It is very difficult to thoroughly understand the symbolic and control meaning of geometric tolerances, and to correctly understand the concept of dimensional tolerances.
This article focuses on the "reading" and "measurement" of geometric tolerances, and explains them in the most easy-to-understand language.
No.1
What is Geometric Tolerance?
ISO将几何公差定义为“Geometrical product specifications（GPS） −Geometrical tolerancing− Tolerancing of form, orientation, location and run-out”。
In other words, "geometric properties" refer to the shape, size, positional relationships, etc., and "tolerances" refer to "allowable errors". The characteristic of "geometric tolerance" is that it defines not only the size, but also the allowable error of shape and position.
1. The difference between dimensional tolerance and geometric tolerance:
The annotation methods of design drawings can be roughly divided into two categories: "dimensional tolerance" and "geometric tolerance". Dimensional tolerances govern the length of the sections.
Geometric tolerances control shape, parallelism, inclination, position, runout, etc.
Dimensional tolerance drawings
Geometric tolerance drawings
This means "Please process the parallelism of the shown surface (A) not more than 0.02".
2. Advantages of geometric tolerance:
For example, when a designer orders a plate part, the dimensional tolerance is indicated as follows.
However, according to the above drawings, the manufacturer may deliver the parts shown below.
Such parts may become unsuitable or defective.
The reason for this is that parallelism is not marked on the drawing. The corresponding responsibility lies not with the processor, but with the designer's tolerance marking.
Annotating a drawing of the same part with geometric tolerances gives you a design drawing as shown below. In addition to the dimensional information, geometric tolerance information such as "parallelism" and "flatness" is added to the figure. In this way, problems caused by simply dimensioning tolerances can be avoided.
If you annotate a drawing of the same part, you can get a design drawing as shown below. In addition to the dimensional information, geometric tolerance information such as "parallelism" and "flatness" is added to the figure. In this way, problems caused by simply dimensioning tolerances can be avoided.
In summary, the advantage of geometric tolerances is that they can accurately and efficiently convey the designer's intent that cannot be reflected by dimensional tolerances.
3. The principle of independence
Dimensional tolerances are not the same as those for geometric tolerances. Dimensional tolerances control length, while geometric tolerances control shape and position.
As a result, there is no superiority or disadvantage between dimensional and geometric tolerances, and the combination of these two tolerances allows for efficient tolerance marking.
In addition, dimensional tolerances and geometric tolerances are measured using different measuring equipment and testing methods. For example, if you use a vernier caliper, micrometer, etc. to measure the distance between two points, the dimensional tolerances in the figure below are all acceptable.
However, the geometric tolerance will be judged to be unsatisfactory if the roundness and the position of the central axis are checked using a roundness measuring instrument or a coordinate measuring instrument, depending on the specified tolerance range. In other words, it is judged to be good according to dimensional tolerances and not to be qualified according to geometric tolerances.
Therefore, we can assume that there is basically no correlation between dimensional tolerance control and geometric tolerance control. This way of thinking is known as the "principle of independence".
4. Definition in ISO
The relationship between dimensions and geometric properties is defined as follows.
ISO 8015-1985
Except in the case of specific correlations, the requirements indicated in the drawings, such as dimensional and geometric tolerances, have no relevance to any other dimensions, tolerances or characteristics, and function independently.
As mentioned above, the principle of independence is an international standard that is explicitly defined by ISO. However, in countries such as the United States, some companies may follow ASME (American Society of Mechanical Engineers) guidelines, which do not apply the principle of independence. Therefore, when trading with overseas enterprises, it is recommended to clarify the specifications and requirements through negotiation and other channels in advance.
No.2
Geometric tolerance drawings and symbols
Geometric tolerances are specified by symbols on the sheet. Currently, there are 16 symbols for geometric tolerances, which are classified according to the tolerances of the control.
