Expanding the Scope and Increasing the Functionality of Digital

Twins by Integrating Thermal Simulations

Dorit Kaufmann, Jannis Bojan Weid and Jürgen Rossmann

Institute for Man-Machine Interaction (MMI), RWTH Aachen University,

Ahornstr. 55, 52074 Aachen, Germany

Keywords: Thermal Simulation, Finite Element Analysis (FEA), Digital Twin (DT).

Abstract: The simulation of components, systems and processes is an established tool in research and development

nowadays. When it comes to complex systems and the interaction of components and disciplines, it is crucial

to consider all relevant aspects, thus creating a powerful Digital Twin (DT) of a technical asset. In this work,

an existing simulation framework for DT will be extended by an interface to Thermal Simulations. The latter

one are still widely used as a stand-alone tool due to difficulties on linking the respective models and methods.

Thus, the developed approach has its access point in the DT simulation framework and conducts the thermal

calculations to an external Finite Element Analysis (FEA) solver by exchanging only characteristic variables.

This concept is used as a base for the development of extensions for the DT whose basic functions are the

import and preparation of geometric structures for both models, the management of the calculations of the

external FEA solver and the visual representation of determined temperature distributions and heat fluxes in

the DT.

1 INTRODUCTION

Simulations are a sophisticated and acknowledged

way to improve any design process. If single

components (and at best complete systems) are

depicted computationally, predictions and thus

optimisations of the system or process can be made.

The more complex the system, the more important

interaction gets. Interaction refers to interaction of

single components as well as interaction of different

disciplines (as mechanics, electrical engineering,

material sciences etc.). To enable those interactions,

a complete digital model of all relevant aspects of the

system is needed, i.e. a Digital Twin (DT).

There are powerful simulation frameworks,

where a DT “can live”, i.e. which combine different

simulation procedures and thus enable the interaction

described above (Schluse et al., 2018). Nevertheless,

there are still problems of integrating methods built

up on highly discretised models, as it holds true for

all sort of Finite Element Analysis (FEA). Apart from

the different level of detail of the respective models,

especially the computing time for simulation is rather

different: DTs usually cover controlling and

sometimes further concepts as e.g. hardware-in-the-

loop and thus the calculations are performed quite

fast; some aspects of the simulation are real-time

capable. On the other hand, solving thousands of

coupled differential equations for an FEA needs a lot

of time to converge and to lead to a reasonable

outcome.

One special sector of FEA are Thermal

Simulations. They are very important for all

mechatronic systems, as movements in general and

motors especially always produce heat. It is crucial to

know, where this heat is going, i.e. which

temperatures can be expected where. Simultaneously,

several forms of thermal energy can only be

determined in the context of the whole system, e.g. all

forms of friction between single components.

In this paper, we present a concept to integrate

Thermal Simulations into a DT simulation framework,

thus expand their scope and increase their

functionality. The concept is based on using an

external FEA solver and an automated exchange of

characteristic variables. It was implemented

successfully and first applications scenarios could be

analysed.

The work was conducted as a student project

(Weid et al., 2021) and is based on our previous work

(Kaufmann et al., 2017), (Kaufmann et al., 2019).

Kaufmann, D., Weid, J. and Rossmann, J.

Expanding the Scope and Increasing the Functionality of Digital Twins by Integrating Thermal Simulations.

DOI: 10.5220/0012081600003546

In Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2023), pages 259-266

ISBN: 978-989-758-668-2; ISSN: 2184-2841

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

259

2 KEY METHODS AND

RELATED WORK

When Thermal Simulations are used within DTs to

enlarge their functionality, the underlying

mathematical and computer scientific concepts of

both have to be considered as they form the base of

this work. Thus, they shall be briefly described in this

section together with an overview of the current state-

of-the-art.

2.1 Thermodynamics and Thermal

Simulations via Finite Element

Analysis (FEA)

Whenever temperature propagation or heat flux is

calculated, the general laws of thermodynamics apply.

Most important for this paper are the principles

concerning thermal conductivity, which describes the

propagation of thermal energy due to a temperature

difference ∇𝑇𝒙 in a solid component. A heat

flow 𝒒



𝒙 occurs until a homogeneous temperature

distribution is achieved. The material of the solid

determines how this thermal equilibrium is reached,

therefor there is a specific thermal conductivity value

𝜆 𝑊/𝑚𝐾 for each material, relating both quantities

(see Equation 1).

