Rdq, Wdq, Pdq, RΛq, WΛq, PΛq Rdq (RΔq, Rdelq) is the rms slope of the profile within the sample length. This parameter is very useful for assessing reflectivity, friction, adhesion, vibration etc and is a measurement of the angular slope of the profile. Results are given in degrees. Generally, the lower the angle, the better the reflection, the higher the angle, the greater the friction. Rlq (Rλq, Rlamdaq) - is the root means square wavelength, a measure of the spacings between local peaks and valleys, taking into account their relative amplitudes and individual spatial frequencies. Being a hybrid parameter, determined from both amplitude and spacing information, it is, for some applications, more useful than a parameter based solely on amplitude or spacing. WΔq, Wλq, PΔq and Pλq are the corresponding parameters from the waviness and primary profiles, respectively. Material Ratio Rmr is the length of material surface (expressed as a percentage of the evaluation length L) at a depth (d) below a reference level (c) Material Ratio Rmr (c) is the length of material surface (expressed as a percentage of the evaluation length L) at a depth (c) below the highest peak. Note: Most analysis packages allow the reference line for Rmr to be set from various levels such as using the mean line, the lowest valley, the highest peak or even from a material ratio level. Rpk, Rk, Rvk, MR1, MR2 These parameters were specifically designed for the control of the potential wear in cylinder bores in the automotive industry, They attempt to describe in numeric terms the wear characteristics of the bore by use of a material ratio curve. The filter used to analyse Rk and its associated parameters is a specific filter described in ISO 13 565 Part 1 (DIN 4776) Rpk - means Reduced Peak Height and is a measurement of the peaks of the surface in the cylinder bore. These peaks will be the areas of most rapid wear when the engine is first run. Rk - Kernal Roughness Depth or Core Roughness Depth - the long term running surface which will influence the performance and life of the cylinder. (Also the depth of the Roughness Core Profile or the load bearing area of the surface) Rvk (valley depth) is a measurement of the oil retaining capability of the valleys of the surface produced during the machining process (plateau honing) Mr1 - is the Material Ratio corresponding to the upper limit position of the roughness core. (Where the Rpk and Rk depths meet on the material ratio curve.) Mr2 - is the Material Ratio corresponding to the lower limit position of the roughness core. (Where the Rvk and Rk depths meet on the material ratio curve) A1 - is the 'peak area' of the material ratio curve. It is calculated as the area of a right angled triangle of base length 0% to Mr1 and height Rpk. A2 - is the 'valley area' of the material ratio curve. It is calculated as the area of a right angled triangle of base length Mr2 to 100% and height Rvk. top of page

Introduction. The measurement of surface roughness is defined by a collection of international standards. These standards cover characteristics of the measurement equipment as well as defining the mathematical definition of the many parameters used today. One of the most significant concepts that have been introduced by ISO in recent years is that of bandwidth. This has been introduced in order to improve the comparability and consistency of surface roughness measurements. This article outlines some of the key issues in this important field. Definitions. In any discussion of this type, we need to start with a few definitions. The important ones here are: Roughness – a quantitative measure of the process marks produced during the creation of the surface and other factors such as the structure of the material. Waviness – a longer wavelength variation in surface away from its basic form (e.g. straight line or arc). Filter – a mechanism for suppressing wavelengths above or below a particular value. In surface measurement filtering can arise in the gauging system due to mechanical or electronic constraints, and it can also be applied by the data analysis system (software). Cut-off – the wavelength at which a filter is seen to have some pre-determined attenuation (eg 50% for a Gaussian filter). In roughness there are two different filters, a long wavelength filter Lc and a short wavelength filter Ls which suppresses wavelengths shorter than those of interest. Background. Stylus instruments have been used in the assessment of surface texture for some sixty years. Initially simple analogue instruments were used, employing an amplifier, chart recorder and meter to give graphical and numerical output. Analogue filters (simple electronic R-C circuits) were used to separate the waviness and roughness components of the texture. With the arrival of mini-computers, a little over twenty years ago, numerical analysis of the information obtained became a possibility. Using this new technology a host of parameters became available. It is now commonplace for the filtering to be implemented by means of digital filter algorithms rather than through electronic circuits. With an increase in globalisation it has become even more important to control the comparability of results from different sources. A key area of concern for roughness measurement is the bandwidth of the data. This arises because, as technology has advanced, it has become possible to collect data with an increasing density and hence a higher bandwidth. Without a control on bandwidth, it would be almost impossible to obtain comparable results from measurements using different instrument types. In order to address this issue, ISO introduced the concept of “bandwidth” in the late 1990’s. Under this regime the shorter wavelengths used in surface roughness analysis are constrained by a short wave filter (know as the λs filter – see ISO 3274:1996). The bandwidth is then limited in a controlled way that relates directly to surface features, rather than being limited by the (electrical) bandwidth of the measuring system. Key concepts. In most circumstances a single measurement will be made on the surface in order to assess the texture. This measurement must be representative of the surface and appropriate to the purpose of the measurement (e.g. measuring normal to the lay of the surface, or in the indicated direction). The most important concept is to know what you are dealing with. From a knowledge of the roughness amplitude and wavelength values expected from the surface, it is possible to select the appropriate instrument settings for a reliable roughness measurement. The most important factors will be the selection of stylus tip and the roughness filters. Effects of the stylus tip. The stylus tip radius is a key feature that is often overlooked. Assuming that a conisphere stylus is being used, the profile recorded by the instrument will in effect be the locus of the centre of a ball, whose radius is equal to that of the stylus tip, as it is rolled over the surface. This action broadens the peaks of the profile and narrows the valleys. For simplicity, if we consider the surface to be a sine wave, then this distortion is dependent both on the wavelength and the amplitude.

