Let's first take a brief look at this simple diagram. What do the annotations in the diagram represent? Can you understand them easily?
01 What is Geometric Tolerance?
(1) The Difference between Size Tolerance and Geometric Tolerance
The methods of marking on design drawings can be roughly divided into two categories: "size tolerance" and "geometric tolerance".
Size tolerance controls the length of each part. Geometric tolerance, on the other hand, controls shape, parallelism, inclination, position, run - out, etc.
[Insert size tolerance drawing]
[Insert geometric tolerance drawing]
It means "Please perform machining so that the 'parallelism' with the indicated surface (A) does not exceed '0.02'."
(2) The Advantages of Geometric Tolerance
Why is it necessary to mark geometric tolerance? For example, when a designer orders a certain plate - shaped part, the following markings are made through size tolerance.
[Insert relevant drawing]
However, according to the above drawing, the manufacturer may deliver a part as shown below.
Such a part may become an unfit or defective product.
The reason for this is that the parallelism is not marked on the drawing. The corresponding responsibility does not lie with the processing manufacturer, but with the designer's tolerance marking.
The drawing of the same part marked with geometric tolerance can be obtained as the following design drawing. Based on the size information, geometric tolerance information such as "parallelism" and "flatness" is added to this drawing. In this way, problems caused by simply marking size tolerance can be avoided.
In summary, the advantage of geometric tolerance is that it can accurately and efficiently convey the designer's intentions that cannot be reflected by size tolerance.
(3) The Principle of Independence
Size tolerance and geometric tolerance control different tolerances. Size tolerance controls length, while geometric tolerance controls shape and positional relationships.
Therefore, there is no superiority or inferiority between size tolerance and geometric tolerance. The combined use of these two types of tolerances can achieve efficient tolerance marking.
In addition, size tolerance and geometric tolerance are measured using different measuring equipment and inspection methods. For example, size tolerance uses vernier calipers, micrometers, etc. to measure the distance between two points. At this time, all the size tolerances in the following figure are qualified.
However, geometric tolerance uses a roundness measuring instrument, a coordinate measuring machine, etc. to detect roundness and the position of the central axis. According to the specified tolerance range, it may be judged as unqualified. In other words, it may be judged as qualified according to size tolerance, but unqualified according to geometric tolerance.
Therefore, we can consider that there is basically no correlation between size tolerance control and geometric tolerance control. This way of thinking is the "Principle of Independence".
(4) Definition in ISO
The relationship between dimensions and geometric characteristics is defined as follows.
ISO 8015 - 1985
Except in cases where a correlation is specifically specified, each requirement indicated on the drawing, such as size tolerance and geometric tolerance, has no connection with any other dimensions, tolerances, or characteristics and functions independently.
As mentioned above, the Principle of Independence is an international standard clearly specified by ISO. However, in countries such as the United States, some enterprises may follow the ASME (American Society of Mechanical Engineers) standards where the Principle of Independence does not apply. Therefore, when conducting trade with overseas enterprises, it is recommended to clearly define the specification requirements in advance through negotiation and other means.
02 Geometric Tolerance Drawings and Symbols
Geometric tolerance is specified on the drawing through symbols. Currently, there are 16 symbols for geometric tolerance, which are classified according to the controlled tolerances.
(1) Classification and Symbols of Geometric Tolerance Characteristics
The symbols of geometric tolerance are as follows. The "independent element" of the "applicable element" refers to an element that is not related to the datum (no need to mark the datum). The "datum" is a theoretical ideal element set to determine the attitude, position, and run - out. The "related element" is an element related to the datum and is used to specify the attitude, position, and run - out tolerances.
[Insert geometric tolerance symbol list (related specification: ISO5459)]
(2) True Position Theory (The dimension value enclosed in a box)
The way of thinking of marking geometric tolerance (position, profile, inclination) with "Theoretically Exact Dimension (TED)". TED will enclose the theoretically correct dimension with a box (□), and fill the geometric tolerance related to this position into the feature control frame.
