L11 Virtual prototyping in machine tool design

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1 Simulation and Control of Production Plants L11 Virtual prototyping in machine tool design Dipl.-Ing. Dipl.-Wirt. Ing. Benedikt Sitte Steinbachstr. 53 B, Room 408 Tel.: 0241/ Aachen, December 2011

2 Structure Integrated Design of Machine Tools inite-element-analysis Structure Optimisation Rigid Multi-Body-Simulation Coupled flexible Multi-Body-Simulation Page 1

3 Structure Integrated Design of Machine Tools inite-element-analysis Structure Optimisation Rigid Multi-Body-Simulation Coupled flexible Multi-Body-Simulation Page 2

Development with virtual Prototypes V2 V1 CONCEPT DESIGN PHYSICAL PROTOTYPE TESTING CHANGE O DESIGN CHANGE O PROTOTYPE SETTING-UP OPERATION TRADITIONAL DEVELOPMENT TIME DEVELOMENT

4 Development with virtual Prototypes V2 V1 CONCEPT DESIGN PHYSICAL PROTOTYPE TESTING CHANGE O DESIGN CHANGE O PROTOTYPE SETTING-UP OPERATION TRADITIONAL DEVELOPMENT TIME DEVELOMENT TIME WITH VIRTUAL PROTOTYPES VIRTUAL PROTOTYPING VERIIKATION CONCEPT DESIGN TIME SAVING START O PRODUCTION PHYSICAL PHYSICAL PROTOTYPE PROTOTYPE TESTING SETTING-UP OPERATION V2 V1 Page 3

5 Integrated Development of Machine Tools Calculation of Components inite-element-analysis and Optimisation Coupled flexible Multi-Body-Simulation z y x Control Loop Drive (1) Control Loop Drive (2) (t) E-Beam-Model of the Spindle x Control Loop M Drive (3) 1. Eigenfrequency f=331 Hz Simulation 2 Measuring lexibility [µm/n] p Co n ce y-axis [mm] Re a on ati x-axis [mm] t li s acceleration Matching of Simulation and Measuring Design Phase 3D-CAD Design and Kinematics Optimisation requency [Hz] Page 4

6 Prototypes in the Development Process virtual real Concept Design Verification + early evaluation of the machine characteristics + fast and easy creation of simulation models + suitable for concept comparisons Ο only rough information about the static/dynamic behaviour Ο neglect of design details + higher accuracy of the simulation results + comprehensive optimisation of a chosen concept little influence on the product costs complicated simulation models high level of required user-specific knowledge + exact information about the static, dynamic and thermal behaviour from measurements necessary for adjustment of the simulation models measures for improvement only effective for following machines Page 5

7 Structure Integrated Design of Machine Tools inite-element-analysis Structure Optimisation Rigid Multi-Body-Simulation Coupled flexible Multi-Body-Simulation Page 6

8 Analysis Types of the inite-element-analysis Analysen der inite-elemente-methode Analysis types of the inite-element-analysis Lineare Statik Linear Static Nichtlineare Statik Non-linear Static Dynamik Dynamic Thermik Thermal linear loaddeformationbehaviour buckling material contact snap through following load linear normal mode analysis response-analysis analysis in time domain (t) crash analysis v r t analysis of steady state temperature fields T(t) = const. analysis of transient temperature fields T(t) const. radiation, convection Q(t) Q(t) non-linear thermal material behaviour Page 7

inite-element-analysis of Machine Tools Ableitung dese- Modells aus

the EA-Model Berechnung des statischen & Optimisation of the n

dynamischen n Calculation & Optimisation of the Maschinenverhaltens

9 inite-element-analysis of Machine Tools Ableitung dese- Modells aus n Defeaturing of the 3D-CAD-Model dem 3D-CAD Modell and setup of the EA-Model Berechnung des statischen & Optimisation of the n Calculation Maschinenverhaltens static behaviour Berechnung des dynamischen n Calculation & Optimisation of the Maschinenverhaltens dynamic behaviour k x k Spring = k y k z c ati St x CAD EM Dy na mi c Page 8

10 Definition of a inite-element-analysis Aims of Analysis static / dynamic deformation behaviour stress distribution temperature fields Boundary conditions foundation fixed points joints prestress temperature x Part Properties part geometry internal joints elastic and thermal Material properties Loads forces, moments heat sources Page 9

11 Steps of the inite-element-model Generation analysis and definition of engineering problem model abstractions partitioning mesh generation clamping and loading E-model generation Page 10

12 Structure Integrated Design of Machine Tools inite-element-analysis Structure Optimisation Rigid Multi-Body-Simulation Coupled flexible Multi-Body-Simulation Page 11

