SAMTECH Group SAMTECH Group Machine Tools Applications Machine Tools Applications August 10, 2004 August 10, 2004 29/06/04, Page 1 SL/04/SAM/MKG_ppt/28an_a
SAMTECH Mechatronic Mechatronic Solution Solution SAMTECH using Finite Element Method using Finite Element Method for the Machine Tools Industry for the Machine Tools Industry 29/06/04, Page 2
Scope of the presentation � What is the problem of High Speed Machine Tools? � Why is it difficult to analyze numerically Machine Tools? � Methodology suited to compute dynamic behavior of vibrating mechanical systems � SAMCEF for Machine Tools � Presentation of examples � Conclusions and future investigations&developments � Questions/Answers 29/06/04, Page 3
What is the problem of High Speed Machine-Tools ? � In order to increase the productivity, it is more and more necessary to increase the velocity of Machine Tools moving parts � If maximum velocities are higher and higher, accelerations are increasing significantly � Accelerations prescribed by controllers are generating huge inertia forces due to the mass of moving parts � If the mass of moving parts is reduced due to the removal of material, there can be a loss of stiffness and thus of precision � Inertia effects are thus major excitations for vibrations of High Speed Machine Tools in working conditions � Vibrations cannot be cut in pieces 29/06/04, Page 4
What is the problem of High Speed Machine-Tools ? In conclusion: � Need of a coherent global model describing the whole dynamic flexible behavior of the Machine Tool (mechanisms + structures + controllers) � Sensitive components are the ones transmitting the vibrations (guideways, linear motors, ball screws…) � These components have to be modeled using advanced numerical computation techniques able to manage the interactions between moving flexible bodies � NL Finite Element coupled with kinematical constraints and large relative motions contact techniques are appropriate to achieve this goal � SAMTECH has been working on this innovative approach since 15 years and brought recently this new powerful and integrated technology to the market, starting with the sector of Machine-Tools 29/06/04, Page 5
Why is it difficult to analyse numerically Machine Tools ? Examples of possible sources of “Non-Linearities” involved in FEM models of Machine Tools: � Large relative displacements & rotations � Linear motors � Ball screw � Guideways � Gearing systems � Belts � Bushings � Friction effects � Interaction with controllers � Visco-elastic material behavior… Need of an implicit unconditionally stable time integration scheme: � Control of time integration error during discontinuities � Reliable description of shocks due to sudden change of motion sense 29/06/04, Page 6
Methodology suited to compute dynamic behavior of vibrating mechanical systems Coupling mechanism and structural analysis Mathematical background r r r r r ⎡ & & ⎤ = = − − M & externa l internal inertia q g ( q , q , t ) g g g Classical non-linear Finite Element equations ⎢ ⎥ r = + internal & ⎣ ⎦ with g C( q ) K( q ) Mixed system of equations in FEM-DOF and Lagrange Multipliers: r r r r r r r ⎡ & & ⎤ + λ + φ = = − − M B T & externa l internal inertia Augmented Lagrangian q ( k p ) g ( q , q , t ) g g g ⎢ r ⎥ form of the equations of φ = ⎣ ⎦ k ( q , t ) 0 motion λ : Lagrange multiplier M: Mass matrix B : Gradient of the constraint matrix p: Penalty factor φ : Kinematical constraints k: Scaling factor Equations are solved iteratively each time integration step: “HHT-Form” ⎧ ⎫ + − α + α = − α + α M & & B T λ B T λ g & g & q ( 1 ) ( 1 ) ( q , q , t ) ( q , q , t ) [ ] + + + + + + α ∈ ⎨ n 1 n 1 n 1 n n n 1 n 1 n 1 n n n ⎬ 0 , 1 / 3 − α φ + αφ = ⎩ ⎭ k ( 1 ) ( q ) k ( q ) 0 + n 1 n HHT-Form of discretised equilibrium equation 29/06/04, Page 7
SAMCEF for Machine Tools Integrated Multi-Disciplinary Solution General integrated environment giving access to different levels of model fidelity and different analysis types from the same CAD based model 29/06/04, Page 8
SAMCEF for Machine Tools scope Suits to all kinds of Machine Tools Translation axis High speed dynamics Parallel C-Frame Gantry Box-In-Box Flexible Screw Linear Motor Rotational axis 29/06/04, Page 9
SAMCEF for Machine Tools Global solution for the modeling of Machine Tools Very general computation scheme 29/06/04, Page 10
