Surface Roughness Modeling Using Q-Sequence

Abstract

Dynamical systems play a vital role in studying highly non-linear phenomena. One of the families of the dynamical systems is integer sequences. There is an integer sequence called Q-sequence: Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n − 2)); for n = 3, 4, . . . ; and Q(1) = Q(2) = 1. It exhibits a unique chaotic-order that might help develop approximate models of highly nonlinear phenomena. We explore this possibility and show how to modify a segment of the Q-sequence so that the modified segment becomes an approximate model of surface roughness (a highly non-linear phenomena that results from the material removal processes (e.g., turning, milling, grinding, and so on). The Q-sequence-based models of surface roughness can be used to recreate the surface heights whenever necessary. As such, it is a helpful means for developing simulation systems for virtual manufacturing.

Fundamental Issues of Concept Mapping Relevant to Discipline-Based Education: A Perspective of Manufacturing Engineering

“…Manufacturing (or production) systems have continuously been evolving under the influence of information and communication technology. As a result, a concept of new-generation manufacturing systems has been evolved, which is referred to as Industry 4.0, smart manufacturing, connected factory, Society 5.0, Made in China 2025, and alike [26][27][28][29][30][31][34][35][36][37][38][39][40]. The primary goal is to achieve an active collaboration among hardware devices (e.g., machine tools, robots, measuring instruments), software systems (CAD/CAM, ERP, and SCM systems), and human resources on a real-time basis by exchanging the required data, information, and knowledge [34][35][36][37][38][39][40].…”

“…As a result, a concept of new-generation manufacturing systems has been evolved, which is referred to as Industry 4.0, smart manufacturing, connected factory, Society 5.0, Made in China 2025, and alike [26][27][28][29][30][31][34][35][36][37][38][39][40]. The primary goal is to achieve an active collaboration among hardware devices (e.g., machine tools, robots, measuring instruments), software systems (CAD/CAM, ERP, and SCM systems), and human resources on a real-time basis by exchanging the required data, information, and knowledge [34][35][36][37][38][39][40]. For achieving this goal, a set of relevant technologies has been introduced, namely, human-cyber-physical systems, digital twins, and the Internet of things [26][27][28][29][30][31][34][35][36][37][38][39][40].…”

“…The primary goal is to achieve an active collaboration among hardware devices (e.g., machine tools, robots, measuring instruments), software systems (CAD/CAM, ERP, and SCM systems), and human resources on a real-time basis by exchanging the required data, information, and knowledge [34][35][36][37][38][39][40]. For achieving this goal, a set of relevant technologies has been introduced, namely, human-cyber-physical systems, digital twins, and the Internet of things [26][27][28][29][30][31][34][35][36][37][38][39][40]. Numerous authors have studied these technologies.…”

“…They have emphasized that the human-cyber-physical systems or the systems that reside in the fog (the mid-wear between edges and cloud) must be populated with the contents called digital twin (computable virtual abstraction of real objects, processes, and phenomena). Ullah [30,38] and Ghosh et al [40] described that there are three kinds of digital twins, namely, object twin, process twin, and phenomenon twin. Among these twins, phenomenon twin is the most challenging twin to construct because the construction of phenomenon needs stochastic dynamical systems-based formulation and user-defined technique to capture the dynamics of the underlying phenomenon [38,40].…”

Elucidating Grinding Mechanism by Theoretical and Experimental Investigations

“…For the sake of quantification, the primary profile data is processed in both conventional and non-conventional ways, as described in [35,36]. As a part of conventional way, the surface roughness parameters denoted as P a (arithmetic average height) and P z (peak and valley height) are calculated using the surface height data points as shown in Figure 11 and Figure 12.…”