In this paper, fractional calculus is used to develop a generalized fractional dynamic model of an electrohydraulic system composed of a servo valve and a hydraulic cylinder, where a fractional position controller $P{I}^{\gamma }{D}^{\mu }$ is proposed for minimizing the performance index according to the integral of the time-weighted absolute error (ITAE). First, the general mathematical equations of the cylinder and servo valve are used to obtain the transfer functions in fractional order by applying Caputo’s definition and a Laplace transform. Then, through a block diagram of the closed-loop system without a controller, the fractional model is validated by comparing its performance concerning the integer-order electrohydraulic system model reported in the literature. Subsequently, a fractional PID controller is designed to control the cylinder position. This controller is included in the closed-loop system to determine the fractional exponents of the transfer functions of the servo valve, cylinder, and control, as well as to tune the controller gains, by using the ITAE objective function, with a comparison of the following: (1) the electrohydraulic system model in integer order and the controller in fractional order; (2) the electrohydraulic system model in fractional order and the controller in integer order; and (3) both the system model and the controller in fractional order. For each of the above alternatives, numerical simulations were carried out using MATLAB^®/Simulink^® R2023b and adding white noise as a perturbation. The results show that strategy (3), where electrohydraulic system and controller model are given in fractional order, develops the best performance because it generates the minimum value of ITAE.

This research presents an experimental study focused on measuring temperature at the tool flank during the up-milling process at high cutting speed. The proposed system deals with emissivity compensation through a two-photodetector system and during calibration. A ratio pyrometer composed of two photodetectors and a multimode fiber-optic coupler is employed to capture the radiation emitted by the cutting insert. The pyrometer is calibrated using an innovative calibration system that addresses theoretical discrepancies arising from various factors affecting the measurement of cutting temperature. This calibration system replicates the milling process to generate a calibration curve. Experimentally, AISI 4140 steel is machined with coated tungsten carbide inserts, using cutting speeds of 300 and 400 m/min, and feed rates of 0.08 and 0.16 mm/tooth. The results reveal a maximum recorded cutting temperature of 518 °C and a minimum of 304 °C. The cutting temperature tends to increase with higher cutting speeds and feed rates, with cutting speed being the more influential factor in this increase. Both the pyrometer calibration and experimental outcomes yield satisfactory results. Finally, the results showed that the process and the device prove to be a convenient, effective, and precise method of measuring cutting temperature in machine processes.

Surface roughness is affected by the tool geometry, feed rate, overcutting by built-up edge, and tool vibration in the depth of the cut direction. However, dividing the roughness value into each component is difficult. Therefore, a new prediction method for the position of the tool contour on the roughness curve is proposed to divide the measured roughness value into components. This proposed method consists of two processes. In one, the roughness curve is divided into the roughness curve formed during each revolution of the work material regardless of the clarity of the feed marks. The other is the process that predicts the vertical position of the tool contour. If the vertical position of the tool contour can be predicted, the vibration and overcutting components of roughness can also be predicted. In this study, the transition of roughness components such as the theoretical roughness, vibration width, and overcutting is studied with the increase in the cutting distance in the turning of chromium molybdenum steel, JIS SCM435. When supplying a 10% emulsion mist, the measured R_z is smaller than that of the dry condition. In both the dry and mist supply conditions, the measured R_z increases from the beginning of cutting then decreases and then increases again with the increase in the cutting distance. The largest component of the total roughness in both the dry and mist supply conditions is the theoretical roughness R_th. The ratio ranges between 50.3% and 78.7%. Regardless of the cutting conditions, the vibration width in the depth of the cut direction is relatively constant. The overcutting slightly increases after the start of cutting, then decreases when the maximum contact length exceeds approximately 0.1 mm. The proposed method verifies the ratio of the surface roughness components and is an effective method for improving the surface roughness.