Understanding Surface Roughness Parameters

Surface roughness is a measure of the texture of a surface. It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. These deviations are often expressed as a single number, which is one of the many surface roughness parameters.

The question asks for the parameter that represents the average height from a mean line of all ordinates of the surface, regardless of sign. Let's look at the common parameters mentioned in the options:

• Ra value (Arithmetic Average Roughness): This is the most widely used parameter. It is defined as the arithmetic average of the absolute values of the profile deviations from the mean line over the evaluation length. The phrase "regardless of sign" implies taking the absolute value of the deviations before averaging. This definition matches the description in the question.
• Rz value (Average Maximum Height of the Profile): This parameter is typically the average of the ten point heights (or five peaks and five valleys) over the evaluation length or the average of the maximum peak-to-valley heights over several sampling lengths. It focuses on the extreme deviations.
• RMS value (Root Mean Square Roughness): This parameter is calculated by taking the square root of the average of the squares of the deviations from the mean line. Squaring the deviations makes all values positive before averaging, but the final value is influenced more by larger deviations compared to Ra. It is calculated as $\sqrt{\frac{1}{L} \int_0^L y(x)^2 dx}$ or for discrete data as $\sqrt{\frac{1}{N} \sum_{i=1}^N y_i^2}$, where $y(x)$ or $y_i$ are the deviations from the mean line.
• Rm value (Maximum Profile Peak Height): This parameter measures the height of the single highest peak within the evaluation length.

Based on the definitions, the parameter that represents the average height from a mean line of all ordinates of the surface, regardless of sign, is the Ra value.

The formula for Ra is often given as:

$\text{Ra} = \frac{1}{L} \int_0^L |y(x)| dx$ (for a continuous profile over length L)

Or, for discrete measurements:

$\text{Ra} = \frac{1}{N} \sum_{i=1}^N |y_i|$ (for N points with deviations $y_i$)

In both formulas, $|y(x)|$ or $|y_i|$ represents the absolute value of the deviation from the mean line, ensuring that the sign does not affect the averaging, which aligns exactly with the question's description.