surface load of radial and circumferential stresses was investigated. The analytical technique constructed previously, the Fourier integral technique with respect to the axial coordinate, and the Fourier series technique with respect to the circumferential coordinate were employed. Then the three-dimensional distributions of the electroelastic field quantities, such as displacement, electric potential, electric field, strain, stress, and electric displacement, were determined. In addition, the resultant forces and moments on the axial section were formulated. Using numerical calculations assuming health monitoring or NDE techniques, it was found that the structures of the electroelastic field were dependent on the composition of the combined load even when the integrated effect of the combined load was constant and that the detailed three-dimensional analyses were absolutely significant. Then, the primary coupling behavior in the D∞ bodies was investigated for health monitoring, and it was found that the stress-strain relationship was substantially elastic but the developed electric displacement was affected by both of the piezoelectric and dielectric effects comparably and that the coupled analyses were also significant. Moreover, an elementary methodology to decompose the combined load into components was suggested and was successfully implemented for a concrete example.
The geometrical features of internal surfaces are important parameters in the field of non-destructive testing such as corrosion inspection or artistic qualities of material surfaces. Although stylus profiling and optical scattering are commonly used for measuring both random and periodically rough surface topography, they are only applicable to accessible surfaces. However, there are many cases in which the surface to be evaluated is inaccessible. For example, integrity monitoring of inner surfaces of pipes is required to ensure proper functions and safeguard quality. Unfortunately, little attention has been paid to the measurement of inaccessible periodic surfaces. Since inaccessible surfaces do not permit contact or optical measurement, application of ultrasonic technique from back side is an appropriate candidate among others. In this paper, an ultrasonic pulse-echo technique is investigated to evaluate the pitch of periodically rough surfaces which is inaccessible or hidden on the back side. The pitch of back surface profile is evaluated based on the diffraction grating theory for oblique incidence of P-wave, SV-wave, and SH-wave. The applicability of the proposed technique was verified by both numerical simulation and experiment. It is found that the angle of incidence should be larger than 45° to enhance the accuracy. SH-wave shows better results compared with SV-wave due to the effect of mode conversion. Moreover, using SH-wave is an effective way for evaluation of the pitch because SH-wave is more sensitive than P-wave with shorter wavelength. On the other hand, P-wave is the best solution to obtain the highest resolution of measurement with higher signal to noise ratio.
Fretting fatigue behavior of Ni-base superalloys used in gas turbine blades and disk assemblies have been investigated under ambient and high temperature conditions. A major emphasis was placed on the influence of experimentally measured tangential force coefficient on the fretting fatigue life prediction of a single crystal superalloy. Significant differences in the experimental fretting fatigue lives with respect to contacting superalloy combinations were found. These experimental findings were correlated with an analytical approach for the estimation of fretting fatigue life. The predicted results employing the crack analogue model provided good agreement with the experimental results. Also, the influence of secondary crystal orientation of single crystal superalloy on the frictional response and fretting fatigue life prediction was highlighted.
Macroscopic failure of polystyrene has been investigated under pure shear and simple tension by isochronal static tests in air at room temperature. A number of crazes were clearly observed under both stress states. The craze initiation identified under pure shear provides an obvious counterevidence to the current criteria, which involve explicitly the dilatational stress term as a requisite for craze initiation. A criterion expressed by a product form of the maximum principal stress and the maximum principal shear stress with an isotropic stress term was examined. The proposed criterion was marked to predict α priori a peculiar feature that the craze initiation never takes place under biaxial compression. A theoretical ratio of critical stress for craze initiation under pure shear to that under simple tension coincided with the experimental result.
This study analyzes the brake operation behavior of drivers when a pedestrian runs out onto a road with good visibility. For this purpose, 15 subjects were observed in a driving simulator. As the evaluation criteria, we adopted the TTC to avoid the collision to pedestrian in the front/back direction at the start of braking and the spare distance between the pedestrian and the vehicle in the sideways direction at the start of braking. To determine the reliability of these test results, we also analyzed the initiation timing of a driver's braking operation in a real road environment using drive recorders and compared these results with those test results. Then, based on the results of this driving simulator test, we proposed the lowest 1% of the cumulative frequency of the driver's operation timings as the time of starting the brake operation in autonomous emergency braking. Finally, this proposed brake control timing's adequacy was validated in an experiment. The system's brake control did not interfere with the drivers' brake operation, confirming that driver overconfidence in the system was controlled.
