# Optimizing the performance and production of a stone crushing process

Researchers from the Centre for Rapid and Sustainable Product Development (CDRSP), a research unit of the Polytechnic of Leiria, in collaboration with a metallomechanics engineering company from the region of Leiria with several years of experience in the stone industry are working together on a mathematical model to develop an optimized algorithm to be used in a stone industry equipment. The goal is to improve the performance and production of a stone crushing process.

A hammer is used to crush a block of natural stone until the volume of the small pieces is under a specified value defined according with the application. These small stones can be applied in the construction sector, for example.

What was the previous solution used by the company?

The natural stone block was normally fed into a pneumatic crusher equipped with a mobile hammer. Initially the hammer was crushing the stone using a simple trajectory, running left horizontally through adjacent points, moving one step further orthogonally and continuing horizontally to the right and so on. The process was not optimized because sometimes the impact occurred in an empty position where there was no stone. This contributed to wasted time and a waste of energy that could be optimized by applying mathematics to this process.

Different researchers from the Polytechnic of Leiria (Paula Faria, Rui Fonseca-Pinto, Jorge Fatelo, Svilen Valtchev and João Marcelino) and from the University of Coimbra (João Luís Soares), with diverse but complementary backgrounds, were involved. Several meetings and experiments were held in the company’s laboratories and, based on this work, a mathematical model and a computational algorithm were developed to meet the challenge proposed by the company.

The proposed solution

The algorithm developed by the mathematicians contributed to optimise the time of the stone crushing process. Image processing techniques and optimization techniques such as the Garcia-Castellanos and Lombardo method were used to provide the machine with the ability to understand where the positions of the stone fragments are and, based on this information, calculate where the mobile hammer should crush in its next action.

The mathematical application developed allows the process described to be automated, reducing execution time and the financial costs involved. This collaboration has led to a better positioning of the company in the market.

The CDRSP has collaborated and led several R&D projects, working together with different companies in different sectors of economic activity, both in Portugal and on board, with the aim of collaborating to make a better future! We highlight the research being done in additive manufacturing and its vast applications, which is the central theme of research at CDRSP. For more information, please visit: https://cdrsp.ipleiria.pt/

João Marcelino, Researcher of CDRSP – Politécnico de Leiria and Master student in Mathematics of the University of Coimbra

Paula Pascoal-Faria, Head of the Mathematics Department @ESTG and Researcher of CDRSPPolitécnico de Leiria