Ø Introduction to Shafts
Ø Definition of Torsion
Ø Torsion of Shafts (Torsional Shafts)
Ø Shaft Distress and Failure Modes
Ø Understanding the factors causing Shaft Failure
Ø Different types of failures of torsional shafts
Ø Appearance of some common shafts failures
Shafts are one of the most common components in machinery. They show up everywhere from small motors, pumps and compressors to large rolls in paper mills, steel mills and power generating facilities. Properly designed and maintained they are expected to operate for years without problem. However, shafts still represent one of the most common types of machinery failures. When a failure occurs it can result in either a minor inconvenience
or it can be sudden with catastrophic results and expensive business interruption.
Understanding the specific cause of a failure can help determine if it was truly sudden and unexpected or simply the result of long-term wear and tear. In some cases, poor workmanship, material defects or inadequate design can be identified to assist in subrogation efforts to recover losses. All of these failure analyses require both the knowledge of materials and metallurgical concepts as well as engineering and experience of the entire machine components and functions.
TORSIONAL Failure (fracture)
Definition of Torsion (In Solid Mechanics):-
In solid Mechanics, torsion is the twisting of an object due to an applied torque. In circular sections, the resultant shearing stress is perpendicular to the radius.
For solid or hollow shafts of uniform circular cross-section and constant wall thickness, the torsion relations are:
· R is the outer radius of the shaft i.e. m, ft.
· τ is the maximum shear stress at the outer surface.
· φ is the angle of twist in radians.
· T is the torque.
· ℓ is the length of the object the torque is being applied to or over.
· G is the shear modulus or more commonly the modulus of regedity.
· J is the torsion constant for the section. It is identical to the polar moment of Inertia for a round shaft or concentric tube only. For other shapes J must be determined by other means. For solid shafts the membrane analogy is useful, and for thin walled tubes of arbitrary shape the shear flow approximation is fairly good, if the section is not re-entrant. For thick walled tubes of arbitrary shape there is no simple solution, and finite element analysis may be the best method.
· The product GJ is called the torsional regedity.
Torsion of Shaft:-
Shear Stress in the Shaft
When a shaft is subjected to a torque or twisting, a shearing stress is produced in the shaft. The shear stress varies from zero in the axis to a maximum at the outside surface of the shaft.
The shear stress in a solid circular shaft in a given position can be expressed as:
σ = T r / Ip
σ = shear stress (MPa, psi)
T = twisting moment (Nmm, in lb)
r = distance from center to stressed surface in the given position (mm, in)
Ip = "polar moment of inertia" of cross section (mm4, in4)
The "polar moment of inertia" is a measure of an object's ability to resist torsion.
SHAFT DISTRESS AND FAILURE MODES:-
The performance of a gear set is dependent on the shafting for the gear elements. The shafting must be rigid enough to prevent excessive deflection that would result in abnormal load distribution on the gear teeth. The fits between the shafts and the bearings and between the shaft and the mounted gears must be proper so that mounted members are not too loose nor too tight as either condition can contribute to shaft failure. The shafts must be strong enough to resist permanent yield from shock loads and they must be strong enough to resist the reverse bending fatigue loads that are superimposed on the transmitted torsional loads. In many cases a careful inspection of the shaft surface and the face of the fracture will reveal clues as to the probable cause of failure. When the clues are not obvious, it is helpful to know the function of the shaft in the drive system and to know the type of service in order to assess the primary cause of fracture.
In general, fractures resulting from bending stresses are perpendicular to the shaft axis, see figure (B), whereas fracture resulting from fatigue type torsional stresses most frequently are disposed at a 45° angle to the shaft axis see figure (A).
(A) TORSIONAL FRACTURE (B) BENDING FRACTURE
(C) SHAFT FRACTURES (D) SHAFT FAILURE (PEELING)
Figure (C) shows a torsional fatigue failure originating at the keyway and progressing as a result of a reversing torque in the system due to dynamic effects. The final fracture zone is typical of a torsional failure occurring along a plane approximately 45° to the axis of the shaft.
Torsional fractures are more complex to analyze than bending fractures. Fracture due to a single overload in a ductile material may develop along the longitudinal shear plane, but in a brittle material the crack may develop on a 45° spiral angle perpendicular to the principal tensile stress. Torsional fatigue cracks may grow because of shear or tensile stresses or both, figure (D).
On this bases we can classify the different causes of failure(fracture) of shafts:-
· fractures resulting from bending stresses
· fracture resulting from fatigue type torsional stresses
Understanding Factors That Cause Shaft Failures:-
To understand shafts and why they fail, you need to understand the relationship between stress and strain for steel. Stress is the force carried by a material per unit area, measured in psi (pounds per square inch) or Mpa (Megapascals or Mega newtons per square meter). If a material is under tension, the stress is acting to pull apart the molecules that make it up, making it longer; if the material is under compression, the stress is pushing the molecules together, causing the material to get shorter (and fatter as the compressed material “bulges” outward) if enough tress is applied.
Strain is the change in the length, or elongation per unit length, of a material under a tensile stress. Most shafts are made of hot-rolled carbon steel, but for more specialized loads or environments, you may see shafts that are made of alloyed or stainless steel. When a tensile stress is added to a material, the material begins to
deform at a certain level of stress. This applies to steel, wood, concrete or any other “engineering” material. In the case of a motor shaft, the material is steel. The deformation due to the tensile stress is elastic until the stress reaches its yield strength point for the steel (typical carbon steel = 73000-psi or 503-Mpa). The yield strength will vary with the material. For example, a 416 stainless steel shaft, while offering corrosion resistance, will actually have slightly lower yield strength than a typical 1045 hot-rolled carbon steel.
Different Types of failure of torsional shafts:-
· Ductile materials generally fail in shear. Brittle materials are weaker in tension than shear.
• When subjected to torsion, a ductile specimen breaks along a plane of maximum shear, i.e., a plane perpendicular to the shaft axis.
• When subjected to torsion, a brittle specimen breaks along planes perpendicular to the direction in which tension is a maximum, i.e., along surfaces at 45o to the shaft axis.
Ductile Vs Brittle Failure:-
Appearance of the Some Common Shaft Failures:-
· Torsional failures have a “twisted” appearance. Their appearance will depend on the amount of torsional loading and whether the material is ductile or brittle. This particular shaft shows some twisting before failure. If the shaft material is ductile, it will twist more before failing. If the shaft is more brittle, or subject to extreme torsion, the fracture will have a rougher appearance.
· A brittle failure due to a sudden torsional load results in a diagonal break with a rough surface. Possible causes include an equipment jam, high-impact loading or a voltage transient.
The study of different types of failure of torsional shafts includes the study of shafts and torsion of shafts. , Torsion is the twisting of an object due to an applied torque. In circular sections, the resultant shearing stress is perpendicular to the radius. For solid or hollow shafts of uniform circular cross-section and constant wall thickness. Shafts distress and failure modes gives the clear picture of different stress which can cause fracture which is indeed failure in shafts .thereby we conclude the causes and effects of failure of torsional shafts.
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