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The relationship between dimensional tolerance, geometric tolerance, and surface roughness values

May 13, 2024

1、 The relationship between dimensional tolerance, geometric tolerance, and surface roughness values:

 

1. The numerical relationship between shape tolerance and dimensional tolerance

 

After the accuracy of the dimensional tolerance is determined, there is an appropriate value corresponding to the shape tolerance, which is generally about 50% of the dimensional tolerance value as the shape tolerance value; About 20% of the dimensional tolerance values in the instrument industry are used as shape tolerance values; The heavy-duty industry uses approximately 70% of the dimensional tolerance value as the shape tolerance value. From this, it can be seen that the higher the accuracy of dimensional tolerances, the smaller the proportion of shape tolerances to dimensional tolerances. Therefore, when designing dimensions and shape tolerance requirements, except for special circumstances, when the dimensional accuracy is determined, 50% of the dimensional tolerance value is generally used as the shape tolerance value, which is beneficial for both manufacturing and quality assurance.

 

2. The numerical relationship between shape tolerance and positional tolerance

 

There is also a certain relationship between shape tolerance and positional tolerance. From the perspective of the causes of errors, shape errors are caused by machine tool vibration, tool vibration, spindle runout, and other factors; The positional error is caused by the non parallelism of the machine tool guide rail, the non parallelism or non verticality of the tool clamping, and the clamping force. From the definition of tolerance zone, positional error includes the shape error of the measured surface, such as flatness error in parallelism error, so positional error is much larger than shape error. Therefore, in general, if positional tolerances are given without further requirements, shape tolerances are no longer given. When there are special requirements, both shape and position tolerance requirements can be marked at the same time, but the marked shape tolerance value should be less than the marked position tolerance value. Otherwise, parts cannot be manufactured according to the design requirements during production.

 

3. The relationship between shape tolerance and surface roughness

 

Although there is no direct numerical or measurement relationship between shape error and surface roughness, there is also a certain proportional relationship between the two under certain processing conditions. According to experimental research, surface roughness accounts for 1/5 to 1/4 of the shape tolerance in general accuracy. It can be inferred that in order to ensure shape tolerance, the maximum allowable value of the corresponding surface roughness height parameter should be appropriately limited.

 

In general, the tolerance values between dimensional tolerance, shape tolerance, positional tolerance, and surface roughness have the following relationship: dimensional tolerance>positional tolerance>shape tolerance>surface roughness height parameter

 

It is not difficult to see from the numerical relationship between size, shape, and surface roughness that the design should coordinate and handle the numerical relationship among the three. When marking tolerance values on the drawing, it should follow the following principle: the roughness value of the same surface should be less than its shape tolerance value; The shape tolerance value should be less than its positional tolerance value; The difference in position should be less than its dimensional tolerance value. Otherwise, it will bring various troubles to the manufacturing. However, the most involved aspect in design work is how to handle the relationship between dimensional tolerances and surface roughness, as well as the relationship between various fitting accuracies and surface roughness.

 

Generally, it is determined according to the following relationship:

1. When the shape tolerance is 60% of the dimensional tolerance (moderate relative geometric accuracy), Ra ≤ 0.05IT;

2. When the shape tolerance is 40% of the dimensional tolerance (higher relative geometric accuracy), Ra ≤ 0.025IT;

3. When the shape tolerance is 25% of the dimensional tolerance (high relative geometric accuracy), Ra ≤ 0.012 IT;

4. When the shape tolerance is less than 25% of the dimensional tolerance (ultra-high relative geometric accuracy), Ra ≤ 0.15Tf (shape tolerance value).

 

The simplest reference value: The dimensional tolerance is 3-4 times the roughness, which is the most economical

 

2、 Selection of geometric tolerances

 

1. Selection of Geometric Tolerance Items

 

The function of comprehensive control projects should be fully utilized to reduce the geometric tolerance items and corresponding geometric error detection items given on the drawings.

 

On the premise of meeting functional requirements, items with simple measurement should be selected. For example, coaxiality tolerance is often replaced by radial circular runout tolerance or radial circular runout tolerance. However, it should be noted that radial circular runout is a combination of coaxiality error and cylindrical surface shape error. Therefore, when replacing it, the given runout tolerance value should be slightly greater than the coaxiality tolerance value, otherwise the requirements will be too strict.

 

2. Selection of tolerance principle

 

According to the functional requirements of the tested elements, the function of tolerance should be fully utilized, and the feasibility and economy of adopting this tolerance principle should be fully realized.

 

The principle of independence is used in situations where there is a significant difference between the requirements for dimensional accuracy and positional accuracy, and they need to be met separately, or when there is no connection between the two, to ensure motion accuracy, sealing, and unmarked tolerances.

