Modeling and stress analysis of wire ropes with parametric equations

Tel halat geometrisi imalat tarzından dolayı karmaşık bir yapıdadır. Halatın temel öğelerinden birisi halatın özünü oluşturan Bağımsız Tel Halat Çekirdeği (BTHÇ)’dir. BTHÇ ise ortasında yedi telden oluşan basit düz bir demet ve onu çevreleyen altı adet helisel sarılmış demetten oluşmaktadır. BTHÇ’nin merkez demeti ile dış demetinde yer alan helisel tellerin geometrileri arasında önemli bir fark vardır. Merkez demetin dış telleri tek helisel yapıya sahip iken, dış demeti oluşturan dış teller çift helisel yapıdadır. Bu sebepten ötürü dış demete ait dış çift helisel tellerin modellenmesi özel yöntemlerin kullanılmasını zorunlu kılmaktadır. Bu makalenin amacı, BTHÇ ile tel halatların modellenmesi için yeni bir tekniğin tanıtılması ve bu teknik ile elde edilecek sonuçların literatürde mevcut bulunan sonuçlarla karşılaştırılmasıdır. Öncelikle BTHÇ’nin merkezinde bulunan basit düz tel demetinin modeli oluşturularak modelin doğruluğu kanıtlanmıştır. Ardından BTHÇ’nin dış demetindeki dış tellerin çift helisel geometrisi incelenerek modellenme tekniği üzerinde durulmuştur. Farklı sarım teknikleri ile modellenmesi yapılan BTHÇ’lerin modelleri anlatılmıştır. BTHÇ’nin sonlu elemanlar kullanılarak analizleri sonucunda tel bazında elde edilen sonuçların analitik sonuçlarla mukayesesi yapılmıştır. En son olarak BTHÇ’nin öz olarak kullanıldığı Seale tipi tel halatların modellenmesi ve analizi yapılmıştır. Elde edilen sonuçlar literatürde bulunan analitik ve test sonuçlarıyla karşılaştırılmış ve iyi uyum sağladıkları görülmüştür. Sonuç olarak tanıtılan yeni modelleme tekniği kullanılarak kolay ve daha efektif bir biçimde sayısal analiz yapma olanağı sağlanmıştır. Aynı zamanda uygulanan yöntem daha basit ve daha pratiktir.  Anahtar Kelimeler: Tel demet, bağımsız tel halat çekirdeği, çift helisel geometri, Seale tipi halat modelleme.Loads and moments over an helical wire geometry is the fundamental starting point of the wire rope theory. The equilibrium equations are derived from the equilibrium of this wire and it has been presented by Love (1944) in his well-known treatise. Solution of the equilibrium equations under axial loading and pure bending is presented by Love (1944). Frictional and contact effects are not included in the theorethical investigations of the problem due to the complicated geometry. Without taking into account the frictional effects, nonlinear problem of wire rope theory is solved using linearization of the equilibrium equations. A simple wire strand is composed by a straight wire which is wrapped by six outer single helical wires. An independent wire rope core (IWRC) is composed by a simple straight strand as a core strand which is wrapped around by six outer helical strands. The outer wires of the core strand is helical shaped wires while the outer wire of the outer strands is double or nested helical wires. Double or nested helical wire geometry is not included in the analytical solution procedures during the development of the theory of wire ropes. Superposition theory is used for the solutions of the IWRC which takes into account core strand as a straight wire while the outer strands as a single helical wire. IWRCs are widely used as a core for more complicated wire ropes at present. Most of the well known structures are Seale and Warrington IWRC. IWRCs are preferred when the wire rope is run under large lateral compressive loads and additional axial loading capacity is required (Velinsky, 1989). During the literature survey, the first analytical analysis are done by Hruska (1951, 1952, 1953). Hruska did not take into account the frictional effects due to contacts while solving the equilibrium equations given by Love (1944). Only geometrical aspects, axial loading and pure bending are discussed during the early studies. Since then Costello (1990), and later, Utting and Jones (1987) have followed a more fundamental approach. They treat each wire of wire rope as a helically curved rod but make differing assumptions relative to the rope geometry or the interwire contacts. The different theories produce results, which remain close to the experimental values presented by Utting and Jones (1987), but the question of the actual relative displacements and forces within a rope is nevertheless still open. Early studies of the wire ropes under axial loading condition obtained by using finite element analysis are given by Jiang and Henshall (1999). Then this study is extended to three layered strand by Jiang et.al. (1999,2000). These analysis are based on a simple sector of 1/12 or 1/6 of the wire rope cross-section, an arc length or a percentage of the pitch length is taken into account generally. Meanwhile during the literature survey, analytical models conducted for IWRC have not mentioned double helical wire geometry until 2004. Most of the analitical analysis rely on homogenization process except theoretical studies of Elata et.al. (2004), Usabiaga and Pagalday (2008). In this article, wire rope geometry is modelled in a more realistic manner taking into account the double or nested helical geometry of the outer wires of the outer strands for IWRC. To accomplish this, a code is generated named Wire Rope Skeleton (WRS) which creates the centerline of the specified wire in a strand, IWRC or Seale IWRC. Proposed modeling scheme considers each wire with its real solid behaviour. Thus analysis over the wire rope with proposed structure gives more realistic results. To model long wire rope models in 3-D is a cumbersome issue due to the irregularities encountered on the surface of the wires while meshing. The proposed modeling scheme solves the meshing problems of long wire ropes. Also the interactions between wires are defined by contact definitions and friction is taken into account. Realistic material properties are defined and analytical results, test results available in the literature and the finite element analysis results are compared simultaneously. It has been concluded that the proposed modeling procedure works for a wire strand and its development to IWRC and Seale IWRC also gives reasonable results. This analysis technique gives more information about the interwire contacts. As this face this modeling scheme and analysis methodology gives oppurtunity for the future analysis. Keywords: Wire strand, independent wire rope core, double helical geometry, Seale type rope modeling.

