Geometric dimensioning and tolerances are a standard system for communicating technical tolerances and design intentions through technical drawings. The flatness symbol is one of the central concepts in GD&T, commonly used by designers to control flat surfaces.
In this article, we discuss what flatness is in GD&T, the name of flatness, explain how to measure flatness, and present a brief comparison between straightness and flatness.
What is flatness in GD&T?
Flatness in GD&T is one of many engineering tolerance tools available for designers to control the size and shape of their designs. Flatness tolerance is applicable to surfaces whose flatness must be maintained within certain limits for the part to function properly. It is a common method of controlling the shape of a surface where flatness is a design requirement.
For example, the jaws of a lathe are ground with high precision so that they can grip parts with sufficient force and apply uniform force to the gripped surfaces. If they are not flat, the cable may come loose and damage the part due to stress concentration.
Flatness label and symbol
Flatness in GD&T has a special flatness label to indicate tolerance details of a part. In this section, we briefly explain the feature control for the flatness symbol. A typical flatness label is shown in the figure below, showing the symbol position and tolerance value in the feature control structure.
No reference point is needed for the flatness symbol, as we will explain in the next section. Therefore, the label only contains the flatness symbol and the tolerance value.
Flatness Tolerance Zone
Flatness in GD&T has a 3D tolerance zone defined by two parallel surfaces above and below the reference surface. The entire surface must be within these two virtual levels to meet the defined quality requirements.
The distance between these planes defines the “tightness” of the flatness tolerance. Based on the design intent, the designer sets a tolerance value according to the level of accuracy required and defines how much room the surface has for deviations from its true shape.
As mentioned above, the flatness symbol does not require a reference because it does not control the referenced feature relative to a standard reference feature. That is, it imposes an independent form of tolerance on the surface, regardless of its position or orientation in relation to other features of the part.
For example, the following figure indicates the flatness on the top surface of the part. All that matters is how flat the top surface is within the 0.1 inch tolerance zone. It doesn't matter if it is inclined in relation to the bottom surface of the part.
How to apply flatness in GD&T?
There are several ways to apply flatness in GD&T, with small differences between each option. While flatness is an easy-to-use GD&T tool, when designing parts with different geometries and quality requirements, it can be helpful to understand the different applications.
Flatness on a surface
This is the most common application of the flatness symbol. It is the same as described above. The surface flatness tolerance zone consists of two parallel planes above and below the surface.
In this case, the flatness label points directly to a flat surface or is on a line extending from the reference surface.
There is no restriction on the positioning of the flat surface for the flatness symbol to be applicable. The referenced surface can be inclined, inside a crack, or even discontinuous as shown in the image below.
Flatness in a Derived Mean Plane (DMP)
Flatness in a DMP is another way to use flatness in GD&T. In this case, the flatness symbol is applied to a sized feature and not a surface. The controlling resource is the virtual DMP of the referenced size resource. This has many practical applications, especially with stacked components.
Another point to keep in mind when using the flatness symbol in a DMP is that the Maximum Material Condition (MMC) and Lowest Material Condition (LMC) modifiers also apply to it. The flatness label in the following image includes the MMC modifier symbol ( 
).
In the example above, according to the tolerance, the thickness of the part should be in the range of 0.995-1.005 at all points. However, due to the display of flatness with the MMC modifier, the overall shape of the part (curvature, waviness in DMP) can still vary by up to 0.01.
Therefore, the actual functional tolerance zone (in GD&T parlance “Virtual Boundary Condition”) is 0.005 + 0.01 = 0.015. Takes into account deviations in size and shape.
Local flatness per unit
Local flatness tolerance is sometimes defined separately on the drawing when local flatness requirements differ from general surface flatness requirements. This happens in cases where the reference surface is very large and difficult to control or when local flatness is a functional requirement.
For example, sealing elements such as O-rings do not need to be completely flat in general, but they still need to be very flat in small local areas to ensure an effective seal.
Local flatness can be defined per unit length or surface area. Below are some examples. The surface must be within local tolerance limits for all possible local zones. For example, if there is a flatness tolerance of 0.01 by ⌀25, there should be no local circular zones ⌀25 on the surface where the 0.01 tolerance is exceeded.