1) Position Specification
When specifying the position as shown in the following figure, both the reference dimension and the tolerance marked by the size tolerance will become the sum of the size tolerances (cumulative tolerance), and the correct position cannot be specified. When using TED for marking, since it does not come with a tolerance, the problem of cumulative tolerance will not occur.
2) Tolerance Zone Specification
When specifying the tolerance zone, the true position theory will correctly mark the position to be controlled by TED at the center of the tolerance value.
When the element is a point, the tolerance zone is a circle (a) or a sphere centered on this point; when the element is a line, the tolerance zone is two parallel planes (b) that are correctly separated from the line by half of the tolerance value, or a cylindrical tolerance zone (c) centered on this line.
03 What is a Datum?
A datum is a surface, line, or point used as a reference during machining and dimensional measurement.
(1) Definition in ISO
ISO 5459:2011 defines: The tolerance zone of position (tolerance) and/or attitude (tolerance), or the set element (one or more) applied to the actual constituent element (one or more) selected to define the ideal element representing the execution state.
(2) Types of Datums
Datums are divided into "datum feature" and "simulated datum feature". There is also a "datum system" that combines two or more datums to specify an element.
Datum Feature: The actual element of the target object used to set the datum (the surface of a part, holes, etc.).
Simulated Datum Feature: The actual surface (flat plate, bearing, mandrel, etc.) that is in contact with the datum feature when setting the datum and has an extremely precise shape.
Datum System: A group of datums that combines two or more different datums to set the datum of a toleranced element.
The surface of the part marked as the datum does not have a perfect shape. Therefore, it is necessary to use a flat plate, ruler, mandrel, etc. with a more precise surface as a practical datum for contact.
(3) Drawing Marking of Datum Feature
The datum can be marked through the following symbol (datum symbol). The datum symbol is marked with an open or filled - in triangle. The English letter representing the datum must be in the same direction as the drawing.
In addition, the area as the object will vary depending on the position of the datum symbol in the drawing. Pay attention to the position of marking the datum to accurately convey the design intention.
1) When Marking the Axis or Center Plane
Combine the dimension line and the datum to mark the datum feature. The center of the marked datum feature will become the datum axis or the datum center plane.
2) When Marking the Generatrix
Mark the dimension line and the datum of the datum feature separately. The center of the marked datum feature will become the datum axis or the datum center plane.
04 Feature Control Frame
Geometric tolerance is marked with a "feature control frame". The feature control frame should contain the following elements.
a: Geometric Characteristic Symbol: Mark the type of geometric tolerance.
b: Diameter Symbol (when necessary): The geometric characteristics that must be marked are as follows.
In a two - dimensional circular area: position, concentricity
In a three - dimensional cylindrical area: straightness, parallelism, perpendicularity, inclination, position, coaxiality
In a three - dimensional spherical area: position
c: Geometric Tolerance Value: The value of the tolerance. The unit is "mm (millimeter)".
d: Material Condition, Common Tolerance Zone, etc.: Mainly include "(Maximum Material Requirement)", "(Least Material Requirement)", "CZ (Common Zone)", etc. And others.
e: Primary Datum: Designate the part that the designer needs to set as the datum with priority as the datum. When marking multiple datums, mark them in the order from left to right, with the priority decreasing from left to right.
Usually, the designer determines the letters of the datums according to the priority order, so the earlier the letter, the higher the priority.
05 Types of Geometric Tolerance
Currently, there are 14 symbols in the geometric tolerance classification. If classified in other ways, there are 15 symbols.
These symbols belong to "shape tolerance", "orientation tolerance", "position tolerance", and "run - out tolerance". With these tolerances, all shapes can be specified.
The "Maximum Material Requirement" is indispensable in designs such as shaft - hole fitting, and the "Least Material Requirement" is an effective means to design parameters necessary for maintaining strength such as the thickness of a pipe. The following also introduces the general outlines of these methods.
