A preview for vehicle driveability characterization on subsystem level powertrain

Abstract

The increasing complexity of driving functions at the overall vehicle level results in a corresponding increase in complexity in the validation process. To expedite this process, validating overall vehicle characteristics at the subsystem level is also beneficial. Validating on subsystems is discussed using the example of the characteristic longitudinal vehicle shuffle as an overall vehicle property concerning the powertrain subsystem. The publication aims to demonstrate, through a literature review, the extent to which consideration of driveability-relevant properties already occurs at the physical subsystem level, with a focus on the frequency range of up to 30 Hz. The literature research shows that the considerations concerning driveability at the subsystem level are currently neither state of the art nor scientific, especially about the increasing number of electric vehicles; the level of knowledge is low. In the second step, this theoretical use case will be presented, in which a physical prototype (powertrain) is used to examine superimposed overall vehicle characteristics (longitudinal vehicle oscillation frequency (shuffle frequency)). For this purpose, a Hardware-in-the-Loop (HiL) approach is presented, which consists of a device under test (DUT) and two highly dynamic, permanently excited synchronous machines as load machines. A suitable manoeuvre (Tip-In) is shown, which makes it possible to evaluate the longitudinal vehicle shuffle. The analysis of the results of a coupled vehicle simulation in the HiL shows evident discrepancies in the verification of the demand values. Concerning a Tip-in, deviations of at least 70% can be determined for the speed required by the whole vehicle simulation and the system response (actual speed signal of the load machines) as a result of the step function. The wheel slip calculated from this propagates the error in the calculation of the virtual vehicle’s longitudinal shuffle frequency. Analyzing the results makes it currently impossible to validate the longitudinal vehicle shuffle at the subsystem level. Finally, there is a discussion about what significant changes are needed to achieve the required goal of vehicle driveability characterization at the powertrain level.

Keywords

driveability electrical powertrain hardware-in-the-loop vehicle shuffle frequency torsional dynamics

Introduction

The vehicle development process can be described by the V-model, which comprises system design and system integration. This approach originates from software development and is primarily determined by concept development. At the macro level, the V-model consists of three levels: system, subsystem and component level. Property verification and validation are conducted continuously at each level of the development process, taking systemic interactions into account. The complexity of the systems increases during the ongoing validation process.¹

Validating an increasing number of driving functions means an increase in the complexity of the validation process¹ and, therefore, a high time expenditure. By combining a prototypical test specimen with a cyber-physical complete vehicle environment, a system can be created in which the real hardware behaves in the same way as if it were implemented in a real complete system. The results of the DUT directly influence the calculations of the coupled simulation. This approach is generally referred to as HiL.²

Transitioning from real-world driving to test rigs is also referred to as ‘road-to-rig’. It is characterised in particular by the reproducibility of the tests, the minimisation of expensive prototype vehicles, flexibility and variability. This leads to optimisation and shortening of the validation process and even makes it possible in special cases. The result of the test rig is strongly dependent on the test rig itself, the DUT, the degree of abstraction of the coupled simulations, and their real-time capability.^2–4

Depending on which driving function or vehicle characteristic is to be analysed, different challenges arise for the validation process. One characteristic vehicle property is longitudinal vehicle shuffle, which describes the oscillation of the entire vehicle in the direction of travel. This phenomenon is attributed to the first natural frequency of the powertrain, which can be perceived as unpleasant by occupants and is therefore a significant factor in driving comfort.⁵

Vibrations up to 30 Hz can be categorised as relevant for driveability. Due to their perception of vibration, humans perceive frequencies up to 10 Hz as particularly unpleasant, which collides with the longitudinal vibration of the vehicle and emphasises the importance of driveability tests.^6,7

This article will therefore examine the extent to which the consideration of driveability as an important comfort feature at the overall vehicle level is taken into account in the validation process at the subsystem level so that the development process can be optimised.

The article is organised as follows: first, a comprehensive literature search is presented, and the sources to be considered are pre-sorted according to the criteria presented. In the next step, these sources are analysed and sorted by subject area. In the following, the articles dealing with the validation of driveability on the complete vehicle are analysed in greater depth. The gaps in the current state of research are identified and pointed out.

