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The actuators required for a wearable system need to be flexible so as not to injure the body. The purpose of this study is to develop a flexible and lightweight actuator which can be safe enough to be attached to the human body. In the previous study, a new type of McKibben artificial muscle that had a long stroke of more than 80 % of its original length was proposed and tested. However, the damages on the tube of the actuator were found. They are caused by a large friction between the slide stage and the tube. Therefore, the life time of the actuator becomes shorter. In this paper, the improved McKibben actuator which consists of a McKibben artificial muscle on the market (FESTO Co. Ltd.), steel balls as a cylinder head and two pairs of slide stages is proposed and tested. The slide stage has steel balls set on the inner bore of the stage to decrease the friction. The steel ball in the McKibben actuator is held by two pairs of slide stages from both sides of the ball. As a result, the minimum driving pressure of the improved actuator decreases about 68 % compared with that of the previous one. The actuator can realize both pushing and pulling motion even if it has flexibility. By using these properties of the actuator, the various rehabilitation devices were proposed and tested.

In this paper, the effect of magnetic field on fretting wear under gross slip was investigated in ranging number of cycles from 102 to 105 under the Hertz-type contact of steel ball to steel plate. The amount of fretting wear volume was evaluated by wear occurring on the surface of the steel plate with and without magnetic field. The experimental results show that the wear region spreads under the magnetic field and the worn volume is increased resulting from accumulation of the wear particles near contact tracks under the magnetic field. It is concluded that the wear particles trapped along the contact annulus increase the worn volume by abrasive and/or pile up action under magnetic field.

This paper is the first in a series of studies on the effects of magnetic field on fretting wear damage of ferromagnetic materials. The effect of frequency of fretting vibration was tested in ranging 10 to 150 Hz under the basic Hertz-type contact between a steel ball and a steel plate. Two levels of magnetic fields of 0.08 and 0.22 T were applied with DC electronic magnets. The effects of worn volume and worn depth were examined through factors of frequency and number of cycles of fretting vibration, and morphology of appearance of worn surface. As a result, the following conclusions were derived : magnetic field increases fretting wear damage at lower frequencies, and decreases it at higher frequencies. The deference in the amounts of fretting wear debris formation is examined.

In the present paper, temperature dependence of damage on CFRP laminates subjected to collision of steel ball was considered from viewpoint of impact load and impulsive stress. The histories of impact load and transverse stresses in a CFRP laminate are analyzed theoretically by means of three-dimensional theory and Hertzian analysis of contact with anisotropic thermoviscoelastic property. Impact damages were generated by collision of steel ball under various thermal conditions. As a result, the maximum of transverse stresses subjected to collision of steel ball are influenced by impact load and they suddenly decrease over the primary glass transition temperature. When transverse stresses are compared with delaminations, large transverse shear stress occurs in the direction where delamination progresses greatly. Therefore the direction to progress of a delamination is explained by the transverse shear stress distribution. And the transverse stresses and delamination areas are small under high thermal environments.

Spin angle controlled ball lapping method developed recently, is to have an excellent performance to lap the ball, in which V-groove lapping plates are separated into two parts and three plates are able to rotate independently. Present paper focuses on an effect of degradation of grain size on finishing characteristics of a steel ball. It is found that degradation of grain size has yielded greater stock removal and has brought smaller sphericity of the ball. Experiments show that the stock removal is dependent upon spin angle θ which is closely related to slipping distance of the ball. Measurements of the sphericity of lapped ball indicate that geometry of lapping plate has small effect with respect to improvement of it, but causes larger stock removal rate and very smooth surface.

The precision of products in plastic rolling bearings has been significantly improved by advances in molding technology and assembly technology. However, the idea that these bearings are still used only as miscellaneous mechanical parts is one of the problems that has not yet been wiped away. The reason why reliability has not yet been recognized is the lack of detailed reports about the characteristics of these bearings capable of supporting designs as data. Therefore, in order to define the operating characteristics of the latest plastic rolling bearings, the coefficient of friction of plastic ball bearings has been clarified in this report. Also using similar experiments carried out on steel ball bearings, the results have been compared and investigations have been carried out regarding practical use of plastic rolling bearings as mechanical parts of copy machine and so on.