(1) Shape Tolerance (Shape Deviation)
Shape tolerance is the basic geometric tolerance that determines the shape of the target object (part). These are all geometric tolerances that can determine the shape independently without a datum.
1) Straightness
A parameter that specifies "straightness", indicating how straight it should be. It is applicable to straight - line rather than plane objects and represents the bending of the center line, generatrix, etc. Therefore, it can be used to set the allowable warping of long - sized objects.
Marking Example
Drawing Interpretation
When the dimension representing the diameter of the cylinder is connected to the feature control frame, the axis of the cylinder must be within a cylinder with a diameter of 0.1mm.
2) Flatness
Specifies the "surface unevenness", indicating how flat the surface should be. The most protruding part and the most concave part must be within a certain distance between two separated upper and lower planes.
Marking Example
Drawing Interpretation
This surface must be between two parallel planes that are only 0.3mm apart.
3) Roundness
A parameter that specifies "circularity". It represents the circularity of circular cross - sections such as shafts, holes, and cones, indicating how circular it should be.
Marking Example
Drawing Interpretation
The outer circumference of any cross - section perpendicular to the axis must be between two concentric circles that are only 0.1 mm apart on the same plane.
4) Cylindricity
A parameter that specifies "circularity" and "straightness". It represents the distortion of a cylinder, indicating how cylindrical it should be.
Marking Example
Drawing Interpretation
The surface in question must be between two coaxial cylindrical surfaces that are only 0.1mm apart.
(2) Shape Tolerance, Position Tolerance (Profile of a Line, Profile of a Surface)
Profile of a line and profile of a surface are also used for position tolerance. The method of marking in the feature control frame for shape tolerance and position tolerance is the same.
1) Profile of a Line
This is a parameter that indicates whether the "actual curved surface of the designed part is consistent with the designed ideal value", representing the distortion of the contour line (the line element presented by the surface cross - section). The cross - section line of the specified curved surface must be within the tolerance zone.
Marking Example
Drawing Interpretation
The contour of the object in any cross - section parallel to the projection plane must be centered on the line with the theoretically correct contour and between the two envelope lines generated by a circle with a diameter of 0.03mm.
2) Profile of a Surface
A parameter that indicates whether the "actual curved surface (surface) of the designed part is consistent with the designed ideal value". Different from the profile of a line, the profile of a surface takes the entire specified curved surface as the object.
Marking Example
Drawing Interpretation
The object surface must be centered on the line with the theoretically correct contour and between the two curved lines generated by a sphere with a diameter of 0.1 mm.
(3) Orientation Tolerance
Orientation tolerance is the tolerance that determines the appropriate orientation of a corresponding element relative to a certain datum. Before specifying the orientation tolerance, the datum must be determined. Therefore, orientation tolerance is a geometric tolerance of a related element, that is, an element related to the datum.
1) Parallelism
Similar to flatness, there is a datum (the plane or line used as the datum) in parallelism. Parallelism specifies "the degree to which two lines or two planes are parallel to each other".
Marking Example
Drawing Interpretation
The surface pointed by the marking line arrow must be between two planes that are parallel to the reference plane A and only 0.05mm apart in the direction of the marking line arrow.
2) Perpendicularity
Specifies the "correct degree of a right - angle" relative to the datum (the plane or line used as the datum). The unit of the value specified by perpendicularity is not an angle, but mm.
Marking Example
[Insert relevant drawing]
Drawing Interpretation
The plane pointed by the marking line arrow must be within a cylinder with a diameter of 0.03 mm perpendicular to the reference plane A.
3) Inclination
When the specified line and plane are not 90°, it specifies "whether it presents a correct inclined state relative to the datum (the plane or line used as the datum)". The unit of the value specified by inclination is not an angle, but mm.