SAMCEF for Machine Tools Components of SAMCEF for Machine Tools � Finite Element Analysis using SAMCEF • SAMCEF Mecano : Mechanisms&Non-Linear Dynamic Structure/Contact FE Analysis • SAMCEF Asef : Linear static FE analysis • SAMCEF Dynam : Modal FE analysis + Super-element creation/restitution • Interface between mechanical analysis (mechanisms&structures) and controller design: • Import of MATLAB Simulink controllers inside SAMCEF Mecano • Export of state space (A,B,C,D matrices) from SAMCEF Mecano to MATLAB Simulink • SAMCEF Field : User Friendly CAD Based Modeling and Post- Processing Environment � Optimization of parameterized mechatronic systems using BOSS quattro 29/06/04, Page 11
SAMCEF Mecano Integrated Non-Linear Mechanical Analysis NL Finite Elements (linear motor…) Rigid kinematical joints and S.E. • • SIMULINK SIMULINK • … … • Digital Control Flexible kinematical joints (Sensors and Actuators) (Guideways, flexible ball screw…) 29/06/04, Page 12
SAMCEF Mecano Integrated Non-Linear Mechanical Analysis � Description of all the parts and the connection devices of the mechanical system � Different Model Fidelity levels (rigid body, detailed meshed structure or Super-Element) � Different types of connection devices (rigid or flexible kinematical joints, contact/friction conditions) � “Sensors” and “actuators” to be connected to the digital control boxes � Output of linearized mechanical models for control design 29/06/04, Page 13
SAMCEF Asef & SAMCEF Dynam Linear Analysis � Linear Static Analysis (SAMCEF Asef) � Modal Analysis (SAMCEF Dynam) � Super-Element creation and restitution (SAMCEF Dynam) � Integrated environment with MBS and NL FEA Modal Analysis (SAMCEF Dynam) 29/06/04, Page 14
SAMCEF-Digital Control Interface Communication between SAMCEF and embedded controllers SAMCEF Current Time Mecano Sensor Vector State Variable Next Sample Time Command Vector Control Box Updated State Variables Inputs and outputs of Controllers � Sensor Variables: � Positions, Displacements, Velocities, Accelerations and/or Reaction Forces � Command Vector: � Forces, Displacements, Velocities, Accelerations and/or functions 29/06/04, Page 15
SAMCEF-Digital Control Interface � Controllers can be imported from a Controller Design Software (for example MATLAB Simulink using Real Time Workshop (RTW) to generate C subroutine) � They can also be fully written by the user (open to in-house controllers) � Linked with SAMCEF Mecano 29/06/04, Page 16
SAMCEF-Digital Control Interface � Positions, displacements, velocities, accelerations as well as reaction forces are provided independently by SAMCEF Mecano to the controller � Activation and deactivation times � Several controllers can be used at the same time � The same controller can be used several times � Different schematic boxes (sensors, controllers and actuators) can be connected between them � Prescribed values and gains can be defined through the SAMCEF data set 29/06/04, Page 17
SAMCEF-Digital Control Interface Time step control � The computation time step is bound to the time discretization of the Controller tComp <= t Controller � Automatic time step choice between instants of “Rendez-vous” 29/06/04, Page 18
29/06/04, Page 19 Integrated Modeling Environment SAMCEF Field
SAMCEF Field Integrated Modeling Environment � Modeling defined directly on the CAD geometry � Easy modifications of the modeling fidelity for bodies • Rigid Body • Meshed body with any type of material, including composites • Super-Elements generated by SAMCEF or imported from another FE package � Easy modifications of the modeling fidelity for connections • Ideal kinematical joints • Rigid-flexible contact conditions • Flexible-flexible contact conditions � Easy switch from an analysis type to another one ( SAMCEF Mecano , SAMCEF Dynam , SAMCEF Asef …) � Import of controllers from MATLAB Simulink 29/06/04, Page 20
SAMCEF Field Five modules to manage the global to the detailed analyses 29/06/04, Page 21
CAD creation Geometry import Geometry creation 29/06/04, Page 22
29/06/04, Page 23 Structural elements of a Machine Tool Parameterized components
29/06/04, Page 24 Placement and use Super-Element creation Component creation and use Super-Element model reduction
29/06/04, Page 25 Linear and non-linear data Data definition
Data creation Association of Data, Mechanism, Motion Unit using geometry Guideways: Flexible slider, Bushing… 29/06/04, Page 26
Recommend
More recommend
