Hierarchical Design Models in the Mechatronic Product

8/11/2019 Hierarchical Design Models in the Mechatronic Product

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tions3 and 4presents an approach for hierarchical design models

for mechatronic systems. A definition of a mechatronic module is

presented which utilizes several domains (disciplines) of mecha-

tronics (e.g. mechanics, automatic control techniques etc.) merging

the respective domain-specific components. Section 5 describes

the modelling of a mechatronic application, a permanent magnet

synchronous machines. Conclusions are drawn in Section 6.

2. Background and objectives

2.1. Requirements on product development processes

Especially in todays economic environment with its global

competition, high dynamics and shorter and shorter time to mar-

ket, a superior design concept for a product is crucial as it pre-

determines the main part of product success. For any new product,

the question is less how to realize it, than to find a promising supe-

rior product concept. In the traditional linear model of design, the

process flows from synthesis over analysis to evaluation. Design

methodology at the conceptual level includes as a mission the cre-

ation of innovative concepts, comprising a description in low detailbut with sufficient relevance for the evaluation of their essential

properties in comparison to other concepts. The products main

properties (e.g. performance, behaviour, function, weight, costs)

quantified by significant parameters are fixed during the concep-

tual design phase in the product development process [4,5].

If a system (overall system, sub-system or component) is de-

signed totally new, the conceptual design process leading to the

preferred design concept(s) for the system is usually a mentally

intensive and challenging work. As this step fixes the main portion

of success of the new product, it should be done by excellent engi-

neers. Due to mechatronics, the toolbox for solution principles is

widely extended; hence, the variety and complexity of different

solution concepts is drastically increased. This is the reason, why

conceptual design of mechatronic systems will be investigated inmore detail.

Amongst the variety of information available to the designer,

standards, directives and suppliers data generally provide specifi-

cations and specific aspects of products and their requirements. On

the other hand, the engineer has to follow several design rules (e.g.

design for manufacture) representing general information. Both as-

pects require a more detailed knowledge of the structure of the

product to be developed, of its functions and production in order

to make reliable predictions regarding the (technical) properties

and costs of the product. Although the properties of the product

are influenced to the greatest extent during its design, the informa-

tion for design, as a general rule, is still mainly derived from expe-

rience that can only be gained from the phases of the product life

cycle following design, which requires knowledge management.

2.2. Demands for hierarchical models in the mechatronic design

process

A mechatronic system is defined as a box, comprising several

design inputs and outputs for the different design requirements. As

a rule, mechatronic systems are assumed to be complex and to in-

clude a lot of internal couplings between different domains. The

system may contain mechanical, electrical, controller and other

typical components of mechatronic systems[6].

Therefore, a method should be available, which allows to derive

a specific design view from an overall model. In general, such an

overall model will be less sophisticated than more detailed sub-

models for one specific aspect. From this point of view it is con-

cluded that models should cover the different views on a system

as well as the different degrees of detailing. Nevertheless, all these

models (for the different views and at different levels of detailing)

should be consistent to one another as much as possible. One key

idea should be that the task of modelling mechatronic systems can

be viewed as a cooperative activity, which exploits the contribu-

tions from several separate models of the system, each of them

comprising a specific type of knowledge for the corresponding

view on the system as well as for the degree of detailing.

The task of designing models is based on two fundamentalmechanisms, namely operations inside a single model and opera-

tions across models. The proposed models may represent struc-

tural knowledge (e.g. about the topology of the system, the

properties of its elements and their interactions), behavioural

knowledge (about the (desired) behaviour of the system, its com-

ponents or sub-systems) and functional knowledge (how to fulfil

specific functions by the implementation of suitable components

using physical or other solution principles). The interactions can

be classified into two types (see also[7]). The internal interactions

describe the connections between the elements. On the other hand

external interactions represent the connections through the sys-

tem boundary.

The different models are integrated by using relations between

system structure and system behaviour, and by links betweenfunction and behaviour implementing the function. To derive

abstractions from different points of view and detailing allow

building multiple models of a mechatronic system. These abstrac-

tions are interconnected through the model of the whole system

(overall model). The interconnections (interfaces) are used to man-

age the interdependencies between the different models. Accord-

ing to these considerations, the different views representing a

mechatronic model can be defined by the according system prop-

erties and areas of application (see[7,8]).

2.3. Background on characteristics of mechatronic design

VDI2206[9]is devoted particularly to the design methodology

for mechatronic systems and suggests to carry out the develop-ment process of mechatronic systems according to the so-called

MechanicalConstruction

SimulationDesign Models

Control UnitDesign

Control UnitImplementation

Physical Prototype, Mechatronic Product

MechanicalDesign

Integration and Interaction in Design

ElectricalDesign

ElectricalCircuit Diagram

Integration

Fig. 1. Mechatronic design activities.