Transient vibrations in a clamped isotropic rectangular plate caused by the impact of a steel ball are investigated numerically and experimentally. In the numerical approach, the contact law between the plate and the steel ball is approximated by the Hertzian contact theory which was proposed for a static contact problem. The in-plane forces due to the deflection of the plate are not taken into consideration. Since the effect of the in-plane forces is negligible in the case of a very small plate deflection, the numerical approach is justified by comparing the numerical results with the experimental results. The effect of the in-plane forces on the collision between the plate and the steel ball is evaluated by comparing the numerical results with experimental results for various impact velocities and plate thicknesses. Although the contact force cannot be measured experimentally, the effect of the plate thickness and the plate shape on the contact force is evaluated numerically.

The behavior of elastohydrodynamic lubrication(EHL) films formed between a steel ball and an oscillating glass disk is examined by means of the optical interferometry technique, and the results obtained are compared with those of tests conducted under unidirectional conditions. The surface traction is also measured. The film profile in the contact area breathes cyclically because the wedging and squeezing actions are not in phase. In reciprocation under pure sliding, the thick oil film entrapped between both surfaces at the stroke end moves towards the exist side at about half the velocity of the glass disk. Under conditions of a short stroke and a high frequency, air bubbles produced in the downstream result in oil starvation in the next stroke, so that the EHL film collapses. In the full EHL regime, the central oil film thickness and the surface traction at the stroke center are almost the same as those under unidirectional conditions. It is also found that the oil behaves like a non-Newtonian fluid, and as a result the behavior of EHL films varies with oil and type of motion.

The elastohydrodynamic oil film formed between a steel ball and a sapphire disk was observed by an optical interference method. In this study, the influence of a slip on the elastohydrodynamic oil film was investigated by creating a difference between the steel ball velocity and the sapphire disk velocity. The experiment shows that the film thickness formed under the condition of a constant mean velocity decreases with the increase of the slip. This finding is entirely different from the isothermal elastohydrodynamic theory. There is a possibility that this experimental result is due to the effect of oil temperature increase caused by the shearing heat and the effect of the non-Newtonian response of oils.

This report describes an analysis of the steel ball lapping process by use of lap plates with V-shape grooves. An evaluation of three-dimensional sphericity in terms of spherical functions enables quantitative analysis of this process. The angle of the contact points between the steel ball and the lap plays an important role in this process because the interference value between the ball and the lap is related to this angle. The rate of sphericity improvement is strongly dependent on the contacting point angle. Experimental results show that the contacting point angle increases with increasing wear of lap. This increase in the angle increases the rate of sphericity improvement in second-order waviness, and decreases that in third-order waviness, which are included in the form error. Furthermore, the rate is also related to the total number of balls processed at one time.

A precision steel ball is attached to the end-face of the spindle and an electronic capacitance-type transducer mounted on the tool slides of a three-dimensional sliding stage. Relative displacement in the axial direction between the ball and the transducer is detected during spindle rotation. The measurement principle of the central position is based on the fact that the undulation component synchronized with the rotational speed of the spindle in the displacement signal reaches a minimum value at the central position of rotation. The results of preliminary experiments are summarized as follows. ( 1 ) The new method allows detection of the central position with a resolution of 0.5μm. ( 2 ) In the case of the spindle with hydrodynamic bearings, the rotational speed of the spindle and the resonance vibration of the headstock affect the central position of the spindle rotation.

In general, when a slider is about to be moved, friction is always at the maximum. This phenomenon has made it difficult to locate a slider at a definite position with submicron accuracy. The authors attempted to challenge this widely accepted concept in this paper. The basic idea is to strike a guideway from the side with a small steel ball, so that stress waves are generated in the body of the guideway. The stress waves induce slight movement of the asperities on the surface of the guideway. The movement will lead to the breakage of metal-to-metal cohesion and will cause considerable decrease in friction. The idea was tested using a steel block with a hardened surface for a guideway and another smaller block for a slider. The results obtained are as follows. (1)Even a small ball can induce a considerable change in the relative slding speed of metal-to-metal contact regions between the guideway and the slider. The relative movement is strongly dependent on the kinetic energy of the ball. (2) The above movement causes a great reduction in the friction coefficient. When a ball of 25.4mm diameter is dropped from a height of 80mm, the coefficient of friction drops from 0.37 to 0.05 when the slider speed is 1 × 10-2mm/sec. (3) Though the low friction level is sustained for only 0.02sec, this period is long enough for a slider to start moving. (4) The lower the slider speed, the greater the reduction in friction.

