**1. Introduction**

Honing is an abrasive machining process in which a honing head provided with abrasive stones combines alternate linear movement with rotation in order to machine the internal surfaces of cylinders. The main goal of honing is to obtain a cross-hatched pattern with channels that favor oil flow in combustion engines or hydraulic cylinders. Several authors have indicated the key role of the surface topography of the cylinders' liners on the friction coefficient in the piston/cylinder assembly as well as on the amount of oil consumption. Thus, selecting proper honing parameters can reduce the emission of toxic compounds during the operation of combustion engines [1–3].

Some researchers have studied the honing process by means of statistical models. For example, Troglio [4] considered the grain size of the abrasive, lubricating oil and workpiece material as variables, and studied different roughness parameters, such as average roughness Ra and parameters of the Abbott–Firestone curve (Rk, Rpk, Rvk, Mr1, Mr2). Kanthababu et al. [5] varied rotation speed, linear speed, pressure, honing time and plateau-honing time. Responses were roughness parameters of the Abbott–Firestone curve. Roughness was mainly influenced by pressure and honing or plateau-honing time. Wos and Michalsky [6] found that main roughness parameters improving aircraft piston engine performances (output power, torque, fuel consumption and total efficiency) are Rvq and the linear triangle area for valleys A2, although they provide a higher oil consumption and greater emissions. More recently, Vrac et al. [7] obtained exponential models for roughness

**Citation:** Buj-Corral, I.; Roderode-Lamo, L.; Marco-Almagro, L. Optimization and Sensitivity Analysis of the Cutting Conditions in Rough, Semi-Finish and Finish Honing. *Materials* **2022**, *15*, 75. https://doi.org/10.3390/ ma15010075

Academic Editors: Gilles Dessein and J. Antonio Travieso-Rodriguez

Received: 25 November 2021 Accepted: 19 December 2021 Published: 23 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

and material removal rate as a function of process parameters, such as pressure or speed. In another study with diamond stones of grain size 151 and 181, they found that pressure was the most influential factor on roughness, followed by cutting speed and feed [8]. Vrabel et al. [9] analysed the influence of cutting speed, machining allowance and stone pressure on surface roughness, specifically on roughness parameters, the height of peaks (CR), the depth of the profile (CF) and the relative height of the holes (CL). On the other hand, Buj-Corral et al. searched for statistical models for both roughness and material removal rate in rough honing as a function of the main process parameters. They found that, in the range studied, abrasive grain size and pressure were the main parameters influencing both roughness and material removal rate [10]. Material removal rate values between 0.015 and 0.020 mm/s (0.090 and 0.120 cm/min) were found by Szabo [11] using cubic boron nitride (cBN) stones. In rough honing, Bai et al. [12] observed that the material removal rate increases with circumferential speed, reciprocate speed and cross-hatch angle, but decreases when the two speeds take too high values.

The semi-finish process was also studied, in which, as a general trend, roughness and material removal rate increase with grain size and density [13]. The finish honing process has been less well studied in the literature. For instance, Arantes et al. [14] compared the surface finish obtained in both conventional honing and flexible honing processes, including amplitude parameters, Rk family parameters, volume and feature parameters. In finish honing, Bai et al. [12] found that surface finish in finish processes improves when circumferential speed increases. Cabanettes et al. [15] studied the relationship between tool wear and different roughness parameters. They reported that only areal reduced summit height, arithmetic mean summit curvature and core roughness are correlated with tool wear.

Multi-objective optimization by means of the desirability function was developed by Derringer and Suich [16]. It has been applied in the past to machining processes, such as turning [17,18] or milling [19,20]. As for abrasive machining processes, Mukherjee et al. employed the desirability function and a metaheuristic technique for optimal process design [21]. Regarding honing processes, Lawrence and Rammamoorthy used robust process design and gray-relational analysis to define recommended values for process parameters in order to obtain required values for roughness Rz, roughness parameters from the Abbott–Firestone curve and honing angle, for three honing stages: rough, semi-finish and plateau-honing [22]. Nguyen et al. [23] carried out multi-response optimization of finishing honing with respect to surface finish and production rate. They noticed that both surface roughness and machining time depended mainly on grit size, followed by tangential speed and linear speed.

