ADVANCED ENGINEERING DESIGN - WERKTUIGBOUW.NL

1 ADVANCED ENGINEERING DESIGND esign for ReliabilityBook: ADVANCED ENGINEERING DESIGN , edition 2015 Website: Manual: Last update Sept 5, Anton van BeekDelft University of TechnologyMechanical Engineering2 DESIGN for lifetime performance and reliabilityRecent updates from Sept 5, updated DESIGN for lifetime performance and reliability3 Problems Chapter 1 Problem : L10 service life Consider a quantity of 10 components that all fail within a year of service. Calculate the L10 service lifewith 90% reliability and 10% failure probability assuming a normal failure Problem : Tolerance field The diameter of a batch of shafts is normally distributedwith of the shafts within the tolerance field 20h9, itis between 20mm +0 / 52 m.

2 Calculate the size of the tolerance field with 95%probability. Problem : Driving torque interference fit An interference fit is realized with 20 H7/r6 hole/shaft tolerances. Thedimensions of the components are assumed to be normally standard deviation is calculated from the assumption that thetolerance interval is a 3 interval. Linear elastic deformation is to beconsidered which implies the torque that can be transmitted isproportional to the diametrical interference . The torque that can be transmitted, based on the mean value of the diametrical interference, is T50 [Nm].

3 It is the torque with 50% failure probability. The torque that can be transmitted with 1% failureprobability is denoted as T1. The variation of performance, relative to the mean, is a measure of reliability. The coefficient of variationis defined as CV = deviation/mean. Calculate CV = (T50 T1)/T50. Problem : Driving torque tapered shaft hubs The torque T that can be transmitted by a tapered shaft hub connectionis proportional to the clamping force, the bolt preload Fi. The preloadFi is proportional to MA / where MA is the tightening torque thecoefficient of friction in the screw assembly.

4 The coefficient of friction is managed by using a proper thread lubricant and varies between Calculate the coefficient of variation CV =(T50 Tmin) /T50 whereTmin is the least torque that can be transmitted by the shaft for lifetime performance and reliabilityProblem : Interference fit with hollow shaft A gear is to be press fitted over a hollow shaft of 20 mm the interference = mm. The strain is that much thatthe hollow shaft will deform plastically. The tensile stress in the plastic regime varies much less with the strainthan in the elastic regime.

5 The tensile stress in the plastic regime of the steel shaft is approximatedby linear interpolation between (g= ) = 350 MPa and (g= ) =450 MPa. Calculate the coefficient of variation CV =(T50 Tmin) /T50 whereTmin is the driving torque that can be guaranteed for all : Estimation of service intervalFrom a series of experiments it isfound that the component life is =150 103 km and = 20 103 km. Acomponent reliability of 90% isspecified with L10, of 99% with the value L10 and L1 and theratio a1 = L1/L10.

6 Problem : Conversion of MTBF to Reliabilitya)Estimate the MTBF for N=10 devices that aretested for Ttest=500 hours and during the test r=2failures )Estimate the probability that any one particulardevice will be operational at the time equal to theMTBF? c)Estimate the probability that the component willwork for 50% of the MTBF d) Estimate the percentage of the MTBF whereR(t)= for lifetime performance and reliability5 Problem : Fault Tree AnalysisConsider the fault tree with the component reliability given in the table below and calculate the failureprobability F(t) of the system for a service life CDE FGR(t).

7 Bearing reliability, deep groove ball bearingCalculate the operating reliability R(t=1000hr) of a deep groove ballbearing. The calculated L10 life expectancy of the ball bearing is L10 =500A106 rev. The rotational speed is 4000 : The life expectancy of the ball bearings is related to the L10 basicrating life according (eq. , page 19). Problem : Reliability factor for Fatigue strength A power supply is cooled by 3 fans. The correct functioning of at leastone of the three fans is required to maintain sufficient cooling.

8 Theoperating reliability of the system needs to be 99% for a service life hr, Rs ( hr) = The rotational speed is 4000 ) Estimate the required operating reliability Rj of the individual ) Calculate the required L10h of the individual ) Calculate C/PProblem : Reliability factor for Fatigue strength Data published of the endurance strength are always mean values. InNorton (2000) is reported that the standard deviation of the endurancestrength of steels seldom exceeds 8% of their mean. Estimate a correctionfactor for the endurance strength if a 99% probability is for lifetime performance and reliabilityProblem : Component reliability Calculate the component reliability of a drive shaft(motor shaft) loaded in the High Cycle Fatigue (HCF)regime with Ln=2A105 load the calculated fatigue life of L50 = 3A105load cycles and a standard deviation of =.

9 Problem : Stress concentration factor "A chain is only as strong as its weakest link, regardless of the strength of the stronger links". Do youagree and what do you think about the reliability if the failure mode is fatigue?Problem : System reliabilityCalculate the failure probability F(100 hr) of twocritical components of a system connected in product catalogues it is found that the reliabilityof one component is specified with = 150 hr and = hr, the other component is specified with = 120hr and = hr.

10 Hint: first step is to calculate R(t) of both : System reliabilityA heavy duty motorized frame features a quad drivesystem using two high power DC motors and four drivebelts. All four belts are required to maintain optimalcontrol. From field testing it is found that the service lifeof the belts under heavy duty operating conditions isnormally distributed with a mean = 200 hr and astandard deviation of = . Calculate the operatingreliability of the set of 4 belts for a service life of 150 for lifetime performance and reliability7 Problem : System reliability There is a rule of thumb that says that the bearing load P relatedto the dynamic load rating of the bearing C is:Light loaded bearings P # loaded bearings < P # loaded bearings P > a motor drive equipped with two ball bearings.