Torsion Of Shaft Research Articles

Research on the Marine Shafting Torsional Vibration with Gears Transmission

Abstract The torsional vibration of marine propulsion shafting has been studied for more than a century. With abundant research achievements and experiences, a systematic approach of vibration calculation has been put forward for ship industrial applications. However, literature review indicates that when processing the gear transmission in the shaft line, the meshing motion has been treated as rigid mass in the equivalent equation of energy conservation, which leads to a certain error between the theoretical and experimental results of torsional vibration. Hence, to improve the calculation accuracy, a new method which considers the gear meshing stiffness is proposed in this paper. By taking the propulsion shafting of 3700DWT IMO TYPE II CHEMICAL TANKER as the research object, the forward computing formula of the shaft torsional vibration was first obtained using gear system dynamics theory. Then, the gear mesh stiffness was derived from the length variation of gear contact line. Finally, the free torsional vibration frequency was calculated considering the influence of the gear meshing force. The real marine test was implemented to verify the proposed method. The calculation results show that the new approach can track the actual torsional vibration more precisely than that without taking the gear meshing impact into account.

Saint-Venant’s torsion of composite shafts reinforced with arbitrarily or periodically dispersed coated fibers

It is known that a circular shaft containing a number of composite cylinders, upon suitably designed material parameters, is an exactly solvable configuration under Saint-Venant’s torsion [Chen, T., Benveniste, Y., & Chuang, P. C. (2002). Exact solutions in torsion of composite bars: Thickly coated neutral inhomogeneities and composite cylinder assemblages. Proceedings of the Royal Society A, 458, 1719–1759]. Here we consider the boundary value problem of a circular shaft containing coated fibers under torsion without any restrictions on the material parameters. The formulation is based on a complex variable method together with simple mapping techniques, representing the warping fields in Laurent or Taylor series based on different origin points. Particularly when the coated fibers are periodically dispersed inside the host shaft, we show that the unknown coefficients for each coated fiber are correlated in specific manners, and thus rendering the governing framework much simplified. We verify analytically that our results conform with the exact results of partly neutrality and complete neutrality of the exact solvable configuration of a circular shaft containing neutral coated fibers. This work presents a feasible solution procedure that complements the exact configurations in which the material parameters must follow restrictive constraint, and also provides an estimate for the torsional rigidity in which the bounds are not sufficiently close.

PI Control, PI-Based State Space Control, and Model-Based Predictive Control for Drive Systems With Elastically Coupled Loads—A Comparative Study

Three different control methods for the speed control of drive systems with elastically coupled loads are presented and compared. In drive applications where the load is connected to the driving motor with a drive shaft that has a finite stiffness, unwanted mechanical dynamics can occur. These unwanted dynamics can stress both the mechanical and electrical drive components. Furthermore, the shaft torsion, if neglected in the control synthesis, can dramatically reduce the achievable control performance. To overcome these challenges, the design, analysis, and comparative study of three speed control methods for a drive system with resonant loads are carried out. The considered control methods are the following: a conventional proportional-integral (PI) control, a PI-based state space control, and a model-based predictive control. To ensure a suitable basis for their comparison, the three different speed control methods are designed with equal bandwidths and are verified with the same test setup. Furthermore, all speed control methods presented use only the drive-side speed measurement to control the drive speed.

Study of femoral torsion during prenatal growth: Interpretations associated with the effects of intrauterine pressure

The developing fetus is protected from external environmental influences by maternal tissues. However, these structures have a limited elasticity, such that the fetus must grow in a confined space, constraining its size at the end of pregnancy. Can these constraints modify the morphology of the fetal skeleton? The intensity of these constraints increases between 5 months and birth, making it the most appropriate period to address this question. A sample of 89 fetal femora was analyzed, and results provide evidence that during this period, the torsion of the femoral shaft (quantified by means of a new three-dimensional method) increases gradually. Two explanations were considered: this increase could signal effects of constraints induced by the intrauterine cavity, developmental patterning, or some combination of these two. Different arguments tend to support the biomechanical explanation, rather than a programming pattern formation. Indeed, the identification of the femur as a first degree lever, created by the hyperflexion of the fetal lower limbs on the pelvis, could explain the increase in femoral shaft torsion during prenatal life. A comparison with femora of infants is in accordance with this mechanical interpretation, which is possible through bone modeling/remodeling. Although genetic and epigenetic mechanisms may regulate timing of fetal development, our data suggest that at birth, the fetal skeleton also has an intrauterine mechanical history through adaptive bone plasticity.

