What Is Engineering Tolerance?

The dimensional tolerance is referred to as tolerance, which refers to the allowable absolute value of the difference between the maximum limit size and the minimum limit size, or the difference between the allowable upper deviation minus the deviation. The dimensional tolerance is an absolute value without a sign. Limit deviation = limit size-basic size, upper deviation = maximum limit size-basic size, lower deviation = minimum limit size-basic size. Dimension tolerance refers to the allowable variation in the size of the part during cutting. With the same basic dimensions, the smaller the dimensional tolerance, the higher the dimensional accuracy.

Dimension tolerance refers to the fact that there is always a certain error in the actual dimensions after completion due to factors such as processing or measurement during the part manufacturing process. In order to ensure the interchangeability of parts, the actual size of the parts must be controlled within the allowable range of change. This allowable amount of dimensional change is called dimensional tolerance . ^[1]

The national standard GB1800.1-2009 will determine the dimensional accuracy

Research Background

Tolerances run through the entire product life cycle, affecting product quality, processing technology routes, testing, manufacturing costs, and final product assembly. However, although existing CAD systems can provide accurate mathematical representations of actual objects, tolerance information is only a symbolic representation, lacks effective engineering semantics, does not contain all the information useful for downstream work, and it is difficult to truly implement CAD and CAPP. Integration with CAM. The integration of CAD, CAPP and CAM needs to include tolerance information in the system and be able to make a correct and reasonable interpretation of the contained tolerance information. This is also the task of modeling and representing tolerance information. Since the computer-aided tolerance design was put forward in the late 1970s, there have been a lot of researches on mathematical models for tolerance information modeling. Tolerance mathematical models based on mathematical definitions are one of the research hotspots. The study applies SDT (small displacement torsor) to tolerance modeling, and proposes a new method for planar dimension tolerance modeling. The plane dimensional tolerances are divided into two categories according to the constraints, and SDT is used to describe the tolerance domain, and a mathematical model of the corresponding dimensional tolerance is established, and this model is used to verify the tolerance synthesis.

Classification of plane size tolerance

A set of interconnected closed-size combinations arranged in a certain order forms a dimensional chain. general

Figure 1 Classification of dimensional tolerances

In other words, the dimensional chain always consists of several constituent rings, starting from a certain benchmark. For the first constituent ring, among the constrained end point features, only one of the end point features has tolerance. This kind of constituent ring is called a type I constituent ring. For other constituent rings, the positions and directions of the two endpoint elements are variable. This kind of constituent ring is called a type II constituent ring.

Dimensional tolerance is the tolerance assigned to a pair of features (points, lines, faces). For each feature, all points on it must be located between a pair of parallel planes (straight lines) at a certain distance, and The distance between lines) is equal to the given dimensional tolerance.

ASME does not have a strict and clear mathematical definition of dimensional tolerances. To establish dimensional tolerance domains, mathematical vector equations must be used to define dimensional tolerances in the same way as other defined tolerance types. Let T _SU and T _SL be the upper limit and the lower limit of the dimensional tolerance. The position vector of the center plane of the two dimensional tolerance domains may be fixed (for type I ring) or it may not be fixed (for type II ring) ), The position of the dimensional tolerance domain may have a translational displacement in the direction of the parallel plane (straight line) of the dimensional tolerance domain.

Modeling of plane dimensional tolerances

For each planar feature, define the bureau

Figure 2 Schematic diagram of the assembly of tolerances

The local coordinate system (LCS) is specifically: the z-axis is parallel to the normal vector of the nominal plane and the direction is outward. In the nominal plane, (x, y) forms a rectangular coordinate system. For a rectangular plane, the origin is The center of the plane. For a non-rectangular irregular plane, a rectangular bounding box can first be found as a valid tolerance boundary, and the origin is at the center of the rectangular bounding box. Therefore, the ideal plane can be expressed as z = 0, and the variation parameters of this plane can be expressed as (d _x , d _y , 0, 0, 0, dz) ^T using SDT.

Tolerance synthesis is to determine the economic and reasonable tolerances between the constituent rings under the requirements of product assembly technology. On the basis of the aforementioned dimensional tolerance model, only the components in the SDT are given to obtain the dimensional tolerance value. Figure 2 is a simple assembly diagram. The fitting dimensions of part 1 are unconstrained, the fitting dimensions of part 2 are constrained, and the two parts are assembled. The tolerances of the relevant dimensions are now determined. ^[2]