𝒒





𝒙



𝜆𝛻𝑇



𝒙



(1)

This and further equations can be found in much

more detail in many textbooks (Baehr et al., 2019).

Nevertheless, depending on the complexity of the

geometry, material properties and boundary

conditions, it becomes impossible to find an

analytical solution, so a numerical approach via

simulations is required.

Thermal simulations cover a wide spectrum of

application areas, as e.g. component development and

thermal testing for automotive and aerospace, (Bu et

al., 2020), as well as the development of electronic

components in general (v.d. Broeck et al., 2017).

Concerning the underlying models and methods

of Thermal Simulations, one important distinction

has to be made: whether the component of interest is

fluent or solid. In the first case, the simulations are

performed via Computational Fluid Dynamics (CFD),

as it holds true for e.g. the integration of heat

exchangers in modern vehicles (Deng et al., 2013).

For solids, usually Finite Element Analysis (FEA) is

used, as e.g. in the simulation of heat propagation in

brake discs (Cho et al., 2008).

In this work, the application scenarios covered by

DTs are mostly built around mechatronic systems,

where the behaviour of one single component is

examined. Thus, only the FEA version of Thermal

Simulations is of interest herein.

The thermal impact itself can be physically seen

as a load, while the consequences on the component

always result in a distribution (of heat/

deformation…). Thus, as it holds true for any FEA,

the first step is to mesh the component, i.e. discretize

it into several elements connected via a defined set of

nodes. The partial differential equations can now be

set up element-wise and are coupled. The boundary

conditions indicate which outer impacts are acting on

the component and are considered in the system of

equations as well. This concludes the preprocessing.

Next, the FE model can be transferred to a solver

whose task is to obtain the numerical solution of the

system of equations. It is always an approximation of

the actual values and the quality of the results depends

on several factors set during the preprocessing, as the

resolution and nature of the meshing, as well as

previously defined termination criterions. Due to an

exponential relationship between these factors and

the computational steps required to solve the

equations, an increase in the computational effort

beyond a certain point can no longer be compensated

by additional computing power, so the calculations

take more time. Since the simulation of thermal

processes can take several days even for small

structures, it is only recommended to carry out the

FEA with sufficient experience in order to obtain

usable results within a manageable time frame.

In the last step, the determined thermal models are

processed for a descriptive presentation. This is the

task of postprocessing.

2.2 Digital Twins (DTs)

Simulations are nowadays a recognized standard in

many industries, as mechanical or electrical

engineering, material sciences, robotics and many

more. Simulation methods and algorithms are used

throughout the entire development process and

lifecycle of a single component or a complete system.

Although each simulation method provides

valuable insights separately, there is a lack of a cross-

system and cross-discipline approach that also takes

into account the interplay of components,

environment and disciplines.

A Digital Twin (DT) as a virtual representation of

its Real Twin solves this problem, as it considers

many (in best case: all relevant) aspects of a complex

scenario. Thus, it combines all these simulation

domains and the cross-lifecycle use of simulation in a

SIMULTECH 2023 - 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

260

comprehensive concept. At the same time, simulation

becomes one of the enabling technologies for DT.

Michael Grieves established the use of the term

DT in relation to technical systems in 2002 (Grieves,

2016). In 2010, NASA applied the concept to

aerospace and used it to refer to "ultra-realistic

simulation" (Shafto et al, 2010). Subsequently, the

term was illuminated from many sides and got

common in various disciplines, e.g. from the

perspective of simulations, cyber-physical systems or

production engineering.

In 2018, Gartner classified DT as part of the

digitized ecosystem as one of the five definitive

technological trends and predicted the technology to

reach the "productivity plateau" in 5-10 years

(Panetta, 2018).

2.3 Coupling of DT and Thermal

Simulations

Designing a DT that includes both the thermal

behaviour and crucial functions of mechatronic

systems (as communication or controlling interfaces)

usually leads to a challenge. It emerges from the fact

that FEA requires a lot of time for exact results, while

simulations of real-time processes such as interaction

with other DT or RT (hardware-in-the-loop) shall

compute results in the shortest possible time -

preferably in real time.

