Eksenel Yüklü Tel Halat Demetlerinin Bilgisayar Ortamında Yorulma Ömürlerinin İncelenmesi
Eksenel Yüklü Tel Halat Demetlerinin Bilgisayar Ortamında Yorulma Ömürlerinin İncelenmesi
Dosyalar
Tarih
2012-01-18
Yazarlar
Anıl, Ali Semih
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Eski çağlardan günümüze kadar kullanımı oldukça yaygın olan tel halatların kentsel ulaşım, taşımacılık, madencilik, denizcilik, vb. pek çok uygulama alanı bulunmaktadır. Bu yüksek lisans tez çalışmasında eksenel yüklü tel halat demetlerinin bilgisayar ortamında yorulma ömürleri incelenmiştir. Bu amaç doğrultusunda tel halatların sonlu elemanlar analizi ile ilgili oluşturulan modeller, yapılan araştırmalar ve tel halatların yorulma durumundan sorumlu olan çekme-çekme, makaralar üstünde eğilme, serbest eğilme ve burulma mekanizmaları incelenmiştir. Sonrasında eksenel yüklü tel halatların yorulması ile ilgili yapılan deneysel çalışmalar incelenmiş ve sonuçları verilmiştir. Sonlu elemanlar yöntemi ile yapılacak yorulma analizi için yöntemin temel ögeleri araştırılmış ve doğrudan yaklaşım üzerinden yöntemin teorisi açıklanmıştır. Tel halat demetinin sonlu elemanlar analizi için oluşturulması gerekli model göz önüne alınarak matematiksel demet modeli araştırılmıştır. Love’ın geliştirdiği teoriye dayanarak bir tel için denge denklemleri elde edilmiş ve bu bilimsel çalışma tel halat teorisi için başlangıç olarak alınmıştır. Sonrasında Costello‘nun eksenel yüklü tel demetin davranışına yönelik oluşturduğu denklemler sunulmuş; demet geometrisi, basit demetin eksenel davranışı, basit demet için yük - şekil değişimi ilişkisi incelenmiştir. Tel halat ve demetlerin geometrik olarak oluşturulabilmesi için helisel eğriler matematiksel olarak tanımlanmıştır. Geometrik transformasyonların bileşimi, tel eksenlerinin parametrik olarak elde edilmesinde bir yöntemdir. Geometrik transformasyonlar kullanılarak tel halat ve demetlerde helisel olarak sarılan tel eksenlerinin tanımlanması için parametrik denklemler formunda analitik tanımlamalar türetilmiştir. Türetilen parametrik denklemler demetin yapısında bulunan bir telin geometrisi ve konumunu tanımlama olanağı sunmaktadır. Dolayısıyla bu denklemler bir demetin üç boyutlu matematiksel modelinin tasarlanmasında yeterlidir. Basit demetin modellenebilmesi amacıyla dış tellerin birbirine temas etmemesi için Costello’nun sunduğu gerekli koşul tanımlanmış ve basit demetin belirlenen geometrik değerleri kullanılarak oluşturulan model doğrulanmıştır. Sonlu elemanlar analizinde kullanılacak 1+6 telli basit demetin üç boyutlu katı modeli bir bilgisayar destekli tasarım yazılımı olan SolidWorksTM ile oluşturulmuştur. Oluşturulan modellerde teller arasındaki temas durumu göz önüne alınarak belirli bir kritik uzunluğun üzerinde kalınmıştır. Basit demetin yorulma analizi bir sonlu elemanlar analizi yazılımı olan ANSYSTM ile gerçekleştirilmiştir. Oluşturulan demet modelleri için eksenel yük altında yorulma ömrü ve göz önüne alınan değişkenlerin çekme-çekme yorulma ömrüne olan etkisi incelenmiştir. Basit demet modellerinin sonlu elemanlar yöntemi ile analizi için temas durumu, sınır şartları ve malzeme tanımlanmıştır. Costello’nun eksenel yük altındaki basit demetin davranışı ile ilgili oluşturduğu denklemler temel alınarak sonlu elemanlar analizi sonuçları kıyaslanmıştır. Eksenel birim uzama sonucunda sabit uç durumu için sonlu elemanlar analizi ile elde edilen kuvvet değerleri teorik olarak elde edilen değerlerle uyum göstermektedir. Sonlu elemanlar analizi ile elde edilen moment değerleri ise teorik olarak elde edilen değerlerle benzer eğilimlidir. Demet uzunluğu, helis açısı ve kuvvet aralığı olmak üzere 3 farklı değişken kullanılarak deney grupları oluşturulmuştur. Deney grupları için ANSYS/Workbench ile sonlu elemanlar analizi gerçekleştirilmiş; aynı koşullar altında eşdeğer birim uzama dağılımı, eşdeğer (von-Mises) gerilme dağılımı ve Goodman yaklaşımına göre yorulma ömür dağılımı elde edilerek eksenel yüklü 1+6 telli basit demetin yorulma ömür değişimini gösteren grafikler oluşturulmuştur.
