Abstract: |
The contributed talk presents a novel strategy for reducing the geometric error of a particular product - a vehicle headlamp equipped with a set of calibration screws. The calibration screws are used to adjust the optimum position of the headlamp. The automated product adjustment procedure was designed to find an optimal configuration for a combination of calibration screws, i.e. a position of the screws in which the distances between the test points and their prescribed positions are minimal and geometric error is minimized.
Our strategy involves solving two sub-problems: the design of a digital twin for a headlamp and optimization using calibration screws. We propose a general method for designing and implementing the digital twin, which can be used to minimize overall geometric error. The main idea of developing a digital twin for a headlamp (the first sub-problem) is based on the assumption that the product is a rigid body. We formulated optimal product adjustment (the second sub-problem) as minimizing the locally Lipschitz continuous cost function, which in our case is continuously differentiable and subject to inequality constraints, i.e. it is written as a problem of constrained minimization. We used the gradient method and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method to solve the optimization problem. In this talk, we present numerical experiments illustrating the solution of both subproblems and the use of our approach.
The proposed digital twin allows finding optimal compensatory element settings, leading to minimal total geometric error. Products are automatically adjusted by these settings during the manufacturing process. The novel strategy allows producing parts with approximately 30% more precise tolerances than previously used approaches. Our deployed implementation in C# language running on a regular industrial computer requires only a few seconds (1s to 5s), and the entire machine cycle takes approximately 40 seconds. It means that one machine can adjust more than 2,000 parts per day. In a previous approach, one produced part per day was taken from a production line and precisely adjusted manually by the operator using a screwdriver and a coordinate measuring machine measurement. The same calibration screw setting was used for every part that followed that day, so the same geometric error for each piece was expected.
The solution presented in this talk is currently applied in the automotive industry and has been used to adjust approximately 200,000 headlamps. The proposed approach was introduced in the paper [1].
References
[1] Jaromír Konečný, Michaela Bailová, Petr Beremlijski, Michal Prauzek, Radek Martinek: Adjustment of Products with Compensatory Elements using Digital Twin: Model and Methodology, PLOS ONE (under review). |