All CAD and analysis data used or created in the learning tasks are stored in an archive file, that can be downloaded via the Internet see following link and should be used to reproduce
Trang 2Peter Binde
Simulations with NX
Kinematics, FEA, CFD, EM and Data Management With numerous examples of NX 9
Trang 3Peter Binde, Dr Binde Ingenieure, Design & Engineering GmbH, Wiesbaden
Translated by the authors with the help of Dimitri Albert, Jan Helge Bøhn, Martin Geyer and
Andreas Rauschnabel
Distributed in North and South America by Hanser Publications
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All rights reserved No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, with- out permission in writing from the publisher.
© Carl Hanser Verlag, Munich 2014
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Trang 4Preface 1
1 Introduction 3
1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book 5
1.2 Work Environments 7
1.3 Working with the Book 8
2 Motion-Simulation (Multibody Dynamics) 11
2.1 Introduction and Theory 11
2 1 1 Simulation Methods 12
2 1 2 Restrictions 14
2 1 3 Classifications of MBD 14
2.2 Learning Tasks on Kinematics 15
2 2 1 Steering Gear 15
2 2 2 Top-down Development of the Steering Lever Kinematics 33
2 2 3 Collision Check on Overall Model of the Steering System 50
2.3 Learning Tasks on Dynamics 59
2 3 1 Drop Test on Vehicle Wheel 59
2.4 Learning Tasks on Co-Simulation 68
2 4 1 Balancing a Pendulum 68
3 Design-Simulation FEM (Nastran) 79
3.1 Introduction and Theory 80
3 1 1 Linear Statics 81
3 1 2 Nonlinear Effects 83
3 1 3 Influence of the Mesh Fineness 85
3 1 4 Singularities 86
3 1 5 Eigenfrequencies 87
3 1 6 Heat Transfer 89
3 1 7 Linear Buckling 90
Trang 53.2 Learning Tasks on Design Simulation 90
3 2 1 Notch Stress at the Steering Lever (Sol101) 91
3 2 2 Temperature Field in a Rocket (Sol153) 139
4 Advanced Simulation (FEM) 149
4.1 Introduction 150
4 1 1 Sol 101: Linear Static and Contact 151
4 1 2 Sol 103: Natural Frequencies 151
4 1 3 Sol 106: Nonlinear Static 152
4 1 4 Sol 601/701: Advanced Nonlinear 152
4.2 Learning Tasks on Linear Analysis and Contact (Sol 101/103) 154
4 2 1 Stiffness of the Vehicle Frame 154
4 2 2 Size and Calculation of a Coil Spring 185
4 2 3 Natural Frequencies of the Vehicle Frame 199
4 2 4 Clamping Seat Analysis on the Wing Lever with Contact 207
4.3 Learning Tasks Basic Non-Linear Analysis (Sol 106) 229
4 3 1 Analysis of the Leaf Spring with Large Deformation 229
4 3 2 Plastic Deformation of the Brake Pedal 239
4.4 Learning Tasks Advanced Nonlinear (Sol 601) 249
4 4 1 Snap Hook with Contact and Large Deformation 249
5 Advanced Simulation (CFD) 271
5.1 Principle of Numerical Flow Analysis 272
5.2 Learning Tasks (NX-Flow) 273
5 2 1 Flow Behavior and Lift Forces at a Wing Profile 273
6 Advanced Simulation (EM) 297
6.1 Principles of Electromagnetic Analysis 298
6 1 1 Electromagnetic Models 299
6 1 2 Maxwell Equations 300
6 1 3 Material Equations 302
6 1 4 Model Selection 303
6 1 5 Electrostatics 306
6 1 6 Electrokinetics 306
6 1 7 Electrodynamics 306
6 1 8 Magnetostatics 307
6 1 9 Magnetodynamics 307
6 1 10 Full Wave (High Frequency) 307
6.2 Installation and Licensing 308
Trang 66.3 Learning Tasks (EM) 310
6 3 1 Coil with Core, Axisymmetric 311
6 3 2 Coil with Core, 3D 326
6 3 3 Electric Motor 330
7 Management of Analysis and Simulation Data 351
7.1 Introduction and Theory 351
7 1 1 CAD/CAE Integration Issues 351
7 1 2 Solutions with Teamcenter for Simulation 352
7.2 Learning Tasks on Teamcenter for Simulation 354
7 2 1 Carrying out an NX CAE Analysis in Teamcenter 355
7 2 2 Which CAD Model Belongs to which FEM Model? 362
7 2 3 Creating Revisions 365
8 Manual Analysis of a FEM Example 371
8.1 Task Formulation 371
8.2 Idealization and Choice of a Theory 372
8.3 Analytical Solution 372
8.4 Space Discretization for FEM 373
8.5 Setting up and Solving the FEA System of Equations 374
8.6 Analytical Solution Compared with Solution from FEA 376
Bibliography 379
Index 383
Trang 7Virtual product development has gained significant importance in particular through the integration of 3D solid based modeling, analysis and simulation Supported by the rapid enhancement of modern information and communication technology application inte-grated virtual product development has become an essential contribution in higher engi-neering education, continuing education as well as in industrial advanced and on-the-job training.
Since 2003 Technische Universität Darmstadt has been selected and approved as PACE university and has become a part of the international PACE network PACE stands for
Partners for the Advancement of Collaborative Engineering Education and is a sponsoring
program initiated by General Motors Corp (in Germany Adam Opel GmbH) PACE is driven by General Motors Corp., Autodesk, HP (Hewlett Packard), Siemens, Oracle, and further well acknowledged companies of the virtual product development branch (www pacepartners.org) Donations and sponsoring through the PACE partner companies has
facilitated the preparation and the publishing of this book
This publication has been developed based on cooperation between Dr Binde nieure – Design & Engineering GmbH (www.drbinde.de) and the Division of Computer
Inge-Integrated Design within the department of Mechanical Engineering of Technische versität Darmstadt (www.dik.maschinenbau.tu-darmstadt.de).