1. Classification and symbolization of geometric tolerance characteristics
The symbols for the geometric tolerances are shown below. The "independent elements" of the "applicable elements" are those that are not associated with the datum (no datum is required). "Datum" is a theoretical ideal element set to determine attitude, position, and runout. On the other hand, "Associative Features" are features that are associated with the datum and are used to specify attitudes, positions, and runout tolerances.
List of Geometric Tolerance Symbols (Related Specifications: ISO5459)
2. True position theory (size value enclosed by a box)
Use "Theoretically Exact Dimension (TED)" to indicate the way of thinking about geometric tolerances (position, profile, inclination). TED encloses the theoretically correct dimensions with a box (□) and fills in the body control box with the tolerances associated with that position.
Assignment of location
When you specify the position as shown in the figure below, both the datum size and the tolerance marked by the dimensional tolerance are the sum of the dimensional tolerances (cumulative tolerances), and the correct position cannot be specified. On the other hand, when labeling with TED, there is no tolerance attached, so there is no problem with accumulated tolerances.
Specification of tolerance zones
When specifying tolerance zones, True Position Theory correctly indicates the position that needs to be controlled with TED in the center of the tolerance value.
When the feature is a point, the tolerance zone is a circle (a) or spherical centered on the point, and if the feature is a straight line, the tolerance zone is a parallel two plane (b) with the line individually correctly leaving half of the tolerance value, or a cylindrical tolerance zone (c) centered on the line.
No.3
What is a datum?
Datum is a surface, line, or point that is used as a datum for machining and dimensional measurement.
1. Definition in ISO
ISO 5459:2011 Definition: A tolerance zone for position (tolerance) and/or attitude (tolerance), or a setting element (more than one) to which the actual component elements (1) are selected to define the ideal element to represent the execution state.
2. Types of benchmarks
Datums are divided into "datum features" and "simulated datum features". There is also a "datum system" that combines two or more datums and specifies elements.
Datum features
The actual features of the target (surfaces, holes, etc.) of the part that are used to set the datum.
Simulate datum features
Extremely precisely shaped physical surfaces (plates, bearings, mandrels, etc.) that are connected to the datum elements when setting the datum.
Benchmarking system
In order to set datums with tolerance features, use a combination of two or more datum groups with different datums.
The faces of the parts marked as datums do not have a perfect shape. Therefore, it is necessary to make contact with flat plates, rulers, mandrels, etc., which have more precise surfaces, as practical benchmarks.
3. Drawing annotation of datum elements
Datums can be labeled with the following symbols (datum symbols). Datum symbols are marked by openwork or blacked-out triangles. The English letters representing the datum must be consistent with the orientation of the drawing.
In addition, the area that is an object varies depending on the position of the datum symbol in the sheet. In order to convey the design intent in a rigorous manner, please pay attention to the location of the datum.
When the axis line or center plane is marked
Merge dimension lines and datums in one place to indicate datum features. The center of the datum feature is marked as the datum axis or datum center plane.
When the busbar is marked
When marking, you need to stagger the dimension line and datum of the datum element. The center of the datum feature is marked as the datum axis or datum center plane.
No.4
Body Control Frame
Geometric tolerances are indicated by the Body Control Frame. The following elements should be included in the body control frame.
a: Geometric property symbol
Indicates the type of geometric tolerance.
B: Diameter symbol (if necessary)
The geometric properties that must be annotated are shown below.
The area in the circle in a two-dimensional plane: position, concentricity
Cylindrical area in 3D space: straightness, parallelism, straight angle, inclination, position, coaxiality,
The area in the sphere in 3D space: positionality
c: Geometric tolerance value
The value of the tolerance. The unit is "mm (millimeter)".
d: Solid tolerance, common tolerance zone, etc
It mainly includes "(Maximum Solid Requirements)", "(Minimum Solid Requirements)", "CZ (Common Zone)", etc. And so on, etc.
e: Priority benchmark
Designate the part that the designer needs to prioritize as a baseline. When annotating multiple datums, label them from left to right and from highest to lowest.
Typically, the designer decides on the alphabet of the datum in order of priority, so the higher the letter, the higher the priority.