Sensitivity analysis is usually carried out in optimization problems, in order to assess the effect of the modification of either the objective function or the variables on the optimized values [24]. Different methods have been used in the past for performing sensitivity analysis after optimization. For example, Arsezer defined a methodology that consists of varying the parameters of the desirability function and analyzing their effect on desirability [25]. Malenovic et al. used a similar methodology for performing sensitivity analysis on the results of multi-objective optimization in a microemulsion LC system, and found the most sensitive parameters among importance, weight and ranges of the different responses [26]. In turning processes, Souza Rocha et al. [27] optimized tool life, surface roughness Ra and the ratio material removal rate/cutting force as a function of cutting speed, feed rate and depth of cut. They found that the weights used in the multi-objective optimization process influence the prediction variance. Mudhukrishnan et al. [28] optimized drilling parameters, such as spindle speed, feed and drill material, with respect to thrust force and torque, and performed a sensitivity analysis to assess the impact of control variables on the responses.

On the other hand, mixture design is a methodology that allows different kinds of mixtures to be tested; for example, in the formulation of cement or concrete pastes [29] or in the food industry [30]. This method is usually employed to determine the best composition of a certain product. In the manufacturing area, for example, Misra et al. [31] employed mixture design to find the optimal electrolyte composition in electrochemical honing of gears.

In the present paper, regression models were obtained for average roughness Ra, material removal rate and tool wear for the three steps of the honing process, namely, rough, semi-finish and finish honing. Afterwards, multi-objective optimization was carried out by means of the desirability function. Importance values were defined for each response in the three honing steps, according to users' requirements. However, the selection of certain importance values for the responses could affect the results of the optimization process. Thus, in order to test the influence of the importance values on the optimal values of the variables in this work a sensitivity analysis was carried out. Mixture design was used to define different importance values to be tested. In order to assess the variability, the coefficient of variation CV was calculated for each response, considering different percentages of variation of the importance values.

This paper has two essential contributions. First, the recommendations for selecting the most appropriate parameters in each honing operation (rough, semi-finish and finish). Second, the final guidelines on how to define the importance of each parameter for the multi-objective optimization in each of the phases of the honing process.

#### **2. Materials and Methods**

#### *2.1. Honing Experiments*

Steel St-52 cylinders of 80 mm interior diameter and 390 mm length were machined in a Honingtec industrial machine (Honingtec S.A., Els Hostalets de Balenyà, Spain). This material is usually employed to manufacture hydraulic cylinders. Figure 1 shows the industrial machine used.

**Figure 1.** Industrial honing machine used in the experiment.

A central composite design was used to define the experiments in each one of the honing steps (rough, semi-finish and finish), which is explained in Section 2.5. Honing time was 30 min in all experiments. Two replicates were performed for each experiment.

Cubic boron nitride (cBN) honing stones were used with metallic bonds. Figure 2 depicts the honing head employed.

**Figure 2.** Honing head used in the experiment.

For each of the three experimental designs, three responses were measured: roughness (Ra), material removal rate (Qm) and tool wear (Qp).

#### *2.2. Roughness Measurement*

Arithmetical mean roughness Ra was measured with a Hommel-Etamic W5 contact roughness meter (Hommel-Etamic GmbH, Villingen-Schwenning, Germany), according to standard ISO 4287 [32] (Figure 3).

**Figure 3.** Contact roughness meter.

Nine measurements were taken along a diametral circumference in the internal surface of cylinders at a distance of 195 mm from the end of the cylinders. The average value of the nine measurements was calculated. The cut-off length was 0.8 mm and the measuring length was 4 mm.