Uni-We thank very much Mr Haiko Klause for his support to chapter 7 and Mr Andreas chnabel for his contribution to the Motion and FEM examples for Version 9 of the CAD system NXTM Furthermore we are grateful for the support of Carl Hanser Verlag, mainly Mrs Julia Stepp A very special thank you is dedicated to Prof Dr Jan Helge BØhn who supported us through his excellent cross-reading Last but not least we thank all readers who encouraged us to prepare this book also in English
Raus-We wish all readers and users a successful application of the selected examples and fully a beneficial knowledge acquisition usable for both, the successful graduation and the successful knowledge application during the industrial career
hope-August 2014
Prof Dr.-Ing Reiner Anderl
Dr.-Ing Peter Binde
Trang 81 Introduction
Engineering science has seen significant changes take place during the past two decades
These changes have been driven by a powerful development of information and
commu-nication technologies and their introduction into both the product development process
and the products themselves In essence, it has enabled computer integrated virtual
prod-uct development, complete with integrated 3D modeling, analysis, simulation, and
optimi-zation
The primary goal of virtual product development is the efficient development of
innova-tive product solutions that satisfy the customers’ needs Consequently, the integration of
computer-based methods into the digital workflow of the product development process
has become critical to the success of virtual product development
Engineering, designing, and detailing are all essential tasks for the development of
inno-vative product solutions, as is the ability to accurately predict the product’s behavior
subject to the multitude of potential use cases and operating conditions Fortunately, with
the continuous improvement of information and communication technologies, and with
the subsequent improvements in integration of computer aided design, analysis,
simula-tion, and optimizasimula-tion, it has become increasingly easier to complete these essential
prod-uct development tasks
Information and communication technologies (ICT) are increasingly influencing the
prod-uct development process, especially as the process becomes increasingly virtualized This
influence results from:
Rapid information acquisition from sources worldwide;
Availability of new computer-based methods for product development and design –
such as for product modeling (e. g., parametric, feature based, and knowledge-driven
CAD); analysis, simulation and optimization (e. g., finite element analysis (FEA),
multi-body simulation (MBS), and computational fluid dynamics (CFD)); rapid validation and
verification (e. g., digital mock-up (DMU)); rapid prototyping (e. g., virtually by using
vir-tual and augmented reality, or physically by using generative manufacturing machines);
and processing product data in successive process chains (so called CAX processes); and
Mapping of the organizational and workflow structures within product data
manage-ment (PDM) systems, with the aim to provide easy, intuitive, and immediate access to
development status, progress, and results
Impact of information and communication technologies on product development
Trang 9The concept of virtual product development has clearly been shaped by the deep tion of ICT into the product development process, to provide seamless flows of product data Virtual product development can be systematically achieved over an escalating set
penetra-of levels (see next figure) These levels consist penetra-of:
Assembly-+ information + Functionalinformation
Assembling-+ Material+ (SoftwareLogics)
+ Production+ Controlling+ Logistics+ Finances+ Marketing
Virtual Prototype/
Virtual Product
Virtual Factory
Product Data Management
3D CAD is the fundamental basis for describing product geometry; usually modeled as solid geometry These digital product descriptions involve single-part modeling as well as assembly modeling, and generally describe a product structure This modeling is typically parametric and feature-based
Digital mock-ups (DMU) provide a visual representation of the product structure, ing the part and assembly geometries These geometries are typically approximated using triangles When the part and assembly models are represented as solids, and comple-mented by material data, then mass properties, such as mass and center of gravity, can be estimated Digital mock-ups enable virtual prototyping for simulating assembly and dis-assembly processes, and for investigating collision detection
includ-Virtual prototypes – often referred to as digital prototypes – include material and physical properties in addition to part geometries and product structures These prototypes can therefore be used to simulate the functional and physical behavior of a product while
Levels of virtual product
development
3D CAD is the
fundamental basis
DMU
The most important
simulation methods are
FEA, MBS and CFD
Trang 10visualizing its behavior The functional and physical modeling within a virtual prototype
tends to be application and discipline specific Typical applications include stress analysis
using finite element analysis (FEA) based on the finite element method (FEM), multi-body
simulation/dynamics (MBS/MBD), or fluid dynamic simulation using computational fluid
dynamics (CFD) Simulations may also integrate thermal analysis, electromagnetic
analy-sis (EM), or kinematic analyanaly-sis, or their combinations, usually based on FEA, to more fully
investigate and understand the product behavior
The term virtual product refers to the aggregation of a product’s physical properties
to-gether with its logical dependencies to produce a comprehensive, interoperable product
model
The term virtual factory refers to the digital representation of a factory, including its
physical properties and manufacturing processes The objective is to facilitate simulation,
analysis, and optimization of factory operations, including material flows, logistics, and
order processing
Product data resulting from the application of the various modeling, analysis, simulation
and optimization software systems is stored as files in the product data management
(PDM) system, enhanced by meta-data representing organizational and workflow
informa-tion such as release status, effectivity, identificainforma-tion, classificainforma-tion, and version numbers
The increasing use of 3D CAD in industry leads to an increasing need to integrate
nu-merical analysis, simulation, and optimization methods and tools With this integration,
product data, once it is described or generated, can then be used and reused in successive
processes to avoid manual reentry errors, and to identify errors and mistakes early This
in turn enhances product quality and increases the efficiency of the virtual product
devel-opment process and successive physical product realization
■
■ 1.1■ Learning Tasks, Learning Objectives,
and Important Prerequisites for
Working with the Book
Based on the objective to use 3D CAD data for analysis, simulation and optimization, the
question of how 3D CAD data can be further used follows For this purpose representative
example scenarios for the procedures of the finite element method, the multi-body
simula-tion, fluid dynamics and the electromagnetic simulation have been developed in this
book, by which the integration of modeling, analysis and simulation will be presented
The here outlined scenarios are based on the 3D CAD system NX9 and its integral
analy-sis and simulation modules
To facilitate understanding the methodology and to shorten the training period, a single
contiguous assembly was chosen for most learning tasks of this book This is the CAD
model of the legendary Opel RAK2 that was created in student projects as a 3D CAD solid
The PDM system manages all product data generated through virtual product develop- ment
The training content is taught on the basis of methodology examples
Trang 11model in the past at the Department of Computer Integrated Design (DiK, TU Darmstadt), for which to take this opportunity, any party shall be gratefully acknowledged.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
In 1928, Fritz von Opel, grandson of Adam Opel, built the rocket driven cars RAK1 and RAK2 for testing purposes With RAK2 he reached a speed record of 238 km/h on the AVUS, the Berlin high speed track, on 23/05/1928 The RAK2 was powered by 24 solid-
The CAD model of the
Opel RAK2 forms the
basis for learning tasks:
The figure shows some
sample images
Trang 12fuel rockets, which were filled with 120 kg of fuel This attempt to establish the rocket
engine was followed by further attempts by road, rail and air
All CAD and analysis data used or created in the learning tasks are stored in an archive
file, that can be downloaded via the Internet (see following link) and should be used to
reproduce the examples
The following Internet link must be used to download the archive file This
file contains all CAD models, analysis and result files Furthermore, the
installation files for the electromagnetic solver are included in this file The
size is 188 MB
download link: www.drbinde.de/index.php/en/203
The training content is taught using practical examples Functions of the NX system are
therefore not explained isolated, but always in connection with an example Since this is
similar to learning from real-world projects, this method is efficient, memorable and
mod-ern didactic
The chapters are structured in a way that follows the didactic concept of continuous
learning progress, but also build on the fundamentals of working with 3D CAD, in
par-ticular the system NX9 Therefore, knowledge of the construction of 3D parametric
mod-els and assemblies as well as general technical understanding is required, as it is usually
taught in technical vocational education
The learning objective is to convey to the student designer or analysis engineer the
knowl-edge that he or she needs to solve simple tasks using the finite element method, multibody
simulation, and flow simulation within NX itself, and to develop an understanding of these
technologies in general However one must not expect that complex practical problems
can immediately be solved using the intermediate level of knowledge presented in this
book This would be an excessively high claim that would be placed on the book Instead,
a novice develops into an expert by working through as many as possible practical tasks
and thereby collects valuable experience His experience thus results from successfully
developed projects This book, with its learning examples, provides important basic
expe-riences and thus forms the basis for a systematic expandable wealth of experience
■
■ 1.2■Work Environments
Engineering simulation problems can be subdivided into four classes: rigid bodies, elastic
bodies, fluids, and electrical/magnetic bodies Rigid body systems are simulated using
Multibody Dynamics programs (MBD); elastic and also electric/magnetic bodies are
simu-lated using the Finite Element Method (FEM); and flow tasks are simulated using
Computa-tional Fluid Dynamics (CFD).
