Bolts installed on a production line are tightened with automatic wrenches. They are to be tightened sufficiently to yield the full cross-section in order to produce the highest possible initial tension. The limiting condition is twisting off the bolt head during assembly. The bolts have a mean twisting off torque of 20 Nm with a standard deviation of 1 Nm. The automatic wrenches have a standard deviation of 1.5Nm. What mean value of torque wrench setting would result in only 1 in 500 twisting off during assembly? Give a rough estimate only.
Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
- Bolts installed on a production line are tightened with automatic wrenches. They are to be tightened sufficiently to yield the full cross-section in order to produce the highest possible initial tension. The limiting condition is twisting off the bolt head during assembly. The bolts have a mean twisting off torque of 20 Nm with a standard deviation of 1 Nm. The automatic wrenches have a standard deviation of 1.5Nm. What mean value of torque wrench setting would result in only 1 in 500 twisting off during assembly? Give a rough estimate only.
- A unit has a constant failure rate of 0.3% per 1000 hours. What is its MTBF? What are the probabilities of the unit successfully completing missions of 10000, 100000 and 1000000 hours? Give a rough estimate only.
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