Previous approaches for the realization of an

interaction are either rather specific for a certain

application (Mussalam et al., 2010), (Kral et al.,

2013) or concentrate on theoretical methods (Busch,

2012). Theoretical approaches are usually based on

co-simulation, where quantities are exchanged

between subsystems at runtime at specific time

intervals (Schmoll, 2015). These subsystems are

modelled in a software environment suitable for the

respective problem. However, there is no general

solution for the handling of the different runtimes and

the extrapolation of transferred quantities, what

makes an individual consideration necessary

(Stettinger et al., 2013).

3 CONCEPT

The difficulty of integrating Thermal Simulations

into DTs is to link the respective models and methods.

Compared to previous work on the integration of

Structural Simulations into DTs (Kaufmann et al.,

2017), the developed concept follows a similar

approach. An external FEA solver performs all

Thermal Simulations and the interaction with the DT

simulation framework is realised with the exchange

of characteristic variables.

3.1

Requirements

Analysis

In accordance to previous work (Kaufmann et al.,

2017), three main aspects were defined for a thought-

out integration of Thermal Simulations into a DT

simulation framework:

 Time-efficiency: The interaction only happens at

crucial points.

The usage of the external FEA solver can be

switched on/off. A sophisticated choice of

critical situations (e.g. when maximum thermal

load is expected) saves a lot of computing power

and time.

 Validity: The quality of the simulation methods

is maintained.

FEA is a commonly used and well-tested method

to perform Thermal Simulations (and further

simulations). Using existing meshers and solvers

takes advantage of years of development and

integrates the huge level of detail into the overall

picture of a DT without losing accuracy.

 Usability: The control is done centrally.

Parameters necessary for the Thermal Simulation

are defined in the DT simulation framework. It

forms the access point of the integration and thus

enables a central control of both simulation

methods.

3.2 Workflow: Integrating Thermal

Simulations into DT

Following the requirements, a FEA-compatible model

containing information about geometry and thermal

loads has to be formulated. To achieve maximum

efficiency, this is only done for components of the DT,

which will experience thermal loads.

Figure 1: The developed concept enables the integration of

thermal impacts into a DT by setting up an automated

workflow the user can start if necessary.

Expanding the Scope and Increasing the Functionality of Digital Twins by Integrating Thermal Simulations

261

A simple application scenario of a robot gripping

a sphere illustrates the workflow provided by the

concept (see Figure 1). The sphere is hot and the

impact on the DT – i.e. the robot – shall be analysed.

The gripping process is simulated in the DT

simulation framework (step 1  2). As soon as

contact is made, the gripper experiences a thermal

load. If the user decides a Thermal Simulation is

needed, the affected structures – i.e. the gripper jaws

– have to be identified and the thermal loads – i.e. hot

contact surfaces – have to be converted into boundary

conditions (step 3). The prepared model is transferred

to the Thermal Simulation software automatically,

where the thermodynamics equations are formulated

and solved (step 4). The results (e.g. a temperature

distribution of the gripping jaws) are returned to the

DT simulation framework and thus can be integrated

into the original model (step 5). If the user does not

request a Thermal Simulation, the simulation

continues (i.e. step 5 is reached without any

information about the impacts of thermal loads).

4 REALISATION

First of all, the concept could have been realized with

any software. Nevertheless, general applicability and

usability was considered important and thus suitable

programs were chosen for implementation.

4.1 Choice of Software

In this work, the starting point is an existing

simulation framework for DT. It already includes

many functionalities as dynamics, kinematics,

environmental simulation, controlling, sensor

simulation etc. (Rast, 2015), (Rossmann et al, 2011).

It combines the required models, data and simulation

methods and integrates them into higher-level

processes as well as into real systems (Schluse et al,

2018). The abstract “Versatile Simulation Database”-

(VSD-) class structure allows to implement special

functions in so-called extensions, which can be

dynamically added to the program (see Figure 2).

Nevertheless, consequences caused by thermal

impact cannot be considered yet and thus need to be

integrated in the DT simulation framework.

There are many computational tools being able to

analyse the effect of thermal impact on components.

A thorough analysis of different FEA software was

performed before choosing a certain program. The

selection criteria were accessibility, usability (i.e.

documentation), accuracy, functionality and – of

course – compatibility, as an interaction with the DT

simulation shall be implemented. Finally, defining an

evaluation scheme and distributing points from 1-3

for the different criteria, the open source software

Z88Aurora (Z88, 2023) was chosen.