Prerequisites for working with the book
Objective is to build a fundamental wealth of experience
Trang 13Technical Simula on
Rigid Bodies Elas c Bodies Fluids Electric Bodies Rigid Body Mechanics Structural Mechanics Fluid Mechanics Electromagne cs (EM)
(Mul body Dynamics) (Finite Element (Computa onal (Finite Element
Method) Fluid Dynamics) Method)
Within the NX system there are several modules for engineering simulation The three most important ones used in this book are (in addition to some others that are not covered here):
Motion Simulation for kinematic and dynamic motion simulations with MBD;
Design-Simulation FEM for simple structural, thermal, and eigenfrequency analysis; and
Advanced Simulation for complex simulation tasks: This module is intended for
engi-neers that focus on analysis Additional simulation capabilities include modeling and simulation of complex assembly structures and the choice of various solvers for ad-dressing particular physical phenomena The problem domains that can be addressed include structural mechanics, thermodynamics, fluid mechanics, and electromagnetism (EM)
The working environments for these modules have a common interface, and default to only include those features that are useful in the selected context
This book looks in detail at these working environments Possibilities and limitations will
be illustrated by examples
■
■ 1.3■Working with the Book
The book is organized into chapters as follows:
Motion Simulation,
Design Simulation,
Advanced Simulation (FEM),
Advanced Simulation (CFD),
Advanced Simulation (EM), and
manual analysis of an FEM example
First, we will explore motion simulation (Chapter 2) because this class of analysis is mon in engineering design and is usually carried out first The joint forces that are deter-mined here are often used in subsequent strength analysis using FEM
com-Technical simulation can
be roughly divided into
four parts
The CAD system NX
pro-vides three modules for
technical simulation
Structure of the book
The joint forces are
calculated in Motion
Simulation
Trang 14The chapters can be largely worked through independently That means, those who do not
care for motion simulation, can skip that chapter The one exception is that those
inter-ested in FEM and “Advanced Simulation (FEM)” (Chapter 4), should first read “Design
Simulation FEM (Nastran)” (Chapter 3) to attain the necessary prerequisites
At the beginning of each chapter an introduction to the principles of each topic is given
For the analysis newcomer these statements might sound very theoretical and difficult
But this should not discourage you to begin with the learning tasks on this subject, on
which the focus lies Explanations in the learning tasks usually build on the principles of
the introductions, clarify and expand them A hurried reader therefore can skip these
introductions, and go straight to the learning tasks
The download files belonging to this book (www.drbinde.de/index.php/
en/203) contain the RAK2 folder This includes all outlined learning tasks
to the areas motion, structural, thermal, and flow simulation A second
folder named EM contains installation files and examples for
electromag-netics There are also solution files in the download file available so that
any result can be looked up in it For working through the book this entire
file should be unpacked and copied to a directory on the hard disk of the
computer
The learning tasks of a chapter can best be worked through in the order given, because
all learning content builds on each other In Motion and Design Simulation, as well as EM,
each first learning task is a basic example All important principles and foundations are
taught here, which are necessary to understand and build the following learning tasks
When describing the learning tasks, there is a distinction between background
explana-tions and steps to be carried out (mouse clicks in NX) Steps to be carried out are always
marked with the pin icon:
ÍHere a step to be carried out is described
Very hurried readers can therefore skip the background explanations (hopefully, they
understand intuitively quite a bit) and jump straight from one pin icon to the next
To work through the learning tasks, a computer with NX installation must be available
The examples were calculated by NX9, but should also work in other NX versions e. g
NX8.5 or 10 With a normal installation of NX9, all required modules for simulation,
espe-cially the NX Nastran solver, are automatically installed It is, other than with previous
NX versions, no longer required to define specific environment variables for the
simula-tion manually
Only for electromagnetic simulation (Chapter 6) the installation of some additional files is
required But this is explained at the beginning of the chapter
In addition, the computer hardware should preferably be well equipped We would like to
give the following recommendations:
Processor: The highest possible clock frequency is essential for all simulation problems
A hurried reader can also directly start with the examples
In each case the first example is of fundamen- tal nature
Pin icons indicate steps
to be performed
NX installation and computer performance
Trang 15Multi-Processor: For FEM analyses and some thermal analysis, the use of multiple cessors is supported.
pro-Memory: FEA, thermal and fluid flow analysis need a lot of memory There is a simple rule: the more, the better To work through the examples in this book, we recommend
at least 4 GB of main memory
Hard drive: Again, There should be enough free disk space available For the examples
in this book we recommend at least 2 GB
32-/64-Bit Operating System: For medium to large analysis models 64-bit architecture must be selected, since much more memory can be addressed here The EM installation will only run on 64-bit systems
For more information on these topics, we recommend reading the documents [nxn_paral] for parallel-processing and [nxn_num] for efficient memory usage with NX/Nastran.For motion analysis there are two solvers available: Adams and RecurDyn The learning tasks of this book were carried out with the RecurDyn solver, but can also be run with Adams
Well, our introduction is now complete We wish you fun and success in learning!
Bibliography
[nxn_num] NX Nastran Numerical Methods User’s Guide Online-Documentation to NX
Nastran[nxn_paral] NX Nastran Parallel Processing User’s Guide Online-Documentation to NX
NastranPresetting the motion
solver
Trang 162 Motion-Simulation
(Multibody Dynamics)
In Section 2.1, first the theory, limitations, special effects, and rules of this discipline are
represented This is followed by kinematic learning tasks, which first start with a basic
example (Section 2.2.1) In the second learning task, principle sketches and kinematics
are used to support the early design phase (Section 2.2.2) In the third task, collisions and
assembling of various sub-kinematics are treated (Section 2.2.3) The fourth learning task
deals with dynamic problems and the simulation of contact (Section 2.3.1) and the final
task deals with the coupling of NX-Motion with MATLAB® Simulink® for the so-called
co-simulation (Section 2.4.1)
■
■ 2.1■Introduction and Theory
Motion simulation offers the designer the ability to control the movements of his or her
otherwise statically constructed machine This allows that a better understanding of the
machine can be obtained and it can be checked whether the movement of the
compo-nents leads to collisions It also can be checked if the machine can carry out the desired
movement, or even reach certain positions Often one of the tasks is to adjust the
geo-metrical dimensions suitable The use of parametric CAD is often an important way to
create variants
But also and especially in the early stage of the design process when only first rough draft
designs are available, the use of kinematic analysis is very useful Using the motion
simu-lation application, principle sketches or simple curves can be moved and their
dimen-sions can be optimized Thus, the sketches of the early design phase become
movement-based control sketches In the further design process, the kinematic models can be used
over and over again to check the latest state of the mechanism
As soon as mass properties are assigned to the CAD geometry, motion analysis can be
extended to dynamic analysis In this case bearing forces, velocities and accelerations can
be determined Therefore motion analyses are often preparations for subsequent FEM
analyses because the FEM use bearing forces as boundary conditions Based on the
re-Content of the chapter
Use cases and benefits
of motion simulation in practice
Mass properties of the components expand the area into the dynamics
Trang 17sults (forces and translations) it is possible to choose springs, dampers, additional masses, vibration absorbers, bearings (load capacity) etc from supplier catalogs.
Users of motion simulation should have experience in modeling parts and assemblies with the NX system This is necessary because the examples in this chapter do not only use finished assemblies, but partly also make changes in the construction methodology necessary However, no further previous experience is required
Motion simulation covers the part of the mechanics that deals with rigid bodies Usually there is a plurality of rigid bodies that are connected to each other by joints Such prob-lems appear, for example, in chassis of automobiles The software for the analysis of such tasks is denoted by the term MBD program. MBD means Multibody Dynamics.
