Development and experimental validation of a macroscopic analytical model aiming to generate metal-FRP stacks drilling cutting force and torque

Thomas Beuscart. Machine Design and Production Engineering Lab – Faculty of Engineering, University of Mons, Place du Parc 20, 7000 Mons, Belgium Corresponding author: thomas.beuscart@umons.ac.be Pedro-José Arrazola. Escuela Politécnica Superior de Mondragon Uniberstitatea, Loramendi 4, 20500, Mondragon, Spain Edouard Rivière-Lorphèvre. Machine Design and Production Engineering Lab – Faculty of Engineering, University of Mons, Place du Parc 20, 7000 Mons, Belgium François Ducobu. Machine Design and Production Engineering Lab – Faculty of Engineering, University of Mons, Place du Parc 20, 7000 Mons, Belgium

A Abstr bstract act. . Composites materials and especially FRP are increasingly employed in many fields of applications (transport, aerospace, …) due to the current trend of improving global energy performances of new designs notably by mass saving. However the use of metallic materials such as aluminum and titanium alloys is still necessary in many cases and a lot of structures are made of a dual technology called stacks (panels composed of different layers of FRP and metal bounded together). Combining the different properties of these materials offers many advantages regarding the mechanical and structural aspects. This is nevertheless for the same reason that machining and especially drilling stacks is a laborious task: the tools and cutting conditions are way too divergent to avoid vibrations, problems of dimensional tolerances and delamination of the composite.
The knowledge and characterization of the drilling cutting forces is a first step to solve these issues. The purpose of this article is to provide an accurate macroscopic analytical model fitted for stacks and compare it quantitatively with experimental tests. The given model is divided in two parts (i.e. respectively adapted for the two materials) and is based on the discretization of the cutting edge. The proposed algorithm is able to predict accurately drilling force and torque along time in function of the cutting conditions, the tool and material configurations. A reverse least squared method is used to obtain the empirical input parameters, allowing to minimize the number of experimental drilling tests to obtain the empirical input parameters.
K Ke eyw ywor ords ds. Drilling, Macroscopic, Model, Cutting Force, Stacks, Fiber Reinforced Plastics, Metal 1 Intr 1 Introduction oduction Stacked metals-FRP materials are increasingly employed in many industries such as automotive, railways and aerospace due to the dual properties offered by these materials: lightweight and mechanical resistance. In addition machining process and especially drilling, which is the more common machining operation used for these kind of net-shaped material, can cause a large range of issues: delamination of the composite part by peel up or push up [1], burrs and tearing especially at the exit [2], vibrations [3] and large tool wear [4] due to the changing machining properties between composite and metal [5]. The knowledge of the cutting force and torque is a key point to avoid all these previous problems. It allows comparing it with a critical thrust force and torque for delamination and crack or to establish limit parameters to prevent tool wear and vibrations.
Since 1950s a lot of research works has been carried out to model cutting force for the basic metal machining operations. The Merchant's [6] model of the orthogonal cutting forces by shear plane modeling is the basis for many other models specific to each machining operation. Firsts drilling force models for metals were introduced in 1970s and can be divided into two categories [7]: some using an iterative theoretical energetical pattern based on the shear plane zone theory by assuming that the mechanical properties are known, while some others prefer to use experimental approaches thanks to empirical parameters giving more accurate results. Most of them are based on a 3D spatial discretization combined with oblique cutting or simplified quasi-orthogonal cutting theory and are tool and material specific. This paper present a new drilling cutting force and torque algorithm developed for stacks metal-FRP by using Chandrasekharan and al.'s [8,9] and Langella and al.'s [10] theories which is able to predict with a reduced number of drilling tests accurate non-tool dependent values of the empirical input parameters thanks to a reverse least squared minimisation method.
2 Stack cutting f 2 Stack cutting for orce and t ce and tor orque modelling que modelling Common architecture for metals and composites The suggested model is based on a dual discretization in order to highlight the thrust force and torque value: • A spatial discretization of the cutting edge is set up as shown in figure 1 inspired from Chandrasekharan and al.'s model [8]. Twist drill cutting edges are decomposed in two main parts: chisel edge (central part) and cutting lips (peripheral part) where the cutting phenomena and parameters differ according to the material type and location (described below). The concerned edges are divided into elements of length (mm) in which the infinitesimal force ⃗z and torque C⃗ are computed, the total drilling thrust force ⃗ and C⃗ are then given by the following sums (1) and (2) multiplied by x, the number of cutting lips (2 in this work): The radial coordinate ( )= / of each spatial element is previously necessary to determine the location of the elements (chisel edge of cutting lips) and thus calculate the drilling force by an appropriate equation. • The orthogonal cutting theory is used for chisel edge (with a large negative rake angle) thanks to its radial orientation (which induces that the cutting speed of each discretized edge element will always be orthogonal to its edge direction).
• Cutting lips are not radial and the cutting speed of each discretized edge element is not orthogonal to the cutting edge, this explains why oblique cutting theory (more complex three dimensional problem) is used for this geometric part (this induces the introduction of an inclination angle between the normal direction to cutting speed and the cutting edge).
Cutting forces are then specifically given according to the material, cutting conditions, the tool parameters and cutting zone by Chandrasekharan and al.'s [8] equations (3) and (4)

R Re ev verse model erse model
Finding the associated material parameters can be a hard and specific task especially with energetical and shear plane methods. The choice of the two previous macroscopic cutting force models using empirical parameters has been made consequently taking into account the efficiency and the facility to obtain reliable results. Furthermore many methods can be used to finds these parameters: for instance Chandrasekharan and al. [8,9] use experimental turning tests (orthogonal cutting) while Langella and al. [10] apply experimental drilling tests by approximation using an average constant rake angle α , . The most common problem of using these drilling tests methods is the large tool dependency of the results and the number of experimental tests to be performed to ensure reliability on a large range of cutting parameters. On the other hand applying the turning tests or orthogonal cutting methods for unidirectional FRP is difficult to implement in practise and will not provide efficient results due to the dependence on the fibre's orientation while this drilling method does not take it into account.
In order to solve these problems a least squares function has been developed which allows to find an approached value      [10] empirical material parameters coupled with the developed reverse least squared minimization function allows to find easily non tool dependent parameters, giving first accurate results that will be further developed in the future (on different materials and tools). This type of algorithm allows to find reliable values and temporal evolution of thrust force and torque for stacks metal-FRP (or each of the materials specifically) on a large range of cutting parameters and thanks to a few tests, despite large measurement noise. This will then make it easier to solve problems such as premature wear of cutting tools or vibrations causing bad dimensional tolerances in drilling parts.

A Ackno cknow wledgements ledgements
The autors acknowledge the Région Wallonne for funding the project under convention 1910097.