## Tolerances applied to the assessment of surface finish

The SL sets the limits for the horizontal length to be considered along the surface. By definition, there also needs to be limits defined in the other direction (the vertical). This defines the deviation allowed perpendicular to the surface. This will be the SF tolerance. Like any length dimension, the SF tolerance needs to be in the form of a tolerance band or range within which the 2D parameter may vary. There are two types of tolerance. Firstly, there is an upper one that the measured value must not be greater than and secondly, an upper one and a lower one that the measured value must not be less than. In the first case, there is only one value and this is the upper one. No lower one is specified but, in the case of, say, height parameters it is effectively zero because this is the lowest practical limit.

The standard ISO 4288:1996 provides flexibility with respect to the acceptance or rejection of the measured surface when compared with a tolerance because there are two rules specified in the standard, the and the 'max-rule'. The '16%-rule' allows some of the values to be greater than the upper limit or less than the lower limit (see Figure 6.12). With respect to the upper limit, the surface is considered acceptable if not more than 16% of the measured values of the selected parameter exceed the value specified on an engineering drawing. With respect to the lower limit, the

Upper limit of the parameter

2D Surface

Parameter

Value

Figure 6.12 The 16%-rule and the upper limit for two distributions (ISO 4288:1996)

surface is considered acceptable if not more than 16% of the measured values of the selected parameter are less than the value specified. In cases where the surface parameter being inspected follows a normal distribution, the 16%-rule means that the upper limit is located at a value of the (X + a where is the mean value and cr is the standard deviation of the values. The greater the value of the standard deviation, the further from the specified limit the mean value of the roughness parameter needs to be.