Name: shear flow in thin-walled shafts
Uploaded: 2024-05-23T12:59:41.000Z
Duration: 1 min 15 s
Channel: JoVE

Burulma yüküne maruz kalan 't' kalınlığındaki ince duvarlı içi boş bir şafttan 'dx' genişliğinin küçük bir kısmını düşünün.
Kısım dengede olduğundan, üzerine etki eden tek kuvvet, kısmın uçlarına uygulanan kesme kuvvetleridir.
Kesme kuvvetlerini, küçük yüz ve bu yüzün alanı üzerindeki uzunlamasına kesme geriliminin ürünü olarak ifade ederek, eleman boyunca sabit kalan kesme akışı için bir ifade türetilebilir.
Şimdi, 'ds' uzunluğundaki içi boş şaft duvar bölümünün küçük bir elemanını düşünün. Eleman üzerine uygulanan kesme kuvvetinin büyüklüğü, elemanın kesme akışı ve uzunluğunun ürünü olarak ifade edilir.
İçi boş milin boşluğu içindeki keyfi bir O noktası etrafındaki bu kuvvetin momenti, kuvvetin O noktasından kuvvetin etki çizgisine olan dik mesafe ile çarpılmasıyla elde edilir.
Moment denkleminin entegre edilmesi, ince duvarlı içi boş silindirin tamamına uygulanan torkun ifadesini verir.

İnce duvarlı İçi boş miller

Burulma yüklemesine maruz kalan ince duvarlı içi boş bir milin analizinde, inceleme için dx genişliğinde bir parça izole edilir. Denge durumuna rağmen bu segment uçlarında burulma kesme kuvvetleri ile karşı karşıyadır. Bu kuvvetler, parçanın küçük yüzeyindeki uzunlamasına kayma geriliminin ve bu yüzeyin alanının çarpımı ile niceliksel olarak tanımlanır ve bu da kayma akışı kavramına yol açar. Bu kayma akışının yapı boyunca tutarlı olması, burulma geriliminin düzgün bir dağılımını gösterir.

Daha ileri analizler, mil duvarının ds ile tanımlanan küçük bir bölümünün incelenmesini içerir. Kayma akımının bu bölüme uyguladığı kuvvet, kayma akımının bölümün uzunluğu ile çarpılmasıyla hesaplanır. Mil üzerindeki burulma etkisi, bu kuvvetin mil boşluğu içindeki belirli bir O noktası etrafında oluşturduğu moment hesaplanarak belirlenir. Bu hesaplama, kuvvetin O'dan kuvvet yönüne dik etki çizgisine kadar olan mesafeyle çarpılmasını içerir.

Bu momentin tüm mil boyunca integrali, içi boş silindiri etkileyen toplam torkun ifadesini verir. Bu integral hesaplama, burulma kuvvetlerinin ince duvarlı içi boş millerin yapısal davranışını ve bütünlüğünü nasıl etkilediğine dair daha derin bir anlayış sunarak, burulma yüklemesi altındaki tasarım ve analizlere ilişkin önemli bilgiler sağlar.

<img alt="Equation 1" src="/files/ftp_upload/15623/15623_Equation_1.svg" style="text-align: center; height: 18px;">

İnce Duvarlı İçi Boş Miller

Burulma yüküne maruz kalan 't' kalınlığındaki ince duvarlı içi boş bir şafttan 'dx' genişliğinin küçük bir kısmını düşünün.
Bölümden beri ...

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Torsion

Burulma

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

Thin-Walled Hollow Shafts

shear flow in thin-walled shafts

Shear flow in a thin-walled hollow shaft describes how torsional force is carried through the wall. When a small segment of width dx is isolated, it is still in equilibrium, but it experiences torsional shearing forces at its ends. These forces come from the longitudinal shearing stress on the segment's minor surface multiplied by that surface area.

The result is a uniform shear flow through the structure. To study the wall more closely, a small section with length ds is considered. The force on that section is found by multiplying the shear flow by the section length.

The torque on the shaft is then found by taking the moment of that force about a point O inside the hollow. This means using the force and its perpendicular distance from O to the line of action. Integrating this moment around the full shaft gives the total torque on the hollow cylinder and helps show how thin-walled shafts respond to twisting load.

Shear Flow in Thin-Walled Shafts

stresses in a shaft

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A transmission shaft is sized from the power it must carry and the speed it rotates at. These two design limits guide the choice of shaft material and cross-sectional size. The goal is to keep the maximum shearing stress within the elastic limit while still transmitting the needed power. Power is directly linked to torque, which is the twisting force applied to the shaft. By rearranging the power relation, the torque can be found from the required power and the shaft speed. That torque value...

stress concentrations in circular shafts

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Circular shafts can develop local stress peaks when torque is applied through real machine parts. The elastic torsion formula works best for a circular shaft with a uniform cross-section and rigid plates fixed to its ends. In practice, torque is often passed through flange couplings or gears, and these parts use keys in keyways to connect to the shaft. That loading method changes the stress pattern near the point where torque enters the shaft. The stress distribution no longer matches the...

plastic deformation in circular shafts

Torsional Failure and Plastic Strain in Shafts

Plastic deformation in circular shafts happens when torsional force pushes the material past its yield strength. At that point, the shaft does not return to its original shape. Instead, it keeps a permanent strain. To measure this change, the stress pattern inside the shaft must be understood. The maximum shearing stress is calculated first. Then a shearing-stress-strain diagram can be drawn to find the maximum shearing strain. Shearing strain changes linearly with the distance from the shaft...

circular shafts - elastoplastic materials

Torsion Limits in Circular Shafts

Circular shafts under torsion show a clear change from elastic behavior to plastic deformation as torque increases. In the elastic limit, stress rises in direct proportion to the distance from the shaft’s center. The outer material carries the highest stress first, and the shaft can still return to its original shape. At a critical stress level, the shaft begins to yield. This marks the maximum torque the shaft can carry without permanent deformation. Beyond this point, a plastic region forms...

residual stresses in circular shafts

Residual Stress After Shaft Torsion

Residual stress can remain in a circular shaft after torque causes plastic deformation. This happens in elastoplastic materials, which show both elastic and plastic behavior. The plastic change can come from high shearing stress or large strain. Residual stress is the internal stress that stays in the material after the external force is removed. In a shaft under torque, the angle of twist does not return fully to its original value. That lasting change shows that residual stress is still...

torsion of noncircular members

Torsion in Square and Rectangular Bars

Torsion in square and rectangular bars shows how shape changes the way a material twists. Circular shafts keep their cross-sections nearly unchanged because they are axis-symmetric. That symmetry helps the stress spread evenly, so the shaft can resist torsion without distorting. Square bars behave differently because they do not have the same axial symmetry. When twisted, their cross-sections distort, although the diagonals and the lines connecting the midpoints stay as exceptions. This means...

thin-walled hollow shafts

Shear flow in a thin-walled hollow shaft describes how torsional force is carried through the wall. When a small segment of width dx is isolated, it is still in equilibrium, but it experiences torsional shearing forces at its ends. These forces come from the longitudinal shearing stress on the segment's minor surface multiplied by that surface area. The result is a uniform shear flow through the structure. To study the wall more closely, a small section with length ds is considered. The force...

key terms and concepts

Learn how shear flow and torsional shearing forces act in a thin-walled hollow shaft, and how integrating the moment gives the total torque.

Shear Flow in Thin-Walled Shafts | JoVE K12

JoVE Core Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Shear Flow in Thin-Walled Shafts

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