Determination of Hardening Coefficient of Large Strain Constitutive Model Based on Torsion Tests

Uni-tension test and torsion test with specimens of A3 steel are completed, and deformation rate, the spin of Euler configuration to Lagrange configuration and generalized Jaumann rate of Kirchhoff stress in torsion problem are given. Large strain constitutive relationship with generalized Jaumann stress rate is studied based on torsion test. The simple shear problem is discussed by using the constitutive model given in this paper. The result indicates that the hardening coefficient of constitutive model with generalized Jaumann rate may be given by the same expression as that of constitutive model with Jaumann objective rate when determining by using torsion tests and the shear stress response curve in simple shear problem obtained by using the constitutive model in this paper is similar to the shear stress-strain curve given in solid circular shaft torsion tests.

Investigation on Finite Strain Constitutive Model with Logarithmic Strain Based on Torsion Experiments

In this paper, a finite strain constitutive model was proposed by the additive decomposition of the logarithmic strain rate and the generalization of small deformation constitutive model and a complete analysis was made for an isotropic hardening J2 flowing finite strain constitutive model based on torsion experiments. Logarithmic strain and Jaumann stress rate were discussed in solid circular shaft torsion deformation. Utilizing the results obtained from solid circular shaft torsion experiments, the plastic rigidity function in constitutive model was determined. The simple shear problem was studied by using the constitutive model given in this paper. The results shows that the plastic rigidity function corresponding to logarithmic strain was different from one to Green strain and finite strain constitutive model should be analyzed by logarithmic strain and torsion experiments.

Investigation on the Large Strain Elastoplastic Constitutive Model with Logarithmic Stress Rate Based on Torsion Experiments

A complete analysis was made for an isotropic hardening rate-type elastoplastic constitutive model with the logarithmic stress rate utilizing solid shafts torsion test in the large strain range. The deformation rate, the logarithmic spin, the Kirchhoff stress and the logarithmic stress rate of the Kirchhoff stress were obtained for the free-end solid shaft torsion test when considering Swift effect. Utilizing the results obtained from the solid shaft torsion test, the plastic rigidity function in the isotropic hardening elastoplastic constitutive model was determined at finite strain range. It was shown that the influence of Swift effect on finite strain constitutive model was related to the varying rate of axial deformation and the varying rate of radius deformation to shear strain, and the plastic rigidity function corresponding to the logarithmic stress rate was the same as that corresponding to the Jaumann stress rate when neglecting Swift effect. Solid shaft can achieve very large strain without buckling in torsion test. They can be used to accurately determine the large strain elastoplastic behavior [1-3]. Many researchers are interesting in the theoretical study and experimental study on large strain torsion deformation [1-7]. Jaumann objective stress rate is often adopted for study on constitutive models [1], but Nagtegaa J C [8] discovered that Jaumann stress rate may render oscillatory stress response for anisotropic kinematics hardening simple shear problem. After that, great interests focus on the issues of choosing an appropriate objective stress rate in rate type constitutive models. The expression of logarithmic stress rate with logarithmic spin can be found in Xiao H [9]. It had been proved that among all rate type elastoplastic constitutive models, only those with the newly discovered logarithmic stress rate fulfill the self-consistency criterion. In this paper, the parameter in large strain isotropic hardening elastoplastic constitutive model is determined with logarithmic rate of Kirchhoff stress utilizing solid shaft torsion test.

Remarks on The Use and Misuse of The Semi-Inverse Method in The Nonlinear Theory of Elasticity

We show, by considering some specific examples, that in the nonlinear theory of elasticity the application of the semi-inverse method has to be carried out very carefully. Usually, the strategy followed in applying the semi-inverse method while dealing with complex models is to generalize forms of solutions already known within the framework of a simpler theory. This is a smart strategy from a mathematical point of view, but from the physical point of view, it may be imprudent. For example, in the theory of nonlinear elasticity, we are at times motivated by the results obtained in the incompressible case to arrive at an understanding of what happens in the compressible case, and by doing so, many important exact solutions for special classes of compressible elastic materials have been obtained successfully. Sometimes, the admissibility of a given deformation field is considered to delineate special classes of constitutive laws. We wish to point out that the classes of constitutive equations thus identified from the standpoint that it may admit a type of deformation may lead to models that exhibit physically unacceptable mechanical behavior. To illustrate the dangers inherent to merely turning the mathematical crank to determine classes of constitutive equations where a certain class of deformations are possible, we consider the torsion of a cylindrical shaft and the propagation of transverse waves in a compressible nonlinear elastic material and show that care has to be exercised in appealing to the semi-inverse method.