Evolved model for early fault detection and health tracking in marine diesel engine by means of machine learning techniques

The Coast Guard Command, which has a wide range of duties as saving human lives, protecting natural resources, preventing marine pollution and battle against smuggling, uses diesel main engines in its ships, as in other military and commercial ships. It is critical that the main engines operate smoothly at all times so that they can respond quickly while performing their duties, thus enabling fast and early detection of faults and preventing failures that are costly or take longer to repair. The aim of this study is to create and to develop a model based on current data, to select machine learning algorithms and ensemble methods, to develop and explain the most appropriate model for fast and accurate detection of malfunctions that may occur in 4-stroke high-speed diesel engines. Thus, it is aimed to be an exemplary study for a data-based decision support mechanism

Experimental and theoretical investigation of bending over sheave fatigue life of stranded steel wire rope

Steel wire ropes are used in elevators, cranes, mine hoistings, bridges, offshore and aerial ropeway systems. In this study, bending over sheave (BoS) fatigue lifetimes of 6 × 36 Warrington-Seale steel wire ropes have been determined theoretically and experimentally. Experimental findings have critical importance in identifying behavior of wire rope subjected to bending over sheave fatigue. Experimental studies have been performed to show effects of tensile load and sheave diameter parameters on BoS fatigue lifetimes of 6 × 36 Warrington-Seale steel wire ropes. Besides, a multiple linear regression model has been devised and novel theoretical BoS fatigue life prediction equation has been presented by using the least square method. The results indicate that there is a powerful correlation between the results obtained by theoretical model and experimental data. The BoS fatigue lifetime results can be used in the range of specific tensile loads investigated and diameter ratios used with acceptable error

Experimental determination of degradation influence on bending over sheave fatigue life of steel wire ropes

In this study, effects of internal and external wire breaks, abrasive wear, insufficient lubrication, curling on bending over sheave fatigue life of steel wire ropes have been investigated. Experimental studies have been performed for two different steel wire ropes to investigate how steel wire rope samples are affected by degradations. Experimental results have been compared and the most critical degradation type and severity orders of defects or failures on bending over sheave fatigue life for both ropes have been presented. The most critical degradation type has been found as four adjacent internal strand breaks for rotation resistant rope and 3 × 2 external wire breaks for 6 × 36 WS rope among another degradation types investigated. The results indicate that bending over sheave fatigue life is influenced substantially by degradations artificially created

On the Properties of a Special Function Defined by an Integral

The properties of a special function which is defined by an integral is presented. The numerical values of this function are tabulated correct to twenty decimal places. The curves of this function and its complementary are plotted. Some properties of this function are investigated

Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls

An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for −2, +∞, and −∞ values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed

Discard fatigue life of stranded steel wire rope subjected to bending over sheave fatigue

In this study, discard lifetimes of 6 × 36 Warrington-Seale steel wire ropes subjected to bending over sheave (BoS) fatigue have been determined theoretically and experimentally. Multiple linear regression model has been devised and novel theoretical discard life prediction equation has been presented by using the least square method. The results indicate that there is a powerful correlation between the results obtained by theoretical model and experimental data. The theoretical discard life prediction equation results can be used in the range of specific tensile loads investigated and diameter ratios used with acceptable error when the values of coefficient of determination (r2) and correlation coefficient (r) are considered