Why are there concepts of tolerance and fit?
All manufactured products, no matter how precise the equipment is, and no matter how hard we try, the size and shape cannot fully meet the theoretical numerical requirements. This is the gap between ideal and reality!
So how to meet the interchangeability requirements of parts? That is, any one of a batch of parts or components of the same specification can meet the specified performance requirements without any selection or additional modifications. This requires that the dimensions of the production parts should be within the allowable tolerance range.
01
Terms related to tolerance
During the processing of parts, due to the influence of machine tool accuracy, tool wear, measurement errors, etc., it is impossible to process the dimensions of the parts absolutely accurately. In order to ensure interchangeability, the machining error of part dimensions must be limited to a certain range and the amount of dimensional variation must be specified.
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1) Basic size
The dimensions are determined during design based on the strength and structural requirements of the part.
2) Actual size
Dimensions obtained by measurement.
3) Extreme size
Two limits for allowable size variation. It is determined based on the basic size. The larger of the two limit values is called the maximum limit size; the smaller one is called the minimum limit size.
4) Dimensional deviation (referred to as deviation)
The algebraic difference obtained by subtracting a certain size from its base size. Dimensional deviations include:
Upper deviation = maximum limit size - basic size
Lower deviation = minimum limit size - basic size
The upper and lower deviations are collectively called limit deviations, and the upper and lower deviations can be positive, negative or zero.
National standards stipulate that the upper deviation code of the hole is ES, the lower deviation code of the hole is EI; the upper deviation code of the shaft is es, and the lower deviation code of the shaft is ei.
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▲Tolerance zone diagram
5) Dimensional tolerance (referred to as tolerance)
Variation in dimensions allowed.
Dimensional tolerance = maximum limit size - minimum limit size
=upper deviation-lower deviation
Because the maximum limit size is always greater than the minimum limit size, that is, the upper deviation is always greater than the lower deviation, the dimensional tolerance must be positive.
6) Zero line, PR zone and tolerance zone diagram
The zero line is a reference line used to determine the deviation in the tolerance zone diagram, that is, the zero deviation line. Usually the zero line represents the basic size. Mark "0", "+", and "-" on the left end of the zero line. The deviation above the zero line is positive; the deviation below the zero line is negative. The tolerance zone is an area bounded by two straight lines representing upper and lower deviations. The width and position of the tolerance zone are the two elements that constitute the tolerance zone.
7) Standard tolerance and standard tolerance grade
Standard tolerance is any tolerance listed in national standards to determine the size of the tolerance zone. Standard tolerance levels are levels that determine the accuracy of dimensions. Standard tolerances are divided into 20 levels, namely IT01, IT0, IT1~IT18, which represent standard tolerances. Arabic numerals represent standard tolerance levels. Among them, IT01 level is the highest, the levels decrease in order, and IT18 level is the lowest. For a certain basic size, the higher the standard tolerance level, the smaller the standard tolerance value, and the higher the accuracy of the size.
8) Basic deviation
Used to determine the upper or lower deviation of the tolerance zone relative to the zero line position. Generally refers to the deviation close to the zero line. When the tolerance zone is above the zero line, the basic deviation is the lower deviation. When the tolerance zone is below the zero line, the basic deviation is the upper deviation.
According to actual needs, the national standard stipulates 28 different basic deviations for holes and shafts, as shown in the figure below. The basic deviation values of holes and shafts can be found from the relevant tables.
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▲ Basic deviation series
As can be seen from the above figure:
1) The basic deviation code is represented by Latin letters, the capital letters represent the basic deviation code, and the lowercase letters represent the basic deviation code of the axis. Since the basic deviation in the figure only represents the size of the tolerance zone, one end of the tolerance zone is drawn as an opening.
2) This deviation is from A to H as the lower deviation, J to ZC as the upper deviation, and the upper and lower deviations of JS are +IT/2 and -IT/2 respectively.
3) The basic deviation of the axis from a to h is the upper deviation, j to zc is the lower deviation, and the upper and lower deviations of js are +IT/2T and -IT/2 respectively. Another deviation of the hole and shaft can be calculated from the basic deviation and standard tolerance.
02
Terminology related to coordination
In machine assembly, the relationship between the tolerance zones of holes and shafts that have the same basic size and are combined with each other is called a fit. Because the actual dimensions of the hole and shaft are different, "gaps" or "interferences" can occur after assembly. In the fit between the hole and the shaft, the algebraic difference obtained by subtracting the size of the shaft from the size of the hole is a gap when it is a positive value, and interference when it is a negative value.
(1) Types of coordination
Fits are divided into three categories according to the difference in gaps or interference:
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1) Clearance fit
The tolerance zone of the hole is above the PR zone of the shaft. Any pair of holes that match the shaft will become a fit with a gap (including a minimum gap of zero), as shown in Figure A above.
