# The relationship between geometric tolerances and alternative applications

The national standard GB1182～1184 “Shape and Position Tolerance” includes shape tolerance-straightness, flatness, roundness, cylindricity, line profile, surface profile; orientation position tolerance-parallelism, perpendicularity, inclination; Positioning position tolerance-concentricity, symmetry, position; runout-radial, oblique, circular end face runout, radial and end face full runout. Although some of these items have different concepts, they are closely related. Some items are similar or controlled by other items, some are single tolerances, and some are comprehensive tolerances, which can replace each other under certain conditions. But often fail to pay attention to this problem. Sometimes the designer draws the geometric shape and size of the part, but the labeling of the shape and position tolerance is sloppy, and the phenomenon of improper labeling or repeated labeling often occurs. Sometimes due to the different understanding of it by technicians, it causes confusion in the application and brings difficulties to the manufacture and inspection of parts. Therefore, it is necessary to have a deep understanding of the relationship between shape and position tolerances, and to master their various replacement usages. In this way, when marking the shape and position tolerances of parts, it is the most concise, clearest, most practical, the most economical for processing, and the most convenient for testing when the requirements are met. 1. Shape tolerance 1. Cylindricity, straightness, roundness and cylindricity is an index that limits the amount of change of the actual cylinder to the ideal cylinder surface. Its tolerance zone is the area between two coaxial cylindrical surfaces with the tolerance value t as the radius difference. It controls the various shape tolerances in the cross section of the cylinder and the shaft section, such as roundness, axis straightness, straightness of plain lines, etc. When in use, it is not necessary to mark the roundness and straightness if the cylindricity is generally marked. If the roundness and straightness must be marked separately, the tolerance value must be less than the cylindricity tolerance value (see Figure 1), to indicate that the design requires further requirements for radial or axial shape tolerances.
Figure 1 Cylindricity and roundness or straightness are marked at the same time. Usually, the cylindricity error is detected by a roundness meter or a three-coordinate measuring device equipped with a computer. If these devices are not available, it is best not to use cylindricity. In this case, roundness can be used separately. The parallelism with the cylindrical surface is used instead (see Figure 2).
Figure 2 Combination of roundness and parallelism instead of cylindricity When roundness and parallelism are used instead of cylindricity, the roundness tolerance value and parallelism tolerance value should be determined according to the aspect ratio of the cylinder. ·When the length of the cylinder is greater than its diameter, the parallelism tolerance value of the plain line must be correspondingly greater than the roundness tolerance value (see Figure 3a). ·When the length of the cylinder is equal to its diameter, the parallelism tolerance value of the plain line and its roundness tolerance value should also be equal (see Figure 3b). ·When the length of the cylinder is less than its diameter, the parallelism tolerance value of the plain line must be correspondingly smaller than the roundness tolerance value (see Figure 3c).
a)L＞D b)L=D c)L＜D Figure 3 Determine the roundness tolerance and parallelism tolerance according to the length-diameter ratio of the cylinder 2. Roundness, line profile roundness is to limit the variation of the actual circle to the ideal circle An index of the tolerance zone is the area between two concentric circles with the tolerance value t as the radius difference. The line profile is an index that limits the amount of change of the actual curve to the ideal curve. The tolerance zone is the area between the two envelopes of a series of circles with a diameter of tolerance t. The centers of the circles should be located on the ideal profile. . From the line profile tolerance zone (see Figure 4b), it can be seen that the line profile not only requires its contour shape to be correct, but also has certain size requirements, that is, its ideal shape is related to the size, similar to the size deviation. The roundness is not the case. It only limits the difference between the radii of the two concentric circles. As for the diameter of the two concentric circles, there is no requirement for the diameter of the two concentric circles, and the position of the two concentric circles is uncertain. Therefore, marking the line profile can get an effect similar to the use of the principle of inclusion (as shown in Figure 4c, the actual curve must be located between two concentric circles with a diameter of 79.9mm and 80.1mm). The effects marked in Figure 4a and Figure 4c are actually the same.
Figure 4 Line profile and the principle of tolerance are well known. When the principle of tolerance is applied to a single element, it can comprehensively control the various shape errors of the longitudinal and cross-section of a cylindrical hole or shaft, including roundness errors. Therefore, the roundness error can be completely controlled by marking the line profile without marking the roundness, that is, the line profile can be used instead of the roundness. Generally, it is more intuitive and clear to use roundness for circular curves. Especially in actual production, it is very convenient to use two-point and three-point methods to measure roundness. The line profile is dedicated to non-circular curves. 2. Position tolerance and shape tolerance The actual position and direction of the measured element of a part are always closely related to its actual shape. Therefore, the ideal boundary of the related element controls the actual position and direction of the element, and it inevitably controls the shape error of the element. For the convenience of operation, whether to use a comprehensive gauge or to measure with an indicating gauge, it is generally carried out directly on the contour surface of the measured element. Therefore, the position error is the combined effect of the actual position and the actual shape, that is, the measured position error includes the shape error. So usually the shape tolerance value given by the same element should be smaller than the position tolerance value (see Figure 5).
Figure 5 Simultaneous labeling of shape tolerance and position tolerance 3. Orientation position tolerance and positioning position tolerance The relationship between orientation tolerance and positioning tolerance is the same as the relationship between position tolerance and shape tolerance, usually positioning tolerance can control the orientation requirements, because the actual element being measured is in the positioning tolerance Not only is the position tolerance change (translation) within the belt controlled, but the direction change (angular displacement) is also controlled. 1. Coaxiality and parallelism. The coaxiality tolerance of the axis of the two holes in Figure 6 can completely control the parallelism requirements of the two axes. Because it controls the translation, tilt or bending of the measured axis to the reference, it is not necessary to mark the two Parallelism of the hole axis.
Figure 6 Concentricity comprehensive control parallelism 2. Position degree and perpendicularity position degree is a comprehensive tolerance. As shown in Figure 7, the straightness of the axis of the two holes and the perpendicularity of the axis of the two holes to the reference plane can be comprehensively controlled by the position degree, and there is no need to repeat the marking.
Figure 7 Position degree comprehensive control verticality and straightness 3. Position tolerance (position degree, coaxiality, symmetry) All positioning tolerance items can be replaced by position degree (see Figure 8, Figure 9).
Figure 8 Position degree comprehensive control coaxial degree
Fig. 9 Position degree comprehensive control Symmetry degree a) and b) in Fig. 8 and Fig. 9 have the same control effect, and the tolerance zone shape and detection method are the same. Therefore, the degree of position can be used to replace the degree of concentricity and symmetry. Since marking the coaxiality and symmetry of the above conditions in production is more intuitive and clear than marking the position degree, it is more appropriate to mark the coaxiality and symmetry on the drawing, and the position degree is usually used to limit the position error of points and lines. 4. Various runouts 1. Radial circle runout and radial full runout. The tolerance zone of radial circle runout is any measurement plane that is perpendicular to the reference axis. The difference in radius is the tolerance value t, and the center of the circle is two points on the reference axis. The area between two concentric circles (see Figure 10a), the tolerance zone is limited to two coordinates (plane coordinates).