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V-model (Fig. 2). After analyzing all requirements on the total sys-

tem, the sub-functions and sub-systems are defined (left branch of

the V-model). They are to be developed simultaneously by the

cooperating development teams. After verifying the sub-functions

and testing the sub-systems, they are integrated step by step (right

branch of the V-model). Then the performance of the integrated

system is checked. If it has to be improved, the initial operation

phase will be repeated (iterative process).

Another approach is represented by Axiomatic Design, a general

method enabling designers to structure and understand design

problems, thereby facilitating the synthesis of suitable design

requirements, design solutions and design processes. This also pro-

vides a consistent framework, by the help of which a design con-

cept can be evaluated from this axiomatic point of view.

The design axioms discussed by Suh[10,11]are:

The Independence Axiom: Maintain the independence of func-

tional requirements (FRs).

The Information Axiom: Minimize the information content of

the design.

In an acceptable design, the design parameters (DPs) and the

functional requirements (FRs) are related such that a specific DP

can be adjusted to satisfy its corresponding FR without affecting

other FRs. The relationship between these two vectors can be writ-

ten as.

FR ADP 1

whereA is the design matrix that characterizes the product design.

For a linear design,A is constant, whereas for a nonlinear designAis

a function of the DPs. In common cases there are more DP than FR

andA is a non-quadratic matrix. When the design matrix is qua-

dratic and diagonal, each of the FRs can be satisfied independently

from the other FRs by means of one DP. Such a design is called an

uncoupled design. The independence of FRs can still be guaranteed

if the matrixAis triangular and hence the DPs can be determined ina proper sequence. Such a design is called decoupled design. Any

other form of the design matrix is called a full matrix and results

in a coupled design.

Among design alternatives satisfying the Independence Axiom,

the best one has the minimum information content which results

most likely in successful design. The Information Axiom provides

a quantitative measure of the merits of a given design and estab-

lishes the theoretical basis for design optimization and robust de-

sign. The Information content Iifor a given FR

iis defined in terms of

the probability Pi of satisfying FRi ([10]).

Ii log21

Pi log2Pi 2

A design is called complex if its probability of success is low.

This occurs when the tolerances of FRs for a product are small,

resulting in high accuracy requirements.

System design and evaluation are important topics for which

improved tools and knowledge are ever claimed by the engineering

profession. Axiomatic design can be applied to systematize and

structure the design and evaluation of systems. A system may be

defined as an assembly of sub-systems, hardware and software

components, and people designed to perform a set of tasks to sat-

isfy specified functional requirements and constraints. Systems

may have a hierarchical structure with many layers of sub-compo-

nents and sub-sub-components.

In addition, this system architecture must be clearly known in

order to construct the system, distribute responsibilities, track

the effect of design changes, organize the complex tasks of manag-

ing a large project and create maintenance procedures [10,11].

A conventional way of characterizing systems is based on the

physical size or the number of components of the system. How-

ever, when making design decisions, physical size is of less signif-

icance than the number of functional requirements and constraints

the system has to satisfy and the number of levels of decomposi-

tion required to arrive at a complete design solution.

In Axiomatic Design the process under consideration is system-

atized by the use of four domains (Fig. 3):

The customer domain indicating the needs of the customer.

The functional domain expressing the desired functions

(desired behaviour) of the design object.

The physical domain representing the physical properties of the

design object.

The process domain illustrating how to achieve or produce the

design object.

2.4. Evaluation of product properties by design models

For the exploitation of the potentials of mechatronics, fully con-

sistent models for the product development process and for the

description of complex systems are essential. The interdisciplinary

description and definition of product information from the variousdomains of mechatronics is a necessary requirement for mecha-

tronic design models.

Concerning the product lifecycle management, it is necessary

to consider all product relevant information from all phases of the

product life cycle in a general structure.

With the ever-increasing variety, integration and interconnec-

tions of functions and components of modern mechatronic prod-

ucts, the urgent demand for a combined (integrated)

consideration of all product features is given.

The various individual product life phases and the different

mechatronic disciplines involved require investigations concerning

distinct aspects of the product (object) under consideration. Hence,

a general description of product properties for different views, in

different combinations and grades of detailing should be available(seeFig. 4).

Sy

stemDesign

noit

arg

etnI

met

sy

S

MechatronicProduct

Requirements

Domain-specific Design

Mechanical Engineering

Electrical Engineering

Information Technology

Modeling and Analysis

Performance

Check

Fig. 2. V-model for mechatronic design.

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This description should be able to comprise the consideration

(design, modelling, analysis, testing, evaluation etc.) of certain

properties (deflection, dynamics, transfer function, reference ac-

tion of a control loop, etc.) of mechatronic systems, their power de-

mand, their complexity of manufacturing and assembling or of

operation and handling items.

In this context, different hierarchical models (e.g. cost models)

are useful. On the one hand, these models can be elaborated in

more detail during the product development process, which results

in an improved significance. On the other hand, it is possible to de-

fine rough and simple dimensioning models for the concept phase

by primarily simple models or by an appropriate reduction of morecomplex models.