To clarify the seizure resistance and the frictional characteristics of a stainless steel ball, which was thermally diffused after being Sn-plated, the four-ball test was run under dip-feed lubrication and thin film lubrication. From the seizure test, the following results were obtained. Under dip-feed lubrication, the coefficient of friction was decreased with increasing thickness of the Sn-diffused layer, and the seizure resistance of the ball was increased with increasing thickness of the diffused layer. The seizure resistance of the ball in which the diffused layer was 8 μm thick was about 2.6 times larger than that without a diffused layer. Furthermore, under thin film lubrication, the running time at the incipient stage of seizuring with balls in which the thickness of the Sn-diffused layer exceeded 4 μm was about 5 min, independent of the thickness of its layer, and this was considerably longer than that without a diffused layer.

In the previous report, it was shown that harmonic analysis results on the three-dimensional shape of a steel ball obtained by use of spherical functions gave good evaluations of characteristics of steel balls used in a bearing assembly. However, this type of analysis is inadequate for evaluating the shape of the ball geometrically. In this paper, first, the possibility of three-dimensional geometrical evaluation by spherical harmonic analysis is described. The 'reference direction' is defined as the index for directivity of each order of the spherical component and has no relationship with the coordinates for measurement. This 'reference direction' or the value of each spherical component for which this direction is obtained, is utilized to illustrate and evaluate the spherical shape of the steel ball. Second, the method for estimating the three-dimensional shape of the steel ball by two-dimensional measurement is explained (e. g., a roundness meter). Mean Fourier coefficients of cross-sectional forms of the steel ball are theoretically calculated, and the correlation between this value and the harmonic analysis result obtained through the use of the spherical functions is obtained.

A method for measuring the form error of spherical parts was developed in the previous report. The measured results showed that steel balls used as ball bearing assemblies usually had the form error of three or four undulations. In the present report, a harmonic analysis by the spherical function is introduced to evaluate the sphericities of the steel balls. Dimensional spectra have invariant values for each ball even if the measuring coordinate axes are changed. Steel balls which are sampled in various states of different finishing processes are measured, and the dimensional spectra are calculated. The calculated results show that the dimensional spectra of steel balls that are in the same state of the finishing process have the same values and that the 3rd-order spectrum has a tendency to be left behind selectively by the polishing process. Evidence has been given that the harmonic analysis by the spherical function is successful for evaluating the sphericity of steel balls.

The shapes and thicknesses of the elastohydrodynamic oil films formed between a steel ball and a glass disk are measured using optical interferometry and compared with the established EHL theory. It is found that film profiles and thicknesses are markedly different from those predicted by the EHL theory, and their discrepancies depend upon the non-Newtonian response of oils and the difference in elastic moduli of contacting surfaces. As a result, it is concluded that in order to have a clearer understanding of the cause of surface failure and methods for its prevention, the EHL theory should be reconstructed by considering the solidification phenomenon of lubricating oils and pressure components parallel to the contacting surfaces.

Residual fatigue strength for CFRP (carbon-fiber-reinforced plastic) laminates having impact damage is evaluated with the four-point bending test. A steel ball launched by an air gun collides against CFRP laminates to generate impact damage. The static and fatigue tests are performed to evaluate the residual strength of impacted laminates. After the experiments, the laminates are observed by optical and ultrasonic microscopes. As a result, the static and fatigue residual strengths are reduced compared with virgin laminates, particularly when the impacted side of the laminates is compressed. It is found that the cracks from the impact impression and the delaminations following the cracks influence the fracture of the laminates.