Wire ropes of which usage have been common reasonably from ancient times to present have a lot of application areas as urban transportation, transportation, mining, shipping, etc. Accordingly in this thesis, historical and structural basis of wire rope strands have been presented, and the main components of wire ropes, wire rope and strand types, wire rope manufacturing process and application areas have been explained. In this master thesis, fatigue life of axial loaded wire rope strands have been investigated in computer environment. In accordance with this purpose the generated wire rope models and the conducted researchs about the finite element analysis (FEA) of wire ropes have been investigated by a literature review from past to present. Tension-tension, Bending-over-Sheaves (BoS), free bending and torsion mechanisms which are responsible for fatigue of wire ropes have been investigated. Then the experimental studies about the fatigue of axial loaded wire ropes have been investigated and the results have been given for spiral wire ropes with resin and metal terminations, and round strand wire ropes with resin and metal terminations. The main elements of the finite element method (FEM) have been studied for the fatigue analysis which is done with finite element method, and the theory of the method has been explained via direct approach. Mathematical strand model has been studied by considering the model which is required to generate for the finite element analysis of wire rope strand. The equations of equilibrium for a wire have been derived by based on the theory developed by Love, and this treatise has been regarded as a baseline. Then the equations, which have been derived by Costello for the behaviour of axial loaded wire strand, have been presented, and strand geometry, axial behaviour of simple strand, load-deformation relation for simple strand have been investigated. The helical curves have been expressed mathematically in order to generate wire ropes and strands geometrically. The assembling of geometric transformations is a method for obtaining the wire axis parametrically. In order to express the wire axes laid helically in wire ropes and strands by using geometric transformations, analytical expressions have been derived in the form of parametric equations. The derived parametric equations present expression possibility of the geometry and location of a wire within strand construction. Consequently these equations are sufficient in order to design a 3-D mathematical model of a strand. The condition presented by Costello, which is required not to contact outer wires each other, has been expressed with the purpose of modeling simple strand and accordingly the generated model has been confirmed by using defined geometric values of simple strand. 3-D solid model of 1+6 simple strand, which is used in finite element analysis, has been generated in computer aided design (CAD) software SolidWorksTM. The fatigue analysis of simple strand has been done by finite element analysis software ANSYSTM. Fatigue life under axial loading and the effect of considered parameters on tension-tension fatigue life have been investigated for generated strand models. Contact conditions, boundary conditions and material have been defined in order to analyze simple strand models with finite element method. The equations derived by Costello about the behaviour of simple strand under axial loading have been regarded as a baseline, and finite element analysis results have been compared with theoretical results in order to confirm generated finite element model. Considering the contact condition between center wire and outer wires, generated models have been remained over a critical length. Simple strand lengths have been regarded as 10 to 16 per cent of pitch length for defined geometric values. Jiang and Henshall report that there is no contact between the center wire and outer wires, from the fixed-end to 3 per cent of the pitch length. The contact loads (pressure) increases gradually and there are relative movements through the contact lines between center wire and outer wires for simple strand lengths which are from 3 to 9 per cent of the pitch length. The contact loads (pressure) reaches the uniform value, and relative movements between center wire and outer wires reaches zero value for simple strand lengths which are over 9 per cent of pitch length. Boundary conditions have been considered as one end is encastre while the other end is restrained not to displace in x and y directions. Considered loading condition has been applied to the end, which is restrained not to displace in x and y directions, up to 0,015 strain value in increments of 0,001 linearly by using the displacement equivalent to the axial strain. Material model for finite element analyses is defined as bilinear isotropic (BISO) which is a non-linear material model. The curve in linear region is elasticity modulus of material. Behaviour of bilinear isotropic material is defined with a curve named plasticity modulus after