No.5
Types of geometric tolerances
Currently, there are 14 symbols in the GTOL classification. If otherwise classified, there are 15 symbols.
These symbols belong to Shape Tolerance, Attitude Tolerance, Position Tolerance, Runout Tolerance, and all shapes can be specified with the help of these tolerances.
The "Maximum Solid Requirement" is indispensable in the design of shaft hole mating, etc., and the "Minimum Solid Requirement" is an effective means of designing the necessary parameters for the strength of the pipe, such as the thickness of the pipe.
1. Shape tolerance (shape deviation)
The so-called shape tolerance is the basic geometric tolerance that determines the shape of the target object (component). All of them do not require a datum and can independently determine the geometric tolerances of the shape.
1) Straightness
Specifies the Straightness parameter to indicate how correct the straightness should be. Applies to straight lines rather than planar objects, representing bends of centerlines, busbars, and so on. Therefore, it can be used to set the allowable warpage of long-sized objects, etc.
Examples of annotations
Drawing interpretation
When a dimension representing the diameter of a cylinder is connected to a body control frame, the axis of the cylinder must be within a cylinder with a diameter of 0.1 mm.
2) Flatness
Specify Surface Convexity to indicate how correctly a flat surface should be rendered. The most convex part and the most concave part must be located at a certain distance between the two planes of upper and lower separation.
Examples of annotations
Drawing interpretation
The surface must be located between 2 parallel planes separated by only 0.3 mm.
3) Roundness
Specifies the parameter for Roundness. Indicates the roundness of circular cross-sections such as shafts, holes, and cones, and indicates how correct the circle should be.
Examples of annotations
Drawing interpretation
The outer periphery of a right-angled section of any axis must be located between 2 concentric circles separated by only 0.1 mm on the same plane.
4) Cylindricity
Specify parameters for Roundness and Straightness. Indicates the degree of distortion of the cylinder and indicates how correct the cylindrical shape should be.
Examples of annotations
Drawing interpretation
The faces that are objects must be located between 2 coaxial cylindrical faces that are only 0.1 mm apart.
2. Shape tolerance, position tolerance (line profile, surface profile)
Line and surface profiles are also used for position tolerances. The body control frame annotation method is the same in both shape and position tolerances.
1) Line contour
This is the parameter that indicates whether the actual surface of the design part is as good as the design ideal, and represents the degree of distortion of the contour line (the line feature presented by the surface cut surface). Cut off the section line of the specified surface, which must be within the tolerance zone.
Examples of annotations
Drawing interpretation
The profile of an object in an arbitrary section parallel to the projection plane must be centered on a line with a theoretically correct profile and between the 2 envelopes resulting from a circle with a diameter of 0.03 mm.
2) Surface contour
The parameter that indicates whether the actual surface (surface) of the design part is consistent with the ideal value of the design. A face profile is different from a line profile and takes the entire specified surface as an object.
Examples of annotations
Drawing interpretation
The face of the object must be centered on a line with a theoretically correct contour and between the 2 curved lines produced by a ball with a diameter of 0.1 mm.
3. Attitude tolerance
The so-called attitude tolerance is the tolerance that determines the attitude of the corresponding element relative to a certain datum. Before you can specify an attitude tolerance, you must determine the datum, so the attitude tolerance is the feature associated with the datum, that is, the geometric tolerance of the associated feature.
1) Parallelism
Similar to flatness, there is a datum (a plane, a straight line as a datum) in parallelism. Parallelism specifies "the degree to which 2 straight lines or 2 planes are parallel to each other".
Examples of annotations
Drawing interpretation
The face indicated by the marking line arrow must be located between two planes parallel to the datum plane A and only 0.05 mm apart from the direction of the marking line arrow.
2) Squareness
Specifies the degree of right-angle correctness relative to the datum (plane, line as datum). The numerical unit specified by a straight angle is not an angle, but a mm.
Examples of annotations
Drawing interpretation
The plane indicated by the arrow of the marking line must be located within a cylinder with a diameter of 0.03 mm perpendicular to the datum plane A.
