# Numerical Relationship Among Dimensional Tolerance, Geometric Tolerance And Surface Roughness

## 1. Numerical relationship between form tolerance and dimension tolerance

When the dimensional tolerance accuracy is determined, the shape tolerance has an appropriate value, that is, about 50% of the dimensional tolerance value is generally taken as the shape tolerance value; In the instrument industry, about 20% of the dimensional tolerance value is taken as the shape tolerance value; In heavy industry, about 70% of the dimensional tolerance value is taken as the shape tolerance value. It can be seen that the higher the dimensional tolerance accuracy is, the smaller the proportion of the shape tolerance to the dimensional tolerance is. Therefore, when designing the requirements for dimensioning and shape tolerance, except for special cases, when the dimensional accuracy is determined, 50% of the size tolerance value is generally taken as the shape tolerance value, which is conducive to both manufacturing and quality assurance.

## 2. Numerical relationship between form tolerance and position tolerance

There is also a certain relationship between form tolerance and position tolerance. From the cause of error formation, the shape error is caused by machine tool vibration, tool vibration, spindle runout, etc; The position error is caused by the non parallelism of the machine tool guides, the non parallelism or non perpendicularity of the tool clamping, the clamping force and other reasons. From the definition of the tolerance zone, the position error includes the shape error of the measured surface. For example, the parallelism error contains the flatness error, so the position error is much larger than the shape error. Therefore, in general, when there is no further requirement, the position tolerance is given, and the shape tolerance is no longer given. When there are special requirements, the 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, the parts cannot be manufactured according to the design requirements during production.

## 3. Relationship between form tolerance and surface roughness

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

In general, the tolerance values among dimension tolerance, shape tolerance, position tolerance and surface roughness have the following relationship: dimension tolerance>position tolerance>shape tolerance>surface roughness height parameter

It is not difficult to see from the numerical relationship between size, shape and position and surface roughness that the numerical relationship between the three should be well coordinated during design. When marking tolerance values on drawings, it should follow: the roughness value of the given same surface should be less than its shape tolerance value; The shape tolerance value should be less than its position tolerance value; The difference of positions shall be less than the dimension tolerance value. Otherwise, it will cause all kinds of troubles. However, the most involved in the design work is how to deal with the relationship between dimensional tolerance and surface roughness, and the relationship between various fit precision and surface roughness.

## Generally, it is determined according to the following relationship:

1. When the shape tolerance is 60% of the size tolerance (medium relative geometric accuracy), Ra ≤ 0.05IT
2. When the shape tolerance is 40% of the size tolerance (higher relative geometric accuracy), Ra ≤ 0.025IT
3. When the shape tolerance is 25% of the size tolerance (high relative geometric accuracy), Ra ≤ 0.012IT
4. When the shape tolerance is less than 25% of the dimensional tolerance (superelevation relative geometric accuracy), Ra ≤ 0.15Tf (shape tolerance value).

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