Geometric Dimensioning and Tolerancing or GD&T is a subject that I get asked about frequently. As I wrote before in THIS post about Levels of Control I thought that I would Blog about the subject because I spend quite a lot of time answering friends a colleagues questions about it. Have a look at that post and read the fist couple of paragraphs if you are curious about what Geometric Dimensioning and Tolerancing is.
Size matters and size is what I want to write about in this post. After all having parts that are the right size is what allows them to fit together. What I am going to write about in this post might seem completely theoretical and somewhat pointless in the real world but it isn't. These concepts don't seem practical when you have a drill or a saw in your hand but actually this is all about having parts that you design and build fit together right? Fitting together of course is all about the size of the parts. Geometric Dimensioning and Tolerancing has some basic concepts about size that might seem a bit odd at first but it all makes sense when you think about how small a hole can be and how big a pin that has to fit in the hole might be - and then grab a hammer to force it into the hole.
The first point that I want to make is that all dimensions on drawings have to have a tolerance associated with them. All dimensions on drawings have to have some tolerance placed on them because it’s not possible to make something exact in the real world. If you ask someone “cut that thing into three 1 inch long pieces” you won’t get three exactly 1 inch long pieces. They might all be really close to 1 inch, but not all of them will be exactly 1 inch because exactly is a difficult thing to achieve. How do you know if they are all close enough to 1 inch for whatever you need them for? That’s where the tolerance comes in, it sets an upper and lower limit or a range on what is acceptable as a 1 inch piece for a particular application. Sometimes it might have to be really really close to 1" and the tolerance will be really small, other times it might not matter much and the tolerance can be a lot. That’s the concept anyway and you can apply that to not only dimensions but also other more abstract things like shapes. “Is this thing flat enough?” “is this square piece of metal square enough?” etc.. of course ‘square’ and ‘flat’ will have to have some number associated with them (and a way to measure them) and that number will have a tolerance.
|A Part Made Exactly To The Drawing|
The reason that I am mentioning this is because in mechanical drawings the tolerance on the dimensions plays a big part in what the final product looks like and whether or not it’s going to work. The tolerances control what the shape of the part is or can be and they are just as important as the dimensions themselves. In fact it shouldn't be too surprising to read that in Geometric Dimensioning and Tolerancing it’s all about the tolerances! To get an idea of what I am talking about have a look at the picture below of the square thing with the hole in the center. I have left a few dimensions out of the drawing for simplicity and to explain the concept so don’t worry if it looks incomplete.
In the drawing below the block with the hole in it is dimensioned and each dimension has a tolerance. The dashed lines in the drawing represent the ‘tolerance zone’ for each dimension (and they are not to scale), so in the case of the 1.500+/-.005 hole the inner dashed line represents the 1.495 diameter and the outer dashed line is the 1.505 diameter. The same goes for the block, with the dashed lines showing the extremes of the dimensions tolerance. Tolerance zones are important to keep in mind especially if you are going to make lots and lots of parts. It should be obvious what the tolerance zones mean, the block or the hole can be made so that the edges and surfaces fall anywhere within the tolerance.
In the above picture the block and the hole are both drawn at exactly their Nominal Sizes and the tolerance zones are both inside and outside the block and hole edges. In this special case the part would be considered to be at it's Nominal Size. In addition to Nominal Size there are a couple of other special cases or ‘conditions’ that the part can be in when talking about tolerances. Those conditions are Maximum Material Condition and Least Material Condition shown with either a M in a circle or a L in a circle. Have a look at the pictures below.
Maximum Material Condition
Notice the difference between the two drawings. In the first drawing both the hole and the block are at their Maximum Material Conditions. I put the dashed lines in the picture to show where the tolerance zones and nominal sizes are. In the case of Maximum Material Condition the block (or the outside of the part) is at it's Maximum Size or it's biggest size allowed within the dimensions tolerance and the hole (or the inside of the part) is at it's Smallest Size. Why would the hole be at it's smallest allowable tolerance size if the part is at Maximum Material Condition? Maximum Material Condition is just like it sounds, the part has the maximum amount of material and when you add material to a hole it gets smaller. That's because a hole or any similar 'opening' is an Internal Feature and the outside of the part or the block in this case is an External Feature. When you add material to an internal feature that feature becomes smaller and when you add material to an external feature that feature becomes bigger. Maximum Material Condition or MMC is sometimes thought of as the part being it's heaviest, the heaviest it can be and still be within it's size tolerance. At MMC all the internal features are at their smallest sizes and all the external features are at their biggest sizes allowed by the dimensions tolerances.