Design Objectives during the Optimisation of Machine Tools Reasons for the use of optimisation software Characteristics of components Dismantling of oversize minimisation of mass Improvement of

13 Design Objectives during the Optimisation of Machine Tools Reasons for the use of optimisation software Characteristics of components Dismantling of oversize minimisation of mass Improvement of mass/stiffness relationship Reduction of maximal stress Maximisation of first nature frequency Manufactory Guarantee of Possibility of manufactory (pour, forge) Reduction of manufactory energy (temperature of pour) Support for technical designer Better product Reduction of coats (saving of material & energy) Optimal damping Optimal nature frequency Even distribution of stress at notch Maximal stiffness Minimal weight of moved parts Minimal coats Page 12

14 Optimisation Methods for the Optimisation of Machine Tools Methods of structural optimisation Parameter Optimisation wall thickness cross section fiber orientation Topology Optimisation optinisation with regard of the casting core draw directions design space Topography Optimisation optimisation of creases and reinforcements Shape Optimisation parameter-oriented optimisation parameter-free optimisation optimisation result source: Chiron / WZL source: Altair source: Altair source: Altair Page 13

Example of a Parameter Optimisation 1 vertical table - bottom 2 vertical table - top 3 pallet carrier 4 pallet 5 column 6 head Sprint Z3 7 fixation 1 Optimisation of a Milling Machine optimisation of

15 Example of a Parameter Optimisation 1 vertical table - bottom 2 vertical table - top 3 pallet carrier 4 pallet 5 column 6 head Sprint Z3 7 fixation 1 Optimisation of a Milling Machine optimisation of the design 2 3 comparison of different design-versions consequent realisation of light weight design 4 parameter optimisation of the wall thickness by the use of inite-element-analysis y x z percent [%] percent [%] optimisation column Start design Optimised design over-all mass optimisation table Start design Optimised design over-all mass 1. eigenfrequency 1. eigenfrequency Page 14

16 Example of a Topology Optimisation Original model Design model Bearings (non-design-space) ixation (non-design-space) CAD-surface model Optimisation results Page 15

17 Example of a Topology Optimisation Original model Design model Bearings (non-design-space) ixation (non-design-space) CAD-surface model Optimisation results Page 16

Example of a Shape Optimisation Load Case: 20 kn longitudinal force Y X Original Part mass: 0.55 kg displacement: 0.63 mm restrictions: displacement < 0.

18 Example of a Shape Optimisation Load Case: 20 kn longitudinal force Y X Original Part mass: 0.55 kg displacement: 0.63 mm restrictions: displacement < 0.8 mm stress < 230 N/mm² 33 % weight reduction Optimised Part mass: 0.37 kg displacement: 0.73 mm E-Model for Optimisation optimised E-Model CAD-Geometry Page 17

19 Structure Integrated Design of Machine Tools inite-element-analysis Structure Optimisation Rigid Multi-Body-Simulation Coupled flexible Multi-Body-Simulation Page 18

20 What is Multi-Body-Simulation mechanical system M An amount of rigid bodies that have mass and inertia properties but can not deform. Constraints define how the parts are attached and how they are allowed to move relative to each other. The motion of a part can be dictated as a function of time or as a function of the relative position of several parts. The motion of the mechanical system is described by algebraic, kinematic equations or by differential equations and external forces whereby the motion is described by a physical law. m, J The kinematic and dynamic behaviour of these mechanical systems are characterised by motions with large amplitudes which results in geometrical non-linearities. These non-linrarities affect the algebraic equation and the differential equation of the mechanical system. Page 19

21 Analysis Options in Multi-Body-Simulation systems Kinematic-analysis Dynamic-analysis Inverse dynamic Static-analysis The motion of the mechanical system is independent of external forces. The variation in time of the absolute or relative position of each part is prescribed. The variation in time of the position, velocity and acceleration of the other parts is calculated by the solution of the non-linear system of equation for the position and the linear system of equations for the velocity and acceleration. Motion of the system caused by external forces. A special case is the calculation of the equilibrium under the effect of external forces which are invariant over time. The motion of the mechanical system under the effect of external forces must be consistent with the equation of motion which is predetermined by joints. The dynamic-equations are differential equations or a combination of differential equations and algebraic equations. Hybrid form of the dynamic- and kinematc-analysis. The variation of time of one or several bodies of the mechanical system is dictated and is leading to a complete determination of the position, the velocity and the acceleration of the system. Afterward the algebraic equations of motion are solved by the use of the known positions, velocities and accelerations to determine the forces which causes these motions. The static-analysis determines the position of the mechanical system where the acceleration of the parts which are burdened by external loads and gravity is minimal. The resulting position is the position of equilibrium. Page 20

Applications of the Multi-Body-Simulation in the Machine Tool Design Guiding-systems

Modelling of guiding-systems, ball-screwspindles and bearings as flexible connectors, such

The physical properties of these elements can be linear or non-linear.