3. Design models

3.1. Characteristics of design models

Models are very important for complex engineering design

activities. In the engineering of high performance characteristics,

numerical modelling and simulation, i.e. experimenting with com-

puter-based models, is an increasingly important problem solving

technique. From the viewpoint of engineering design, models are

containers of knowledge, and simulations are activities producing

information that may improve product knowledge and potentially

also the quality of many analyses and decisions made during thedesign process[12].

The aim of a behavioural model, i.e. a model of the (physical)

systembehaviour, is to serve as a tool to find an answer to a design

question, i.e. each model is unique and it has a specific purpose.The preliminary design phase is often characterized by a cas-

cading series of what-if questions. Many of these questions, which

may be of divergent character, are related to the complex depen-

dencies between geometry (shape), topological structure, and

(physical) behaviour.

The complex nature of engineering design, as well as the time-

and cost-constraints on this process, require highly efficient and

flexible procedures to configure system models (overall models)

for non-routine simulations. The modelling challenge may be ad-

dressed by a modular or an integrative model design.

A modular sub-system has interfaces that are well defined and

are shared with only a few other sub-systems. An integrative sys-

tem has interfaces that may be more complex and shared across

the whole system model. The physical behaviour of a technical sys-tem depends on the properties of the sub-systems and their (inter-

nal and external) interactions, which take place at interfaces. An

interface describes the relationship between a pair of mating fea-

tures. Product models are important containers of significant prod-

uct properties such as shape and material. With present state-of-

the-art computer-aided engineering (CAE) technologies, finite ele-

ment (FE) and multi-body systems (MBS), modelling of geometri-

cal objects is a relatively straightforward technique.

The chosen approach to enable innovative mechatronic design,

flexibility, speed, and responsiveness to non-routine design ques-

tions is to rely on a modular model architecture that enables the

configuration of system models from a library of sub-models and

interface models. A sub-model can be a model of a single mechan-

ical component or of a complex system, e.g. a model of an inte-

grated mechatronic system with an embedded control system.

An interface model represents the physical interaction between

two sub-models or between the system model and its environ-

ment. Characteristic properties (e.g. colour of the product) are

stored as attributes (e.g. blue) of the mating features, which are

specialized product features. Each sub-model and each interface

model is a behavioural representation of a product model at a spe-

cific level of abstraction[12].

3.2. Definition of an information model and model conformance

The information model is the conceptual description of ideas,

facts and processes that in total represent the model of the design

product. The object created during the design process is called thedesign object. Design objects may be models of systems, sub-sys-

CustomerNeeds

CN

ProcessVariables

PV

CustomerDomain

FunctionalDomain

PhysicalDomain

ProcessDomain

Functional RequirementsFR

Design ParametersDP

FR = A * DP

Fig. 3. Design domains.

Modelingof

Sensors

Modelingof

Controllers

Modelingof

Reliability

....

MechatronicSystem

Modelingof Drives

Modelingof Strength

Modelingof

Kinematics

DesignStep

DesignStep

SatisfactorySolution

Yes

No

Decision

Ana

lysis and Evaluati

on

Design(Change

)

Fig. 4. Evolution of product properties by design and analysis.



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tems or single elements (e.g. parts or components) representing a

certain structure. There are groups of standard elements that are

used by every information model; according to[12]these groups

would contain the elements entity, property, attribute and

relation.

Model conformance defines as property how well a model

implements its intended functions. Typical model conformance

characteristics are accuracy, speed and flexibility. In the modelling

process, these characteristics must be judged in the context of both

the model purpose and the intended model lifecycle. Non-routine

simulations, which have a tendency to be more explorative and

in many times also more qualitative than routine simulations,

are facilitated by models that are relatively easy to configure and

reconfigure for a slightly different purpose, i.e. models that are

flexible.

4. Hierarchical design models for mechatronic systems

4.1. Definition of a mechatronic module

For the achievement of all aspects discussed in the previous

chapters, a method is needed, which helps the design engineer toanalyze and evaluate functional requirements and design parame-

ters of possible solutions. Our mechatronic pillar design model was

developed to assist the engineer especially in mechatronic design

tasks by structuring the design process and by increasing

transparency.

A mechatronic module (according to [13]) utilizes several dif-

ferent disciplines of mechatronics (e.g. mechanics, automatic con-

trol techniques etc.). In such a mechatronic module exclusively

domain-specific components are merged. This means that a mech-

atronic module can be decomposed only into domain-specific

(non-mechatronic) components, but not into other mechatronic

modules or mechatronic system components. A mechatronic mod-

ule therefore designates a mechatronic sub-system at the lowest

hierarchical level of a mechatronic system and is indivisible within

the set of mechatronic sub-systems. With the mechatronic pillar

design model all couplings between the several mechatronic disci-

plines (domain pillars) can be described in a superior data plat-

form. Each model pillar characterizes a domain-specific sub-

component, which is structured into several hierarchical levels cor-

responding to the proceeding degree of detailing (seeFig. 5). The

above model description has the following implications: Only the

first (highest) level has an interface to the other pillars (compare

with encapsulated modelling) via the mechatronic coupling level.

