公差累积分析.pptx

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,2021/10/3,#,Design Analysis,Design analysis is used in place of test and inspection to find the expected part performance,It basically means we are looking for the mean and sigma of the distribution before we build the parts,Techniques used for design analysis include:,1.Worst Case Analysis,2.Sensitivity Analysis,a)Monte Carlo Simulation,b)Taylor Series Expansion,c)Design of Experiments,1,第1页,1.Worst Case Analysis,Worst case is used to determine what happens when all the parameters are at their limits,Set every parameter to its spec limit,Measure the response,This is the same as adding tolerances,If all the parameters represent 3 sigma limits then,The number of parts bad for one parameter is 0.0026,Four parameters(0.0026),4,=0.00000000000286(3 in a trillion),For 20 parameters we get 2 out of 10,58,bad!,Analysis should limit probabilities to 6 sigma,This is about 3 parameters all at their limits,2,第2页,Tolerance Stack Up,What is the tolerance stack up from the top to bottom?,Will they line up?,3,第3页,Worst Case Analysis Tough!,Shaft 1+-0.002,Hole 1+.003,-.001,Shaft 2+-0.002,Hole 2+-.003-.001,Shaft 3+-.002,Hole 3+-.003-.001,Total Worst case is,.002+.003+.002+.003+.002+.003,=+0.015,-.009,The SHAFT WONT FIT IN THE,LAST HOLE UNLESS ITS.009,SMALLER!,4,第4页,Worst Case,For the first shaft and hole the shaft can be+-.002 and the hole+.003,-.001.,If the hole is small then-.001 and the shaft is large then+.002.The difference between the two must be 0.003 to make sure it fits.,Add another set and the worst case says the second hole and shaft must be 0.006 different in size,A third set would have to 0.009 etc.,The problem with this is it makes for a too conservative design when you stack up tolerances,Perfect,Worst case,5,第5页,2.Sensitivity Analysis,a)Monte Carlo Simulation,Simulate variation in the results,b)Taylor Series Expansion,Mathematical evaluation of variations,c)Design of Experiments,Careful experimentation(testing)approach,6,第6页,2a)Monte Carlo Analysis,Monte Carlo is the name of a gambling city on the Mediterranean Sea.,With MC analysis you“roll the dice”and estimate the outcome many,many times,If you randomize the result often enough you get a good idea of the outcome of a system,You need to know the following,An equation for what you are simulating,The distribution of the parameters so they can vary over time,7,第7页,Circuit Example,Mean Std Dev,V=voltage 100 5,r=resistance 10 1,f=capacitance 50 5,L=inductance .004 .0008,The equation for the current through the circuit is shown.,The voltage of the power supply is usually at 100 Volts but it varies+-5 Volts 1 sigma,1 Sigma means 68%of the time,2 Sigma is 95%and 3 Sigma is 99%,so,the voltage could be 100-3*5=85 Volts some times.,If the package says a 1%tolerance on 10 Ohm resistors,that means the resistors can,be between 9 or 11 ohms 99%of the time(or 3 sigma).,8,第8页,Monte Carlo Analysis,Circuit Example,Mean Std Dev,V=voltage 100 5,r=resistance 10 1,f=capacitance 50 5,L=inductance .004 .0008,(1)V=5*Z+100,(2)R=1*Z+10,(3)f=5*Z+50,(4)L=0.0008*Z+.004,(5)Calculate,I,and plot Z is a random number,(6)Repeat 1000s of times Normally distributed,9,第9页,2b)Taylor Series Expansion,The Taylor Series calculates the system variance based on the derivatives of the function with respect to each parameter,Give the equation g(x1,x2,x3)then,10,第10页,Sensitivity Analysis,The sensitivity of the output to changes in the input can be calculated from the derivatives.,The sensitivity of,I,to changes in V,This means that when V increases from its mean by 1 sigma,I,increases by 0.5,11,第11页,Taylor Series Example,12,第12页,Example,Evaluate the expression for,I,using the mean and standard deviations,13,第13页,Root Sum Squared(RSS),Root Sum Squared is simply the Taylor Series expansion for a linear system,g=x1+x2+x3,This only work for linear system(mechanical tolerances),This is,VERY,popular in industry!,14,第14页,Revisiting Tolerance Stack up,Shaft 1+-0.002 implies that all the units vary by this much.So 3 Sigma is 0.002 and Sigma=0.00067,Hole 1+.003,-.001 implies the 3 Sigma is.001/3=.00033,RSS for 2 parts is SQRT(0.00067,2,+.00033,2,)=0.00075 for 1 Sigma of the system.3 Sigma of the system is then.00225 not 0.003.,For 6 parts in the system you get,SQRT(0.00067,2,+.00033,2,+0.00067,2,+.00033,2,+0.00067,2,+.00033,2,)=.00129 for 1 Sigma.,So 3 Sigma is 0.004 not 0.009 shown by worst case.,15,第15页,2c)Design Of Experiments,DOE is a statistical tool that allows the most information to be extracted from an experiment,Normal experiments hold every variable constant and change one.,In the previous example hold all fixed except R.Change it to its limits and see how the network responds,DOE(also called Taguchi methods)allow more than one variable to change so that multiple interactions can be measured,What happens if R is low and f is high?,16,第16页,D.O.E.Process,First determine the number of factors(controllable variables)you want to change.Call it n.,The number of experiments necessary to test everything at the high and low limits of each variable is 2,n,The minimum number of experiments is the larger of n and 2,x,If we have 5 variables we need 2,5,or 32 experiments,With DOE we need 2,3,or 8 experiments,The math is simple(Excel spread sheet)but it takes some knowledge to set this up and use it.,This is popular for expensive testing in industry.,17,第17页,