11. Simulation of Machining Operations Based on the VMT Concept

The simulation of machining operations in close interaction with the machine tool dynamic behaviour requires two main modelling components. First, to accurately simulate the dynamics of modern high-speed machine tools, a mechanical model that represents the flexibility of all components and their interactions is needed [1]. To create this mechatronic model of a machine tool (virtual machine tool), 3D MBS and FEA methods are used for mechanical aspects and 1D modelling for the CNC. As described in Chap. 2, an integrated methodology is proposed for the mechanical aspects, and it combines MBS capabilities in a nonlinear FEA [2] solver called SAMCEF Mecano [3]. It enables accurate modelling of the machine by considering FEA models of the components connected by a set of flexible kinematical joints. Additional models are implemented to deal with drive-trains and motors dynamics. Furthermore, an integrated cutting force model is used to capture force interactions between the tool and the workpiece to fully capture the dynamic behaviour of the machine tool. Within the scope of the Twin-Control project, the VMT concept was used to model two machines, a high-speed four-axes box-in-box machine from Comau and a large three-spindle five-axes machine from Gepro. The two models are shown in Fig. 11.1.

Furthermore, an integrated cutting force model is used to capture force interactions between the tool and the workpiece to fully capture the dynamic behaviour of the machine tool during the machining operations. This chapter deals with the integration of this cutting force model with the developed VMT module.

The considered cutting simulation approach is compatible with the virtual machining paradigm. Derivation of the forces acting on the cutting edges of the milling tool is a two-step procedure. First, the geometric and volumetric properties of the removed material are computed. Second, process dependent heuristic is applied on the tool move spatial data to compute cutting force components. The process for obtaining cutting forces is illustrated in Fig. 11.2. This method is widely described in Chap. 3 of the book. This section focusses only on its integration in the Mecano software.

The cutting force module [4], originally developed in MATLAB, is converted to a single DLL to be called in the SAMCEF simulation. An overview of the cutting force module structure is shown in Fig. 11.3. The cutting force module is composed of three primary sections (labelled a–c in Fig. 11.3) which execute the key functions of the cutting force model. These sections are combined into a single module, and the different sections are only called as necessary using the desired RunFlag input value. The first step of the cutting force module, Fig. 11.3a, generates the discretized tool mesh based on the tool dimensions and mesh resolution data. The constant edge effect vectors, \(F_{{{\text{e}},XYZ,el}}\), the cutting force matrices, \(Q_{{{\text{c}},XYZ,el}}\), are also generated in this first step. This first step is only called once at the beginning of the simulation and at each tool change. The second step, Fig. 11.3b, updates the TWE tool mesh and determines average cutting forces based on the nominal feed direction and feed per tooth. The second step of the module is called when the TWE obtained from the ModuleWorks module is updated. The third step, Fig. 11.3c, determines the instantaneous, angle-dependent cutting force based on the tool rotational speed and the current simulation time. Step three is called during for each SAMCEF iteration to access required instantaneous forces.

The mechanical model of the machine tool is coupled with three additional simulation modules (Fig. 11.4). For the CNC modelling, a MATLAB Simulink model that is converted to C-code is used and included in a dynamic library thanks to MATLAB Coder capabilities. As the cutting force module is also based on MATLAB programming, the same approach of creating a dynamic library from C-code generated by MATLAB Coder is selected. The simulation C++ program for tool-workpiece engagement (TWE) computation is also converted to a dynamic library that can be called from C-code functions.

In SAMCEF Mecano, two specific elements have been developed to manage these dynamics libraries. The first one, called DIGI element, allows coupling the mechanical model to any Simulink model and, in particular, control systems. The implemented staggered method is a fixed time step sampling, where both codes will exchange data (positions, forces …). Both codes manage their own time step and can compute several instants between two sampling times without updating exchanged data. This weak coupling is usually stable thanks to the small sampling times imposed by the control loops, which imposes passing times to the Mecano solver.

A strong coupling between the mechatronic model of the machine tool and the machining simulation tool is implemented. Practically, a specific cutting force element, called TOOL element, has been developed. It considers the dynamics of the tooltip combined with the tool-workpiece engagement (TWE) determined from ModuleWorks toolpath generation and simulation libraries. The resulting relative motion of the tool with respect to the workpiece (TP) is used as input to generate cutting forces (CF). These are applied on the machine model at the spindle tip and generate some excitation to the model. To fulfil equilibrium at each step of the time integration process a Newton–Raphson iterative scheme is used, where cutting forces are updated, and the associated iteration matrix is generated at each iteration. As explained in Sect. 2.​1 of this book, the computation of cutting forces is done in a single module that can be called in three different ways. Before starting the time integration (or when the tool is replaced/changed for the considered spindle), the module is initialized. Once the process starts, the TWE is computed for each current individual cut, and the machining module is updated. Finally, the module is called every time that force evaluation is required. Cut definition is obtained from the tool computed kinematics projected in the workpiece reference frame. According to a user-defined cut length, TWE is updated as soon as (Tc time) the tool as moved of this characteristic length since previous update. For accurate TWE computation, the cut length should be chosen significantly bigger than the spatial discretization used in ModuleWorks software. As TWE computation changes the workpiece geometry when a cut is performed, the corresponding DLL can only be called once during the considered cut. The flow chart of Fig. 11.5 has been implemented to combine this constraint with the need of having a strong coupling between the machine model and the cutting forces.

The VMT concept is used for virtual prototyping of machine tools in working conditions. The proposed technology has been applied to build mechatronic flexible multibody models of several machines. This virtual machine tool is fully coupled to a cutting force module. This approach provides comprehensive simulations capabilities for virtual machine tool prototyping in machining conditions. The resulting Twin-Control simulation package is intended for both machine tool builders for design activities and machine tool users to improve their processes. In both cases, this virtual model can be used to avoid performing many costly physical tests.