All couplings between the model pillars (e.g. design parameters

and requirement parameters affecting multiple disciplines) are

captured and described at the mechatronic coupling level. The

model structure has to be adapted if additional couplings between

domain-specific components are detected during a design iteration

(design, analysis, integration, performance check etc.). This is also

true if new or additional domains (pillars in the model) come into

consideration.

4.2. Using hierarchical models for conceptual design

In the context of mechatronic design processes, the phenomenaunder consideration are mainly physical or chemical. The models

consist of a set of parameters as well as a set of logical and quan-

titative relationships between those models. Models are important

components of scientific theories. Modelling is the process of

establishing a model, which is a very challenging and creative

work. The challenging work in engineering design is to compose

(combine) suitable effects to a beneficial solution concept as well

as to describe and evaluate the resulting technical system with

all its relevant, usually well known phenomena. When establishing

a model, some kind of idealization is necessary, this means that the

model is intrinsically tied to explicit assumptions which do not

represent reality in a complete or perfect way. Appropriate

assumptions are keys to get simple models which still are signifi-

cant representations of reality whereas the exact description ofreality is not possible in general.

4.3. Hierarchy of design parameters

The hierarchy of the design parameters are investigated sepa-

rately for each domain. It is very useful if not necessary to fix some

important parameters at an early stage of the design process. De-

sign decisions bring a system from the initial design stage, through

several intermediate design stages, to the output of the design pro-

cess, the complete final documentation of the product. Both, the

initial stage as well as the design goal are generally described in

vague terms, which are not definitive. This is one of the reasons

why in many applications it can be observed that the number of

design parameters (DPs) to be fixed is much higher than the num-ber of well defined functional requirements (FRs). Some of the

superfluous design parameters are indeed not essential for the

solution (e.g. the height of a shafts shoulder), but others give rise

to significant optimization potentials of the solution. As another ef-

fect that can be seen is that one FR at level i can affect several FRs

at leveli + 1 via the DPs at leveli (Fig. 6).

The process of defining hierarchical levels must be repeated un-

til elementary FRs (e.g. proven solutions, standard components)

with their associated, well known DPs are achieved. This means

that switching between the functional and the physical approach

during the product development process is necessary. The design

parameters at one level can be classified into two categories. One

subset comprises nex= ni+1 external parameters representing

requirement parameters for the next level. The other nin

parame-

ters are exclusively local at the active level for dimensioning the

component at this level (internal design parameters). In the follow-

ing describes chapter 5 the modelling of a mechatronic application

(a permanent magnet synchronous machines) with the usage of

the presented approach.

5. Permanent magnet synchronous machines modelling of a

mechatronic application

Synchronous machines have been used for decades mainly as

generators in electric power plants featuring a rated power of sev-

eral MW and above. In the area of small machines, covering for

example the whole region of automotive applications, a classical

DC machine has been the first choice for a long time. In this fieldof application the power ranges from lW up to a few kW. It can

MechanicalSystem

ControlSystem

DriveSystem

Domain-specific Components

Mechatronic Module

....

Mechatronic Coupling Level

Pillar 1 Pillar NPillar 2

Fig. 5. Mechatronic module.



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be seen as an impact of a mechatronic design which changed these

classical application fields of electrical machines completely

[14,15]. The brushes of DC machines have to be maintained, lead

to an increased complexity, need considerable space, increase

weight and not least costs and therefore are seen as parts that

should be replaced.

On the other hand, a change of requirements and the need of,

for example, highly efficient machines lead to the implementation

of completely changed machine structures including applications

that were formerly not powered by electricity.

Combined with the development of new materials as well asmore powerful electronic components, synchronous machines

gained a new field of application. Excited by permanent magnets,

brushes became obsolete as well as commutators, while the power

density could be increased even compared to DC motors. On the

other hand more or less sophisticated power electronics are now

necessary to achieve the same favourable torque to speed charac-

teristics as a DC machine. This includes the knowledge of the rotor

angle and can be implemented as vector oriented control [14,16].

Hence, control changed from an add-on to an intrinsic part of the

drive system and opened the way to the implementation of even

more features, which were at first enabling the vast variety of pos-

sibilities known from todays permanent magnet synchronous ma-

chines (PMSM).

5.1. Mechatronic modules of a permanent magnet synchronous

machine

Permanent magnet synchronous machines (PMSM) are known

for their mechanical robustness and their comparably simple

mechanical design [14]. However, there would be no point in using

them, if there would not be the possibility of powerful and flexible

control. This clearly separates the drive system into three mecha-

tronic modules: A mechanical system controlled with suitable

powerelectronics. As it is an inherent characteristic of mechatronic

devices to interact with the surrounding application, a boundary

has to be drawn. The selected boundary does not change the sys-

temitself but affects the number of parts that are identified as indi-

vidual mechatronic modules. Without a loss of generality, a powerconnection, a top level control command (torque, speed or position

for example) and a shaft to provide the output torque, are defined

as system interfaces. Therefore, only the components inside this

boundary are investigated further.