How to measure flatness using different methods?
The next question to be answered is how to measure flatness. Once the part has been manufactured, it goes to the quality department along with its technical drawing, where a quality control specialist assesses whether the flatness tolerance is met or not.
There are numerous ways to measure flatness with varying degrees of accuracy. In this section we discuss the main methods and compare them in terms of accuracy, effort and time.
Altimeter
A common method for evaluating flatness in GD&T is to use a height gauge. The operator places the bottom of the part in three columns of equal height. The operator then adjusts the height of these columns to simulate a completely flat plane.
The altimeter needle is then moved over the surface and its deviation is monitored throughout the process. If the needle runout remains within the flatness tolerance, the part has passed the quality test.
This is the standard method of measuring flatness and is generally accurate for general engineering purposes. However, the operator must pay attention to some things. Firstly, the flatness of the three-point assembly must be ensured. Otherwise, the measurement would be inaccurate due to the resulting tilt of the reference surface.
As the piece also rests on three pillars, some parts of it are suspended in the air, like a bridge. For this reason, delicate geometries, such as thin sheets, can bend under gravity or under the effect of the altimeter. This would also lead to an incorrect measurement.
Surface plate
This method is similar to the one described above, but the part rests on a surface plate. The surface plate is usually a flat granite table as it provides good thermal stability and cushioning.
Once the dial indicator is securely placed, it is similarly slid across the surface and its deviation is monitored.
Even in this scenario, there is a potential problem that quality professionals need to resolve. The measuring plate itself must be flat and properly aligned. If the slab is tilted, the height gauge will measure the parallelism between the bottom of the slab and the reference surface, which does not meet flatness tolerance specifications.
Therefore, the measuring plate must be particularly flat and horizontal to ensure accurate measurement.
Coordinate Measuring Machine (CMM)
Coordinate measuring machines are the most accurate devices for measuring flatness in shape and position (GD&T). Unlike the previous two methods, they are automated, accurate, and independent of layer orientation. Additionally, coordinate measuring machines are compatible with CAD software, providing engineers with more flexibility and convenience when performing quality inspections.
A coordinate measuring machine works by scanning the surface at multiple points and creating a 3D point cloud. The number of measurements depends on the size of the part and the level of accuracy required. The coordinate measuring machine software then evaluates the point cloud to check the flatness tolerance. The software can use several algorithms for this calculation. The two most common methods are the best-fit plan algorithm and the minimum zone algorithm.
For the best fit plane, the algorithm fits the best possible plane to the collected Cartesian points and then calculates the maximum deviation of that plane with respect to the extreme points on both sides. This value serves as a flatness tolerance value.
In the minimum zone method, the algorithm adapts two parallel and closest possible planes of the entire point cloud. These planes define the tolerance zone and the distance between them is the flatness of the surface.
Differences between flatness and straightness
The symbols for straightness and flatness in GD&T are often confused. Their applications are quite similar, so confusion is natural. Essentially, flatness in GD&T is the 3D version of straightness.
In this section, we provide a comparison between straightness and tolerance to help designers better understand these concepts when designing products.
| planicity | righteousness |
| Flatness controls a 2D plane. | Righteousness controls a 1D line. |
| The flatness tolerance zone is the 3D space between two parallel planes. | The tolerance zone is the 3D space within a cylinder around the reference line. |
| Applies to a flat surface or DMP. | It applies to straight lines or axes and does not necessarily need to be on flat surfaces. |
| Applications generally focus on maintaining adequate contact between mating surfaces. | Applications of straightness include alignment of linear features and axes. |
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Concluding
Flatness in GD&T is an important concept in design engineering that provides engineers with a tool to define critical production requirements. This article explains the flatness symbol, the flatness label, and the different ways to use them.
Common questions
What standards are used to apply flatness using GD&T?
ASME Y14.5 is the most common GD&T standard for tolerances, including flatness. It contains guidelines for applying flatness, its use cases, and notes.
Can flatness be used to evaluate tolerance piles?
Flatness is regularly used to control tolerance stacks. It is used to refine the size tolerance of stacked resources and helps maintain the total length of the stack.
Is a reference point for flatness necessary?
No reference point is required for the flatness symbol.