Technical Simula on
Rigid Bodies Elas c Bodies Fluids Electric Bodies Rigid Body Mechanics Structural Mechanics Fluid Mechanics Electromagne cs (EM)
(Mul body Dynamics) (Finite Element (Computa onal (Finite Element
Method) Fluid Dynamics) Method)
Within the CAD model, the user defines moving rigid bodies (links), joints, drivers, and possibly external forces or constraints Even springs and dampers may be involved
Definition of links
Creation of geometry joints and driversDefinition of Solving the solution Post processing of results
Links are usually defined using CAD geometry (components and assemblies) In addition, the CAD system, with its powerful capabilities, can also be used to define, for example, cams or other control elements
2.1.1■Simulation Methods
It is difficult to generalize how MBD methods work because the different solvers, ing RecurDyn and ADAMS, work quite differently For a detailed description on ADAMS, see [adams1]; and for a detailed description on RecurDyn, see [RecurDyn1]
includ-Internally, the moving bodies, joints and drivers are converted into a mathematical tem of differential equations, which is then solved to determine the desired quantities This includes the displacements, velocities, and accelerations of the moving bodies and joints, as well as the reaction forces at the joints
sys-Each component that is defined as moving body has to be cut free, and six dynamic tions (describing forces and accelerations) and six kinematic equations (describing posi-tions and velocities) in the translational and rotational directions are established These equations thus form a system of equations describing the motion
equa-Subdivision of technical
simulation in four fields
Process steps in the
MBD analysis
Additional literature
Trang 18The number of unknowns in the system of equations can be reduced by adding
con-straints Each joint that restricts the possibility of movement of two bodies may be
ex-pressed in the form of additional equations in the system of equations For example, a
revolute joint between two moving bodies leads to a reduction of five unknowns in the
system of equations because only one rotational degree of freedom remains where once
there were six
gm1
m2
Motion drivers, which define the displacement, the velocity or the acceleration, also
re-duce the degrees of freedom (DOF) A rotational driver, for example, with an enforced
speed of 360 deg/sec, reduces the number of DOF by one On the other hand, forces and
torques, appearing on the motion model, neither bring additional unknowns into the
sys-tem nor reduce the count of DOF
That way, the count of the DOF is reduced either to zero (in which case the system of
equa-tions can be solved directly) or to a number greater than zero In the second case, the
system can be solved by adding initial conditions and integrating the equations over the
time In the case of zero degrees of freedom, we have a kinematic system; otherwise we
have a dynamic system to be solved
It also should be noted that the resulting system of equations is either linear or nonlinear,
depending on the correlations in the system that the various types of joints introduce
While simple types of joints such as revolute, slider, or spherical joints behave linearly,
complex joints such as the point on curve connections require nonlinear equations Linear
equation solvers – as they are usually used for FEM – are therefore not used for solving
MBD systems For MBD rather such solvers with ability to reduce the order are used
After solving the system of equations, the following variables are available for
post-pro-cessing:
translational velocity
rotational velocity
A differential system of equations is set up
Drivers and constraints reduce the number of unknowns
Some kinds of joints cause nonlinearity in the system of equations
Trang 19coordinates of center of gravity
orientation angles
applied, external Forces
Forces in joints and constraints
2.1.2■Restrictions
A very basic property and restriction of MBD is given by the rigidity of the considered body A link can be moved in space, but cannot be deformed For MBD, real bodies are reduced to their mass and inertia properties and their geometrical dimensions, while their deformation properties are neglected This is the fundamental difference from the structural mechanics, which uses FEM to consider flexible bodies, including their defor-mations and stresses The disadvantage of linear FEM compared to MBD is that no move-ments and only small deformations can be simulated The assumption of rigidity in the motion links in MBD therefore has the advantage of simplifying the analysis and reducing the computational effort, thus enabling even complex motions of large assemblies to be analyzed
In reality, however, there are some effects that are difficult to model using MBD These include clearance, tolerance, and flexibility Because such effects are often not taken into account in the MBD model, in some cases it may appear, for instance, that a clamping situation has occurred, when in reality there is a slight clearance in the joints or there is some flexibility in the body to ensure motion without any problems
Clearances can be considered in MBD as well, but then the corresponding parts must be considered dynamic and the contacts with restoring forces must be modeled If so, the system will have open degrees of freedom, which will make the problem significantly more difficult to solve
2.1.3■Classifications of MBD
For a classification of motion simulation we refer to the classification of mechanics as it is, for example, described in [HaugerSchnellGross] Accordingly, the mechanics may be di-vided into kinematics and dynamics.
The kinematics is the science of the temporal and spatial movement, without regarding
forces as a cause or effect of the movement The dynamics, however, deals with the
inter-action of forces and movements It is divided into the statics and kinetics The statics deals
with the forces at stationary bodies (e. g., a truss in equilibrium), while the kinetics ines actual movements under the effect of forces
Trang 20Technical Simulaon
Rigid Bodies Elasc Bodies Fluids Electric Bodies
Rigid Body Mechanics Structural Mechanics Fluid Mechanics Electromagnecs (EM)
(Mulbody Dynamics) (Finite Element (Computaonal (Finite Element
Method) Fluid Dynamics) Method)
Degrees of freedom = 0 Forces and moons
Forces without moons Degrees of freedom > 0
All these phenomena can be analyzed with NX Motion, with the restriction of rigid bodies
in the MBD Furthermore, starting with version NX 7.5, it has also been possible to take
into account single flexible bodies in the MBD These bodies must be prepared in advance
using FEM, which means that the stiffness matrix must be determined (in reduced form)
and included as Flexible Body in the MBD system.
Kinematic systems are characterized by the fact that all degrees of freedom of a moving
body are determined This determination may be made either by joints or by driver rules
Such systems are predictable to a certain extent, and can also be referred to as
motion-driven systems (tied movement)
Kinetic systems are available if one or more degrees of freedom are undetermined The
motion then results from external forces (untied movement) For example, the force of
gravity can lead to a swinging movement of a lever with rotational DOF Kinetic systems
are therefore also known as power-driven systems
■
■ 2.2■Learning Tasks on Kinematics
2.2.1■Steering Gear
This basic example will explain the most important issues that are necessary for a simple
motion analysis using the NX system The example will take the user through the process
of generating links (the motion bodies in NX) and basic joints, and uses the articulation
function as the driver since it is well suited for purely kinematic motion simulations In
addition, the function for dynamic analysis will be used as a method for detecting
indefi-nite degrees of freedom
Classification of MBD Simulations
Flexible bodies are a special case
Determined and undetermined degrees
of freedom
Trang 21This kinematic model is here first created as a single mechanism In a later example, this mechanism will be modularly assembled with other mechanisms to form a larger motion model.
