Rigidity Of Shaft Research Articles

Surface roughness discrimination with the long cane: Effects of cane tips, handle, shaft rigidity, and swinging speed

This study examined the effects of cane tip type, cane tip size, cane shaft rigidity, cane handle material, and cane swing speed on the cane user’s ability to discriminate surfaces of different roughness. A repeated-measures design with block randomization was used for each of the three studies. Blindfolded sighted and visually impaired participants attempted to identify which of the two grooved aluminum plates was rougher by swiping the plates using different cane tips, shafts, handles, and swing speeds. Participants correctly identified the rougher plate at a higher percentage with smaller cane tips (77.6% ± 8.7%) than with larger cane tips (72.1% ± 7.2%), p = .029, r = .54. Pencil tips (76.9% ± 8.4%) were more advantageous than ball tips (72.8% ± 6.5%), p = .028, r = .55. Slower cane swing speed (84.4% ± 2.6%) also allowed the participants to better discriminate the surfaces than faster swing speed (76.6% ± 6.0%), p = .002, r = .80. However, the cane shaft rigidity ( p = .499, r = .22) and cane handle material ( p = .694. w2 = 0.02) did not have a significant effect on the cane user’s ability to discriminate the surfaces of different roughness. Given these findings, a cane user may want to use a smaller and/or cylindrical cane tip as opposed to larger and/or spherical cane tip for better surface texture change detection. In addition, a cane user may not want to swing the cane too wide or walk too fast since wider cane swing and faster walking speed tend to result in faster cane swing speed, which can compromise one’s ability to detect sudden changes in walking surface texture. That being said, an Orientation and Mobility (O&M) specialist should assess each person’s traveling environment when determining which cane tip and swing speed to use in a given situation.

PROPELLER SHAFTING DYNAMICS UNDER IMPULSE ACTION

Propeller shafts and countershafts are bent quite often on sea and river vessels. The cause of the curvature is a strong load on this node of the ship’s power plant. In addition to bending, the shafting experiences longitudinal and transverse loads with a dynamic and static component. A large number of scientific papers have been devoted to the study of the dynamics of the propeller and shafting. However, the problem has not been completely solved, and the increase in damages during the shafting operation and its intensive wear only confirm the relevance of further research in this direction. The aim of the work is to determine the dynamic forces in the shafting, which occur during impulse action due to the propeller impact on the ice. A model of a two-stage elastic rod with inert disks at the ends is presented in the paper. It allows considering different situations of dynamic impact on the shafting and propeller. The following design features such as different stiffness of the shaft sections, different speed of elastic waves of deformation (different densities and modules of elasticity on the shaft sections), reduced inertial load from the moving parts of the drive, can be taken into account in the model. It is concluded that the frequency of the main form of oscillations mainly depends on the inertial loads concentrated at the ends and the shaft rigidity. The proposed simplified model of the inertialess shaft makes it possible to determine the angles of rotation of the shaft sections with sufficient accuracy. For different sections of the stepped shaft, the dynamic torque coefficient can differ significantly.

Straightening of low-rigid cylindrical details. Part I. Justification of the type of loading and modes at transverse straightening

For straightening of low-rigid cylindrical details like shaft and axes different types of loadings are considered which form tension different in size and in distribution. As the perspective direction, it is possible to consider correction by a bend at the influence of the distributed loading with the subsequent hardening of a billet by superficial plastic deformation based on a cross cheesing of it by flat plates. Purpose of the work was to define tension of the billet at cross correction for the choice of more effective type of loading and processing rational modes. The mathematical apparatus was used based on laws of the theory of an elastoplastic solid and Ansys Workbench software package. Novelty is the research of effective methods of loading at cross correction of cylindrical details. As a result of analytical calculations, value of the residual tension providing correction of cylindrical details was determined. Residual tension necessary for correction of cylindrical details depends on an initial deflection, material and preparation rate. Tension of cylindrical details was defined depending on a type of the application of cross loadings. Bend tension for correction of a shaft at distributed loading is less, than tension from action of cross force. For correction of a shaft with a diameter of 10 mm, 200 mm long and an initial deflection of 0.5 mm it is necessary to create bend tension equal to about 370 MPa. An effective method of loading at cross correction of cylindrical details is the bend at influence of the distributed loading. The received extreme values of bend coefficients are from 5.3 to 5.5 for all cases of shaft rigidity at correction by cross bend at distributed loading with l/L relation equal to 0.8. The developed mathematical model gives quite reliable values of the residual tension providing correction of cylindrical details. The analytical dependence for determination of the size of general deflections and definition of an effective loading type can be recommended for practical use in production for achievement of precision accuracy of low-rigid details like shaft.

