## 1 Introduction  
The valves of the design shown in Figure 1 have a wide range of applications for media flow control in industrial automation systems. To ensure the correct tightness of such a valve, it is important that the valve spindle, operating under sliding friction conditions in a reciprocating motion, has an optimal shape and an appropriate surface condition. Figure 1: Control valve: (**a**) design overview and (**b**) valve steam-to-stuffing sealing principle; (**c**) valve stem overview: 1—valve stem, 2—gland, and 3—sealing pack. During the initial stage of operation, the mandrel is lapped, and its working surfaces are subject to relatively quick wear. After the running-in stage, they reach the equilibrium surface texture, followed by a normal operating period, in which the wear of the friction pair becomes less intense. For a specific pair of materials and operating conditions, the amount of wear depends on the hardness and state of stresses in the surface layer and on the initial condition of the surfaces of the mating parts [1; 2]. The closer the input condition of the surface layer is to an equilibrium surface texture, the less time it takes to run it in, and the longer the normal operating period. This was demonstrated in ref. [3], where the running-in time was reduced by shaping (at the finishing stage of the mandrel) the optimal surface condition by burnishing, thus extending the valve's normal operation time. In addition, in ref. [4], it was found that the condition of the mating surfaces (and the amount of wear during running-in) has a significant impact on later wear (operational), which is related to parameters _Sku_, _Sdq_, and _Svk_. The use of _Rk_ parameters to assess the surface condition to ensure lower wear and better durability of the pin-seal assembly was reported in refs. [5; 6]. In ref. [7], the use of the Abbott-Firestone curve for the same purpose for hydrocylinder liners is mentioned. However, in ref. [8], as many as 17 parameters of the surface texture were used to assess tightness and wear in a reciprocating motion. This is in line with the principle that when assessing the surface condition in the context of predicting tribological properties, not only standard (commonly used) _Sa_ (_Ra_) or _Sz_ (_Rz_) parameters should be considered, but a number of other parameters that better allow the assessment of these properties should also be considered. This was confirmed in ref. [9], the results of which showed that (morphological) surface parameters such as skewness and kurtosis show a better correlation with tool wear and life than amplitude parameters such as _Sa_ and _Sq_. However, in ref. [10], parameters _Rvk_ and _Rpk_ were used to assess the degree of grinding wheel wear, and in refs. [11; 12], parameters _Rvk_, _Rpk_, _Mr2_, and _Rk_ were used to assess the amount of wear during sliding friction. Investigating the relationship between the friction coefficient and some non-standard surface texture parameters, the authors of ref. [13] found that parameters _Sq_, _Ssc_, and _Sdq_ are positively correlated with the value of the sliding friction coefficient, whereas _Sal_ and _Sk_ are negatively correlated with the value of the sliding friction coefficient. The same authors in ref. [14] used a number of non-standard roughness parameters to analyse the surface texture and its resistance to micropitting. They found that the severity of micropitting was positively correlated with parameters _Sbi_, _Sku_, _Sv_, and _Sal_ but negatively correlated with _Ssc_ and _Ssk_. By examining the relevant dependencies on the four-ball tester in work [15], a relationship between parameters _St_, _Ssk_, _Spk_, and _Svk_ and the amount of wear was found. On the other hand, in the work [16] it was found that _Sku_, _Ssk_, and _Svk_ parameters showed a good correlation with the tribological properties of the mating surfaces. In ref.