The graphic inFig. 7shows the interconnections of three mod-

ules that can be identified on the mechatronic coupling level.

I. The first module comprises the electro-mechanical hard-

ware of the actual drive. Here, according to the presented

mechatronic design model, three pillars can be identified.

Noticeable is the electro-magnetic domain, which includes

the magnetically active parts of rotor and stator irons, thepermanent magnet excitation as well as the copper wind-

ings. Due to the close coupling of electric and magnetic

effects, a separation of these two areas does not make sense

in the context of the pillar model. The electro-magnetic parts

are mainly designed to show a good electro-magnetic per-

formance, which results in the desired shaft torque. That

indicates to select the mechanical domain as the second pil-

lar. It includes bearings, shaft, housing, electrical connectors

and the mechanical insulation of the copper against the iron,

which is usually achieved using coil bodies. Forming the

basis and the support for the rotating parts and being the

output interface for the generated torque, is the main task

of this pillar. Thirdly, thermo-dynamics has to be mentioned.

The components of this section include the whole coolingequipment ranging from cooling fins to enlarge the surface

of the housing to a complex water cooling equipment, which

consists of a pump, hoses, cooling tubes through the motor

and a heat exchanger with a fan for the cooling liquid. Espe-

cially this third pillar is usually highly interconnected with

the surrounding application. According to the definition of

mechatronic modules it does not reduce generality to draw

the model boundaries around the machine in this case, as

it just means that the interconnections cut by these bound-

aries are seen to be sufficiently significant for this modelling

process.

II. The second mechatronic module can be found in the control

system. Here the challenge is not only to achieve the top

level control task, speaking of speed, torque or position con-trol in general, but also to perform the underlying control

FRi

DPi

DPi+1,1 DPi+1,2

FRi+1,1FRi+1,2

1 FRi n DPi+1 i+1

InternalDesign Parameters

ExternalDesign Parameters

(Requirement Parameters)

DPi+2,1 DPi+2,2

FRi+2,1FRi+2,2

1 FRi+1 n DPi+2 i+2Iteration

and

Feedback

Fig. 6. Hierarchy of parameter.



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tasks of a field oriented control to achieve the desired

dynamic and static behaviour. In the sense of components

this module consists of the control electronics, which is

made up of a micro-controller and several sensors. In a typ-

ical application, current and position sensors are used, but

they can partially be replaced to a limited extent. As a con-

sequence these parts would be implemented as observers

in software. If a micro-controller is used, software is the

main component of this module.

III. Finally, the third mechatronic module is represented by the

power electronics. The task is here to convert the power

input to a multiple phase voltage system using the com-

mands of the control algorithm. An example for a typicalthree phase power electronics would be a pulse-width mod-

ulation (PWM) inverter featuring three half bridges[17].

The intra domain specific interconnections of the electro-

mechanical system are shown in Fig. 8. It has to be mentioned that

the interconnections shown here are not necessarily complete and

not ordered in any kind with respect to their importance. It will be

the task of the subsequent modelling process to answer the ques-

tion how this can and should be done.

5.2. Limitations, assumptions and idealizations

Models in the sense of representations of reality exist on vari-

ous levels of abstraction. The appropriate level is always a compro-mise between simplicity, calculation speed, accuracy and

requirements. Though all criteria have in common to be based on

assumptions and idealizations, it is crucial for the chosen level of

abstraction to define its limitations. Hence, these preliminary set-

tings define quality and validity of the model output and are influ-

enced by requirements and constraints.

Keeping the PMSM drive system in mind, a simple level of mod-

elling could be to define the requirements to average torque and

speed in addition to limitations for current and voltage. This keeps

many design variables free for choice, which are usually selected in

a way to obtain the simplest possible model. Any further require-

ments or limits like for instance costs, dynamic behaviour, reduc-

tion of cogging torque, extremely high speed, etc. would imply

an almost completely different modelling procedure (compareSection2).

However, these models show interconnections and dependen-

cies. Thus the next step is to bring these models into a hierarchal

structure. This order reflects the rising number of requirement

parameters, but not necessarily a rise of the complexity of the sys-

tem. The intention is to find the simplest model capable to describe

the system. Therefore, possible idealizations have to be considered

carefully. Note that they can change at different levels to obtain

flexible models.

5.3. Hierarchical design models of a PMSM

It is apparently useful to base the description of hierarchical de-

sign models on a hierarchical structure of design parameters. Cus-tomer requirements stand at the beginning of the design process,

which are translated into functional requirements to result in a

solution that meets the demands (see Fig. 3). The hierarchical

structure of the selected sets of design parameters leads to differ-

ent definitions of functional requirements for different customer

requirements. It is expected that the demanding customer require-

ments do not directly indicate the way the design parameters have

to be chosen. It is assumed that the simplest model to fulfil the cus-

tomer requirements is the best choice.

