# Validation of a Manual Methodology for Measuring Roundness and Cylindicity Tolerances
## 1 Introduction  
In the industrial field, the search for constant improvement of manufacturing processes and the quality of manufactured parts due to technological evolution leads to a demand for qualified professionals in the field of dimensional metrology, responsible for the control and verification of product shapes and tolerances. The industrial engineer emerges as a key figure in this type of task, as they have versatile training in terms of manufacturing, materials science, metrology, process control, and automation [1]. For these reasons, curricula and training methodologies in a high-level technical environment need to be updated, as well as methods sought to encourage conceptual understanding, which reinforces users' working skills and brings them closer to the conditions typically found in the industrial background [2, 3]. It is therefore essential that the training activities carried out herein provide professionals with a comprehensive knowledge of different procedures to deal with design, production, and their relationship with the standard system of Geometrical Product Specifications (GPS) [4]. As future users in the field of dimensional metrology, some Mechanical Engineering students have been chosen to experiment with the efficiency of the technological proposal that is explored in this paper. Dimensional tolerances are used in manufacturing to control the actual sizes, shapes, and geometrical characteristics of parts to meet their functional requirements and to ensure parts' interchangeability [5]. Therefore, tolerancing has evolved as an important activity that is related to design, manufacturing organization, and inspection, significantly affecting the economics of manufacturing processes, which has a significant effect on the development of precision products [6; 7]. However, it has been detected that the understanding of some of these concepts, especially those related to roundness and cylindricity tolerances, is not easy for technicians, as it is not clear how to visualize them graphically, i.e., it is not easy to try to make them understand the theoretical and analytical procedures if there is no practical activity involved. In addition, there is no commercial software on this topic that offers a training approach and supports virtual learning. Thus, the calculation and testing of roundness and cylindricity tolerances pose a problem when they must be applied to the verification of solids of revolution. Typical methods to measure roundness and cylindricity tolerances are those that use a table, and particularly, specific measuring machines are common in industrial environments or metrological verification laboratories [8]. In some cases, it is necessary to control workpieces either during the manufacturing process without being disassembled from the machine, or on working parts. For those cases, the V-block method [9; 10; 11], systems based on the laser [12], or inductive or capacity sensor systems [13], have been developed. The V-block method is an adaptation of the typical one based on V-blocks on a table, but some sensors and monitoring computers are necessary for this to be performed [10; 11]. Laser triangulation is a typical non-contact method that has the advantage of high accuracy and efficiency. Nowadays, even some laser systems supported by digital twin technology are being examined [14]. Some recent research has been carried out to apply machine vision to determine deviations of rotational parts [15], but there is no standard equipment in the industry and more research is necessary in this context [16]. Specifically, automated cylindricity measuring equipment (CME) is designed for the evaluation of roundness and cylindricity tolerances. Basically, a stylus takes a lot of readings on the surface of the part with respect to a reference axis while it rotates. The measurement process is usually simple and even intuitive, but not the mathematical and conceptual one.