Increase of bending rigidity of long-dimensional shaft by surface plastic deformation

The results of computer simulation of bending stiffness of cylindrical part are presented. The effect of residual stresses on the maximum bending is considered. It is established that the formation of residual stresses in the surface layers of a certain thickness have a positive effect on increasing the rigidity of the cylindrical pieces. The influence of the degree of relative deformation with the covering surface plastic deformation on the flexural rigidity of long shafts is determined. It is established that the degree of relative deformation in the range from 0.4 to 1.0% has a positive effect on the flexural rigidity of the shafts. The process in question can be implemented without the use of environmentally hazardous lubricating cooling technological means, which makes it possible to attribute it in the future to one of the types of green mechanical processing technologies.

Straightening of Relatively Flexible Cylindrical Parts. Part I. Establishing the Loading Conditions in Transverse Straightening

Relatively flexible cylindrical parts (shafts and axles) may be straightened by loads produced by different stresses in different distributions. A promising method is straightening by flexure under a distributed load, with subsequent strengthening of the workpiece by surface plastic deformation based on transverse rolling between flat plates. The goal in the present work is to determine the stress state of the workpiece in transverse straightening so as to select the best type of load and treatment conditions. The mathematical analysis is based on the theory of an elastoplastic solid; ANSYS Workbench software is employed. Effective methods of loading in the transverse straightening of cylindrical parts are determined. Analytical calculations yield the residual stress corresponding to straightening of the cylindrical parts. The residual stress required for straightening depends on the initial flexure, the material in the workpiece, and its size. The stress state of cylindrical parts is determined for different types of transverse loading. The flexural stress for straightening of a shaft under a distributed load is less than the stress due to a transverse force. To straighten a rod (diameter 10 mm, length 200 mm) with initial flexure 0.5 mm, flexural stress of about 370 MPa must be created. In the transverse straightening of cylindrical parts, flexure under the action of a distributed load is an effective loading method. Limiting flexural coefficients of 5.3–5.5 are obtained for all values of the shaft rigidity in straightening by transverse flexure under a distributed load when l/L = 0.8. The proposed mathematical model correctly determines the residual stress corresponding to straightening of the cylindrical parts. The formula derived for calculating the total flexure and determining the effective load may be recommended for practical use in production conditions so as a ensure precise straightening of relatively flexible parts such as shafts.

Investigation of the fluctuation of the static axial rigidity for double-nut preloaded ball screws

This article aims to investigate the fluctuation of the static rigidity for preloaded ball screws. Based on the correlation between preload and friction torque, a new model to calculate the contact rigidity by friction torque is proposed. Meanwhile, a novel test bench is constructed to measure the static stiffness at different positions. The experimental results agree well with the theoretical values, which proves the validity of the model. Furthermore, it is found that the screw shaft rigidity has the greatest influence on the system stiffness fluctuation, compared to the bearing rigidity, and the torsional rigidity. For the feed system, increasing the bearing rigidity, which is the lowest stiffness of the whole system, is an effective method to increase the system stiffness. The study provides an accurate method to obtain the stiffness fluctuation in the effective travel of ball screws, which is significant for improving the positioning accuracy of ball screws and computer numerical control machine tools.

