ADVANCED ENGINEERING DESIGN - TRIBOLOGY …

1 ADVANCED ENGINEERING DESIGND esign for ReliabilityBook: ADVANCED ENGINEERING DesignEdition, ManualLast updated Feb 16, Anton van BeekDelft University of TechnologyMechanical Engineering2 DESIGN for lifetime performance and reliabilityRecent updates:Feb 27 Chapter 4, problem and updated, problem 6 Chapter 3, problem , and newChapter 3, problem 9 Chapter 3, Problem 10 Chapter 3, Problem 12 Chapter 3, Problem solution updatedChapter 3, Problem newChapter 3, Problem newMarch 20 Chapter 6, Problem and 5, Problem 1 Chapter 3, Problem solution updatedChapter 3, problem solution 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.

2 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 field20 Then 95% of the shafts will have a diameterwithin a tolerance field of 20 mm A mm. a) What is A? b) What is the coefficient of variation CV ? CV is defined as the maximum deviation of the meandivided by the : 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.

3 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].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 = (T1 T50)/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.

4 The preloadFi is proportional to MA / where MA is the tightening torque thecoefficient of friction in the screw assembly. 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.

5 The tensile stress in the plastic regime varies much less with the strainthan in the elastic regime. 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 least torque that can be : Chain dimensioningThe illustration below shows a simpledrawing of a part made by the symmetrical toleranceinterval of A with 99% probability,assuming all tolerances are normallydistributed within the 3 interval andindependent.

6 Problem : Number of measurements needed to obtain a reliable estimation When the measurement of the coefficient of friction is repeated one will find a large variation. Considerthe measured values , , , and a) Calculate the 95% interval over which coefficient of friction may lie. b) What number of measurements are needed to estimate the mean with 95% reliability within for lifetime performance and reliability5 Problem : Estimation of service intervalFrom a series of experiments it isfound that a 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.

7 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)= : 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) for lifetime performance and reliabilityProblem : Bearing reliability, deep groove ball bearingCalculate the operating reliability R(t=1000hr) of a deep groove ballbearing.

8 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 129). 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. 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.

9 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 : 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 = .Problem : Stress concentration factor "A chain is only as strong as its weakest link, regardless of the strength of the stronger links".

10 Do youagree and what do you think about the reliability if the failure mode is fatigue? DESIGN for lifetime performance and reliability7 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. 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.