Time to read: 9 min
In the world of mechanical product design, engineers and designers complete what is known as a tolerance analysis or tolerance stack up analysis on an assembly as they prepare to send the components out for manufacturing. This is done to ensure when you order parts, they are manufactured to dimensions that保证the components within an assembly fit together.
For this post, I’m going to focus on how to conduct a tolerance analysis specifically for 3D printed components, reviewing:
- How to conduct a positional tolerance analysis
- 如何进行线性公差分析
- Final pro tips and tricks
Download our free tolerance analysis calculator here
Tolerance Stack and Interference Example
让我们开始详细说明当我们说“宽容堆积”和相关的问题 +解决方案时，我们就会详细介绍。
如果您查看下面的组件，您会发现一系列¼-20个插座盖螺钉用于将盖子（灰色）固定在基座上（绿色）。
The fasteners have a maximum outer diameter of 0.250”, but they will also have to pass through holes in the lid and thread into the tapped holes in the base. For a 0.250” diameter fastener to pass through a plain hole, the diameter of the hole would have to be just larger than 0.251”. However, when these components are manufactured, the holes will not be in the exact same locations as the model due to machine capabilities.
The image below demonstrates what happens when we add .030” of positional error to the screw holes outward (relative to the vertical center plane) for the lid and the inward for the base (note：the screws have been colored blue for clarity).
In the enlarged view, we can see the hole mismatch between the lid and the base for the features on the left, but the center screw holes are perfectly aligned. This means that our lid will never install properly with all of the screws in place. If we had done a proper tolerance analysis, we wouldn’t be in this situation and for the remainder of this article we’ll detail how to conduct such an analysis.
Example 1: How to Conduct a Positional Tolerance Analysis
Now that we’ve reviewed a basic example of tolerance stacking, let’s look at an example that details the steps to perform a tolerance analysis as it relates to the position of features such as bolt holes. The steps will be completed using an excel calculator built specifically for a 3D printing tolerance analysis.
In the spreadsheet, there are separate tabs for positional and linear tolerance studies and the lighter columns on the left require user input and the darker two columns on the right are the calculated spreadsheet output.
Here are the four steps for completing the analysis using the spreadsheet:
Step 1– Define the Machine or Process Capabilities
首先，我们定义机器或过程的技术功能。beplay客户端下载在一个Stratasys发表的研究, their Fortus 360mc/400mc FDM machines have a dimensional accuracy of ±.005” or ±.0015 in/in. For our example, we’re going to use the tolerance specification of ±.005” for this FDM machine.
Step 2——定义Interfacing Components and Associated Dimensions
接下来，我们需要定义接口功能及其各自的维度。在我们的示例外壳的情况下，接口功能是螺丝孔和螺钉。这些是我们需要确保所有内容都会对齐并安装在一起的功能。
Note that the description here is simply for our benefit when we review these calculations at a later time. The interface OD (outer diameter) is the最大将进入孔的螺钉或紧固件外径（在我们的情况下为.250英寸）。
Step 3– Calculate the Necessary Clearance
The next step is the fun part: Calculations! In our example, the base (green part) has threaded holes, while the lid (gray) has through holes. This is what we call a “fixed fastener case” and a further explanation can be found in Appendix B paragraph B4 ofASME Y14.5。The formula we’ll use is slightly different because we’re dimensioning the parts based on the performance specification of the machine:
This formula is based on the fact that if the axes of the holes are displaced relative to each other at the maximums of each tolerance, the displacement will be equal to the hypotenuse of a right triangle with sides equal to .010”. The image below illustrates a ±.005” tolerance zone, and the associated hypotenuse. Note that the sides are .010” which is simply twice the .005” we are using for the machine tolerances.
因为任何displacem我们双斜边ent between hole axes, we need twice the increase in clearance from a diametral standpoint. Finally, we’re adding in the tolerance again because the hole may come in undersized by the tolerance amount. If we were to use this formula in our example, we would see that the clearance holes in the lid need to be dimensioned as follows:
Fortunately, we’ve built a handy excel calculator that solves these formulas for us since we don’t want to calculate these items separately every time. The snapshot below shows the spreadsheet doing its magic:
Notice that the “Tolerance Type” has a drop down menu. We can select “Fixed” or “Floating” based on the type of holes we’re using.
Floating fastenerssimply have two through holes and will use a fastener and a nut instead of threading directly into one of the parts. If we use floating fasteners, the required clearance is cut in half and each hole is expanded by that amount. The example part in this case isFixed, so we’ve selected that option accordingly.
步骤4 - 相应调整CAD模型
Now that we have all the necessary dimensions for our design to ensure it fits together on the first try, we’re going to modify our CAD models to reflect these dimensions.
The drawing image below details what the nominal dimensions and tolerances are for the hole size and spacing that we’ve calculated:
The models for both the lid and the base will have the holes spaced at 2.150” and 1.500” from the center planes of the part, while the through holes in the lid will be modeled to a diameter of 0.283”.