FINITE ELEMENT ANALYSIS OF CENTRELESS-LUNETTE TURNING OF HEAVY SHAFT

Dynamics of huge renovated lathe is simulated. Turning scheme concerns to heavy rotor shaft finishing. Lofty parts and milling head may create dynamic problems. Static, modal and harmonic frequency response function simulations were provided. Bearing system consists of bed, support, tool, lunettes, tailstock. Headstock didn’t take part in shaft holding. Static and dynamic rigidities founded 3–4 times less for support than for shaft. Tool rigidity lessens from 186.5 to 11.9 N/µm for speeding from slow to near resonance turning. Twelve lathe eigenmodes were evaluated. Two eigenmodes are most dangerous. It is “shaft swinging on lunettes” (M1, 26.7 Hz) and “support pecking” (M3, 54.4 Hz). Bed has excessive flexibility due to through holes and lack of inner ribbing. Polymer concrete filling is moderately effective. Changing two-lunette (2L) scheme to three-lunette (3L) increases rigidity of shaft at 2.09 times at statics but gives limited action in dynamics. Resonant peaks on frequency response function are lowered only at 1.32 times for M1, M3. Effect of dynamic damping is revealed under condition of proximity middle lunette to lofty support. Support serves as tuned mass damper. Measures of machine tool reinforcement are simulated. Shaft swinging according to M1 may hardly be blocked by passive means. It would be better to bypass it. “Support pecking” resonance (M3) succumbs to only full set of measures. Small effect of partial reinforcement is predicted. Three frequency intervals are recommended for turn-milling at huge lathe: pre-resonant (<20 Hz), inter-resonant (35–45 Hz) and post-resonant (>65 Hz). The last one is more suited. Next design step is to create triangle inner ribbing system or caissons inside of bed.

Giant scaffolding protein AHNAK1 interacts with β-dystroglycan and controls motility and mechanical properties of Schwann cells.

The profound morphofunctional changes that Schwann cells (SCs) undergo during their migration and elongation on axons, as well as during axon sorting, ensheathment, and myelination, require their close interaction with the surrounding laminin-rich basal lamina. In contrast to myelinating central nervous system glia, SCs strongly and constitutively express the giant scaffolding protein AHNAK1, localized essentially underneath the outer, abaxonal plasma membrane. Using electron microscopy, we show here that in the sciatic nerve of ahnak1(-) (/) (-) mice the ultrastructure of myelinated, and unmyelinated (Remak) fibers is affected. The major SC laminin receptor β-dystroglycan co-immunoprecipitates with AHNAK1 shows reduced expression in ahnak1(-) (/) (-) SCs, and is no longer detectable in Cajal bands on myelinated fibers in ahnak1(-) (/) (-) sciatic nerve. Reduced migration velocity in a scratch wound assay of purified ahnak1(-) (/) (-) primary SCs cultured on a laminin substrate indicated a function of AHNAK1 in SC motility. This was corroborated by atomic force microscopy measurements, which revealed a greater mechanical rigidity of shaft and leading tip of ahnak1(-) (/) (-) SC processes. Internodal lengths of large fibers are decreased in ahnak1(-) (/) (-) sciatic nerve, and longitudinal extension of myelin segments is even more strongly reduced after acute knockdown of AHNAK1 in SCs of developing sciatic nerve. Together, our results suggest that by interfering in the cross-talk between the transmembrane form of the laminin receptor dystroglycan and F-actin, AHNAK1 influences the cytoskeleton organization of SCs, and thus plays a role in the regulation of their morphology and motility and lastly, the myelination process.

Determining the reliability of the cantilever shaft in a conical gear transmission with limited statistical information

A method is proposed for estimating the reliability of a shaft with limited information regarding the parameters of the limiting state. It may be used to estimate the reliability in terms of static strength, fatigue strength, and shaft rigidity, so as to ensure safe operation.