22 Applications of the Multi-Body-Simulation in the Machine Tool Design Guiding-systems Spindles Modelling of frame components as rigid bodies or flexible bodies. Modelling of guiding-systems, ball-screwspindles and bearings as flexible connectors, such as spring-dampers and bushings. The physical properties of these elements can be linear or non-linear. δ Modelling of the feed drives by the use of a closed control loop. Bearings Static-analysis: Deformation at the tool centre point caused by static forces (e.g. cutting process) Dynamic-analysis Deformation at the tool centre point caused by dynamic forces (e.g. cutting process) Deflection at the tool centre point by proceeding along a programmed path. (dynamical path variation) Page 21

23 Structure Integrated Design of Machine Tools inite-element-analysis Structure Optimisation Rigid Multi-Body-Simulation Coupled flexible Multi-Body-Simulation Page 22

24 The mechatronical System Machine Tool Mechanic Process Product requirements Requirements on Machine Tools high static and dynamic stiffness high dynamic Control loop properties of the feed drives high accuracy low path deflections Page 23

25 Dynamic lexibility Behaviour of Machine Tools Page 24

26 Model Assembly in Multi-Bodies-Simulation System generation of the several flexible bodies of the machine (Step 1 to 6) generation of the guideways, bearings and mounting element with flexible connectors (Step 7) Order of the Modelling in the MBS-System 5 Bushing Element 7 6 Page 25

27 Craig - Bampton Theorem for the Modelling of flexible Bodies Boundary-conditions of the E-Model for the calculation of the Craig- Bampton - Modes Constraint modes z y x x x ixed-boundary normal modes Page 26

nut stiffness GUIDING SYSTEMS k D { } = [ k] { u} + [ D] { u& } + {

28 Modeling of mechanical Components DRIVES fixed bearing L(t) k D + + E A k =,D L ball screw spindle + M k D 2 π h a = M h spindle nut nut stiffness GUIDING SYSTEMS k D { } = [ k] { u} + [ D] { u& } + { } v MOUNTING DEVICES k D { } = [ k] { u} + [ D] { u& } + { } v Page 27

29 Coupling of the MBS-Model and the Control Loops force excitation TCP control loop of the direct drive (x-y) K R a,t el Regelkreis des linken a Regelkreis K R A Linearmotors,T el desk i,t ni ia u A isoll linken x ist s - x Linearmotors ist - eis K i,t ni i soll - Stromregelkrei K p,t np K p,t np control loop of the direct drive (x-y) a K E KL Geschwindigkeitsregelkr - - current Lageregelkreis controller K v - - s soll 1 ssoll 2 orce 0 x ist x ist velocity controller position controller Displacement 0 Time 1,0 displacement TCP 0 0 Time 1,0 y z x flexible multi-body model control loop of the ball screw drive (z) K M i A M M n ist z ist R A,L A K E u A K i, T ni i soll K p,t np i ges K L z soll current controller velocity controller position controller Page 28

30 Simulation of a requency Response unction Z-Axis K M =0,93 Nm/A K L =70 1/s K P =2,71 Nms/rad T np =10 ms Lineardrive K =103 N/A K L =70 1/s K P =3500 As/m T np =8 ms Simulation Results simulation of frequency response functions (R) lexibility [µm/n] with control loop without control loop estimation of interactions between mechanical structure and control influence of the controller parameters on the dynamic behaviour at the tool centre point (TCP) overshooting of the feed drives 0 requency [Hz] Page 29

Simulation of a Positioning Operation jerk acceleration Positioning operation of the Z-unit (5mm) [m/s³] 0 [m/s²] 0 M (t) [m/s] 0 0 0 Time

31 Simulation of a Positioning Operation jerk acceleration Positioning operation of the Z-unit (5mm) [m/s³] 0 [m/s²] 0 M (t) [m/s] Time velocity Time [m] Time position Time Input control loop z-axis control loop linear drive 1 =0 control loop linear drive 2 = 0 (t) (t) Page 30

32 Results of the Simulation of a Positioning Operation Displacement [mm] displacement T 3 Þ f 3 r=730 m/s³ r=650 m/s³ r=550 m/s³ r=450 m/s³ desired path lexibility [µm/n] R G xx G yy G zz Time [sec] l f 3 = 61,0 Hz Excitation of the third è Excitation of the third eigenfrequency of the of the machine requency [Hz] Page 31

Expedient Modeling of Ball Screw Feed Drives

S. Frey a A. Dadalau a A. Verl a Expedient Modeling of Ball Screw Feed Drives Stuttgart, February 2011 a Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), University of