Least Material Condition
Have another look at the above drawing and compare the Maximum Material Condition and the Least Material Conditions. Notice that they are opposite one another in the sense that in Least Material Condition the hole is at it's Largest Size and the block is at it's smallest size. Least Material Condition or LMC is the same concept as MMC in that when something has the Least amount of material the hole (or all internal features) are at their largest sizes and the external features are at their smallest sizes allowed by the dimensions tolerance. LMC is sometimes thought of as the condition where the part weighs it's least or the minimum weight allowed by the dimensions tolerance.
Maximum Material Condition and Least Material Condition are extremely important concepts in Geometric Dimensioning and Tolerancing and are used all the time. How they are used is a little bit complicated and I'll explain more about that later. For now understanding the concepts is enough.
So far I have mentioned the Nominal Size, The Maximum Material Condition and the Least Material Condition as three different states that a part in theory can exist. In practice nothing is ever perfectly manufactured or ever perfectly in any one of these three states completely. Normally what you get is something closer to the picture below.
The drawing above shows one state that the part could be manufactured to and still meet all the conditions of the dimensions tolerances. The tolerances are not to scale and realistically a part probably wouldn't be manufactured like the above drawing shows but it could be! Notice that the hole isn't really all that round and the block really isn't very rectangular but at no point is any surface outside the tolerance zones so the part is acceptable. This is important because the tolerances are controlling the Shape (or Form) of the part. If the tolerances were smaller the hole would be rounder and the block would be more of a rectangle. Geometric Dimensioning and Tolerancing has a name for this concept of the dimensions tolerances controlling the parts Shape and it used to be called Rule 1. It's not called rule 1 anymore but it should be because it's important and here is what it says more or less:
When a drawing has only dimensions with tolerances and no other shape or form controls, those dimensions and tolerances control the parts size and it's shape.
I'm paraphrasing a little but that is essentially what it says. Another way to look at this is if you are creating a drawing and you put a dimension someplace with a tolerance, that dimension and it's tolerance will control not only the size but also how the part could be shaped. So unless otherwise specified the dimensions and tolerances prescribe the limits of how much the shape can vary in a part. If you want to control the shape more than the tolerances are allowing you have to add some other type of control. More about the types of control later.
Perfect Geometric Form at MMC
There is one more thing to mention regarding LMC, MMC and Rule 1. There is a concept called Perfect Geometric Form at Maximum Material Condition. That's a fancy way to say something that I will try to explain in plain terms because I don't like fancy names unless I made them up myself.
Have a look at the first three drawings above of the part at Nominal Size, MMC and LMC. In each one of those drawings the hole is drawn perfectly round and the block is drawn perfectly rectangular. All the edges of the block are straight and the corners are perfect right angles. In each one of those drawings you could say the the part has Perfect Geometric Form because it's perfect! Geometric Dimensioning and Tolerancing doesn't allow Perfect geometric Form at any condition other than at MMC. If you refer to something at MMC it must have perfect geometric form. A round cylindrical rod at MMC would be perfectly round, perfectly straight a perfect cylinder. So the concept of Perfect Geometric Form at Maximum Material Condition means that if a drawing states that something it to be considered at MMC then it is also considered to be perfect. Perfect in this case means perfectly round, straight, flat, square etc... The rule of Perfect Geometric Form doesn't apply to a part produced at LMC, in that case it's allowed to deviate as much as the tolerances allow. If you refer to it at LMC it could be perfect but it isn't necessarily so.
LMC, Nominal and MMC can be applied and thought of in any combination of ways. For example the block in the drawing above could be at MMC (Big) and the hole at LMC (Big) or any combination of the three.
Why is all this important?
This all probably seems pretty academic and not at all related to the real world but in reality it's quite the opposite. When you are designing a particular part it usually has to attach to something else and fit right. For example you might have a hole that a pin has to fit through and you have to be sure that the hole is big enough for the pin. In this case you will want to consider how big the hole is going to be at MMC because that would be the smallest the hole could ever be. While the hole is at MMC (or smallest size) you would have to also consider the pin at MMC (biggest size) and be sure they will fit together. The MMC sizes in this case would be the 'worst case' fit for the pin and the hole. When you are designing and fabricating your own stuff from a sketch this isn't too important but if you sketch something and have someone else make it the dimensions and their tolerances become really important. Even more so if you ask someone to make 1000's of parts from your drawing and you want all of the parts to fit correctly. I'll write more later about how these concepts work together to ensure that every part always fits together in all cases.