Dimensional tolerance means that in the manufacturing process of parts, due to factors such as processing or measurement, there will always be some errors in the actual dimensions after completion. In order to ensure the interchangeability of parts, the actual size of parts must be controlled within the allowable range, which is called dimensional tolerance. [ 1]

Example:

1, basic size design given size: 30mm.

2, the limit size allows two limit values of size change:

Maximum limit size = 30+0.0 1 = 30.0 1 mm.

Minimum limit size = 30-0.0 1 = 29.99 mm.

3. Limit deviation, the algebraic value obtained by subtracting the basic size from the limit size. That is, the algebraic difference between the maximum limit size and the minimum limit size MINUS the basic size is the upper deviation and the lower deviation respectively, which are collectively called limit deviation. The upper and lower deviations of holes are indicated by capital letters es and EI respectively:

Upper deviation es = 30.01-30 =+0.01.

Lower deviation EI=29.99-30=-0.0 1.

4. Dimensional tolerance: the allowable dimensional variation, that is, the maximum limit dimension minus the minimum limit dimension, is also equal to the algebraic difference obtained by subtracting the upper deviation from the lower deviation. Dimensional tolerance is an unsigned absolute value.

Tolerance: 30.0 1-29.99=0.02.

Or 0.01-(-0.01) = 0.02.

Tolerance standard

The national standard GB 1800. 1-2009 divides the standard tolerance grade for determining the dimensional accuracy into 18 grades, which are IT 1, IT2, ... and IT 18 respectively. From IT 1 to IT 18, the corresponding tolerance values increase in turn and the accuracy decreases in turn.

The dimensional accuracy obtained by cutting is generally closely related to the equipment used, cutting tools and cutting conditions. The higher the dimensional accuracy, the more complicated the technological process of parts and the higher the processing cost. Therefore, when designing parts, we must ensure the performance of parts.

Tolerance almost runs through the whole product life cycle, affecting product quality, processing route, inspection, manufacturing cost and final product assembly. However, although the existing CAD system can provide an accurate mathematical representation of the actual object, the tolerance information is only a symbolic representation, which lacks effective engineering semantics and does not contain all the information useful for downstream work, so it is difficult to truly realize the integration of CAD, CAPP and CAM. The integration of CAD, CAPP and CAM needs to include tolerance information in the system and make a correct and reasonable explanation of tolerance information, which is also the task of tolerance information modeling and representation. Since the computer-aided tolerance design was put forward in the late 1970s, a lot of research has been done on the mathematical model of tolerance information modeling, and the mathematical model of tolerance based on mathematical definition is one of the research hotspots. In this paper, a small displacement torsion device is applied to tolerance modeling, and a new method of tolerance modeling for plane dimensions is proposed. According to the constraint conditions, the plane dimensional tolerance is divided into two categories, and the tolerance domain is described by SDT, and the mathematical model of the corresponding dimensional tolerance is established, and the tolerance synthesis is verified by this model.