5.3.1. Models based on characteristic diagrams and table data

One of the most elementary models possible is to directly try to

express the result in terms of customer requirements. Such a pro-

cedure can be found in the selection of components based on tabledata and characteristic curves.Fig. 9shows model for a PMSM mo-

tor drive based on characteristic diagrams. The customer require-

ments of a certain amount of power P, which should be

transferred via the output shaft at a rotational velocity x , is ex-pressed as an array of curves of the torque-speed relation of motors

of a selected type series. This simple motor model is on top of the

hierarchy of functional requirements, followed by the selection of

the power electronics and the control unit, because these two com-

ponents do not directly reflect the customers requirements. Inter-

connections do occur, but they are limited to the interfaces of these

components.

5.3.2. Simple analytical model

Though it is very common for component selection, it is certainthat the table based model can meet only very limited demands.

Fig. 7. Mechatronic modules of the PMSM drive system.



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Special applications, tight limitations as well as more sophisticated

control algorithms require a more detailed view on the functional

requirements. Each of the three components need to be described

in more detail. Exemplarily this will be shown here for themechanical system.

The customer demands may be expanded by the fact, that a DC

power supply, e.g. a battery, with a voltage level V is provided to

power the system. Therefore the number of windings Nhas to be

adapted to match the voltage level.

The underlying set of functional requirements for a vector ori-

ented control is shown in Fig. 10. Tdenotes the shaft torque, xthe rotational speed, k1 the motor constant of one winding, ~wfthe

rotor flux,pzthe number of pole pairs, Nthe number of windings,

Vand V1the phase voltage and the phase voltage with one winding

respectively, Lmd the mutual inductance in direct axis and i sq the

amplitude of the phase current in q-axis. The mechanical system

is characterized using the overload factorS, diameterdof the shaft

and the allowable shear stress rT. Temperature is denoted as #.To keep the model simple it has been assumed that

inductance is independent from the rotor angel,

leakage flux can be neglected,

stator resistance has negligible effects on the stator voltage

(negligible losses).

This model features no loops or feedbacks and therefore no de-

grees of freedom for an optimization. Top of the parameter hierar-

chy is, according to the specifications, the output power of the

drive system. The selection of a different top level parameter is

possible but would lead to another hierarchal model.

5.3.3. Analytical model including optimization possibility

Optimizations need feedback and recursion across hierarchal

levels, functional parameters and therefore degrees of freedom.

This is originated by the need for an optimization, which can be ex-

pressed as a global or local extremum of one of the functional

parameters and may result from additional demands.

As possible customer demand a torque ripple that does not ex-

ert a specified percentage of the average torque may be requested.

Additionally, the motor should be fit for sensorless control even at

zero speed. Furthermore, it should be agreed that if different solu-

tions are possible the one that leads to the simplest and cheapestmechanical design should be chosen.

These aspects are not covered by the simple analytical model

and consequently need investigations in more detail. The first as-

pect causes the need to model the angular change of magnetic en-

ergy stored in the air gap. Sensorless operation on the other hand is

known to need a specific inductance difference in d- andq-axis of

the rotor, as this is one of the possibilities to achieve observability

even at zero speed. Thus the new model has to express the induc-

tance Las a function of the rotor angle u. Hence, a detailed analysis

of the motor cross section is inevitable.

Moreover, also control needs a closer look, as the quality of a

sensorless operation is coupled with geometrical properties. A

sensorless oriented motor design can simplify the control algo-

rithm. The design potential on both sides can be validated as will

be later shown in principle in Section 4.6.

The functional requirements of the model inFig. 10can now be

extended to meet these requirements, but still keeping the original

structure unchanged. As the new demands affect exclusively the

torque production, only this part of the model has to be changed.

One possibility for an analytical approach is the model explained

in[18].

As the fundamental field equations cannot be solved analyti-

cally on an arbitrary motor cross section, simplifications are

needed. They are found in this case in the restriction to linear ef-

fects and ring shaped layers. All functional parts of the motor cross

section are modelled as regions arranged like onion rings. This al-

lows the field equation

@2Az@r2

1r2

@2Az@u2

1r

@Az@r

Brem;u

r B

rem;u

@r 1

rBrem;r@u

3

with the magnetic vector potentialAzand the magnetic remanence

Brem,u andB rem,r to be solved analytically. The problem is now re-

duced to the description of the magnetic field in the different areas.

Two important effects in these regions are identified to significantly

influence torque ripple and inductance variation. As rotors with sur-

face mounted magnets show hardly any angular change of induc-

tance, a possible choice is a rotor with interior permanent

magnets, as shown inFig. 11.These rotors generally feature mag-

netic saturation bars, which cannot be modelled using a linear

approach.