但是，如果机器在公差区的极端产生零件，我们可能会得到以下尺寸的零件：
We can see that the lid (top) and the base (bottom) have parts produced at the opposite extremes of their tolerance bands.
这些维度制造的零件是不太可能的情况，但是考虑到机器的性能规范，这并非不可能。此外，零件永远不会像模型中的尺寸一样进入。
The image below shows our assembly with the tolerance offsets given in the drawing images above.
It’s obvious that even with the most drastic offsets in part dimensions, the parts still fit together. Statistically speaking, it’s very unlikely that all of these dimensions will come in at these extremes, but this method will ensure the parts fit together the first time, every time, with no modification.
Example 2: How to Conduct a Linear Tolerance Analysis
Conducting a linear stack of tolerances uses the same basic steps as a positional tolerance analysis.
For this second example, we’re working with a linear stack of tolerances, looking at how multiple interfaces affect parts and their spacing relative to each other. We’re going to follow the same basic steps used in our first example and continue to use machine tolerances of ±.005” for simplicity.
我们的下面示例详细介绍了矩形插头进入矩形插座的简单表示。
我们希望插头的较大肩膀与插座的顶部联系，以确保插头不会底部。如果我们查看下面的图纸，我们会了解我们在这种安排中正在使用的公差。
Referring back to our spreadsheet (using the linear tab this time), I can put these dimensions into the cells to calculate the dimensional extremes as follows:
If the part is manufactured to the nominal dimensions, we can see there will be .015” of clearance between the end of the plug and the bottom of the socket cavity. However, this clearance gap can be reduced as low as .005” if the part is produced to the tolerance extremes of the machine as detailed in the image below.
NOTE:We can use our spreadsheet to calculate these clearances by subtracting the max plug depth dimension (0.990) from the min socket depth dimension (0.995).
In this case, we know the plug will not bottom at the tolerance extremes so we have no concern. But when we add other interfacing components such as faceplates, we’ll see how the tolerances begin to stack up and pose a concern.
The assembly in the following images places the plug in a housing and includes a faceplate on top of the socket.
现在，很明显，我们已经以不利的方式堆叠的公差机会的数量增加了一倍，但是我们的名义清除率与第一种案例完全相同。
The image below details a worst case scenario for interference:
There’s now .005” ofinterferenceinstead of a worst case of .005” ofclearance。This is because the two components between the plug and the socket each have a tolerance of ±.005” (.010” of additional tolerance stack).
Referring back to the spreadsheet, we can perform the same math to determine the extremes of our interfacing features:
The math is simple: We subtract the maximum plug length from the sum of the minimum dimension for the other features that separate the interference we’re worried about. That’s to say:
Clearance/Interference = .870 + .120 + .120 – 1.115 =-.005
A negative value in this instance means we’ll have interference, while a positive value would indicate how much clearance we have in the worst case scenario.
为了在维持0.005英寸的清除率的同时容纳面板和外壳设计，我们需要在.010的标称尺寸上添加额外的许可。这将使我们的名义间隙差距.025“。
很容易看到接口零件之间增加了多少组件，以加在一起以在设计过程中引起挑战。
3个最终技巧和技巧
现在，我们已经完成了详细的计算和分析，我为您提供了一些最终技巧和技巧。
1.如果您不愿意或不能打开足够的公差，以确保根据机器功能确保100％拟合，则beplay客户端下载you can reduce the clearance if you’re ok with a few things：
- You have to be ok with some clean-up work if things don’t fit perfectly together. This means sandpaper, reaming holes or other minor subtractive modifications.
- You have to be ok rolling the dice. Remember, tolerance stack ups are a game of statistics, and the further you deviate from a guaranteed fit, the greater your chances of “busting” are.
2. From a tolerance stack point of view,减少必须融合在一起的组件之间的接口数是有益的。您拥有的界面越多，耐受性堆栈的机会就越多，可以干扰组件的组装。
3。如果您需要维度精度，请限制组件的大小并相应地选择制造过程。许多高端流程（例如Polyjet) will produce more accurate parts, and nearly all machines will hold tighter tolerances as your parts get smaller as long as it doesn’t exceed the feature size capability of the machine.
What About Statistical Studies?
Note that these examples have looked only at a worst case tolerance analysis which is typical of parts that are ordered in lower quantities or that are required to serve as a drop in replacement on an existing assembly.
当处理更高的体积或极度的公差时，通常进行统计研究以量化零件不适合宽大范围的零件范围的概率。
如果您想在最坏情况下的值之外的值尺寸，则可以以较小的数量进行此操作。一种常见的方法是执行Monte Carlo simulationbased on a normal distribution from a root sum square analysis. Through this approach, you can quantify the statistical probability of parts fitting together or not fitting together.
Main Takeaways
通过这些例子,我们看到tolerance analysis isn’t as daunting as it may have seemed at first. As you become more familiar with this analysis and the machine capabilities, the dimensional limits can be pushed with less risk and uncertainty. You can在此处下载我们的免费耐受分析计算器to put your skills into practice and also checkout Fictiv’s3D printingandCNC加工服务for precision tight tolerance parts.