Marking Example
[Insert relevant drawing]
Drawing Interpretation
The surface pointed by the marking line arrow must be accurately inclined at 45° relative to the reference plane A and be between two parallel planes that are only 0.3 mm apart in the direction of the marking line arrow.
(4) Position Tolerance
Position tolerance is the tolerance that determines the position (true position) where a corresponding element should be relative to a certain datum. Before specifying the position tolerance, the datum must be determined. Therefore, position tolerance is a geometric tolerance of a related element, that is, an element related to the datum.
1) Position
Specifies the "accuracy of the position relative to the datum (the plane or line used as the datum)".
Marking Example
[Insert relevant drawing]
Drawing Interpretation
The center point of the circle pointed by the marking line arrow must be within a circle with a diameter of 0.1 mm.
2) Coaxiality
Specifies "the degree to which the axes of two cylinders are coaxial (no deviation of the central axis)".
Marking Example
[Insert relevant drawing]
Drawing Interpretation
The axis of the cylinder pointed by the marking line arrow must be within a cylinder with a diameter of 0.03 mm, with the reference axis line A as the axis.
3) Concentricity
Specifies the "accuracy of the degree to which the axes of two cylinders are coaxial (no deviation of the center point)". The difference from coaxiality is that the datum feature is the center point (plane).
Marking Example
[Insert relevant drawing]
Drawing Interpretation
The axis of the cylinder pointed by the marking line arrow must be within a cylinder with a diameter of 0.05 mm, with the reference axis line A as the axis.
4) Symmetry
Specifies the "accuracy of maintaining symmetry relative to the datum (the plane used as the datum)".
Marking Example
[Insert relevant drawing]
Drawing Interpretation
The center plane pointed by the marking line arrow must be between two parallel planes that are symmetrically spaced 0.05 mm from the reference center plane A.
(5) Run - out Tolerance (Run - out Deviation)
"Run - out tolerance" is a geometric tolerance that controls the run - out variation value of the elements of a target object (part) by setting a certain line as the rotation axis and rotating the target object. Before specifying the run - out tolerance, the datum must be determined. Therefore, run - out tolerance is a geometric tolerance of a related element, that is, an element related to the datum.
1) Circular Run - out
Specifies the "run - out of any circumferential part when the part rotates". Circular run - out - that is, the run - out of the measured value when the part rotates, must be within the specified range.
Marking Example
[Insert relevant drawing]
Drawing Interpretation
When rotating one full turn around the reference axis line, in any measurement plane perpendicular to the reference axis line, the radial run - out of the cylindrical surface pointed by the marking line arrow shall not exceed 0.03mm.
2) Total Run - out
Specifies the "run - out of the entire surface when the part rotates". Total run - out - that is, the run - out of the measured value of the entire cylindrical surface, must be within the specified range.
Marking Example
[Insert relevant drawing]
Drawing Interpretation
When rotating the cylindrical part around the reference axis line, at any point on the cylindrical surface, the total radial run - out of the cylindrical surface pointed by the marking line arrow shall not exceed 0.03mm.
(6) Maximum Material Requirement (MMR) and Least Material Requirement (LMR)
The Maximum Material Requirement (MMR: Maximum Material Requirement) is used to mark the tolerances of fitting parts such as shafts and holes. The Least Material Requirement (LMR: Least Material Requirement) is used to specify the strength of holes around the end face and the thickness of pipes.
1) Marking Methods
When applying the Maximum Material Requirement (MMR) to certain dimensions, it is necessary to mark Ⓜ either after the geometric tolerance value or after the datum symbol within the feature control frame. When applying the Least Material Requirement (LMR), mark Ⓛ.
Marking Example
2) Advantages of the Maximum Material Requirement and the Least Material Requirement
These requirements can correctly implement volume - related control based on the deviations of size tolerances and geometric tolerances, enabling reasonable tolerance setting. When used for tolerances of components such as shafts and holes, they can accurately represent the volume of the parts. This has the advantages of reducing processing costs and improving quality.