yield stress. In consequence of axial strain for fixed-end case, force values obtained by finite element analysis are in accordance with Costello’s theoretical force values. Then also moment values obtained by finite element analysis are in similiar trend with Costello’s theoretical moment values. Experimental groups have been generated by using 3 different parameters which are strand length, helix angle and force range. Strand lengths are 15mm, 17,5mm and 20mm with 78,2° helix angle and 0,006 axial strain for each model. Helix angles are 75°, 77,5° and 80° with 15mm strand length and 0,006 axial strain for each model. Force range has been changed by using the axial strains equivalent to the axial forces. Axial strains are 0 ~ 0,006, 0,0015 ~ 0,006, 0,003 ~ 0,006 with 78,2° helix angle and 15mm strand length. Finite element analyses have been done by ANSYS/Workbench for each experimental group. Graphics, which show fatigue life variance of axial loaded 1+6 simple strand under the same conditions, have been created by obtaining equivalent strain distribution, equivalent (von-Mises) stress distribution and fatigue life distribution according to Goodman approach. According to analysis results, tension-tension fatigue life increases approximately linearly with the increase in strand length for variable strand length. It is supposed that the reason for the longer fatigue life of the longer strands is the relaxation of the structure can be compensated better. Tension-tension fatigue life increases with the increase in helix angle for variable helix angle. It is supposed that the reason for the longer fatigue life of the higher helix angle can be the less contact between center wire and outer wires per unit length and hence less force requirement in order to overcome friction. Tension-tension fatigue life increases with the increase in pre-strain, in which axial strain is equivalent to the axial force, for variable force range. The smaller force magnitude can be regarded as superiority in similiar engineering applications. Fatigue life increases by decrease in additional force applied to the strand. In all experimental groups it seems that the most effective parameter on number of fatigue cycle is helix angle. Although strand length seems a little more effective than force range on number of fatigue cycle, they both are in similiar trend approximately.
Wire ropes of which usage have been common reasonably from ancient times to present have a lot of application areas as urban transportation, transportation, mining, shipping, etc. Accordingly in this thesis, historical and structural basis of wire rope strands have been presented, and the main components of wire ropes, wire rope and strand types, wire rope manufacturing process and application areas have been explained. In this master thesis, fatigue life of axial loaded wire rope strands have been investigated in computer environment. In accordance with this purpose the generated wire rope models and the conducted researchs about the finite element analysis (FEA) of wire ropes have been investigated by a literature review from past to present. Tension-tension, Bending-over-Sheaves (BoS), free bending and torsion mechanisms which are responsible for fatigue of wire ropes have been investigated. Then the experimental studies about the fatigue of axial loaded wire ropes have been investigated and the results have been given for spiral wire ropes with resin and metal terminations, and round strand wire ropes with resin and metal terminations. The main elements of the finite element method (FEM) have been studied for the fatigue analysis which is done with finite element method, and the theory of the method has been explained via direct approach. Mathematical strand model has been studied by considering the model which is required to generate for the finite element analysis of wire rope strand. The equations of equilibrium for a wire have been derived by based on the theory developed by Love, and this treatise has been regarded as a baseline. Then the equations, which have been derived by Costello for the behaviour of axial loaded wire strand, have been presented, and strand geometry, axial behaviour of simple strand, load-deformation relation for simple strand have been investigated. The helical curves have been expressed mathematically in order to generate wire ropes and strands geometrically. The assembling of geometric transformations is a method for obtaining the wire axis parametrically. In order to express the wire axes laid helically in wire ropes and strands by using geometric transformations, analytical expressions have been derived in the form of parametric equations. The derived parametric equations present expression possibility of the geometry and location of a wire within strand construction. Consequently these equations are sufficient in order to design a 3-D mathematical model of a strand. The condition presented by Costello, which is required not to contact outer wires each other, has been expressed with the purpose of modeling simple strand and accordingly the generated model has been confirmed by using defined geometric values of simple strand. 