Cyclic stress
Encyclopedia
Cyclic stress in engineering refers to an internal distribution of forces (a stress) that changes over time in a repetitive fashion. As an example, consider one of the large wheels used to drive an aerial lift
such as a ski lift
. The wire cable
wrapped around the wheel exerts a downward force on the wheel and the drive shaft supporting the wheel. Although the shaft, wheel, and cable move the force remains nearly vertical relative to the ground. Thus a point on the surface of the drive shaft will undergo tension when it is pointing towards the ground and compression when it is pointing to the sky. Because the wheel rotates many times during the use of the machine, this cycle of tension and compression is repeated many times — hence the name cyclic stress.
), which must support the mass of people as they jump off structures such as bridges. When a person reaches the end of a cord, the cord deflects elastically and stops the person's descent. This creates a large axial stress in the cord. A fraction of the elastic potential energy stored in the cord is typically transferred back to the person, throwing the person upwards some fraction of the distance he or she fell. The person then falls on the cord again, inducing stress in the cord. This happens multiple times per jump. The same cord is used for several jumps, creating cyclical stresses in the cord that could eventually cause failure if not replaced.
Cyclical torsional stresses are stresses repetitively applied tangent to an axis. As an example, consider a compact disc
drive. Each time a disc is inserted into the drive, a motor applies torque
to the disc via a drive shaft. Once disc reaches the desired rotational velocity
, relatively little torque is required to maintain the speed. Thus the torque varies over time as the drive spins up a disc and slows it down. Unlike the ski lift example above where the torque is relatively constant but the load due to cable tension created a bending moment
, compact disc drive shafts have little to no bending movement applied, but have a torque that varies significantly over time.
. Fatigue failure is typically modeled by decomposing cyclic stresses into mean and alternating components. Mean stress is the time average of the principal stress. Alternating stress is the difference between the mean and the maximum or the mean and the minimum value the principal stress takes on. Engineers try to design mechanisms whose parts are subjected to a single type (bending, axial, or torsional) of cyclic stress because this more closely matches experiments used to characterize fatigue failure in different materials.
Aerial lift
An aerial lift is a means of transportation in which cabins, cars, gondolas or open chairs are hauled above the ground by means of one or more cables.Types of aerial lifts include:...
such as a ski lift
Ski lift
The term ski lift generally refers to any transport device that carries skiers up a hill. A ski lift may fall into one of the following three main classes:-Lift systems and networks:...
. The wire cable
Wire rope
thumb|Steel wire rope Wire rope is a type of rope which consists of several strands of metal wire laid into a helix. Initially wrought iron wires were used, but today steel is the main material used for wire ropes....
wrapped around the wheel exerts a downward force on the wheel and the drive shaft supporting the wheel. Although the shaft, wheel, and cable move the force remains nearly vertical relative to the ground. Thus a point on the surface of the drive shaft will undergo tension when it is pointing towards the ground and compression when it is pointing to the sky. Because the wheel rotates many times during the use of the machine, this cycle of tension and compression is repeated many times — hence the name cyclic stress.
Types of cyclic stress
Cyclic stress is frequently encountered in rotating machinery where a bending moment is applied to a rotating part. This is called a cyclic bending stress and the aerial lift above is a good example. However, cyclic axial stresses and cyclic torsional stresses also exist. An example of cyclic axial stress would be a bungee cord (see bungee jumpingBungee jumping
Bungee jumping is an activity that involves jumping from a tall structure while connected to a large elastic cord. The tall structure is usually a fixed object, such as a building, bridge or crane; but it is also possible to jump from a movable object, such as a hot-air-balloon or helicopter, that...
), which must support the mass of people as they jump off structures such as bridges. When a person reaches the end of a cord, the cord deflects elastically and stops the person's descent. This creates a large axial stress in the cord. A fraction of the elastic potential energy stored in the cord is typically transferred back to the person, throwing the person upwards some fraction of the distance he or she fell. The person then falls on the cord again, inducing stress in the cord. This happens multiple times per jump. The same cord is used for several jumps, creating cyclical stresses in the cord that could eventually cause failure if not replaced.
Cyclical torsional stresses are stresses repetitively applied tangent to an axis. As an example, consider a compact disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...
drive. Each time a disc is inserted into the drive, a motor applies torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
to the disc via a drive shaft. Once disc reaches the desired rotational velocity
Rotational speed
Rotational speed tells how many complete rotations there are per time unit. It is therefore a cyclic frequency, measured in hertz in the SI System...
, relatively little torque is required to maintain the speed. Thus the torque varies over time as the drive spins up a disc and slows it down. Unlike the ski lift example above where the torque is relatively constant but the load due to cable tension created a bending moment
Bending Moment
A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres , or pound-foot or foot-pound...
, compact disc drive shafts have little to no bending movement applied, but have a torque that varies significantly over time.
Cyclic stress and material failure
When cyclic stresses are applied to a material, even though the stresses do not cause plastic deformation, the material may fail due to fatigueFatigue (material)
'In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The nominal maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material.Fatigue occurs...
. Fatigue failure is typically modeled by decomposing cyclic stresses into mean and alternating components. Mean stress is the time average of the principal stress. Alternating stress is the difference between the mean and the maximum or the mean and the minimum value the principal stress takes on. Engineers try to design mechanisms whose parts are subjected to a single type (bending, axial, or torsional) of cyclic stress because this more closely matches experiments used to characterize fatigue failure in different materials.