# The Effect of Stick-Slip Friction on the Stability of Nanostructuring Burnishing
## 1 Introduction  
Surface treatment technologies have become an integral part of engineering design, due to their ability to considerably extend the functional performance, reliability, and longevity of machine parts. Anodizing [1], electro-polishing [2], plasma treatment [3], and hard coatings [4] are some of the most popular methods, but mechanical surface treatments are gaining importance as well [5]. The process of nanostructuring burnishing is one such process, which consists of passing a hard spherical indenter (e.g., diamond) in many overlapping passes over a rotating workpiece [6]. Process parameters are chosen such that the contact area undergoes severe plastic deformation and the material therein reforms into a very hard nano-crystalline surface layer. This layer, despite having the same nominal composition as the bulk metal, may show several times higher hardness and wear resistance. Compared to coating technologies, nanostructuring burnishing is much more constrained in terms of geometry, but where applicable, it provides a cost-effective and high-quality surface finish that is not subject to chipping or flaking. Production of high-quality surfaces via nanostructuring burnishing requires careful choice and control of processing parameters, including burnishing force, velocity, temperature, number of passes, lubrication, damping, etc. [7; 8; 9; 10]. When process parameters are not selected appropriately, self-excited vibrations tend to be produced, and these may be exacerbated further by repeated passes over the uneven surface produced previously. In the worst case, this results in a corrugated surface and an effectively ruined workpiece. Frictional instabilities and self-excited vibrations are commonly encountered in highly loaded frictional contacts, and there is an extensive body of research concerning them in areas including machining [11], brakes [12], and rail-wheel systems [13]. An excellent overview of such phenomena was compiled by [PERSON] [14]. The suppression of these instabilities can be achieved by damping or adjusting process conditions, e.g., in the case of nanostructuring burnishing studied here, very high sliding velocities tend to exacerbate the instability, while many other systems tend towards unstable stick-slip at lower velocities. In either case, sliding friction can be effectively stabilized by making the surrounding system extremely stiff, as discovered by [PERSON] [15], but this is often not a practical option. Instability suppression through external ultrasonic vibration may be applicable in some cases [16]. An illustrative example of such a process instability is shown in Figure 1. At the top, one can see a steel valve spindle shaft subjected to nanostructuring burnishing. At the bottom is a close-up of the burnished section, which initially shows stable surface smoothing but eventually transitions into an unstable oscillatory regime. (Note that the tool makes circular passes, slowly progressing from left to right). A further close-up can be seen in Figure 2. The pictured shaft has a length of 380 mm and a diameter of 30 mm, and the visible self-excited oscillations occurred on the first tool pass during processing on the MULTUS 300B machine in the following processing mode: normal force 300 N, indenter radius R = 2 mm, smoothing speed (circumferential sliding of the natural diamond indenter) vs = 2.42 m/s, axial feed rate fb = 0.025 mm/rev \(\approx\) 0.642 mm/s. The workpiece material was AISI 420 (steel 20 \(\times\) 13) with hardness 269 HB. Figure 1: Top: photo of burnished workpiece under consideration. Bottom: burnished section with surface irregularities. The subject of this paper is the investigation of one possible mechanism of such failures of stabilization. It was originally supposed [17] that the oscillations produced in the above two figures must be due to dynamical effects in the direction normal to the surface and possibly related to the flex of the workpiece itself, which represents a long bar mounted at the ends.