Convergence of solutions for noncanonical bodies found by the boundary-shape perturbation method

The exact solution of the problem of the torsion of a solid cylindrical shaft with an ellipsoidal cavity is expanded into a series in powers of an eccentricity parameter. At the points of the cavity where the stress concentration is maximum (minimum), the expansion coefficients for the exact and approximate solutions coincide. The approximate solution is obtained by the first version of the boundary-shape perturbation method, which is used to solve three-dimensional problems of elasticity for bodies of revolution with nearly canonical shape. Successive approximations as an iteration process are shown to converge to the exact solutions

Finite element modeling of warping in smart piezoelectric noncircular shaft

Torsion often occurs in real engineering structures such as beams, shafts, and framed structures in conjunction with bending actions. This work mainly focuses on torsion of shafts with noncircular sections. Generally, torsion of beam with noncircular cross-section produces warping or nonuniform out-of-plane displacements in the cross-section. Warping introduces longitudinal strains as the section twists and significantly affects the torsional stiffness. The principal objective of this work is the development of a smart structure technique, which involves piezoelectric materials that necessarily involve coupled mechanical and electrical field, for the control of warping displacement of twisted noncircular shafts. In this work, expressions for warping displacement and shear stress at a section have been derived for the coupled load case. This work focuses on two interrelated cases in relation to the warping of the noncircular bar. Firstly, the warping of cross-section of host structure is analyzed. Secondly, the warping control of a smart shaft with selected noncircular cross-section is analyzed. The paper also describes a Finite Element procedure for the 2D and 3D analysis. In this paper, numerical results have been generated and plotted using MATLAB® for different cases like pure mechanical loading, pure electrical loading, and the coupled field loading with a view to quantify the stiffness characteristics of smart shaft. The finite element calculations are made with ANSYS® for the present analysis work.

Using linear and geometric morphometrics to detect intraspecific variability and sexual dimorphism in femoral shape in Alligator mississippiensis and its implications for sexing fossil archosaurs

ABSTRACT Sexual size dimorphism (SSD) is prevalent among extant vertebrates and presumably was as common among fossil archosaurs. Here, we test the hypothesis that femur shape is a reliable indicator of sex among archosaurs using linear and geometric morphometric analyses on a large sample of sexed Alligator mississippiensis femora. Linear regression of femoral dimensions onto femur length in alligators shows that male femora are the largest and stoutest in midshaft and articular dimensions, whereas females show more variation in their midshaft dimensions. Using thin-plate splines analyses, regression of partial warps onto alligator femur length revealed that with increasing size the midshaft expands whereas shaft torsion diminishes, that femur shape differs according to sex, and that females show the maximum amount of shape variation at a size 72% that of the largest males. However, sexual dimorphism accounts for only 3% of the total femur shape variation in the sample. Differences in reproductive physiology (e.g, shelling eggs in females) may account for some of the fine morphological differences between males and females. However, size and individual variation appear to effect femur shape the most. These results have significant implications for inferring fossil archosaur sex from femoral dimensions and shape.

Coupling Vibrations in Rotating Shaft-Disk-Blades System

Applications that have coupling among shaft, disk, and blades are investigated. A shaft-disk-blades unit often seen in engineering is presented. The governing relations for shaft torsion, disk bending, and blade bending are derived. Free vibration is then studied and the results show that shaft-blade (SB), shaft-disk-blades (SDB), disk-blades (DB), and blade-blade (BB) type coupling modes exist. The SDB and DB modes are observed to be evolved from the original SB and BB modes in a previously studied case of a rigid disk case. The effects of stagger angle (β) on the coupling of the components are also examined. In the two extremes at β=0, the disk is uncoupled, and at β=π∕2, the shaft is uncoupled. In between, the three components are coupled. As β increases, the disk participates more strongly, but the shaft behaves in exactly the opposite way. A SB mode at β=0 will transfer into a SDB mode as β increases, eventually becoming a DB mode at β=π∕2. Basically, as β increases, the disk flexibility contributes more and reduces the natural frequencies. The effect of rotation is the last to be discussed and the results show that frequency bifurcation and loci veering occur as the rotation rate increases because of disk flexibility. For SD and SDB modes, the frequency loci veer and merge at certain rotational speeds. In these regions, there exist mode exchange and instability problems.

