MECHANICAL DESIGN ENGINEERING – Geometrical Dimensioning and Tolerancing_What is the CYLINDRICITY tolerance?

2 simple geometrical elements are responsible to describe any geometrical shape. These are the Straight Line and the Circle. If you connect a line with at least one external non-collinear point you get a plane. If you extrapolate a circle towards an external point in perpendicular direction to the center point you get a cylinder.

If you continue to add external points and connect the basic elements made from lines and circles you get objects of complex shapes. So before to understand how mechanical design of things works you must understand the 2 basic geometrical elements first.

The same as the plane is the 3D for the Line, also the cylinder is the 3D of the circle. In this post let´s have a look at the CYLINDRICITY.

Description

Cylindricity is a geometrical condition of a machined part with surface of revolution, a 3-dimensional tolerance that controls the overall form of a cylindrical feature to ensure that it is round enough and straight enough along its axis. Cylindricity is independent of any datum feature, the tolerance needs to be less than the diameter dimensional tolerance of the part. Cylindricity essentially forms a perfect cylindrical boundary around the object that the entire 3-Dimensional part must lie in.

We can also say that the Cylindricity tolerance extends the Circularity tolerance with 1 dimension, namely: the length. Thus Cylindricity tolerance applies both longitudinal and circular element of the surface and controls the entire surface of a cylinder and is applied to an individual surface.

Most of measurement characteristics valid for Circularity egually apply to Cylindricity too. (YOU CAN UNDERSTAND THE CYLINDRICITY ONLY IF YOU UNDERSTAND THE CIRCULARITY).

Symbol: The Cylindricity symbol is a circle between 2 parallel slashes, imaginable as the addition of parallel surface lines to the circular shape. The Cylindricity symbol is used to describe how close an object conforms to a true cylinder.

FIGURE 1. – THE CYLINDRICITY SYMBOL

The Cylindricity tolerance call out

The cylindricity tolerance is practically prescribed only for real cylindrical surfaces (Outer or Inner), it does NOT apply for derived elements such as axis and center lines. Therefore the tolerance control frame leader must not be placed on the dimension line.

FIGURE 2. – Cylindricity drawing callout

Tolerance zone

A Cylindicity Tolerance is a composite control of form that includes circularity, straightness, and taper of a cylindrical feature. A cylindricity tolerance specifies a tolerance zone bounded by two concentric cylinders whose radii differ by an amount equal to the tolerance value tC (Figure 3). The entire feature surface shall be contained within the tolerance zone (between the two cylinders). The tolerance zone cylinders may adjust to any diameter, provided their radial separation remains equal to the tolerance value. This effectively removes feature size from cylindricity control. As with circularity tolerances, a cylindricity tolerance must be less than half the size tolerance to limit multi-lobed form deviations. Since neither a cylindricity nor a circularity tolerance can nullify size limits for a feature, there’s nothing to be gained by modifying either tolerance to MMC or LMC.

FIGURE 3. – Cylindricity tolerance zone

Cylindrical form deviation: the cylindricity deviations can be imagined as overlaps between Circularity, Straightness and Parallelism. Depending on manufacturing process, for short cylinders the circularity form deviation often predominates on slender cylinders versus the deviations in length.


Included deviations: The tolerance zone of cylindricity is the same like the one for circularity on front view and the same with the straightness in the side view (Fig 3). therefore the following statement can be said:
The circularity deviation (dR) of each individual cross-sections as well as the straightness deviation (dS) of the surface lines , cylinder axis included, can not be bigger than the Cylindricity tolerance tC.

FIGURE 4. – Cylindricity related to Straightness and Circularity

The parallelism deviation dP of the surface lines with the axis which can have the value tC, can reach 2tC on the opposite surface lines. The parallelism deviation is a position deviation and occurs when the tolerated cylinder turn out to be a conical.

FIGURE 5. – Cylindricity related to Parallelism

For length deviations the typical idealized cases are shown in Fig. 6

FIGURE 6. – Cylindricity form deviations

The shape d in fig. 6 is the only one with an odd axis. This can happen as result of overlaying with roundness deviations which occur for examples due too machine vibrations, screw-type bodies or multiple other things during the manufacturing process.