This basic example should be performed by everyone who wants to work with NX Motion
2.2.1.1■Task
A designer has redesigned the levers for the steering gear Now he or she has to check if collisions occur Therefore, a kinematic model must be created that allows the rotational movement of the steering wheel, and (associated with it) of the pitman arm
In this task, the steering gear of the RAK2 and its steering wheel and pitman arm are used The steering gear is accommodated in a housing and connects the steering wheel with the pitman arm
For this task, the simulation should only be used for visual control, however, the tion of minimum distances to other components, the study of the resulting reaction forces
examina-in the joexamina-ints and collision checks would be possible examina-in further analyses
In the following section some principles are explained at first Thereafter, the solution steps for this task are presented Very urgent readers can skip the next section and move straight to the creation of the model (see Section 2.2.1.4)
2.2.1.2■Overview of the Functions
In the kinematics application (Motion Simulation) the kinematic or kinetic model is
estab-lished and the simulation is performed and evaluated The following figure shows the
Motion toolbar that appears after changing to the module The toolbar contains all the
main features of the Motion module that are used Usually, this toolbar is along the left
edge of the NX window
The aim is to control
the design
Trang 22The following is an overview of the main functions of the Motion module, which already
refer to the later use Very hurried readers can skip this section and proceed immediately
to the creation of the model (Section 2.2.1.4)
The function Environment allows the basic setting of the system for kinematic or
kinetic properties (herein called Dynamics) For our task, we will adjust “Dynamics”,
although it is actually a kinematic model The reason for this approach is, that the user
has more possibilities, which contribute to a better understanding and error
identifica-tion In addition, advanced solution options can be selected in the Environment function,
for example the option of Co-Simulation to use control engineering elements with
MATLAB Simulink, the Motor Driver option for accessing electric motor libraries or the
option of Flexible Body Dynamics The option Component-based Simulation is suited for
assemblies, because it activates the filter for assembly components when generating
moving bodies
In addition to the links, the user defines joints, which specify how the connected
links can be moved In this context the function Driver is also used, which is
neces-sary to drive the joints If the Joint function is opened, you can find a lot of different joint
types as a selection These are the most important joints:
The Solution function must be activated by the user to specify the type of solution
that is desired The options include the Normal Run, the Articulation, and others.
The main elements for the definition of the motion model are the moving bodies
(links) With this function the user defines which geometry or component should be a
part of the moving system
In addition to the links, joints are defined by the user, which describe the possible
movement of the links to each other or to the environment In this context, the Driver
function also is used to define a constant or time depending driver on a DOF of the
joint If the Joint function is selected, a lot of different joint types are listed These are
the most important joint types:
Overview and brief explanation of the main functions for NX Motion Simulation
Trang 23 The revolute joint only allows a rotation.
The slider allows a translational displacement between two parts or one part
and the environment
The cylindrical joint allows the rotational and translational displacement along
one axis
The screw forces a rotation if a part is displaced in translational direction.
The universal joint allows tilting movements between two parts, however, a
rota-tion around the main axis is transmitted to the other part Depending on the angular position of the axes it can cause uneven rotational speeds as in real universal joints This non-uniformity can be avoided by use of the constant velocity joint described
below
The spherical joint allows all rotational movements.
The planar joint allows the frictionless sliding of two parts in a plane.
The fixed joint eliminates all degrees of freedom so that there is no displacement
between a part and the environment, or between two parts
In addition to the conventional joints, which are based on the model of realistic joints, there are some joint primitives that offer more precise control of the DOF of the connected
links So it is possible to fix every single degree of freedom with the help of joint tives Here you can find some of the useful joint primitives:
primi- Constant Velocity: This joint works very similar to the universal joint described
earlier But unlike the universal joint, the rotational velocity is constant on both sides and even angles with over 90° are possible too
Inline fixes two translational DOF, so that the both links could be moved on one axis
to each other (similar to Point on Curve).
Parallel: A joint that keeps two faces, lines or axes in parallel Two rotational DOF
are fixed
The Orientation primitive fixes all rotational DOF between two links but it allows
the translation in all three directions
Further functions are:
Smart Point: A general CAD point that is associative to the geometry it was assigned
to
Marker: A marker that is used to request results such as the velocities and
accelera-tions on certain posiaccelera-tions of the link
Sensor: Enables the user to record motion results such as displacements, velocities,
and accelerations relative to other results or markers
The joint primitives
Sensors etc
Trang 24Further functions of the Motion Simulation toolbar:
The function Master Model Dimension could be used to alter the CAD parameters of
the underlying CAD model in a motion model The special thing about this feature is
that the changes only affect the motion model, and the underlying CAD model itself is
not changed Therefore this function can be used for “what-if” studies
The Function Manager is used to define more complex functions, such as a driver
whose control that is time- or motion-dependent Simpler functions, however, are
usu-ally available directly in the appropriate motion features Therefore in such a case, the
function manager is not needed
The Flexible Link function allows calculated flexible links, which previously had
been calculated with FEM, instead of solely using rigid bodies
Another group of special joint are couplers and gears The user can choose between the
following options:
Gear: Defines the relative motion of two revolute joints or a revolute and a
cylindri-cal joint with a defined ratio
Rack and Pinion: Defines the relative motion of a revolute and a slider joint with a
defined ratio
Cable: Defines the ratio of the relative translational motion of two slider joints.
2–3 Joint Coupler: Defines the relative motion between 2 or 3 revolute, slider and
cylindrical joints
The next group of special joint types summarizes the connections:
Spring: Flexible element that is defined between two joints, or a joint and the
envi-ronment or on an existing joint with stiffness value, preload and damping coefficient
Damper: Damper element defined like a spring, but with a damping coefficient This
results in a velocity-dependent force between the respective links
Bushing: A cylindrical combination of spring and damper (stiffness and damping
coefficient in all directions)
The 3D Contact and the 2D Contact are special contact functions because they
allow the impact on each other and the lifting of each other Strictly speaking, these
contact definitions are no joints, but force objects that respond by restoring forces in the
event of contact In this case, friction and contact damping can play a role too and can
be replicated using assigned parameters While the 3D Contact is applied to the whole
solid, the 2D Contact is a simplification that may be used in the case of planar curves
These two contacts should be used with caution due to their complexity If possible, the
following constraints should be used instead
Now a group follows, in which the constraints are summarized These include:
Point on Curve forces a point on a link to move along a desired curve.
Couplers
The elements for connections are collected in a group
Various types of constraints
Trang 25 Curve on Curve: Two curves are forced to slide tangentially on each other Both
curves have to be coplanar With this function most of the cam disc tasks are solved
Point on Surface: A point on a link is forced to slide on a selected surface.
Additional motion features in the toolbar belonging to the group of loads These include:
Torque, which are available as vector or scalar approach.
Some advanced features are only available after appropriate adjustment of the settings in the environment dialog These include:
PMDC-Motor: defines the electrical parameters of a motor, such as voltage,
resis-tance, and inductance
Signal Chart: provides an input signal to the PMDC motor
Plant Input: defines the control variables that are read from the optional Matlab
Simulink control and which are provided to the MBD model, for example as a driver
Plant Output: measured value, which is fed to the Matlab Simulink loop.
For running the analysis, first a solution has to be created and then the following function
Interference checks the model for collision and could create intersection solids
Measure for measuring distances and angles
Trace for recording the geometry during the movement
The last function group provides five methods for post-processing:
Animation displays the calculated movements of the model
Graphing for the graphical evaluation of motion results
Populate Spreadsheet for editing, re-using, and saving of motions using a
spread-sheet as input
Create Sequence saves a motion animation in an assembly sequence so that the
motion sequence is also available in the master assembly
Load Transfer for transferring reaction forces from the kinematics analysis in the
Trang 262.2.1.3■Overview of the Solution Steps
To solve this exercise, a Motion Simulation file must first be created in the NX system
Then the geometry that should be movable in the motion system has to be defined with
the Link function The creation of two revolute joints, one gear, and a driver on the
steering wheel follows The time-dependent Normal Run is used to find accidentally
indefinite degrees of freedom, and the Articulation function is used to manually move
the actuator on the steering wheel
2.2.1.4■Creating the Motion Simulation File
According to the master model concept, all elements that are used for motion analysis
(links, joints, drivers), are stored in a separate file (i. e., the kinematic sim-file; see the
fol-lowing figure) This kinematic file is connected to an assembly file via an assembly
refer-ence, which means that the kinematic file is a quasi-assembly comprised of the assembly
part to be analyzed as a single component In addition to these assembly references, other
associative connections are similarly added to reflect the associative relationships
be-tween the joint and link objects defined in the kinematics file with the geometry objects
describing these components (curved arrows in the figure) This way, the NX Motion
ap-plication is fully integrated into the master model concept, similar to how, for instance,
the NX Drafting application is
Assembly
Part1
(…) Part2 steering wheel Part3 (…) Part4 (pitman arm)
Kinematics (Joints, Links)
Reference of MBD Objects (associative)
ÍLoad the assembly from which you want to create a simulation in the NX system For
our exercise, the assembly file ls_lenkgetriebe.prt The files are located in the RAK2
directory of the DVD
ÍNext, start the Motion application.
