## 1 Introduction  
Chromium-nickel austenitic stainless steels (CNASSs) are the most common class of stainless steels. CNASSs are used in many industrial applications due to their superior corrosion resistance, excellent formability, good machinability, and weldability. However, a key disadvantage of these steels is their poor strength and hardness, which, due to their austenitic structure, cannot be increased by the application of heat treatment. Heating the specimen to 1100 \({}^{\circ}\)C, holding it at this temperature to dissolve the carbides, and subsequently rapidly cooling the specimen in water results in a larger-grained alloyed austenite structure. Accordingly, the sample's strength decreases, while its plasticity and corrosion resistance both increase [1]. A slight improvement in hardness, static strength,and fatigue strength (under steady-state loading) of AISI 302 steel can be achieved by deep cryogenic treatment [2; 3]. However, these mechanical characteristics may drastically increase in response to cold plastic deformation due to the strain-hardening effect, which can be either volumetric [4; 5] or surface [6; 7; 8], i.e., surface cold working (SCW). Besides strain hardening, cold working also leads to the \(\gamma\rightarrow\alpha^{\prime}\) phase transformation, forming so-called strain-induced \(\alpha^{\prime}\)-martensite, which increases the strength and hardness of the specimen but worsens its corrosion resistance [1]. SCW is a surface engineering approach to modify the surface layers of metal components through mass conservation. Static and dynamic SCW methods increase the surface microhardness and introduce compressive residual stresses in the surface and subsurface layers of the sample. In addition, static SCW methods, known as burnishing methods, drastically reduce the specimen's roughness height parameters, which may produce mirror-finished surfaces. One of the static SCW methods is diamond burnishing (DB) [9], which is implemented on conventional machine tools and those with computer numerical control (CNC) and forms part of the technological process used to produce rotary details and less often those with flat surfaces. The interface between the deforming diamond insert and the treated surface is characterized by sliding friction. Due to the heat generated, mostly from friction, the DB process is usually implemented with lubrication under cooling conditions. Since DB is a finishing process, i.e., realized after machining on the same machine tool (turning, milling, drilling, and, in some cases, grinding), the environmental and human impacts of using lubricating cooling liquid (LCL) during cutting [10] are also relevant for DB when it is performed in the presence of LCL. Conventionally, DB is usually implemented under flood lubrication conditions, which involve the use of extensive LCL. The purpose of LCL in cutting and burnishing processes is to reduce the heat generated by friction and plastic deformation, wash chips from the cutting area, and inhibit corrosion, with the aim of improving the quality of the machined surface, reducing tool wear, and increasing productivity [11]. However, the widespread usage of LCL (with over two billion gallons of cutting fluids used by North American manufacturers alone in 2002 [11]) can cause economic, ecological, and human health problems. LCL costs typically range between 7 and 17% of total production costs [12; 13] and may increase by a further 20% for difficult-to-cut alloys [14]. The cost of recycling spent LCL is two to four times that of buying new LCL [15]. In addition, disposal of purified LCL can contaminate natural resources including rivers, lakes, air, and groundwater [11]. LCL can harm human health, causing skin infections, pneumonia, and lung cancer [16; 17; 18; 19; 20]. LCLs also commonly generate a mist in the air that can cause respiratory diseases and several types of cancer [21]. Various approaches have been developed to control LCL mist, including kinematic coagulation, innovative machine tool design, and dry machining [21].