Keeping the ease to manufacture in mind, a system of concen-

trated windings is chosen, that can be externally wound and arepushed on straight teeth without pole shoes (Fig. 11a). However,

Fig. 8. Example of domain specific interconnections within the electro-mechanical

hardware.

Fig. 9. Simple model based on characteristic diagrams.



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a layout without pole shoes generally increases torque pulsationand cogging torque. Therefore, the effect of the stator slots on

the air gap field cannot be neglected as well.

According to[18]it is possible to model these two facts inde-

pendently from one another as their nonlinear effects are locally

limited. An equivalent magnetic circuit model shows that the sat-

uration bars can be modelled as small substitute permanent mag-

nets with linear characteristics. The effect of slotting is inserted

using a SchwarzChristoffel transformation of the air gap field.

Hence, it results in linear models with nonlinear parameters for

these two layers as shown inFig. 12.

Thus the assumption of linearity is valid and the magnetic field

equations can be solved. As a result all geometry parameters like

diameters and width of the stator teeth, back iron and permanent

magnets have now a direct influence on torque and therefore forma feedback loop.

Assumptions and simplifications still apply, but on a different

level of hierarchy. Now linearity in combination with ideal mate-

rial parameters, except for the specially treated areas, symmetry,

and the reduction to a 2D problem are necessary.

New or more detailed demands lead to a continuing refinement

of one or more of the functional requirements. As torque is the

product of the field provided by the permanent magnets and the

stator current, it is desirable to find the specific combination of

both that produces minimum losses. Usually this leads to the use

of rather large amounts of magnetic material. However, there are

limits due to iron saturation and an effect of demagnetization of

the permanent magnets. The influences of rotor geometry on

demagnetization are investigated in [19]. Accordingly a clear state-

ment, based on analytic calculations, can be given to estimate the

working point of the magnet. The parameters investigated are the

number of pole pairs, the influence of the magnetic cross section,

the air gap in combination with rotor eccentricity, the layout of

saturation bars and armature reaction.

5.3.4. Finite element model including nonlinear effects

As third level of model hierarchy, finite element based model-

ling is mentioned. If the demands concerning torque pulsation

and cogging torque are seen as factors of major importance for

the system, further details of geometrical design gain importance.

This can no longer be described in a simple analytical way and

makes numerical investigations such as finite elements analyses

inevitable. Especially nonlinear effects like saturation can now be

easily handled.

It can be shown that the inductance of the machine is not only

dependent on the rotor angle, but also on the phase current. This

leads to load dependent torque pulsations as well as load depen-

dent inductance variations with negative effects on both thesmoothness of torque[20]and the ability to observe the rotor an-

Fig. 10. Simple analytic model of the electro-magnetic system.

(a) (b)

Fig. 11. Motor cross sections that show different inductances in d- andq-axis.



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gle at different start-up conditions[21]. These effects are strongly

coupled with the actual layout of the machine cross-section.

Finite element calculations eliminate the problems of model-

ling, reduce the number of restricting conditions but still will not

work with at least some assumptions. These usually means a

restriction to a 2D analysis wherever possible to limit calculation

time, as well as some assumptions concerning material properties

and interconnections with other domains like direct magnetic-

thermal, or magnetic-mechanical couplings.

While the interrelationship between electric and magnetic cir-

cuits for a dynamic calculation can be expressed in rather simple

analytical formulas as given inFig. 10, it is rather complex to set

up a model incorporating the reaction of the magnetic nonlineari-ties on the dynamic behaviour. The model in [22] shows an ap-

proach to extract a completely nonlinear dynamic model from

2D finite element calculations saving most of the originally neces-

sary calculation time. This can be described in terms of a hierarchal

structure as shown inFig. 13.

A recursion exists due to geometric aspects, which have not

only an impact on the torque generation, but also a connection

to the control module, as geometry strongly affects angular induc-

tance variation. Moreover, the hierarchy of models within a hierar-

chical structure is clearly visible. The quasi-static finite element

(FE) simulation serves as a model to obtain a precise nonlinear

description of the flux distributionW. Later on, an optimized ver-

sion of these results is used to set up a nonlinear dynamic model.

5.4. Validation of the couplings between domains

An analysis of the different coupling parameters, allows to eval-

uate the interactions between the different domains. With the pre-

sented Mechatronic Design Model, a method is available that helps

to analyze and evaluate functional requirements and design

parameters of possible concepts and solutions. All couplings be-

tween the several mechatronic domains (discipline pillars) are de-

scribed in a superior data platform (coupling level). According to

Fig. 10 the interaction between the mechanical and the electrical

domain is analyzed. The considered coupling parameter DP is the

torque T.

In the mechanical domain it is limited by the diameter d of the

rotor, the allowed maximum shear stress rTand the overload fac-torSvia the formula

Tmech1

S

p

16d3rT 4

From the mechanical point of view all parameters have a design

range given by the different possibly used materials (rT min, rT max),

by geometrical constraints like the size of the bearings (dmin,dmax)and the variation of safety factor according to different application

Fig. 12. Incorporating specific models for layers with complex characteristics.