2) Interference fit
The tolerance zone of the hole is below the tolerance zone of the shaft. Any pair of holes that match the shaft is a fit with interference (including a minimum clearance of zero), as shown in Figure b above.
3) Overcooperation
The tolerance zones of the holes overlap with the tolerance zones of the shaft. If any pair of holes matches the shaft, there may be a gap or an interference fit, as shown in Figure c above.
(2) Coordinated benchmark system
National standards stipulate two benchmark systems, as shown in the figure below.
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▲Two benchmark systems
1) Basic hole system
The tolerance zone of the hole with a certain basic deviation and the tolerance zone of the shaft with the basic deviation constitute a matching system, as shown in Figure a. That is, in a fit with the same basic dimensions, the hole's tolerance zone position is fixed, and different fits are obtained by changing the shaft's tolerance zone position. The hole made of the basic hole is called the datum hole. The national standard stipulates that the lower deviation of the datum hole is zero, and "H" is the basic deviation code of the datum hole.
2) Basic shaft system
The tolerance zone of the shaft with a certain basic deviation and the tolerance zone of the hole with different basic deviations constitute a system of various fits, as shown in Figure b. That is, in a fit with the same basic dimensions, the tolerance zone position of the shaft is fixed, and different fits are obtained by changing the tolerance zone position of the hole. The hole drilled in the base shaft is called the base sleeve. The national standard stipulates that the upper deviation of the base shaft is zero, and "h" is the basic deviation code of the base shaft.
It can be seen from the basic deviation series chart:
In the basic hole system, the reference hole H matches the shaft, a~h (11 types in total) are used for clearance fit; j~n (5 types in total) are mainly used for over-fitting; (n, p, r may be over-fitting) or interference fit); p~zc (12 types in total) are mainly used for interference fit.
In the basic shaft system, the datum axis h fits with the hole. A~H (11 types in total) are used for clearance fit; J~N (5 types in total) are mainly used for over-fitting; (N, P, and R may be over-fitting. or interference fit); P~ZC (12 types in total) are mainly used for interference fit.
03
Shape tolerance
Shape tolerance refers to the total amount of variation allowed in the shape of a single actual feature. Form tolerance is expressed in form tolerance zones. The shape tolerance zone includes four elements: shape, direction, position and size of the tolerance zone. The shape tolerance items include 6 items: straightness, flatness, roundness, cylindricity, line profile, surface profile, etc.
1) Straightness
Straightness refers to the condition that the actual shape of the straight line elements on the part maintains an ideal straight line. This is what is commonly referred to as straightness. Straightness tolerance is the maximum allowable variation of an actual line from an ideal straight line. That is, what is given on the drawing is used to limit the allowable variation range of the actual line processing error.
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▲Pattern example 1: In a given plane, the tolerance zone must be in the area between two parallel straight lines with a distance of 0.1mm.
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▲Pattern example 2: Add the mark φ before the tolerance value, and the tolerance zone must be within the area of the cylindrical surface with a diameter of 0.08mm.
2) Flatness
Flatness refers to the actual shape of the plane elements of the part and the condition of maintaining an ideal plane. This is what is commonly referred to as flatness. Flatness tolerance is the maximum allowable variation of an actual surface from a flat surface. That is, it is given on the drawing to limit the allowable variation range of the actual surface processing error.
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▲Pattern example: The tolerance zone is the area between two parallel planes 0.08mm apart.
3) Roundness
Roundness refers to the actual shape of the elements of a circle on a part, equidistant from its center. That is commonly referred to as the degree of roundness. The roundness tolerance is the maximum allowable variation of the actual circle from the ideal circle on the same cross-section. That is, it is given on the drawing to limit the allowable variation range of the actual circle processing error.
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▲Pattern example: The tolerance zone must be on the same normal section, and the radius difference is the area between two concentric circles with a tolerance value of 0.03mm.
4) Cylindricity
Cylindricity means that all points on the cylindrical surface contour of the part are equidistant from its axis. Cylindricity tolerance is the maximum allowable variation from an actual cylindrical surface to an ideal cylindrical surface. That is, what is given on the drawing is used to limit the allowable variation range of the actual cylindrical surface machining error.
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▲Pattern example: The tolerance zone is the area between two coaxial cylindrical surfaces with a radius difference of 0.1mm.
5) Line profile
Line profile refers to the condition that any curve of any shape maintains its ideal shape on a given plane of the part. Line profile tolerance refers to the allowable variation of the actual contour of a non-circular curve. That is, what is given on the drawing is used to limit the allowable variation range of the actual curve processing error.
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▲Pattern example: The tolerance zone is the area between two envelope lines that envelop a series of circles with a diameter of 0.04mm. The centers of the circles lie on lines with theoretically correct geometric shapes.