3-D solid model of 1+6 simple strand, which is used in finite element analysis, has been generated in computer aided design (CAD) software SolidWorksTM. The fatigue analysis of simple strand has been done by finite element analysis software ANSYSTM. Fatigue life under axial loading and the effect of considered parameters on tension-tension fatigue life have been investigated for generated strand models. Contact conditions, boundary conditions and material have been defined in order to analyze simple strand models with finite element method. The equations derived by Costello about the behaviour of simple strand under axial loading have been regarded as a baseline, and finite element analysis results have been compared with theoretical results in order to confirm generated finite element model. Considering the contact condition between center wire and outer wires, generated models have been remained over a critical length. Simple strand lengths have been regarded as 10 to 16 per cent of pitch length for defined geometric values. Jiang and Henshall report that there is no contact between the center wire and outer wires, from the fixed-end to 3 per cent of the pitch length. The contact loads (pressure) increases gradually and there are relative movements through the contact lines between center wire and outer wires for simple strand lengths which are from 3 to 9 per cent of the pitch length. The contact loads (pressure) reaches the uniform value, and relative movements between center wire and outer wires reaches zero value for simple strand lengths which are over 9 per cent of pitch length. Boundary conditions have been considered as one end is encastre while the other end is restrained not to displace in x and y directions. Considered loading condition has been applied to the end, which is restrained not to displace in x and y directions, up to 0,015 strain value in increments of 0,001 linearly by using the displacement equivalent to the axial strain. Material model for finite element analyses is defined as bilinear isotropic (BISO) which is a non-linear material model. The curve in linear region is elasticity modulus of material. Behaviour of bilinear isotropic material is defined with a curve named plasticity modulus after yield stress. In consequence of axial strain for fixed-end case, force values obtained by finite element analysis are in accordance with Costello’s theoretical force values. Then also moment values obtained by finite element analysis are in similiar trend with Costello’s theoretical moment values. Experimental groups have been generated by using 3 different parameters which are strand length, helix angle and force range. Strand lengths are 15mm, 17,5mm and 20mm with 78,2° helix angle and 0,006 axial strain for each model. Helix angles are 75°, 77,5° and 80° with 15mm strand length and 0,006 axial strain for each model. Force range has been changed by using the axial strains equivalent to the axial forces. Axial strains are 0 ~ 0,006, 0,0015 ~ 0,006, 0,003 ~ 0,006 with 78,2° helix angle and 15mm strand length. Finite element analyses have been done by ANSYS/Workbench for each experimental group. Graphics, which show fatigue life variance of axial loaded 1+6 simple strand under the same conditions, have been created by obtaining equivalent strain distribution, equivalent (von-Mises) stress distribution and fatigue life distribution according to Goodman approach. According to analysis results, tension-tension fatigue life increases approximately linearly with the increase in strand length for variable strand length. It is supposed that the reason for the longer fatigue life of the longer strands is the relaxation of the structure can be compensated better. Tension-tension fatigue life increases with the increase in helix angle for variable helix angle. It is supposed that the reason for the longer fatigue life of the higher helix angle can be the less contact between center wire and outer wires per unit length and hence less force requirement in order to overcome friction. Tension-tension fatigue life increases with the increase in pre-strain, in which axial strain is equivalent to the axial force, for variable force range. The smaller force magnitude can be regarded as superiority in similiar engineering applications. Fatigue life increases by decrease in additional force applied to the strand. In all experimental groups it seems that the most effective parameter on number of fatigue cycle is helix angle. Although strand length seems a little more effective than force range on number of fatigue cycle, they both are in similiar trend approximately.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2011
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2011
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2011
Anahtar kelimeler
Tel halat demeti,
Yorulma,
Sonlu elemanlar analizi,
Wire rope strand,
Fatigue,
Finite element analysis