Comparison of performance characteristics between new and reprocessed electrophysiology catheters

Electrophysiology (EP) catheter reprocessing is widespread and previous studies have examined clinical performance, sterility and safety of these reprocessed devices. Here we compare the intrinsic engineering characteristics, electrical, mechanical and safety, between new and reprocessed devices. New (58 devices) and clinically used (five times)/reprocessed (165 devices) EP catheters from five manufacturers were employed to examine and compare catheter electrode continuity, electrode isolation, electrical leakage current, shaft torsion and stiffness characteristics as well as tip buckling and bond strengths. Electrode continuity, isolation and leakage currents for both new and reprocessed EP catheters were within acceptance criteria for electrode continuity (<30 Omega) and shaft electrical leakage (<0.5 mA) as well as electrode isolation (>200 Omega). In addition, reprocessed catheters were equivalent when compared with their new counterparts. While catheter shaft torque forces varied five fold amongst manufacturers, comparison between new and reprocessed devices within a manufacturer showed no significant differences. Likewise shaft stiffness showed no significant difference between new and reprocessed devices. Average tip buckling forces for all catheters were substantially below the acceptance criteria of 0.45 lb (between 0.04 and 0.1 lb) with differences between new and reprocessed catheters not being significant. All bond strengths for both new and reprocessed catheters exceeded the acceptance criteria specified in ISO 10555-1. This study found that reprocessed EP catheters which had undergone five actual clinical use/reprocessing cycles met and exceeded acceptance criteria specified by industry standards as well as individual manufacturer's criteria for both electrical and safety characteristics. We conclude that reprocessed EP catheters exhibit electrical, mechanical and safety characteristics which are equivalent to their new counterparts.

The Influence of a Mistuned Blade’s Staggle Angle on the Vibration and Stability of a Shaft‐Disk‐Blade Assembly

The influence on coupling vibrations and stability among shaft‐torsion, disk‐transverse and blade‐bending of a rotor system with a mistuned blade′s staggle angle was investigated analytically. A shaft‐disk‐blade system has been found existing two types of coupling vibrations, disk‐blade (DB), and blade‐blade (BB) modes when the shaft was assumed rigid. If the shaft′s torsional flexibility was taken into account, an additional type of coupling modes, shaft‐disk‐blade (SDB), appeared. When an angle‐mistuned blade existed, the blades periodicity was destroyed and it was found to change not only the natural frequencies but also the types of modes. Due to blade′s mistune, the shaft torsion had to participate to balance such that DB modes vanished and replaced by SDB modes. A mistuned staggle angle was numerically found to alter the natural frequencies in an almost linear trend. At last, the rotational effects were found to merge frequency loci and eventually reached an instability point. Very interestingly, a mistuned blade diminished the possible instability caused by blade‐dominating modes, which existed in a perfect and periodic rotor. In words, the rotor might benefit from a mistuned blade from the stability viewpoint. The shaft‐dominating mode, yet, was unaffected by the mistune and retained a possible instability.

Individual Blade Pitch Control for the Controls Advanced Research Turbine (CART)

Pitching the individual blades of a horizontal-axis wind turbine allows control of asymmetric aerodynamic loads, which in turn influences structural loads in the nonrotating frame such as tower side-side bending. These loads are not easily controlled by traditional collective pitch algorithms. This paper presents the design of individual pitch control systems for implementation on the Controls Advanced Research Turbine (CART) in Colorado to verify controller performance for load attenuation. The control designs are based on linear time-periodic state-space models of the turbine and use optimal control methods for gain calculation. Comparisons are made between new individual pitch, new collective pitch, and baseline controller performance in both above rated and below rated wind conditions. Results from simulations show the potential of individual pitch to reduce tower side-side fatigue damage in above rated wind speeds (by 70% compared to baseline control) but with no improvement over collective pitch in below rated wind speeds. Fatigue load reductions in tower fore-aft, shaft torsion, and blade flap are also observed. From 13h of field testing, both collective and individual pitch controllers achieve a reduction in fatigue damage. However, the superior performance of individual pitch control observed in simulation was not verified by the field test results.

이동질량에 의한 중공축의 비틀림 진동해석

The analysis of a mechanical system, body traveling along the elastic structure, has been a topic of interest. The establishment of analytical method for the development and control of this system is required in the fields of many machine operations such as modern weapons and high-speed feed drive system for a machine tool. The dynamic equations are derived on the torsion of a cantilever hollow shaft induced by the spin-up of a moving mass and the displacement of the mass. Influences of design parameters such as the inertia ratio, the mass moving speed and the friction coefficient are discussed on the transient response of the system.

