# Surface Roughness: The Comprehensive Analysis

## The concept of surface roughness

Surface roughness is the unevenness of a machined surface with a small pitch and tiny peak valley.

The distance (pitch) between two peaks or valleys is small (less than 1mm), which is a micro-geometric error.

Specifically refers to the degree of Z (height) and S (spacing) condition of the tiny peak valley, which is generally categorized by S.

• S＜1mm is the surface roughness;
• 1≤S≤10mm is the waviness;
• S>10mm is f shape.

## Comparison table of VDI3400, Ra and Rmax

In national standards, three indicators are commonly used to assess surface roughness (unit is μm).

• Average arithmetic deviation of the contours: Ra
• The average height of unevenness: Rz
• Maximum height: Ry

Ra index is mostly used in actual production.

The maximum microscopic height deviation of contour, Ry, is commonly used in Japan and other countries as the symbol of Rmax, while the VDI index is commonly used in Europe and America. The following is the comparison table of VDI3400, Ra and Rmax.

Table: Comparison of Ra, Rmax parameters (μm)

 VDI3400 Ra ( μm ) Rmax (μm ) 0 0.1 0.4 6 0.2 0.8 12 0.4 1.5 15 0.56 2.4 18 0.8 3.3 21 1.12 4.7 24 1.6 6.5 27 2.2 10.5 30 3.2 12.5 33 4.5 17.5 36 6.3 24

## Surface roughness formation factors

Surface roughness is generally formed by the processing method used and other factors.

For example, the friction between the tool and the surface of the part during the machining process, the plastic deformation of the surface layer metal when the chips are separated, the high-frequency vibration in the processing system, and the discharge pits of electrical machining.

Due to the difference in processing methods and workpiece materials, the depth, density, shape and texture of the traces left on the processed surface are different.

## Main effects of surface roughness on parts

The effects on wear resistance.

The rougher the surface, the smaller the effective contact area between the mating surfaces, the higher the pressure, the higher the frictional resistance and the faster the wear.

The effects on the stability of the gap fit.

For gap fit, the rougher the surface, the easier it is to wear so that the gap gradually increases during the working process; for interference fit, because the microscopic convex peak is squeezed flat during assembly, the actual effective interference is reduced, and the connection strength is reduced.

The effects on fatigue strength.

The rough surface of the part has large troughs, which are sensitive to stress concentration, just like sharp-edged notches and cracks, thus affecting the fatigue strength of the part.

The effects on corrosion resistance.

Rough part surfaces are prone to allow corrosive gases or liquids to penetrate through microscopic valleys in the surface into the metal inner layer, which causes surface corrosion.

The effects on sealability.

Rough surfaces do not fit tightly to each other, and gases or liquids can leak through the gaps between contact surfaces.

The effects on contact stiffness.

Contact stiffness is the ability of a part’s bonding surfaces to resist contact deformation under the influence of external forces. The stiffness of the machine depends largely on the contact stiffness between the parts.

The effects on measurement accuracy.

Parts are measured surface and measuring tools measuring surface roughness will directly affect the accuracy of measurement, especially in precision measurement.

In addition, surface roughness has a variable effect on the part’s coating, thermal and contact resistance,  reflectance and radiation properties, resistance to liquid and gas flow, and current flow through the conductor’s surface.

## Evaluation basis of surface roughness

1. Sampling length

The sampling length is the length of a specified reference line for evaluating surface roughness.

According to the formation of the actual surface of the part and texture characteristics, the length that reflects the surface roughness characteristics should be selected and sampling lengths shall be measured according to the general course of the actual surface profile.

The sample length is specified and selected to limit and reduce the influence of surface ripple and shape errors on the surface roughness measurement results.

1. Evaluationlength

The evaluation length is a necessary length to evaluate the contour, and it can include one or several sampling lengths.

Since the surface roughness of the parts of the surface is not always uniform,.

It is often impossible to reasonably reflect a certain surface roughness feature on a sampling length, so it is necessary to take several sampling lengths on the surface to evaluate the surface roughness.

The evaluation length generally consists of five sampling lengths.

1. Baseline

The baseline is the centerline of the profile used to evaluate the surface roughness parameters.

There are two types of baselines:

The least-squares centerline of the contour: within the sampling length, the sum of the squares of the contour offset of each point on the contour line is the smallest, and it has a geometric contour shape.

The arithmetic mean centerline of the contour: within the sampling length, the area of the upper and lower contours on the centerline is equal.

Theoretically, the least-squares centerline is an ideal baseline, but it is difficult to obtain in practical applications.

Therefore, the arithmetic mean centerline of the contour is generally used instead, and a straight line with an approximate position can be used for measurement.

## Evaluation parameters of surface roughness

### 1. Altitude characteristics

Contour arithmetic mean deviation (Ra): the arithmetic mean of the absolute value of the contour deviation within the sampling length (lr).

In the actual measurement, the higher the number of measurement points, the more accurate Ra is.

Contour maximum height (Rz): the distance between the top and bottom lines of the contour.

Ra is preferred in the common range of magnitude parameters.

Before 2006 there was also an evaluation parameter in the national standard for “the height of ten points of micro-unevenness” expressed in Rz and the maximum height of the profile in Ry.

After 2006, the ten-point height of microcosmic unflatness was abolished in the national standard and the maximum height of the profile is expressed as Rz.

### 2. Pitch characteristics

Rsm: The average width of the contour unit, which means the average of the contour micro-unevenness spacing over the sampled length.

The microscopic unevenness distance refers to the length of the profile peak and the adjacent profile valley on the midline.

In the case of the same Ra value, the Rsm value is not necessarily the same, so the reflected texture will also be different.

Surfaces that value texture is usually concerned with both Ra and Rmr metrics.

The Rmr shape feature parameter is expressed as the contour support length ratio, which is the ratio of the contour support length to the sampling length.

The profile support length is the sum of the length of each section of the profile obtained by intercepting a straight line parallel to the center line and a distance of c from the top line of the profile within the sampling length.

## Measurement methods of surface roughness

### 1. Comparative method

It is used for on-site measurement in the workshop, which often used for the measurement of medium or rough surfaces.

The method is to compare the measured surface with a roughness model marked with a certain value to determine the measured surface roughness value.

Roughness comparators are nickel-based electroformed specimens that are ideal for metalworking and are a very effective aid.

The operator simply scrapes his fingernail across each surface in a group, looking for the closest match to the part being compared.

Some people use these model groups as look-up tables, but it is important to note that they are not material standards.

Roughness measuring machines can perform different functions, have different methods of evaluation, and vary in cost.

Before selecting a model, you can consult with a professional manufacturer to select the most suitable model for your needs.

### 2. Stylus method

The surface roughness uses a diamond stylus with a tip curvature radius of about 2μm to slowly slide along the measured surface.

The up and down displacement of the diamond stylus is converted into an electrical signal by an electrical length sensor.

After amplification, filtering, and calculation, the surface roughness value is indicated by the display instrument, and the measured profile curve can also be recorded by a recorder.

Generally, the measuring tools that only display surface roughness values are called surface roughness gauges, while those that record surface profile curves are called surface roughness profilers.

Both tools have electronic calculation circuits or computers that automatically calculate contour arithmetic mean deviation Ra, microscopic unevenness ten-point height Rz, maximum contour height Ry and various other evaluation parameters, which have high measurement efficiency and are suitable for measuring surface roughness with a Ra of 0.025 to 6.3 μm.

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