Rss tolerance stack upformula

A widely used method for performing a statistical stack-up tolerance analysis is the Root-Sum-Squares (RSS) method. Variances (the standard deviation is the square root of variance) can be added. This makes it easy to sum normally distributed tolerances: Ttot = √(T12 + T22 + …. Tn2).

You should read our 6 step guide to drilling through metal because the same rules apply to drilling harder grade alloys.

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A common assumption is that the tolerance limits coincide with the +/-3σ (3x standard deviation) values. As a reminder, the standard deviation is a measure of variation. 99.7% of the population falls within the +/-3σ limits.

It is clear that it is beneficial to consider the probability distribution of the tolerances and perform a statistical analysis

Rss tolerance stack upexample

If you don’t know the distribution of tolerances, you have to make an estimate. It is often assumed that tolerances have a normal (Gaussian) distribution. This is because the normal distribution seems to occur in “almost all cases”. In statistics, this is called the central limit theorem. Roughly speaking, this theorem states that “the sum of a large number of independent and identically distributed random variables, will be approximately normally distributed“. Since the manufacturing process of machined parts consists of many variables, it is safe to assume a normal distribution of tolerances. An added benefit is that it is relatively easy to add up normally distributed tolerances.

In the worst case example above, there was an extreme distribution of tolerances. The question now is what is a (more) realistic distribution. This is not an easy question to answer, but a better estimate would increase the accuracy of your analysis.

Root sum square

If you can drill metal then certainly you should not fear drilling hardened steel because the same techniques apply. Read below what customers say about their experiences drilling hardened metals and then watch the videos of TTP HARD drills in action.

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“These drills perform exceptionally well. They’re far superior to anything I can buy locally. Delivery is extremely fast. I was able to finish drilling a 3/8” hole through 1-1/4” hardened bar stock. I must have gone through a dozen conventional cobalt bits before purchasing this kit. Love ‘em.”

“They are fabulous. I still haven’t had the time to use them for their actual intended purpose – drilling out exhaust manifold studs, but I did try them on a couple of bolts to see how they did and was very impressed! Told a bunch of my friends about them. Hoping to get a joint order together. I want more sizes or one of the sets!”

RMS vsRSS toleranceanalysis

We have selected some customer reviews to give you an idea of some of the hardened metals and steels TTP HARD cobalt drill bits will drill through. You will see that whether you are drilling a hardened 12.9 bolt or an exhaust manifold stud once you follow the basic drilling principles you should have the same level of success.

“I was very happy with my purchase of the tough drill bits, they allowed me to drill out some broken off tensile bolts form a 25 year old motorbike cylinder head, failure in this would have meant finding a new head or abandoning the project.”

A tolerance analysis spreadsheet is available in the Engineering Toolkit of Vink System Design & Analysis. This allows you to quickly start performing tolerance analysis, including the statistical method described here. The advanced method as described in ‘Advanced Method of Tolerance Analysis‘ is also possible.

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Rss tolerance stack uppdf

Rss tolerance stack upcalculator

Watch videos of hardened metal being drilled with TTP HARD cobalt drill bits. You will see how easily Hardox 450 can be drilled using the correct speed, pressure and pleanty of libricant paste. Likewise a 12.9 cap head bolt is easily drilled when the drill bit is allowed to do the work and rest periods prevent the drill bit from overheating. Finally you will see a BMW flywheel and even JCB tow plate steel being drilled without any effort using correct speed, pressure and lubrication.

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RSS tolerancestack-up Excel

The probability of an extreme thickness is 2/16 = 12.5%. If, for example, only the top pile is problematic, the probability is only 6.25%. Note that this is an extreme tolerance distribution with a low probability itself. In practice, the probability of an extreme height is very low.

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“I’ve been at this a long time and I have never seen bits this good. On my test, they breezed through gr 8 bolt on the press with cut oil. When I tested with a chord drill, I found that you could break the bit if you weren’t perfectly square. On the car with the broken exhaust stud, it was fantastic, they bite like crazy. I’m going to give them as gifts to my wrenching friends.”

“These drills perform exceptionally well. They’re far superior to anything I can buy locally. Delivery is extremely fast. I was able to finish drilling a 3/8” hole through 1-1/4” hardened bar stock. I must have gone through a dozen conventional cobalt bits before purchasing this kit. Love ‘em.”

RSS tolerance stack upexample pdf

If similar parts have been produced, you have important data to make a good estimate of the tolerance distribution. But what if you’re working on a new product and don’t have that kind of data to compare?

“They are fabulous. I still haven’t had the time to use them for their actual intended purpose – drilling out exhaust manifold studs, but I did try them on a couple of bolts to see how they did and was very impressed! Told a bunch of my friends about them. Hoping to get a joint order together. I want more sizes or one of the sets!”

We have selected some customer reviews to give you an idea of some of the hardened metals and steels TTP HARD cobalt drill bits will drill through. You will see that whether you are drilling a hardened 12.9 bolt or an exhaust manifold stud once you follow the basic drilling principles you should have the same level of success.

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You should read our 6 step guide to drilling through metal because the same rules apply to drilling harder grade alloys.

Precipitation hardening, also called age hardening, is a heat treatment technique used to increase the yield strength of malleable materials.

In the example above, all tolerances were +/-1, so the total height variation is: Ttot = √(12 + 12 + 12 + 12) = 2. The stack of parts will have a height of 40 +/-2. And 0.3% of the stacks will be smaller or larger (with a height of 36 .. 38 or 42 .. 44).

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Watch videos of hardened metal being drilled with TTP HARD cobalt drill bits. You will see how easily Hardox 450 can be drilled using the correct speed, pressure and pleanty of libricant paste. Likewise a 12.9 cap head bolt is easily drilled when the drill bit is allowed to do the work and rest periods prevent the drill bit from overheating. Finally you will see a BMW flywheel and even JCB tow plate steel being drilled without any effort using correct speed, pressure and lubrication.

If you can drill metal then certainly you should not fear drilling hardened steel because the same techniques apply. Read below what customers say about their experiences drilling hardened metals and then watch the videos of TTP HARD drills in action.

In the Worst-case Tolerance Stack-up Analysis article, you will read about worst-case or linear stack-up analysis. Such an analysis assumes that all dimensions in the tolerance chain have worst-case deviations from their nominal values. A statistical tolerance stack-up analysis considers the probability of a tolerance value and the combination of tolerances. It turns out that the probability of a worst-case combination is negligible for even a small number of parts. Let’s look at the following example. Suppose you are making a stack of 4 identical parts and you want to analyze the total height of the stack. The parts have a height specification of 10 +/-1. Now assume that all parts have a worst-case deviation and are either 9 (part ‘9’) or 11 (part ’11’) high (any dimension, mm, inch, meter, etc.). With only 4 parts, it is still possible to write down all possible combinations.

“I was very happy with my purchase of the tough drill bits, they allowed me to drill out some broken off tensile bolts form a 25 year old motorbike cylinder head, failure in this would have meant finding a new head or abandoning the project.”

“I’ve been at this a long time and I have never seen bits this good. On my test, they breezed through gr 8 bolt on the press with cut oil. When I tested with a chord drill, I found that you could break the bit if you weren’t perfectly square. On the car with the broken exhaust stud, it was fantastic, they bite like crazy. I’m going to give them as gifts to my wrenching friends.”