**Problems due to tolerance stack-ups include:**• Failure to assemble • Interference between parts • Failure of parts to engage • Failure to function as intended**Overview:**Tolerance stack-ups are accumulations of variations on drawings or in part assemblies.**Example: Accumulation of tolerances on a drawing.**3.00±0.01 7.00±0.01 What is the effective dimension and tolerance between the two holes?**In this case the tolerances add directly**The furthest apart the two centers can be is 7.01-2.99=4.02 The closest is 6.99-3.01=3.98 Thus, the effective dimension and tolerance is 4.00±0.02 This addition of tolerances may make it hard to join with a mating part that has two pins that fit in those holes.**The logical thing is to put the dimension and tolerance**directly on the hole spacing if that is the location most important to function. 7.00±0.01**A±a**Gap B±b C±c Example: Assembly of individual parts Suppose we have two blocks, A and B that are to fit into a slot in C, all with tolerances shown.**Let’s look at the largest and smallest gap that we could**have. Largest Gap = (C+c) – (A-a) – (B-b) = C – (A+B) + (a+b+c) Smallest Gap = (C-c) – (A+a) – (B+b) = C – (A+B) – (a+b+c) Consequently the dimension and tolerance of the gap is effectively: {C-(A+B)} ± (a+b+c)**If we have 10 parts (say a clutch pack) that all have to fit**into a housing, the addition of all those tolerances can be significant. If controlling the spacing of the clutches is important to function we have a problem. What can we do as designers?**Solutions**• Tighten up the tolerances on each component so the sum of the tolerances is lower. • Include a spacer that comes in different sizes to take up any slack resulting from the tolerance addition (similar to shimming). • Design so that the tolerance stacks are not relevant to function. • Consider that the variation in each part is likely to be statistically distributed.**Example: 2-D**Consider a swing weight governor similar to the one shown below**L1±l1**H L2±l2 Simplifying further, assume: • Holes are perfectly located • Pins and holes have zero clearance and move freely • Only length of links has tolerance**The height can be found using geometry (specifically, the**Law of Cosines). H2 = L12 + L22 - 2l1l2cosα (where α is the angle between the legs) And Hmax2 = (L1+l1)2 + (L2+l2)2 – 2(L1+l1)(L2+l2)cosα Hmin2 = (L1-l1)2 + (L2-l2)2 – 2(L1-l1)(L2-l2)cosα