Saint-Venant torsion of anisotropic shafts: theoretical frameworks, extremal bounds and affine transformations

We study the Saint-Venant torsion of anisotropic shafts. Theoretical frameworks for torsion of anisotropic composite shafts are derived in terms of warping function, conjugate function as well as stress potential, parallel to the existing frameworks for torsion of isotropic shafts. We prove an extremal property for the torsional rigidity of anisotropic composite shafts. For homogeneous shafts, an affine coordinate transformation is introduced in the formulation, which demonstrates how the cross-sectional shape of the shaft is deformed (stretching and rotation) under the mapping, and how the warping field and the torsional rigidity of an anisotropic shaft are correlated to those of an isotropic one. We find that a certain class of anisotropic elliptical shafts, simply- or multiply-connected, will not warp under an applied torque. Of all homogeneous shafts with a given cross-sectional area and the same shear rigidity matrix, the torsional rigidity, associated with zero warping displacement, can be proven as extremal upper bounds. Finally, families of anisotropic shafts that are equivalent to isotropic ones, including elliptical and hollow elliptical shafts, and cylindrical shafts with specific cross-sections of parallelogram and triangle shape, are characterized.

Effect of Fault Current Limiter on Shaft Torsional Torque

We investigated the influence of a resistive type (R-type) and inductive type (L-type) fault current limiter (FCL) on the behaviour of the shaft torsional torque of a synchronous generator installed in a consumer system connected to a utility distribution system. In the case that the generator has relatively low natural oscillation frequency f 0 under about 40 Hz, the L-type FCL suppresses the maximum value of the shaft torsional torque τ sm to lower level than the R-type FCL. The R-type FCL with low limiting resistance may instead increase τ sm under the condition of low f 0 . On the other hand, for higher f 0 , R-type FCL limits τ sm at any limiting resistance as well as L-type FCL. The limiting effect of R-type FCL on τ sm is larger than that of L-type FCL.

Mechanical Design Analysis and Test in Support of the Market Introduction of a New Vehicle

This paper reports results from a stress, acoustics and vibration investigation of the ride and driveline components of a new 2-seater sports car. The work was aimed at giving design assurance information to designers and vehicle engineers working to compressed timescales. The paper focuses on two particular areas: design of the power train for NVH refinement, and design analysis of a suspension wishbone. In the first case, a dynamic model of drive shaft torsion effects was created to understand design relationships needed for high power, high torque performance car. In the second case, an investigation was made into the integrity of a suspension wishbone component when gauge thickness was reduced from 3 mm to 2 mm. The work described was carried out in a joint industry academic venture sponsored by Knowledge Transfer Partnership (KTP). It is from this background that the authors give some perspectives on vehicle development.

Torsion of an isotropic shaft of arbitrary cross-section embedded with multicoated or graded circular cylinders of cylindrically orthotropic materials

Finding a geometric configuration that is amenable to an exact determination or characterization of the torsional rigidity is a relatively new territory that has only recently begun to be explored. For example, a circular cross-section with an assemblage of composite cylinders was only recently known to be an exactly solvable microgeometry. A host shaft with arbitrary cross-section, equivalent to higher orders of boundary data, necessitates that the coated cylinder be sufficiently multiply coated. The present analysis is to provide a theoretical framework showing how to design a neutral cylinder with any number of coatings or with graded shear moduli in a cross-section under torsion. Specifically we consider that the constituents are cylindrically orthotropic with the shear moduli μ r and μ θ . The host shaft is isotropic with the shear modulus μ 0 . A simple and unified mathematical framework is first proposed for the analysis of a multicoated cylinder. It is proven that only a two by two matrix, resulting from a serial multiplication of matrices of the same order, will enter into the resulting expression. Next, the multicoated cylinder, which consists of piecewise constant shear moduli, is generalized into a graded cylinder, with a continuous variation of the shear modulus along the radial direction. We find that the warping field of a neutral graded cylinder, with varying radial and tangential shear moduli, is governed by a second-order, homogeneous, ordinary differential equation. The method of Frobenius is adopted to obtain series solutions for the warping functions. An interesting result for the neutrality of the embedded cylinders (multicoated or graded) is that when the geometric mean of the shear moduli μ G = √μ r μ θ is identical to the shear modulus μ 0 of the host shaft, the neutrality condition is satisfied for any cross-section of the host shaft. Finally, a condition is given for the torsional rigidity of the host shaft to remain the same with the inclusion of the embedded cylinders.