Interval Rotor-Bearing Systems Stability Via Monte Carlo Simulation

This paper considers the stability problem of a rotor-bearing system with interval parameters. The system comprises a rotor that is supported by two journal bearings with different characteristics. The bearings stiffness and damping parameters as well as the shaft rigidity are assumed known only within lower and upper bounds. Stability analysis of the considered system is treated in this work by applying two approaches, namely; interval analysis and Monte Carlo simulation. The results of the paper show the usefulness of the Monte Carlo simulation approach as applied to the underlying problem as compared to the interval analysis approach.

Bounds for the torsional rigidity of shafts with arbitrary cross-sections containing cylindrically orthotropic fibres or coated fibres

In this paper we derive bounds for the torsional rigidity of a cylindrical shaft with arbitrary transverse cross-section containing a number of cylindrically orthotropic fibres or coated fibres. The exact upper and lower bounds depend on the constituent shear rigidities, the area fractions, the locations of the reinforcements as well as the geometric shape of the cross-sections. Specific bounds are derived for circular shafts, elliptical shafts and cross-sections of equilateral triangle. Simplified expressions are also deduced for reinforcements with isotropic constituents. We verify that when additional constraints between the constituent properties of the phases are fulfilled, the upper and lower bounds will coincide. In the latter case, the fibres or coated fibres become neutral under torsion and the bounds recover the previously known exact torsional rigidity.

Parametric study of dynamics of worm and worm-gear set under suddenly applied rotating angle

The dynamics of a worm-gear set under instantly applied rotating angle are affected by several factors (including the friction force and elastic deformation of the surface between gear teeth). It is found that those factors cause a non-negligible rotational positioning error. The goals of this study are to (1) set up a mathematic model, (2) carry out a numerical simulation, and (3) carry out an experiment and compare it with the numerical results. The experiments and numerical results have very good agreement. In this research, the moment-inertia of fly wheel, friction, rigidity of shaft and rigidity of gear tooth are also studied. The results can be used as error estimations of relevant angles, angular speed and angular acceleration under a suddenly applied rotational angle, and are useful for establishing the error compensation required for position control.

Multiple modulation torque planning for a new golf-swing robot with a skilful wrist turn

A new golf-swing robot that included a feed-forward controller in the shoulder joint and a passive wrist joint was suggested in previous studies to more closely model a skilful golfer. In this study, multiple modulation torque planning for a new golf-swing robot that is capable of modelling a skilful golfer’s swing with a delayed wrist turn was analytically examined. The twostep modulation torque included the effects of whole-body motion on shoulder acceleration, which improved the efficiency index of the swing motion and the club head speed at impact with a correctly timed wrist turn. In addition, it was demonstrated that the optimum moment of inertia and optimum design of club shaft rigidity for several types of golfers could be determined by torque planning in a virtual performance test.

Multiphase two-screw pump A8 2VV 125/40–80/40 for a differential pressure of 40 bar

Characteristics of pump versions with front and rear reducers for pumping I40 oil and water are given. Flexure of the screws and loads on the supports are assessed. It is noted that with respect to screw rigidity and loads on the supports a three-support structure with a front reducer is superior to a structure with a rear reducer. A two-support structure, being inferior in shaft rigidity to a three-support structure, has smaller loads on the supports.

A parametric study on rocking vibration of rotating disk/spindle systems with hydrodynamic bearings: rotating-shaft design

The system studied in this paper is a rotating disk/spindle assembly supported by hydrodynamic bearings with a rotating shaft design. Based on an experimentally verified mathematical model [1, 2], this paper presents how various spindle parameters affect critical vibration modes of the system, such as half-speed whirls and (0, 1) unbalanced modes (i.e., rocking modes). The parameters studied include number of disks, hub/shaft interface stiffness, shaft rigidity, thrust bearing location, radial bearing stiffness, radial bearing damping, and radial bearing locations. To simulate operational tests, the numerical study focuses on frequency response functions (FRF) of rotating disk/spindle systems subjected to linear base excitations. Simulation results show that 1-disk configuration has smaller FRF amplitude than the 4-disk configuration. In addition, the amplitude of half-speed whirl is primarily controlled by the radial bearing stiffness. In contrast, the amplitude of (0, 1) unbalanced modes is dominated by hub/shaft interface stiffness. Finally, radial bearing locations significantly affect the amplitude of half-speed whirls and (0, 1) unbalanced modes simultaneously.

Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type

In this paper, an approximate analytic procedure is developed for solving the strong non-linear differential equations of the Duffing type with complex-valued function which describes the dynamical behavior of many real systems. The method is based on the elliptic-Krylov–Bogolubov procedure where the solutions are the Jacobi elliptic functions. As an example, the self-excited vibrations of the rotor with variable shaft rigidity are considered. The analytical results of this example are compared with numerical ones and excellent agreement is found between them.

Study of Influences of Characteristics of Golf Club on Impact Phenomenon.

In this study, the influences of the characteristics of golf dub, such as the rigidity of shaft and spring constant of head, are examined on the impact phenomenon such as the dynamic deformation of shaft and the release velocity of ball by the analysis on the ball-head hitting line. As the results of numerical analysis, it is seen that the optimum spring constant of head is as same as the one obtained by impedance matching condition even if the dynamic deformation of shaft is considered. It is also seen that the release velocity of ball isn't influenced by the dynamic characteristic of shaft when the impact phenomenon is only considered.

Dynamic Characteristics of Hard Disk Drive Spindle Motors—Comparison Between Ball Bearings and Hydrodynamic Bearings

Recently, many computer hard disk drive companies and spindle motor manufacturers have been looking for a substitute for ball bearings to continue making dramatic progress in increasing the capacity of data storage systems. In this paper, the frequency-forced responses of hard disk drive spindle motors supported by both ball bearings and liquid-lubricated spiral groove hearings (SGBs) were studied experimentally. It is found that both shaft rigidity and disk flexibility have great effects on the natural frequency of the spindle motor conical (rocking) mode. The high damping capacity of the SGB is able to suppress the vibration amplitudes of both motor rocking mode and the flexible disk modes. But at a very low frequency range, the SGB motors displayed a large amplitude in the axial direction vibration test. With an adequate bearing design, the SGB motors have proven their superior dynamic characteristics.

Flexibility control of solar battery arrays (3rd report Vibration and attitude control with consideration of the dynamics of a reaction wheel as an actuator)

An actuator problem is dealt with in this paper in controlling vibrations of flexible solar battery arrays and orienting the array toward the sun correctly. A Lero momentum type of a reaction wheel which is in common use is selected as an actuator in space here. Then the flexible array can be controlled by a reaction force working in the opposite direction of the rotation of the reaction wheel. Therefore, there is close coupling between the flexible array and the reaction wheel. First, the dynamics of the coupling system is derived here including the shaft rigidity between them under the assumption that the flexible array vibrates only in the bending way. Then the feedback control law is given to control the orientation and the vibration of the flexible array, employing the differential solar battery sensors as vibration and orientation measurement. The effect of the inertia moment of the reaction wheel is also considered experimentally with respect to the settling time of the flexible array.

Torsional stress state in a hollow shaft with longitudinal slots

1. Comparatively high stress concentrations arises around the bottom of a slot. A slot whose bottom has the form of a half-circle shows a stress-concentration factorαk=5.67−6, whereαk=σmax/τnom andαIV=2.8[αIV=(σIV)max/(σIV)nom]. 2. There is a general tendency for the stresses near the bottom of the slot to increase with the radius of curvature on account of the reduction in shaft rigidity (αk rises to 7.5–8). 3. Elliptical rounding instead of semicircular rounding reduces the stress concentration, withαk falling to 4.2–4.5 andαIV to 2 (by comparison with 5.7 and 2.8 respectively for semicircles). 4. The stress concentrations increase considerably at points where the direction changes sharply, so particular care should be taken in making shafts to ensure that the shape of the bottom of the slot corresponds closely to the specifications.