6) Surface contour
Surface contour refers to the condition in which an arbitrary-shaped surface on a part maintains its ideal shape. Surface contour tolerance refers to the actual contour line of a non-circular surface and the allowable variation from the ideal contour surface. That is, what is given on the drawing is used to limit the variation range of the actual surface processing error.
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▲Pattern example: The tolerance zone is between two envelope lines that envelop a series of balls with a diameter of 0.02mm. The centers of the balls should theoretically be located on the surface of the theoretically correct geometric shape.
04
position tolerance
Position tolerance refers to the total amount of variation allowed from the datum in the position of the associated actual feature.
(1) Orientation tolerance
Orientation tolerance refers to the total amount of change allowed in the direction of the datum by the associated actual elements. This type of tolerance includes three items: parallelism, perpendicularity, and inclination.
1) Parallelism
Parallelism, commonly known as the degree of parallelism, indicates that the actual elements being measured on the part remain equidistant from the datum. Parallelism tolerance is the maximum allowable variation between the actual direction of the measured element and the ideal direction parallel to the datum.
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▲Example of drawing: If the mark φ is added before the tolerance value, the tolerance zone is within the cylindrical surface with a reference parallel diameter of φ0.03mm.
2) Verticality
Perpendicularity, commonly known as the degree of orthogonality between two elements, indicates that the measured element on the part maintains a correct 90° angle relative to the datum element. The verticality tolerance is the maximum amount of variation allowed between the actual direction of the feature being measured and the ideal direction that is perpendicular to the datum.
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▲Illustration: If the mark φ is added before the tolerance zone, the tolerance zone is perpendicular to the cylindrical surface with a datum diameter of 0.1mm.
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▲Legend: The tolerance zone must be located between two parallel planes that are 0.08mm apart and perpendicular to the reference line.
3) Inclination
Inclination refers to the correct condition of maintaining any given angle between the relative directions of two elements on a part. Slope tolerance is the maximum amount of variation allowed between the actual orientation of the feature being measured and its ideal orientation at any given angle to the datum.
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▲Illustration: The tolerance zone of the measured axis is the area between two parallel planes with a tolerance value of 0.08mm and a theoretical angle of 60° with the datum plane A.
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▲Illustration: Add the mark φ before the tolerance value, then the tolerance zone must be located within a cylindrical surface with a diameter of 0.1mm. The tolerance zone should be parallel to plane B perpendicular to datum A and at a theoretically correct angle of 60° to datum A.
(2) Positioning tolerance
Positioning tolerance is the total amount of variation allowed in the position of the associated actual feature relative to the datum. This type of tolerance includes three items: position, coaxiality, and symmetry.
1) Location
Position refers to the accuracy of points, lines, surfaces and other elements on the part relative to their ideal positions. Positional tolerance is the maximum allowable variation in the actual position of the measured element relative to its ideal position.
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▲Illustration: When the mark Sφ is added before the tolerance zone, the tolerance zone is the area inside the ball with a diameter of 0.3mm. The position of the center point of the ball tolerance zone is the theoretically correct size relative to datums A, B and C.
2) Coaxiality
Coaxiality, commonly known as coaxiality, indicates that the measured axis on the part remains on the same straight line relative to the reference axis. Coaxiality tolerance is the allowable variation of the actual axis being measured relative to the reference axis.
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▲Legend of coaxiality tolerance: When the tolerance value is marked, the tolerance zone is the area between cylinders with a diameter of 0.08mm. The axis of the circular tolerance zone coincides with the datum.
3) Symmetry
Symmetry refers to the state that the two symmetrical center elements on the part remain in the same central plane. The symmetry tolerance is the allowable variation of the symmetry center plane (or center line, axis) of the actual feature from the ideal symmetry plane.
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▲ Legend: The tolerance zone is the area between two parallel planes or straight lines with a distance of 0.08mm and symmetrical arrangement with respect to the datum center plane or center line.
(3) Runout tolerance
Runout tolerance is a tolerance item given based on a specific detection method. Runout tolerance can be divided into circular runout and total runout.
1) Circle jump
Circular runout means that the surface of revolution on the part maintains a fixed position relative to the datum axis within a limited measurement plane. Circular runout tolerance is the maximum variation allowed within a limited measurement range when the actual element being measured rotates around the reference axis for a complete revolution without axial movement.
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▲ Legend 1: The tolerance zone is the area between two concentric circles that are perpendicular to any measurement plane, have a radius difference of 0.1mm, and have the center of the circle on the same reference axis.
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▲ Legend 2: The tolerance zone is the area between two circles with a distance of 0.1mm on the measuring cylinder surface at any radius position coaxial with the datum.
2) Full beat
Total runout refers to the runout along the entire measured surface when the part continuously rotates around the reference axis. The total runout tolerance is the maximum amount of runout allowed when the actual element being measured continuously rotates around the datum axis while the indicator moves relative to its ideal contour.