 

Inclusive requirements are mainly used in situations where strict assurance of compatibility is required.

 

The maximum physical requirement is for the central element, generally used in situations where the accessory requirement is for assemblability (without requirements for fitting properties).

 

The minimum physical requirement is mainly used in situations where it is necessary to ensure the strength and minimum wall thickness of the parts.

 

The combination of reversible requirements and maximum (minimum) entity requirements can fully utilize tolerance zones, expand the range of actual dimensions of the measured elements, and improve efficiency. It can be selected without affecting performance.

 

3. Selection of benchmark features

 

1) Selection of benchmark position

 

(1) Select the joint surface where the parts are positioned in the machine as the reference position. For example, the bottom and side surfaces of the box, the axis of the disc type parts, and the supporting journals or holes of the rotating parts.

(2) The benchmark elements should have sufficient size and stiffness to ensure stable and reliable positioning. For example, combining two or more axes that are far apart to form a common reference axis is more stable than a single reference axis.

(3) Select a surface with relatively precise processing as the reference area.

(4) Try to unify the assembly, processing, and testing standards as much as possible. In this way, errors caused by inconsistent benchmarks can be eliminated; It can also simplify the design and manufacturing of fixtures and measuring tools, making measurement convenient.

 

2) Determination of benchmark quantity

 

Generally speaking, the number of benchmarks should be determined based on the orientation and positioning geometric functional requirements of tolerance items. Directional tolerances mostly only require one datum, while positional tolerances require one or more datums. For example, for parallelism, verticality, and coaxiality tolerance items, generally only one plane or axis is used as the reference feature; For positional tolerance projects, it is necessary to determine the positional accuracy of the hole system, which may require the use of two or three reference features.

 

3) Arrangement of benchmark sequence

 

When selecting two or more benchmark features, it is necessary to clarify the order of the benchmark features and write them in the tolerance frame in the order of first, second, and third. The first benchmark feature is the main one, followed by the second benchmark feature.

 

4. Selection of Geometric Tolerance Values

 

General principle: Select the most economical tolerance value while meeting the functional requirements of the parts.

 

According to the functional requirements of the parts, considering the economic efficiency of processing and the structure and rigidity of the parts, determine the tolerance values of the elements according to the table. And consider the following factors:

The shape tolerance given by the same element should be less than the positional tolerance value;

The shape tolerance value of cylindrical parts (excluding straightness of the axis) should be less than its dimensional tolerance value; Just like on a plane, the flatness tolerance value should be less than the parallelism tolerance value of the plane to the reference.

The parallelism tolerance value should be less than its corresponding distance tolerance value.

The approximate proportional relationship between surface roughness and shape tolerance: Generally, the Ra value of surface roughness can be taken as (20%~25%) of the shape tolerance value.

◆ For the following situations, considering the difficulty of processing and the influence of factors other than the main parameters, while meeting the requirements of the part function, appropriately reduce the selection by 1-2 levels:

○ Holes are opposite to the axis;

Slender and larger shafts and holes; Axis and hole with larger distance;

Surface of parts with a larger width (greater than 1/2 of the length);

○ Parallelism and perpendicularity tolerances between lines and opposite lines relative to the face-to-face.

 

5. Provisions on unmarked tolerances in form and position

 

To simplify the drawing process, it is not necessary to indicate positional tolerances on the drawing, which can be guaranteed by general machine tool processing. If positional tolerances are not indicated, they shall be executed in accordance with the provisions of GB/T1184-1996. The general content is as follows:

 

(1) H, K, and L tolerance levels are specified for unmarked straightness, flatness, perpendicularity, symmetry, and circular runout

(2) The unmarked roundness tolerance value is equal to the diameter tolerance value, but cannot exceed the unmarked tolerance value of radial circular runout.

(3) The unmarked cylindricity tolerance value is not specified and is controlled by the annotated or unmarked tolerances of the roundness tolerance, straightness of the contour lines, and parallelism of the relative contour lines of the features.

(4) The unmarked parallelism tolerance value is equal to the larger of the unmarked tolerance values between the dimensional tolerance between the measured feature and the reference feature and the shape tolerance (straightness or flatness) of the measured feature, and the longer of the two features is taken as the reference.

(5) The coaxiality tolerance value is not specified. If necessary, the unmarked tolerance value of coaxiality can be taken as equal to the unmarked tolerance value of circular runout.

(6) The tolerance values for unmarked line profile, surface profile, inclination, and positional tolerance are controlled by the annotated or unmarked linear dimension tolerance or angle tolerance of each feature.

(7) The full runout tolerance value is not specified.