A precision steel ball mounted at the center of the spindle end and an electronic capacitance type transducer installed on the tool slide with three dimensional sliding stage. Relative displacement in axial direction between the ball and the transducer is detected during spindle rotation. Detecting method of the central position is based on the fact that undulation component synchronized with rotational speed of the spindle in the displacement signal comes into minimum value at the central position of rotation. The results of preliminary experiments may be summarized as follows: (1) The new method is capable to detect the central position better than ±0.1 μm measuring resolution. (2)In case of the spindle with hydrodynamic bearings, central position of the spindle rotation very differs in different rotational speeds.

Square plates of laminated glass, whose interlayer is the polyvinyl butyral, are impacted transversely by a circular steel ball. The impact critical energies Uc and Up, which are the energy to initiate a crack in the outerlayer glasses and penetration energy of the ball, are measured by changing the dropping height of the ball. The static bending strength and Uc are dependent on the total thickness T of glass in the laminated glass. But, Up is independent of T and dependent on the thickness of the interlayer. In the laminated glass, the crack initiates from the glass of the impact side, and the next cracks initiate from the glass of the side on the reverse of the impact side. The penetration fracture of the laminated glasses consists of three steps. The first step is until initial cracks initiate in the outerlayer glasses, the second step is the bending fracture of the laminated glass, and the third step is the fracture due to shearing of the interlayer.

Friction coefficient, relative slip amplitude (fretting amplitude) and dissipation energy per one fretting cycle for steel ball-PMMA (polymethylmethacrylate) in fretting situation are investigated under various levels of normal load and amplitude of steel ball. Friction coefficient increases and relative slip amplitude decreases with fretting cycles in this study. Especially, dissipation energy per one fretting cycle was calculated by inputting a friction force and a relative displacement to a microcomputer. Equations between a tangential force and a tangential displacement based on the theory of elasticity were made by using the results of Mindlin who analyzed the contact of two elastic balls. It was shown that the experimental results of dissipation energy can be explained by these equations.

This paper deals with the acceleration of a steel ball in an annular jet and the impingement on the solid wall. An experiment is carried out using a pressurized water jet from a nozzle with an inner pipe. A steel ball is introduced into the nozzle with air through the inner pipe, and then accelerated by the annular water jet. The results show that the annular water jet with air supply from the inner pipe has a similar velocity distribution along the axial direction as that of normal jet without the inner pipe, which increases the impact velocity of the steel ball against the target plate. The velocity of the steel ball calculated by the equation of motion, taking into account the Basset's force, agrees well with the experimental data.

Fretting damaged surfaces of PMMA (polymethyl methacrylate) and steel balls in contact are directly and microscopically observed by optical microscope for various level of normal load, amplitudes of steel balls and fretting frequencies. It is found that corrugation occurs on the surface of PMMA during fretting and it is closely related with the wear of steel balls. After the initiation of corrugation, two types of wear are observed in our experiments : (a) the steel ball continues to slide on PMMA and the wear debris of the steel ball is enveloped in the softened PMMA ; and (b) the steel ball adheres to the corrugation and the wear debris accumulates at the boundary of adhered area. To study the cause of corrugation, the distribution of temperature of the fretting surface is numerically analyzed by the nonlinear transient heat conduction equation with the heat generated by the dissipation of energy during fretting. As a result, the increase of temperature by the dissipation of energy is very little, and it may be attributed to the viscoelastic property of PMMA.

By applying the extended Meyer's law proposed by the author to the relation among the depth of indentation h, the initial load Po, the major load Pm and the diameter of steel ball D, the following equation was obtained analytically : [numerical formula]where A and n called Meyer's index are constants for the material and Pt=Po+Pm. The relation was verified as correct experimentally. Furthermore, the effects of errors in Po, Pm and D on the hardness HK were calculated from the above relation and verified, and the total error ΣΔHK due to each permissible error of the tester can be restricted to ΣΔHKK/H≒±5 % in the worst case.

In this paper, an attempt is made to analyze the impulsive stresses in a glass plate subjected to the transverse impact of steel balls. For the case of a mass striking an infinite glass plate, the contact force variation is obtained by solving a nonlinear integral equation given by the use of Lagrange's classical plate theory and Hertz's law of contact. By regarding this force as an impact load for the case of the central impact of a steel ball on a supported circular glass plate, the impulsive stresses in a glass plate are analyzed using the three-dimensional dynamic theory of elasticity. Finally, it is shown that these analytical results are in good agreement with the experimental results.