The Motion Navigator appears as the first tab in the resource bar This navigator supports
the work with the Motion application by representing all the features and providing
opportunities for their manipulation
The steps of the exercise
With the help of the master model concept, the entire product is digitally mapped Inter- nal references between geometry and MBD- joints are created
Here the exercise begins.
Trang 27The navigator shows that a motion file named motion_1 already exists This is the already
finished solution of this problem Since you will create an own solution, you should delete this file
ÍDelete the existing simulation motion_1 by opening and executing the Delete function
from the context menu of the simulation
Now the Motion Navigator only shows the master node, i. e., the module that you have opened
ÍCreate a first simulation by clicking on this master node, and invoke the function New Simulation in its context menu.
ÍConfirm the following menu Environment by selecting OK We will come back to it later
on
After activating this function, the system creates a simulation file that is associated with the master model via the assembly structure
In addition, the function Motion Joint Wizard is activated automatically, which tries to
create links and joints according to the existing assemblies Mating Conditions/Constraints.
The Motion Joint Wizard function analyzes each set of constraints with respect to the
de-grees of freedom that exist between the affected assembly components If there is only an indeterminate rotational degree of freedom, then a Revolute is generated If there is an
indeterminate translational degree of freedom, then a Slider is generated An assembly
constraint that links, for example, one point to another, is translated by the Motion Joint Wizard into a Spherical joint An assembly constraint that defines all degrees of freedom
between two parts, is translated into a fixed joint In a similar manner, a few more joints can be generated automatically
The Motion Joint Wizard can therefore automatically create the motion model, or parts
of it, when the assembly on which the motion should be based on, has been constructed
in such a way that the mating already describes the potential movements of the parts This approach can be quite useful, though the following disadvantages must be consid-ered:
The joints automatically generated by the Motion Joint Wizard are not associative to the
geometry That means that in case of changes on the master model, the joints must be adjusted manually A manual creation of the associativity of the joints is subsequently possible
Only the assembly constraints of the top-level assembly are analyzed and converted Constraints from the subassemblies are not considered
The navigator shows the
structure of the model,
and allows the
manipu-lation of its features
The Motion Joint Wizard
implements the Mating
Conditions/Constraints
into motion joints
Advantages and
dis-advantages of Motion
Joint Wizard
Trang 28Assembly constraints are often used for parts that are irrelevant in terms of the motion
model, such as small bolts, nuts and washers In the case of automatic translation by the
Motion Joint Wizard all these parts are made into links The motion model is then
con-siderably more complex than it needs to be One remedy for this problem is to disable
single conditions in the Motion Joint Wizard.
For these reasons, the Motion Joint Wizard should not to be used for the solution of our
problem:
ÍCancel the Motion Joint Wizard with the CANCEL function
The Motion Navigator should now shows a structure as shown in the following figure
A characteristic of the Motion Navigator is that the motion model is represented under
the master model This is done for reasons of clarity, because the motion features that are
generated are displayed in the navigator below the motion model In addition, several
motion models can be clearly displayed side by side in this way if desired
The NX system has thus automatically created a new file that is associated with the
mas-ter model according to the masmas-ter model concept, and the Assembly Navigator can now be
used to represent or to work with the new structure The picture to the right of the Motion
Navigator shows the Assembly Navigator that represents the motion model, now as the
top-level assembly
You should be cognizant of the operating system directories in which the new master file
has been stored, which you can confirm by using the Windows Explorer The following
illustration shows on the left side the master file ls_lenkgetriebe.prt, which can be located
in any folder of the operating system Once a motion model is created, the NX system
creates a subfolder with the name of the master model All the data that is needed for
motion simulation is thus stored in this new subfolder In our case, we see that the folder
now includes motion_1.sim, which is the file for the motion model.
During the following simulation several additional files are created, which are then stored
in this folder as well
We are not using the Motion Joint Wizard
The motion model is a quasi-assembly of the master model
The resulting files of the simulation are stored in
a folder
Trang 292.2.1.5■Selection of the Environment
As a next step, the environment for the motion model should be adjusted This is done using the Environment function There are the two alternatives, kinematics and dy- namics, which correspond to the classes of mechanics that were described at the begin-
ning of this chapter
The following should be observed for the use of these two classes in the NX Motion plication
be determined by joints or drivers
Of course, no conflicts may arise from joints or drives in the movement possibilities determinations that do not lead to conflicts are called redundant degrees of freedom These are allowed, but not recommended, because even the smallest inaccuracies can lead to conflict situations Such very small inaccuracies can occur, even when working really carefully, due to numerical rounding errors during computations Experience has therefore shown that large kinematic models will effectively only work correctly if they are constructed without redundancy Smaller models, however, will usually run with lim-ited redundancy without any problem
Over-The advantage of the kinematic environment is that no mass properties are required for the links The disadvantage is that the user is forced to create a motion system with ex-
actly zero degrees of freedom Until such is created, it is not possible to perform a test run
Dynamics
Dynamic analysis is characterized by the possibility of undetermined degrees of freedom and free movement opportunities Such movements are obtained by including the mass and inertia properties of the links as well as the external forces such as the gravitational
acceleration in the analysis
A dynamic analysis will calculate results even if undetermined degrees of freedom are available, while a kinematic analysis will stop in such a case This is an advantage for dynamic analysis during the model-building phase when the joints have not yet all been defined To do this, the mass properties for each link must be assigned and verified.
For these reasons, the dynamic environment should be chosen for the solution to our problem, even though no indeterminate degrees of freedom are desired We use this method only to simplify the development of the motion model, so that we can temporarily test the model without having fully determined degrees of freedom Once the model is complete, we can then easily switch back to the kinematic environment
In addition, Advanced Solution Options can be selected in the environment settings These
include the Motor Driver, which defines an electric motor based on its electrical
parame-ters and for which a signal diagram can be submitted; the Co-Simulation, which allows one
The decisive factor is
Dynamics also allows
the simulation of
Trang 30to couple controls that have been defined using Matlab Simulink to the NX-motion model;
and Flexible Body Dynamics, with which it is possible to work not solely with rigid moving
bodies, but to also make them partially flexible For this, however, a prior FEM analysis of
the corresponding parts is required
Furthermore, you can choose whether a Component-based simulation shall be used or not
This is useful if assemblies shall be simulated With this option, the link selection filter is
preset to components However, this can always be changed manually
2.2.1.6■Definition of the Links
Now the Links will be created
ÍSelect the Link function.
