Surface quality plays a very important role in the proper formation of the properties of the machine part components. These properties can positively influence, e.g., the resistance to wear, corrosion and fatigue strength. Conventional methods such as machining, turning or milling very often don’t allow to obtain the surface of appropriate parameters of a geometric surface structure. This kind of processing also causes unfavourable tensile residual stresses in the surface layer. These stresses have a negative impact on the resistance to work in fatigue conditions [
1]. Burnishing allows to improve the properties of a surface layer by its plastic deformation. Ball burnishing is a chipless finishing process that allows to reduce the surface roughness and makes the surface work-hardened. In addition, compressive stresses that allow to increase the fatigue strength are introduced in the surface layer. A ball burnishing process consists of pressing and turning a smooth and very hard ball on the material surface in order to achieve plastic deformation of the surface roughness. This process can be implemented for a variety of surfaces, for example cylindrical, flat, internal as well as external. It can be used on conventional and CNC machines. Ball burnishing is very economical and, in some cases, it may replace operations such as grinding or polishing [
2,
3].
Burnishing can be widely used with various materials such as aluminium, steel [
6‐
8], alloys [
9,
10], and brass [
11]. The effect of ball burnishing on the surface stereometric structure is most commonly described in research reviews. The parameters of greatest concern are the feed, force, and speed. The force plays a vital role in the ball burnishing process. From the start of the plastic deformation, increasing the force causes the surface roughness to decrease until it reaches a reasonably low value. However, an excessively high force may result in spalling of the surface [
12].
The conducted literature review indicates that the main research area of different authors include primarily the characteristics of the surface geometric structure after ball burnishing. Most attention was focused on the description of the changes of the surface geometric structure parameters in regard to the process input parameters, i.e., burnishing force, feed rate, burnishing speed or the number of passes. Not much attention was paid to the mathematical description of the input parameters influence on the surface geometrical structure parameters. El-Tayeb et al. [
13] analysed the impact of the following ball burnishing parameters: a ball diameter, burnishing speed, its force and direction on reducing roughness and improving tribological properties of aluminum 6061. Rao et al. [
14] studied the impact of the parameters of burnishing and lubricant on the surface hardness of dual-phase steels. Loh et al. [
15] investigated the possibility of optimizing (minimizing) the surface roughness for aluminum alloy. El-Taweel and El-Axir [
16] studied the applicability of the Taguchi method for optimizing the process of ball burnishing. The parameters such as surface roughness and surface microhardness were taken into account. Shiou and Hsu [
17] analysed the possibility of using ball burnishing for flat surfaces for stainless mould steel with the Taguchi plan for 9 experiments. In his further works Shiou and Cheng [
18] analysed the impact of the ball burnishing parameters for free form surface plastic injection mould in order to obtain the best possible surface quality. Swirad et al. [
19] analysed the influence of a burnishing strategy (raster and spiral) on the obtained surface geometric structure for martensitic steel. The results show that the raster strategy is a good solution for the curved-shaped surfaces due to the process stability in relation to the tool position and burnishing force. In his further works, Swirad [
20] presented the possibility of ball burnishing for alpha-beta titanium alloy (Ti6Al4V). The studies showed that there is a possibility of a significant reduction in the surface roughness in a wide range of the input parameters. In Ref. [
21] the possibility of using hydrostatic burnishing for hard steel 145Cr6 with the hardness of 54 HRC was presented. The results showed that the burnishing force has the least impact on the reduction of the surface roughness. Burnishing width and speed has the biggest impact. In his works, López de Lacalle et al. [
22] used two types of steel, AISI P20 steel of the hardness of HRC 32 and H13 tempered steel of the hardness of 52 HRC. The ball burnishing process was carried out in two directions (perpendicular and parallel) in relation to the preceding milling processing. The results indicate that for the perpendicular direction for the previous treatment a greater minimization of the surface roughness was achieved. In addition, it was revealed that for the steel with the hardness of HRC 32 the best results were achieved for the burnishing force of 15 MPa, while for the steel of the hardness of 52 HRC, it was necessary to apply the force of over 20 MPa. In another work, López de Lacalle et al. [
23] used ball burnishing on the 5-axis CNC machine. As a workpiece, a hemisphere surface of AISI 1045 steel was used. The research findings indicate that continuous burnishing allows to achieve a significant reduction in the surface roughness. However, this treatment is limited by the maximum speed of the machine headstock (or table) rotary axes. In addition, the programming process of a burnishing path is more complex in the continuous five-axis.
In the present work, the Hartley research plan was used in order to obtain a mathematical description in the form of the equation of the input parameters impact of a ball burnishing process on the selected parameters of a geometric structure. As the input parameters, burnishing pressure, speed and width were analysed. The output parameters for the surface texture included Sa, Sv, Sz, and Sq.