Fig. 13. Hierarchal structure of a part of the nonlinearly modelled electro-magnetic

module.



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areas (Smin, Smax). As a result of these considerations the mechanics-

specific design range can be defined by the limits Tmech, max and

Tmech, min (referred to as DH1,1).

In the electrical domain the parameter torque Tis determined

by the number of pole pairs pz, the motor constant of one winding

k1, the number of windingsNand the amplitude of the phase cur-

rent inq-axisisq.

Telect3

2pzk1Nisq 5

From the electrical point of view all parameters have a design

range given by the properties of the motors (k1 min, k1 max, pz min,

pz max, Nmin, Nmax) and the capability of the power electronics ( isq

min,isq max). As a result of these considerations the electric-specific

design range can be defined by the limits Telect, maxand Telect, min(re-

ferred to as DH1,2).

In Fig. 14 the interaction between the two domains (repre-

sented e.g. by two design teams) when defining a single design

parameter DP is sketched. The couplings can be classified into

three types.

For type 1, the two domains compete for the design parameter

DP and so the design range of this coupling parameter is the inter-section of the two domain-specific design ranges of this parameter.

This type of parameter will appear most frequently in practice. In

the case of type 2, the different design ranges have no overlap.

Hence, a successful determination of the coupling parameter is

not possible, which results in a new design iteration, where the de-

sign ranges have to be modified, e.g. by changes in the principal

solutions or adaptation of some requirements. Type 3 illustrates

the contrary case where the design ranges of both domains coin-

cide. This case turns out to have the maximum potential for opti-

mization and improvement of the mechatronic product.

In [23] the characteristic quantities of a heterogeneous elec-

tronic/mechanical design with the definitions of the different types

of Degrees of Mechatronic Coupling (DoMC) for a Mechatronic

Module are analyzed by using the Mechatronic Pillar Design

Model.

The relative Degree of Mechatronic Coupling (DoMCrel) evalu-

ates the intensity of couplings in a selected design structure

independently from the size of the structure (normalized from 0

to 1). First of all, it makes sense to define two ranges for the values

of a coupling parameter. The domain-specific design range DHi,j> 0

characterizes the possible range of design parameter DPiwith re-

spect to pillar j without consideration of the other pillars. The

resulting design range DDiP 0 of the DPi is determined as the

intersection of the domain-specific design ranges.

Derived from this DoMC the Coupling Intensity CI for the cou-

pling parameter DPi can be described for two domains (e.g.

mechanics and electrical system) according toFig. 14.

CIDPi 2 X2j1

DDiDHi;j

! 6

If the resulting design range DDi is zero (type 2), CI reaches its

maximum value, namely

CIDPi 2 7

In this case the metric describes the number of necessary (uni-directional) communication channels between the two domains

involved. If each domain is represented by a specific design team

of a project organization, the half of this number may be inter-

preted as the number of necessary (bilateral i.e. bidirectional) coor-

dination exchanges between the different groups. The Coupling

Intensity describes the density of interactions between the differ-

ent domains by analysing the different coupling parameters. This

helps to evaluate to complexity of different design concepts.

5.5. Reflections to the case study

The example of the design of a PMSM shows the advantages of

analyzing the design process in a hierarchical way. In contrast to a

traditional sequential design process, the parameters needed for anintegrated mechatronic design are identified and moved to the

superior mechatronic layer. This allows to sort the necessary

parameters and to rank the involved domains according to their

impact on the design process.

As a result it not only facilitates the view over the necessary de-

sign parameters, but also brings up the relevant set of parameters

at an earlier stage of the design process, as it would be the case in

traditional design.

At this stage of the design process the hierarchal structure of

the design parameters exhibits its strength. It allows the models

to be set up in a way suitable to achieve an optimal result with re-

spect to the mechatronic context. It has to be kept in mind that the

process of modelling may lead to different results, with respect to

the hierarchy of the selected functional parameters. The hierarchyitself can be implemented using different models, which is shown

using as example the conceptual design of a PMSM. The selection

of the appropriate model directly results from this structure.

Analyzing the interconnections of the functional parameters en-

ables an easy qualification on how a product should be designed to

reduce unnecessary iteration loops. A systematic tool is given in

Section5.4, which is able to evaluate a selected set of functional

parameters with respect to the quality of their couplings.

6. Conclusion and future research

This paper presents an approach for using hierarchical models

in the design process of mechatronic systems, which are as a mat-

ter of principle multi domain systems. Demanding mechatronicsolutions include an optimized result spanning various domains.

Design Team

Mechanics

Design Team

Electrical

System

DP

Requirements to the

Coupling Design Parameter

Type 1

DP10

H1,1H1,2

D1

DP1

H1,1 H1,2

DP1

H1,1= H1,2= D1

Type 2

Type 3

0

0

Fig. 14. Couplings between domains.



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Hierarchical Design Models in the Mechatronic Product

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