Figure 2: The VSD microkernel structure of the DT

simulation framework enables integration of new

functionalities via extensions (cf. Rossmann et al., 2013).

4.2 Implementation

The exchange of characteristic variables between the

DT and the Thermal Simulation is implemented via

an interface (see Figure 3). The relevant pieces of

information for the respective models are transferred

via files (.stl for geometry, .txt for FEA-relevant

information and visualization-input). The files have

the syntax the Thermal Simulation software

Z88Aurora requires. The generation and processing

of the files (i.e. the interface) is controlled by the DT

simulation framework. Two extensions were

implemented that integrate the new functionalities:

Figure 3: Design of the interface. The exchange of

characteristic variables is done with files (middle), which

contain the information for the mesher and solver of the

Thermal Simulation software Z88Aurora (right). The

interface is controlled by two extensions of the DT

simulation framework. One handles the communication to

the Thermal Simulation (i.e. the preprocessing;

corresponding functions marked in blue), the other one the

communication from the Thermal Simulation (i.e. the

visualizations; corresponding functions marked in green).

SIMULTECH 2023 - 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

262

 Z88Extension handles all communication from

the DT to the Thermal Simulation. Besides the

infrastructure for the geometry import via an

(possibly external generated) .stl-file, this

consists mainly of the preprocessing for the FEA

(i.e. meshing control, definition of boundary

conditions, start of the solver, generation of

output files). Z88Extension has its own GUI

element in the DT simulation framework, where

the user can set all relevant parameters.

 VisualizationExtension handles all

communication from the Thermal Simulation to

the DT. This means in specific the processing of

the output files, i.e. the visualization of the

results from the Thermal Simulation.

5 EXEMPLARY USE CASE:

THERMAL SIMULATION OF

THE DT “VEHICLE AXLE”

In the following, the functions of the interface are

described on the basis of a thermal analysis of the

geometry shown in Figure 4 which can be interpreted

as a highly simplified version of a vehicle axle.

Figure 4: The imported geometry as base for the DT

“vehicle axle”.

This use case is only exemplary and shall

emphasize the functionality of the developed

integration of Thermal Simulations into a DT rather

than optimizing a real component. Thus, the object

size is rather small to keep the required computational

power low and thermal conductivity coefficients were

chosen, such that temperature differences and heat

flux could be particularly well illustrated.

Nevertheless, the structure contains subcomponents,

which are also used in the modeling of more complex

structures (cylinders, hollow cylinders, cuboids,

cavities). Furthermore, there is a certain reference to

real application scenarios: operation of a vehicle

generates heat due to friction of rotating shafts or

running gears, which then propagates along the axis.

5.1 Geometry Import and Meshing

The geometry is imported into the DT simulation

framework and thus the DT “vehicle axle” is created.

The geometry comes as an .stl file, which was created

externally with the help of CAD-software, following

the standard design process in mechanical

engineering.

First, the required density of the mesh has to be

defined. This can be easily done in the GUI of the DT

simulation framework by choosing different inputs

for the respective parameter in the Z88Extension.

Figure 5 shows the results for varying the parameter,

i.e. generating a finer mesh. The meshing of Figure

5 c) was taken for the following analyses, since the

FEA nodes are close enough to each other to map

temperature distributions and heat flux with a high

spatial resolution.

Figure 5: Nodes of the mesh for different values of the

respective parameter in the Z88Extension, which controls

the mesher from Z88Aurora out of the DT simulation

framework.

5.2 Temperature Analysis

First, simple temperature distributions are simulated

in the DT of the vehicle axle. Thus, specific

temperatures on the end faces of the axle are defined

via the DT simulation framework as boundary

conditions for the FEA. The GUI element of

Z88Extension provides the respective input options.

The upper boundary surface along the z-axis is

assigned a temperature of 𝑇



 100°𝐶 , the lower

boundary surface a temperature of 𝑇



0°𝐶. Figure

6 a)-c) shows the resulting temperature distributions

for different thermal conductivity coefficients 𝜆



The increasing propagation of temperature within

the component resulting from an increasing thermal

conductivity coefficient can be easily seen. The

temperature variation is typical for this set of

boundary conditions and resembles the results of

other scientific publications (Prabhu et al., 2018).