Every surface has some form of texture that takes the form of a series of peaks and valleys. These peaks and valleys vary in height and spacing and have properties that are a result of the way the surface was produced. For example, surfaces produced by cutting tools tend to have uniform spacing with defined cutting directions whilst those produced by grinding have random spacing. In surface texture there are many factors that, when combined, characterise a surface?s profile. For example:

• the microstructure of the material
• the action of the cutting tool
• the instability of the cutting tool on the material
• errors in the machine tool guideways
• deformations due to stress patterns in the component

We measure surface texture for two main reasons:

1. To try to predict the performance of the component.
2. To try to control the manufacturing process as the manufacturing process leaves its signature in the surface texture.

In the past surface texture has been assessed by the judgement of the inspector either by eye or even fingernail. In order to put a number to the surface texture, we need to use a more accurate means of measurement. A typical surface measuring instrument will consist of a stylus with a small tip (fingernail), a gauge or transducer, a traverse datum and a processor. The surface is measured by moving the stylus across the surface. As the stylus moves up and down along the surface, the transducer converts this movement into a signal which is then exported to a processor which converts this into a number and usually a visual profile.
For correct data collection, the gauge needs to pass over the surface in a straight line such that only the stylus tip follows the surface under test. This is done using a straightness datum. This can consist of some form of datum bar that is usually lapped or precision ground to a high straightness tolerance. On small portable instruments this is not always a good option and can add to the expense of the instrument. In these cases, it is possible to use an alternative means of datum. This is a skid.

A skid is a part of the gauge that has a radius large enough to prevent movement in and out the roughness characteristics of the surface. The stylus and the skid are usually independent in their height (Z) movement but move together in the measurement direction. Surface deviations are recorded as the difference between the stylus and the skid movement in the Z direction. In other words, the skid acts as the straightness datum ? it ?skids? over the top of the surface.

We analyse three main elements of surface texture - roughness, waviness and form.

Roughness ? this is usually the process marks or witness marks produced by the action of the cutting tool or machining process, but may include other factors such as the structure of the material. Waviness ? this is usually produced by instabilities in the machining process, such as an imbalance in a grinding wheel, or by deliberate actions in the machining process. Waviness has a longer wavelength than roughness which is superimposed on the waviness. Form ? this is the general shape of the surface, ignoring variations due to roughness and waviness. Deviations from the desired form can be caused by many factors. For example:

• the part being held too firmly or not firmly enough
• inaccuracies of slides or guideways of machines
• stress patterns in the component

In order to separate the three elements, we use filters. On most surface texture measuring instruments we can select either Roughness or Waviness Filters. Selecting a Roughness Filter will remove waviness elements, leaving the roughness profile for evaluation. Selecting a Waviness Filter will remove roughness elements, leaving the waviness profile for evaluation. Separating the roughness and waviness is achieved by using filter cut-offs.

Electronic or mathematical methods or algorithms which separate out different wavelengths and allow us to see only the wavelengths we are interested in.

In basic terms, a cut-off is a filter and is used as a means of separating or filtering the wavelengths of a component. Cut-offs have a numerical value that when selected will reduce or remove the unwanted wavelengths on the surface. For example, a roughness filter cut-off with a numeric value of 0.8mm will allow wavelengths below 0.8mm to be assessed with wavelengths above 0.8mm being reduced in amplitude; the greater the wavelength, the more severe the reduction. For a waviness filter cut-off with a numeric value of 0.8mm, wavelengths above 0.8mm will be assessed with wavelengths below 0.8mm being reduced in amplitude.