In a theoretical consideration of the Rockwell hardness, the value of elastic recovery of indentation depth which occurs on removal of major load, becomes an important problem. The effects of shape of anvil, and elastic deformation of a frame and an indentor of a testing machine were examined. The true value of elastic recovery of indentation depth could be derived experimentally from the apparent readings of elastic recovery of the testing machine. Experimental results of elastic recovery of indentation depth agreed with the theoretical value calculated by the Hertz's equation. Therefore it may be considered that the elastic recovery of indentation in the case of Rockwell hardness testing is an identical phenomenon of elastic contact expressed by the Hertz's equation. The elastic recovery of indentation depth becomes larger when the major loads is larger, the diameter of the steel ball indentor is smaller, the testing specimen is harder and the Young's modulus of the specimen is smaller. The proportion of the elastic recovery to the total depth of indentation under major load becomes larger when the major load is smaller, the diameter of the steel ball indentor is larger, the testing specimen is harder and the Young's modulus of specimen is smaller.

Succeeding the previous reports, the new-designed spindle with a radial air-lubricated bearing and a thrust bearing made of a steel ball has been investigated. Such design of thrust bearing is taken owing to the fact that the thrust air-lubricated bearings with conical surface are not sufficient to reduce the frictional power as described in the previous reports. But the design of the upper radial bearing is left as same as it was in the 2nd report, because it had the good characteristic. As an exprimental result, it is clarified that the new spindle is superior to the other spindles especially in the range of high speed rotation, and its frictional power at 12, 000rpm is as small as about 25% of the ordinary oil-lubricated spindle, 60% of the air-lubricated spindle in the 1st report and 80% of the spindle in the 2nd report. And moreover, by measuring the flowing quantity of air and calculating the power required to compress air, the total power of the new spindle, that is the sum of the frictional and air-compressing power, is shown to be less than the power of the ordinary oil-lubricated spindle. This fact shows that the air-lubricated bearing is practically useful for the spinning spindles.

The superficial Rockwell hardness tester comes into use for quality control of thin metal sheets because of quickness of testing. Therefore the establishment of JIS (Japanese Industrial Standard) on this hardness tester is urgently needed. This report makes clear the effects of errors in the preliminary load W1 kg, the total load W2 kg and the diameter D mm of the steel ball indenter on the superficial Rockwell hardness reading. The extended Meyer's law that has been successfully used for the Rockwell hardness test is again applied to this test although the loads in the latter are smaller than in the former. The deviation of the hardness reading is theoretically analyzed and the following formula is obtained, taking the Meyer's index n as 2.3. For example, ΔHR30T=(100-HR30T)(0.044 9ΔW1-0.033 7ΔW2+0.466ΔD). A good agreement is observed between the calculated values and the experimental ones. In addition, the authors' proposal for establishing a tentative JIS is shown.

The characteristics of three integral measuring methods of surface roughness which contain the method by means of electric capacity (a), the method by means of the pneumatic micrometer (b) and the method by means of indentation of a steel ball (c), are investigated experimentally on the same test pieces. By the methods (a) and (b), mean depth of surface roughness is indicated and by (c) other indication is given. These integral measuring methods are suitable for testing the surface on the standpoint of wear, for the indications are different by the forms of roughness even if the maximum depth is same.

On the error introduced into Rockwell hardness numbers by the error of steel ball diameters, this paper reports the results of experiment and the caluculated results from Meyer's law. Results obtained by observation and theoretical calculation respectively coincided well with each other. Accordingly, the errors caused by the errors of total load W2 kg, preliminary load W1 kg and diameter D mm are shown as follows : [numerical formula].

There is no method of conversion or comparison between Brinell hardness numbers which are obtained by different steel ball and different load respectively but they satisfying a special condition. In this report, using relations obtained in the former report, the relation to convert between Brinell hardness numbers obtained in all conditions was introduced, which was testified by previous experimental results. To convert the hardness number H1 (the depth of indentation is h1) or H1' (the depth of indentation h1') obtained by a steel ball of radius R1 and load P1 and P1' respectively, to the hardness number H2 which will be obtained with a steel ball of radius R2 and load P2, the conversion equation was given as following : where, [numerical formula]