Question

During the evaluation of surface roughness (in a given sample length), the average height from a mean line of all ordinates of surface, regardless of sign, is the

• A. $R_m$ value
• B. $R_z$ value
• C. $R_p$ value
• D. $R_a$ value

Hint:

Remember: A stands for Average. The $R_a$ value is simply the Arithmetic Average of the profile deviations. It is the most common way to describe how "smooth" a machined surface feels.

Answer 1

The Correct Option is D

Surface roughness is a measure of the finely spaced micro-irregularities on a surface. Engineers use several mathematical parameters to quantify these irregularities to ensure proper friction, wear, and lubrication in machine parts. 1. Defining the $R_a$ Value: The

$R_a$ value, also known as the Arithmetic Average (AA) or Center Line Average (CLA), is the most universally used parameter for surface roughness.

2. Mathematical Evaluation: During evaluation over a specific sampling length ($L$), a mean line is established such that the areas above and below the line are equal. The roughness is calculated by measuring the vertical distance (ordinates $y_1, y_2, ... y_n$) from this mean line to the profile. The $R_a$ value is defined as the arithmetic mean of the absolute values of these ordinates: $$R_a = \frac{1}{L} \int_{0}^{L} |y(x)| dx \quad \text{or approximately} \quad R_a = \frac{\sum |y|}{n}$$

3. Why "Regardless of Sign": In the calculation, the "absolute" values are used. This means that whether a point is a peak (positive) or a valley (negative) relative to the mean line, its distance is added as a positive number. If the signs were not ignored, the positive and negative values would cancel each other out, resulting in a value near zero regardless of how rough the surface actually is.

4. Comparison with Other Values:

• $R_z$: This is the "ten-point height" of irregularities, calculated by the average distance between the five highest peaks and five deepest valleys.

• $R_p$: This is the maximum profile peak height within the sampling length.