First, a link should be defined to describe the steering wheel, and then a second one to
describe the pitman arm
The first selection step concerns the selection of the geometry that should be part of the
link If you have not already selected the setting to filter for components in the
environ-ment, it should be set now This will make it easy to change the geometry of the assembly
components later, without the danger of the links in the motion model losing their
refer-ences
ÍNow select in the graphics window the assembly components that belong to the
steer-ing wheel; that is, all the parts that move together with the steersteer-ing wheel
There are 19 components that belong to the sub-assembly ls_ubg_spindel You can use the
Assembly Navigator to select these components
Once you have selected the components, the mass properties of the link can be defined as
shown in the following selection steps However, this is not necessary in this case because
the system can automatically calculate the mass properties based on the geometry and
the assigned material respectively the density Because these properties are not of
inter-est in this exercise, we will use the automatic mass analysis instead Therefore, keep the
Automatic setting under the Mass Properties option.
ÍIn the field “Name” you fill in an appropriate name, such as “steering wheel”
The menu for the definition of a link
Both components of the assembly, as well as the solids, simple curves, and points, can be moved
Mass properties are determined automati- cally for solid bodies
Trang 31Do not include any spaces or special characters in the name of motion objects.
ÍWith a click on OK or APPLY, the link will be created and displayed in the Motion Navigator under the Links group.
ÍNow, in the same way, create the next link Add the three components hebel, ls_segment, and ls_lenkgetriebewelle, and then name the link “Lenkstockhebel”
ls_lenkstock-(pitman arm)
At this point, all the necessary links have been defined, Next, we will define the joints
2.2.1.7■Definition of Revolute Joints
Now we will define a rotatable bearing between the link steering wheel and the fixed environment Other joints can be defined similarly Proceed as follows:
ÍSelect the Joint function You will see the menu shown below.
At the top of the menu, the type of the desired joint can be selected The default is the
Revolute joint, which is a joint that has only one rotational degree of freedom Since
this is the desired joint, we will proceed with the selection steps
With the first selection step the first link which shall be connected, that is the steering
wheel, is specified In principle, the steering wheel can now be selected in any manner in the graphics window, but it is advisable to take into account the following aspects for the selection:
It is recommended to select a geometry from which the system can derive the desired joint center and the axis of rotation This is possible, for example with a circle: In this case, the circle center becomes the center of rotation and the circle normal becomes the rotational axis But also a straight edge or curve is possible: In this case the next control point becomes the center of rotation and the direction of the edge or corner the axis of rotation
It is also advisable to select a geometry that in the further design history is subjected to
as few as possible changes Because if the selected geometry is subjected to changes, it
is not sure if the joint remains associative to the geometry and is updated automatically For example, if an edge is selected, which is rounded later, the joint loses its associativ-ity to the geometry
For the definition of
revolute joints the
selection should be
done on arcs Then the
point and axis of
rota-tion can be determined
automatically
Trang 32ÍTherefore, select a circular edge on the steering wheel which is not subjected to
sig-nificant changes
In the second step, the origin and orientation of the joint should be selected In the case
of the pivot joint this is the center and the axis of rotation Because these two pieces of
information have been given in the first selection step, this question does not need to be
answered
In the third selection step the second link, which should be connected, can be selected If
there is nothing selected, the system assumes that the joint connects the first link to the
fixed environment Because this is desired here, no selection is made in the third step
ÍAccept with OK to create the revolute joint
In the graphics window and in the Motion Navigator the joint is now displayed
If the symbol of the joint is displayed very small, the size specification can be increased
under Icon Scale in the default settings (MAIN MENU > PREFERENCES > MOTION) for
motion simulation
The best way is to select
on circular edges Then the center point and direction can be used automatically
A joint can often be generated with just two mouse clicks
A joint which is connected to the fixed environment can be identified by its symbol
Trang 33ÍIn the same way you can create a revolute joint which connects the pitman arm with the fixed environment (as you can see in the following figure)
Now you have created a first mechanism with two moving bodies that are connected to the environment, each with a revolute joint But the task is not yet solved In the interest
of better understanding, some test runs are carried out in the following
2.2.1.8■Detection of Undetermined Degrees of Freedom
Due to the missing driver and the absence of a coupling gear, the previously completed mechanism is still underdetermined The number of the undefined degrees of freedom can be determined either by plausibility checking, or by examining the Information win-dow shown in the next figure
ÍFrom the context menu of the motion model in the Motion Navigator, select the tion Information, Motion Connections The information window that then appears lists
func-the number of undetermined degrees of freedom in func-the mechanism (Degrees of dom).
Free-In this case, there are two degrees of freedom because both the steering wheel and the pitman arm can still freely rotate about their respective axes
The pitman arm is also
attached with a revolute
to the environment
For complex
mecha-nisms, the identification
of undetermined
degrees of freedom can
be difficult The function
Information, Motion
Connections helps
Trang 342.2.1.9■Test Run with Two Undetermined Degrees of Freedom
In cases of more complex mechanisms, it is often difficult to identify the undetermined
degrees of freedom of a mechanism only from plausibility considerations One useful
ap-proach in such cases is to perform a test run with, in our case the two open degrees of
freedom, to develop a better understanding of the mechanism
ÍSelect the Solution function Now the dialog appears to define the solution.
In this dialog, you are prompted to select the Solution Type You have the following
op-tions: Normal Run, Articulation, and Spreadsheet Run We accept the default type Normal
Run to perform an analysis that takes into account time and gravity Furthermore, the
simulation Time and the number of Steps can be specified here Additionally, you can
choose Analysis Type to specify a Kinematic / Dynamic Analysis or a Static Equilibrium
Analysis In addition, the direction and the magnitude of the gravitational acceleration
can be set In our case we want to customize it as follows:
ÍIn the dialog, set the Gravity vector to -ZC and verify the direction of the resulting
arrow
This direction of gravity does not correspond to reality, but this way the pitman arm
should fall definitely into oscillation, which is what we want to check in the following
ÍFor our example, leave all other settings as default, and select OK After that, the
solu-tion is created
ÍAfter the creation of the solution, select the Solve function The analysis should be
completed quickly
ÍNow you can start the Animation function The menu to control the animation of
the movements will appear
ÍUse the function Play to view the results of one second of simulation time.
In a dynamic run usually undetermined degrees
of freedom can easily be recognized
The direction of the gravity is important for undetermined degrees
of freedom
Trang 35It should be recognizable that the lever performs approximately one full oscillation The simulation makes it easy to see that there still exists an indeterminate degree of freedom The second undetermined degree of freedom cannot be discovered in this way, because due to symmetry, there is no reason for the steering wheel to move.
ÍCancel the Animation function with CLOSE
2.2.1.10■Definition of a Kinematic Driver
In the next step, a driver is defined on the steering wheel Such a driver can be used both for the Normal Run simulation method and for the Articulation method With Normal Run
it is time-dependent, while with Articulation it is performed after manual specification.
Drivers are defined either directly in the joints or by the Driver function It should be
noted that not all joints can have drivers defined Only the Revolute, the Slider, the drical, and the Point on Curve can have drivers defined If other joints are to be driven,
Cylin-then this must be realized through the use of appropriate joint combinations In the lute joint the driver works as a rotational driver; in the Slider joint the driver works as a
Revo-sliding driver; and in the Cylindrical joint the driver may be a combination of a revolute
and a slider driver The following shows how a revolute joint can be provided with a drive
ÍSelect the Edit option in the context menu for the revolute joint on the steering wheel,
and then select the Driver tab.