This paper considers a particular case of a robot body design method which determines degrees of freedom (DOFs) number and link parameters to maximize a target task performance, and feasibility of this design method is validated by several experiments. In this paper, the target task is to throw a ball a long distance, and a multi DOFs ball throwing robot is designed and manufactured for the experimental validations. Design parameters are the robot body parameters and its motion pattern, and they are designed to maximize ball reaching distance under long throw task conditions. To define the link lengths and the robot DOFs number as design parameters, it is assumed that robot links have identical actuators, and these link parameters are defined as functions of link lengths. This design method is applied to the manufactured ball throwing robot, and its body parameters and motion pattern are designed. The ball reaching distance is changed along with the DOFs number, and as a result, 5 DOFs robot body and its throwing motion are obtained, and the ball reaching distance is maximized. Finally, the ball throwing experiments of the designed 2 DOFs and 5 DOFs robots are executed in each 8 trial. Average values of the ball reaching distance are close to the calculation results, therefore, the feasibility of the calculation results is demonstrated.
A contribution separation technique for estimating road noise and wind noise contributions to vehicle interior noise without using any sound source information was considered when each noise was from multiple sources. In the test, road, wind or mixed noise sources were reproduced from four speakers placed at different positions. The mixed interior noises were recorded at two separate positions surrounded by the speakers. Independent component analysis (ICA) was then applied as the contribution separation method for obtaining them at the target position (driver seat position). As the original condition, ICA was firstly applied to the recorded noises at the driver seat (target noise) and at the assistant seat (reference noise). The result revealed that the estimated contribution was inaccurate due to the low accuracy at the low frequency and the permutation problem, in which the relationship between the calculated contribution and the actual contributions is not retained with changes in frequency. Next, the reference signal was changed to the other noise having lower correlation to the target for improvement of the accuracy and the permutation solution was considered by using the time trend correlation of the calculated contributions of dominant independent component. The modified ICA technique with the permutation solution could estimate more accurate contributions than the original condition.
Recently, in vehicle development, consideration of the human passenger/driver has become increasingly important. In the present study, numerical simulation of human-body dynamics for a human in a vehicle was conducted. Generally, humans are simulated using whole-body models during numerical simulation. However, the whole-body model has multiple degrees of freedom and multiple properties that must be considered. Moreover, the influence of parameters of the human body is uncertain, and it is difficult to accurately set these parameters. Therefore, we herein focus on motion control of the human head and trunk because these parts account for a large portion of the overall human body. A simplified human model that can identify the characteristics of motion control for actual human response was proposed. In the present paper, the parameters of this human motion control are identified based on results obtained experimentally and using a simulation model. The characteristics of motion of an individual human are then considered based on the obtained characteristics of the parameters.
Effects of polymer structure on the electroosmosis in proton exchange membranes (PEMs) have been investigated using a reactive molecular dynamics simulation. An anharmonic two-state empirical valence bond (αTS-EVB) model has been used to describe efficiently excess proton transport via the Grotthuss hopping mechanism. The electroosmotic drag coefficients (i.e., the number of water molecules transferred through the membrane per proton) has been evaluated directly in PEMs consisting of various equivalent weights (EWs). The electroosmotic drag coefficients from the MD simulations are in good agreement with the available experimental values at studied levels of hydration. It is shown that for low water contents the connectivity of the water clusters decreases with increasing EW, leading to a decrease in the electroosmotic drag coefficients. The proton and water mobility is also found to decrease with increasing EW because of the structural changes in the water cluster domains. The present simulations provide quantitative information about the direct link between electroosmosis and nanoscopic water domain structure in different polymer structures
This research aims to reduce the second-order distortion due to diaphragm vibration. The quadratic term of the restoring force of nonlinear springs varies in the pulling and compression directions. Utilising this property, nonlinear springs are attached to the edge circumference of the simple disk model of a diaphragm. The attachment directions of the springs are alternated in the negative and positive directions to reduce the second-order distortion due to diaphragm vibration. A nonlinear response analysis using the finite element method is demonstrated and the efficacy of the proposed technique is confirmed.
In order to improve comfort in soaking in the bathwater, the relationship between the biomechanical load and the bathtub shape has to be clarified. For this purpose, many soaking experiments had to be conducted since it was necessary to measure the reaction forces acting on a human from the bathtub experimentally. The objective of this study was to construct an algorithm to estimate reaction forces from a bathtub in order to calculate joint torque as biomechanical loads without experiments for given bathtub shapes and soaking postures. This algorithm calculates distribution of reaction forces which minimizes weighted summation of i) sum of squares of reaction forces, ii) joint torques of hip and knee joints and iii) friction force on the back, considering gravity, buoyancy and passive elastic joint torque. The weighting coefficients were expressed as a function of bathing posture including parameters determined for each person to reflect influence of differences among the individual. In order to examine this algorithm, an experiment to obtain the bathing posture and reaction forces for 10 participants and 24 posture conditions was conducted. It was found that the estimated reaction forces were consistent well with the measured values.