Expanding the Scope and Increasing the Functionality of Digital Twins by Integrating Thermal Simulations

263

Figure 6: Temperature distributions of the DT are calculated for different boundary conditions (temperatures 𝑇



on different

surfaces) and different thermal conductivities 𝜆



.The upper row shows a typical temperature shift for increasing 𝜆. The lower

row shows mostly asymmetrical and thus more complex boundary conditions.

Figure 7: Heat flux in the DT for different boundary conditions (temperatures 𝑇



on different surfaces) and different thermal

conductivities 𝜆



In a second step, more complex boundary

conditions were applied, i.e. also other faces of the

axle got a defined temperature value as an input (see

Figure 6 d)-f)). While d) shows again a straight

temperature drop along the y-axis due to symmetrical

boundary conditions, the axle was exposed to

asymmetrical boundary conditions in e) and f).

Nevertheless, the resulting temperature distributions

are still reasonable (e.g. the similar temperature of the

connection between the upper cylinder and the cuboid

in e)).

In a last step, the temperature distributions were

calculated in a “pure FEA” in Z88 without the DT

simulation framework. The results were the same in

both cases.

5.3 Heat Flux Analysis

For an exemplary analysis of heat flux, the boundary

conditions of the temperature analyses were taken. In

Figure 7, the colours code for the heat flux balances

of the nodes. In the following, we define a positive

heat flux balance such that the amount of outgoing

heat fluxes exceeds the amount of incoming heat

fluxes. Figure 7 a) shows the heat flux balances of the

boundary conditions from Figure 6 a). The colour

gradient illustrates that changes only occur in the

upper cylindrical subbody. Due to the constant

temperature in the lower part of the axle, this was

expected. Figure 7 b) shows the heat flux distribution

corresponding to Figure 6 c). In contrast to the

previous heat flux distribution, the temperature

changes now also reach the lower face of the lower

cylindrical subelement, so there occur negative heat

flux balances. Figure 7 c) shows the heat flux

distribution of the temperature distribution shown in

Figure 6 d). A constant heat flux balance is again

established inside the body, but is no longer constant

on the boundary surfaces. This can be explained by

the cavity in the centre of the body, where no thermal

SIMULTECH 2023 - 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

264

conductivity was specified, thus acting as an ideal

insulator.

5.4 Discussion

The first example of a DT with integrated Thermal

Simulations was created, examined and

thermodynamically analysed from within the DT

simulation framework.

Thus, the requirements of usability and

enhancement of time-management were met; both

secured by a central point of access for the whole

interaction with the FEA in the DT simulation

framework.

Besides, the resulting temperature distributions

and heat fluxes were the same in the DT simulation

framework as in a “pure FEA” only using the Thermal

Simulation software, which validates the interface

and the approach. Furthermore, they showed the

expected physical behaviour in accordance with other

Thermal Simulation related publications. Thus, also

the required preservation of quality of each

simulation method respectively was validated.

6 CONCLUSION

The aim of this work was the integration of Thermal

Simulations via FEA into an existing DT simulation

framework and thus expanding the scope of DTs.

In the development of the concept for this

integration, a special focus was set on the general

usability and validity. Thus, the DT environment

served as access point to conduct Thermal

Simulations of defined components. This concept

also optimizes time management, as this can be done

when critical situations occur in the application

scenario (contrary to performing an FEA at every

time step).

For the specific implementation, new extensions

for DTs were developed, which manage the

externally performed Thermal Simulations with

Z88Aurora. During the implementation, it was

necessary to convert the DT model to a model that is

FEA compatible. This was achieved by importing the

geometries from external .stl files. The

transformation of the models and the entire setup of

the Thermal Simulation was automated such that a

high degree of user-friendliness can be guaranteed.

The extensions currently include the calculation of

steady-state temperature and heat flux distributions,

where the starting point is a temperature distribution

on the surface.

7 OUTLOOK

Although a first approach of integration of Thermal

Simulations into a DT was successfully performed,

there are still opportunities for future work. For

example, more complex concepts concerning

thermodynamics could be integrated (e.g. thermal

loads due to thermal radiation, convection or electric

currents). In addition, the thermal processes might

result in geometric changes that have been neglected

so far. Thus, a combination with the structural

simulation framework for DT (Kaufmann et al.,

2018), (Kaufmann et al., 2019) will be interesting.

The same holds true for a specific application

scenario in space robotics, where heat influx is

already calculated in a DT, but not connected to FEA

(Rossmann et al., 2018).

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