WHEN is the Cylindricity tolerance is used?

The constraints to cylindricity deviations are needed in the functionality of numerous rotating parts such are gearing elements. Cylindricity tolerance is applied where cylindrical part features must have good circularity, straightness and taper.

Cylindricity is a fairly common callout for shafts, pins and any critical cylindrical element. When a part needs to be both round and straight along its axis, such as a sliding shaft, or a dynamic locating pin, cylindricity is usually called out. You will see this GD&T symbol very often in automotive drawings and mechanical systems.

Example 1 = Cylindricity application over a limited length or area

FIGURE 7. – Cylindricity applied over a limited length area

Some designs require form control over a limited length or area of the surface, rather than the entire surface. In such cases, draw a heavy chain line adjacent to the surface, basically dimensioned for length and location as necessary, as shown in Fig. 7. The form tolerance applies only within the limits indicated by the chain line.

Example 2 = Cylindricity tolerance applied to a shaft

In the cylidricity tolerance zone, the cylindrical surface must lie between two concentric/coaxial cylinders ,these are based on given cylindricity tolerance zone of 0.05 as shown in fig.8. The surface must lie within the given tolerance limits.

FIGURE 8. – Cylindricity tolerance applied to a shaft.

Example 3 = Controlling the cylindricity tolerance without and with the GD & T Symbol

If you had a bushing that was to be pressed into a housing, the bushing would take the form of the housing bore when inserted. To ensure that the bushing maintains its round shape, and wears evenly along its surface, the housing bore needs to be very cylindrical. To do this without GD&T you would need very tight dimensions on the diameter of the bore, which may be very hard to control when being machined (and expensive).

FIGURE 9. – Controlling the cylindricity tolerance without and with the GD & T Symbol

This GD&T control allows the diameter tolerances of the part to be opened up much larger, and better controls the entire length of the bore. You can now accept a much broader range of hole sizes as long as the cylindricity is met.

Gauging/Measurement

Cylindricity is measured by constraining a part on its axis, and rotating it around while a height gauge records the variation of the surface in several locations along the length. The height gauge must have total variation less than the tolerance amount.

Limit deviation and test: The Limit deviation is equal with cylindricity tolerance value (tC). An accurate cylindricity deviation measurement taking into consideration the least material condition (LMC) using conventional measuring devices is hardly possible. There are approximations that can be used to determine the Straightness, Circularity and Dimensional deviations , but all these – depending on type, size and position -can lead to falsified results. The individual deviations do not simple overlap additively. It applies only with a minimal probability of being exceeded.

Therefore a correct cylindricity deviation measurement should be always done with measuring gauges respectively with form testing devices as shown in fig. 10

FIGURE 10. – Cylindricity measuring instrument

If such devices are not available or the workpiece can not be placed on the device, then on the drawing instead of cylindricity it is better to specify functional characteristics based on circularity, straightness and parallelism and determine the cylindricity deviation with the formula as shown.

Or another possibility is to specify a functional characteristic based on total run-out which can be used with the available measuring instrument.

Relation to other GD& T Symbols

Cylindricity is the 3-Dimensional version of circularity along an entire cylinder length. While circularity only is concerned with individual measurements around the surface in one circle, cylindricity takes into account how straight the axial portion of the cylinder is. Thinking of stack of coins, cylindricity would measure to make sure that the entire stack is straight up and that every coin is round. Circularity would only be measurements of the roundness of the individual coins.

Cylindricity is a merger of circularity and surface straightness.

Final Notes

Statistical tolerances: Because cylindricity specifies the form of the surface, it must be considered when calculating a statistical tolerance stack. For example, if you have a part with a diameter and cylindricity callout, you must input both into your statistical stack since the cylindricity can contribute to a large part envelope than just the diameter tolerance alone. There are different theories on doing this and how to implement it; however, it can make a slight impact on skewing the results higher. Normal tolerance stacks do not require this since due to the envelope principle; the maximum radial envelop cannot exceed your maximum diameter tolerance due to rule #1 of GD&T.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s