3) Inclination
If the specified line or plane is not 90°, specify whether it is correctly tilted relative to the datum (the plane or line used as the datum). The numerical unit specified by the inclination is not the angle, but mm.
Examples of annotations
Drawing interpretation
The surface indicated by the arrow of the marking line must be accurately inclined to the theoretical inclination of 45° from the datum plane A, and be located between two parallel planes that are only 0.3 mm away from the direction of the arrow of the marking line.
4. Position tolerance
The so-called position tolerance is the tolerance that determines the position (true position) of the corresponding element with respect to a certain datum. Before you can specify a location tolerance, you must determine the datum, so the location tolerance is the feature associated with the datum, that is, the geometric tolerance of the associated feature.
1) Location
Specify the accuracy of the position relative to the datum (plane, line as datum).
Examples of annotations
Drawing interpretation
The center point of the circle indicated by the line arrow must be in a circle with a diameter of 0.1 mm.
2) Concentricity
Specify the degree to which the axes of the two cylinders are coaxial (no deviation of the central axis).
Examples of annotations
Drawing interpretation
The cylindrical axis indicated by the arrow of the marking line must be located in a cylinder with a diameter of 0.03 mm with the reference axis straight line A as the axis.
3) Concentricity
Specify the accuracy of the degree of axial coaxiality (no deviation at the center point) of the two cylinders. The difference with concentricity is that the datum feature is the center point (plane).
Examples of annotations
Drawing interpretation
The cylindrical axis indicated by the arrow of the marking line must be located in a cylinder with a diameter of 0.05 mm with the reference axis straight line A as the axis.
4) Symmetry
Specifies the accuracy of Maintain Symmetry with respect to the datum (the plane that is the datum).
Examples of annotations
Drawing interpretation
The center plane indicated by the arrow of the marking line must be located between 2 parallel planes symmetrically spaced 0.05 mm from the datum center plane A.
5. Runout tolerance (runout deviation)
The so-called "runout tolerance" is the geometric tolerance that sets a straight line as the axis of rotation, rotates the target (component), and controls the runout change value of the target element. Before you can specify a run-out tolerance, you must determine a datum, so a run-out tolerance is the geometric tolerance of the feature associated with the datum.
1) Circular runout
Specifies the assembly "Runout of any circumferential part when rotating". Circular runout – i.e. the runout of the measured value when rotating the part, which must be within the specified range.
Examples of annotations
Drawing interpretation
When rotating in a straight line around the datum axis for 1 cycle, the runout in the direction of the radius of the cylindrical surface pointed by the marking line arrow shall not exceed 0.03 mm on any measuring plane perpendicular to the straight line of the datum axis.
2) Full runout
Specifies the subassembly Runout of the Entire Surface as Rotated. Full runout – i.e. the runout of the overall measured value of the cylindrical surface, which must be within the specified range.
Examples of annotations
Drawing interpretation
When rotating the cylindrical part in a straight line around the datum axis, the full runout of the radius of the cylindrical surface indicated by the marking line arrow shall not exceed 0.03 mm at any point on the cylindrical surface.
6. Maximum Entity Requirement (MMR) and Minimum Entity Requirement (LMR)
最大实体要求（MMR：Maximum Material Requirement）用于标示轴孔等嵌合部件的公差。 而最小实体要求（LMR：Least Material Requirement）则用于指定端面周边位置的孔的强度及管道厚度。
1) Annotation method
When applying the maximum solid requirement to a partial dimension, it needs to be annotated after the geometric tolerance value, or after the datum symbol in the shape control frame. and should be labeled when the minimum entity requirement applies.
Examples of annotations
2) The advantages of the largest entity requirement versus the smallest entity requirement
It is possible to correctly implement volume-related control according to the deviation of dimensional deviation and geometric tolerance, and realize reasonable tolerance setting. When used for tolerances such as shafts and holes, the volume of the part can be accurately expressed, which has the advantage of reducing machining costs and improving quality.