The definition dialog of the revolute joint appears From here, all the properties of this joint can be changed In the menu item Driver, the parameters describing the different
driver types in the list can be set
The Animation dialog is
used to review the
simu-lated movements of the
mechanism
A driver works like an
additional constraint
Trang 36The Constant driver performs a time-constant motion or acceleration with the solution
type Normal Run It can be specified an Initial Displacement, an Initial Velocity and an
Acceleration.
The Harmonic driver performs a harmonic oscillation during a Normal Run The
oscil-lation Amplitude, the oscillation Frequency, a Phase Angle, and an initial Displacement can
be specified
The Function driver can be used to define more complex motion functions with the help
of the Function Manager
The last driver is the Articulation This driver corresponds to fixing the degree of freedom
in the solution type Normal Run , however, with the addition in the solution type
Articulation , that the driver may also be operated manually.
All types of drivers can be used in the solution type Articulation The modified values are
simply reset and remain irrelevant For the visual control in our example, the Articulation
function should be used, which therefore means that we can use any of the four driver
types
ÍIn order to make good use of simple test runs for both Articulation and Normal Run,
you should use, for instance, the Constant driver with an Initial Velocity of 360 [deg/
sec], as shown in the previous figures
ÍAfter defining the driver, close the dialog box with OK
Using these settings for the driver, and a simulation time of one second, our simulation
should complete exactly one full rotation
2.2.1.11■Creation of a Gear
The gear pair connects the two rotational joints and defines the relative rotational
mo-tions for the two joints
Several types of drivers are possible for example
the constant type
The Harmonic driver
defines a harmonic oscillation
The type Function allows
the access to advanced functions
The Articulation is a
special driver It can be virtually moved by remote control
Two revolute joints could
be coupled by a gear
Trang 37ÍCreate the gear by using the Gear function.
ÍThe first selection step asks you to select the first revolute joint, such as the joint of the steering wheel You can select the joint in the graphics window or in the Motion Navi-gator After this selection the second selection step in the dialog box is activated auto-matically
ÍNow select the second revolute joint, which is the joint of the pitman arm
ÍFor Ratio enter the desired gear reduction or ratio For our example enter a value of 0.25.
ÍAccept with OK The joint will be created
Unfortunately the joint Gear has the following limitation: It can only be
created if the two joints (revolute or cylindrical) have the same base The base of a joint is the link, which has been selected as the second body during the generation of the joint In case of our example, this is the envi-ronment
2.2.1.12■Visual Control through the Use of Articulation
After complete generation of the motion model it could be moved manually with the Articulation function
ÍTo do this, create a new solution and select the Articulation option as Solution Type
After that accept your input with OK
ÍNow select the Solve function The dialog shown in the following figure appears.
ÍTo move the single driver of the model manually, first activate the check box for the joint J001
ÍThen enter the desired Step Size, for example 1 degree.
The Articulation function
is well suited for the
control of movement
sequences
Thereby, it can be
moved forwards and
backwards step by step
Trang 38ÍWith the buttons and , the driver could be moved forward and backward step
by step
ÍWith Number of Steps you can specify a number of steps that are executed at every
mouse click on or
ÍUsing this function, the visual control of the mechanism which is desired in this task
can now be performed
ÍExit the articulation function with CLOSE
ÍSave the file
ÍLeave the motion simulation by execute the function Make Work on the master node
ls_lenkgetriebe in the Motion Navigator and then switch to the Modeling
applica-tion
This completes the first learning task for motion simulation
2.2.2■Top-down Development of the Steering Lever Kinematics
In this example it is shown how kinematics simulations can be used effectively in the
early design phase Background is the usual design methodology in the early phase, in
which a designer does not yet have a detailed idea of the finished product Rather, he tries
to approximate the first very rough drafts to find possible designs, for which the motion
of the planned machine plays an important role In most cases, simple curves, 2D sketches
or coarse solids are used, which can be manipulated easily Only when appropriate
geo-metrical parameters were found, the detailed design begins This includes the structuring
of the geometry objects in assembly components or the definition of sub-assemblies This
type of construction is known as a top-down design, because the product is developed
from the top downwards
In this example, you learn about design methodology, which is used in early design
phases However, the main focus is on the use of motion simulations in the context of
principle sketches and the optimization of geometric parameters It is also shown how the
simulation results are displayed as a graph
2.2.2.1■Task
The aim is the construction of the steering levers which means the left and the right
steer-ing arm and the tie rod The followsteer-ing figure already shows the result of the task With a
parallelogram like geometry of the steering lever it should be achieved, that the wheels
are wrapped unevenly whilst driving through a curve, which helps to improve the
driv-ing dynamics To check the correct movement in this example the different angular
posi-tion of the wheels should be displayed in a graph
An example of the support of early design phases through motion simulation
Trang 392.2.2.2■Overview of the Solution Steps
Before we will start we would like to give an overview of the solution steps first After the required subassembly of the RAK2 is loaded in NX, you will delete or hide the existing components of the steering lever mechanism Then you will create a basic sketch in the context of the assembly, which serves as a rough geometry for the components to be de-veloped
Based on this schematic sketch you will create a motion model that represents the quired movement of the mechanism According to your preference, you can also add the existing wheel geometry to your motion model for visual control
re-Next, a graph is recorded, which represents the angles of the two wheels when the ing wheel is turned The difference of the wheel angles is controlled If desired some changes to the parameters of the schematic sketch can be made and a re-inspection of the wheel angle can be solved
steer-After the geometric variables are appropriately adjusted, you will create assembly ponents from the principle sketch curves To maintain associativity to the principle curves, the WAVE Geometry Linker is used Finally, a new motion control is created includ-
com-ing the solids
2.2.2.3■Preparation
ÍStart with loading the assembly vr_lenkung in NX and have a closer look at the sembly Navigator.
As-ÍMake the Part lenkhebelmechanik the active part (Make Work Part).
The final solution of the learning task consists of the components of the subassembly
lenkhebelmechanik Here are in addition to some small parts the left and right steering
lever vr_lenkhebel_li, vr_lenkhebel_re as well as the tie rod vr_spurstange You will also
find the finished principal sketch lenkhebelmechanik_prinzip.
First, the existing solution should be deleted:
ÍDelete all components of the assembly lenkhebelmechanik, by selecting the
compo-nents in the Assembly Navigator and select the DELETE function in the context menu
Based on principle lines
a mechanism should be
developed
The motion model, and
a motion graph shall be
created The control of
motions is important
The exercise starts
here.
Trang 40The parts are not deleted by this, they are only removed from the assembly structure of
the lenkhebelmechanik.
ÍSave the part lenkhebelmechanik.
If you need the original file lenkhebelmechanik later, create a new copy of the
down-loaded model
2.2.2.4■Creation of a Schematic Sketch of the Steering Levers
Now create a new part and therein the new schematic sketch:
ÍIf not already done: Make the part lenkhebelmechanik active (Make Work Part) (not the
displayed part)
In the following, we will create a new part using the top-down method:
ÍTo do this, use the Create New function in the Assemblies toolbar to create a new
component
ÍIn the window that appears, enter the name lenkhebelmechanik_prinzip2.prt for the
part which should be created
ÍIn the following dialog box Create New Component accept all default settings with OK
The result in the Assembly Navigator should look as shown in the figure below
The next step is to create a schematic sketch in the new created part Proceed as shown
in the steps below which are illustrated in the figures
The use of the top-down method
The principle geometry for the steering system can be created by a parametric sketch or by non-parametric curves