# Roughness Evaluation of Burnished Topography with a Precise Definition of the S-L Surface
## 1 Introduction  
The analysis of surface topography can be valuable in the characterisation of the tribological performance of machined surfaces. Valuable information including those when the surface is generated can be received straight from the surface topography characterisation such as wear resistance [1], lubricant retention [2], sealing [3], friction [4], energy consumption [5], eco-friendly applications and strategies [6], or functional performance [7] in general. The evaluation of surface topography can be significant when there is an assessment of additively manufactured parts [8, 9]. Furthermore, in many cases, it can also be classified as a fingerprint of the manufacturing process [10]. When analysing the surface topography, there are many actions required, some of which can be validated separately. First, many errors can occur [11] when surface topography is measured, considering stylus [12] or non-contact [13] methods. Not only is precise measuring equipment required, but errors in the processing of the received raw measured data can cause a false estimation of the properties of the machined parts. From this perspective, accurate procedures for data characterisation should also be defined. Considering surfaces after different machining processes, it is difficult to define one general procedure for the raw measured data analysis. Regarding this matter, detailed guidance can play a significant role. The whole process of surface topography analysis including, especially the characterisation of machined parts (surfaces), can be roughly divided into several, separate actions,where mutual influence can occur. A necessary preliminary to the numerical assessment of surfaces or their selected profiles is to extract the frequency components, defined as the roughness and to respectively eliminate those that would be irrelevant such as form [14]. The surface topography of machined parts is usually analysed when a form including the shape and waviness is extracted [15]. However, the process of the removal of insignificant components of surface topography can be fraught with many errors, especially when the surface contains some dimples or, generally, deep and wide features [16]. The effect of the depth, size, or density of various features on the results of surface filtering with the general (available in the commercial software) methods has been widely studied previously [17]. It was found that reducing the errors in the raw measured data processing can be placed on an equal footing with errors in the manufacturing process, where an improper data processing approach can lead to the false estimation of surface properties, and the classification of properly made parts as lack and its rejection. When receiving the surface roughness parameters, an appropriate definition of the S-L surface [18], often described as a scale-limited surface, is required. The S-L surface is received when removing small-scale and large-scale lateral components from the primary surface by the application of S-operators (e.g., S-filter) and L-operators (L-filter), respectively. Both operations are considered separately. The L-surface, when removing the long-scale components from the measured data, can be received by the application of digital filtering, often characterised by Gaussian filters [19]. Many Gaussian filter limitations were resolved when introducing its robust modifications [20; 21], especially for surfaces containing some deep features. There were many digital filters provided for the extraction of form from the data such as spline [22; 23], wavelet [24; 25], morphological [26; 27], fast Fourier transform (FFTF) [28; 29], and many others [30]. Very popular in recent studies is multi-scale characterisation [31; 32; 33] or analysis based on feature consideration [34; 35]. These techniques separate the received raw measured data in various frequencies using different methods, and filters in some cases [36]. Alternatively to filters, a form removal process can be provided with a defining reference plane [37].