Finally, the status quo of a highly dynamic test rig coupled with a full vehicle simulation is presented. A Tip-In is used to highlight the challenges that currently exist, making direct analysis difficult. Measures that must be implemented first to enable a valid method for validating the driveability of the powertrain subsystem are discussed.

Method of systematic research

The literature research is intended to identify existing deficits, show the context in which the HiL approach has been used to date concerning the vehicle powertrain and clarify the following questions:

To what extent is the first natural frequency of the powertrain analysed or validated concerning the longitudinal vehicle shuffle in the HiL approach?

How is the representativeness of these results on the HiL compared to the real (prototypical) complete vehicle assessed?

What are the relevant driving manoeuvres for a validation process?

The systematic research and its documentation were carried out according to the PRISMA procedure⁸:

Identification of publications through a systematic search campaign.

Screening of all results found and sorting out based on predefined criteria.

Inclusion of the remaining publications in the review.

An initial literature search was carried out on Scholar on 23 September 2023, and the search operators defined were:

allintitle: (Rig to Road OR in the loop OR validation) AND (powertrain OR drivetrain OR driveline).

This search returned 81 results on the day it was carried out and covered the publication period from 1990 onwards.

The publications identified by the systematic search and additionally found via cross-references were pre-sorted in the second instance based on content criteria. Only sources dealing with motor vehicles were explicitly considered for further evaluation. This applies to series vehicles, as well as prototypes and end-of-life vehicles, which serve as carriers for prototype units.

Explicitly excluded are rail vehicles,⁹ wind turbines,¹⁰ rickshaws,¹¹ commercial vehicles¹² and tractors¹³ etc.

The remaining 84 contributions were taken into account for the evaluation of the initial research. To categorise the content of the remaining sources, they were assigned to categories defined in Table A2. A source can be assigned to several categories.

An examination of the groups in Table A2 reveals that the focus of the investigations on the powertrain in this research is on the topics of energy management, digital twin modelling and reducing the necessary test time (frontloading). None of these dominant groups addressed the issues relating to driveability.

In addition, the analysed sources in each group were subdivided according to the type of mechanical power generation. The following four categories were defined for this purpose:

The internal combustion engine (ICE) serves as the sole drive for the configuration under consideration → ICE.

In the powertrain under consideration, two types of energy converters generate mechanical power. The two drive types cannot drive the vehicle completely decoupled and influence each other in their free oscillation form, for example, a parallel hybrid →Hybrid.

An electric motor (EM) serves as the sole energy converter for the generation of mechanical power. In this analysis, the serial hybrid and a range extender are also assigned to this category, as the combustion engines of these systems are not mechanically connected to the powertrain and therefore have no influence on its free vibration behaviour →EM.

This category summarises all publications that deal with the subject area of methodical validation of components in the X-in-the-Loop (XiL) approach and the significance of the results obtained →None.

The distribution of the categories in the respective groups can be found in Figure 1. For further evaluation, the focus was increasingly placed on electric drives (category 3), as these are the subject of research due to the emphasis on alternative drive types, and their application is also possible in the present test rig.

Figure 1.

Distribution within the groups, 1 development of algorithms/tools, 2 digital twin, 3 frontloading, 4 driveability/torsional dynamics, 5 durability, 6 vehicle control, 7 energy management, 8 history, 9 noise/harshness, 10 safety, 11 XiL method.

Validation of driveability on the subsystem level

To consider and evaluate the vibration behaviour of the powertrain in the HiL, the groups for the description of vibrations on the powertrain (groups 4 and 9 of Figure 1) and the methodical consideration of the XiL (group 11) are presented in more detail below. At the end of this chapter, the three questions defined before are answered.

Frequency evaluation of the powertrain in the XiL complex

The vibrations occurring in the vehicle can be divided into noise vibration and harshness (NVH) depending on the frequency range. Concerning the acoustics of the powertrain, Dupont et al.¹⁴ consider the airborne and structure-borne vibrations of an electric vehicle drive. In contrast, Lucas et al.¹⁵ describe a methodology for calculating noise emissions across the entire vehicle based on measurements of the powertrain subsystem in the HiL network, thereby predicting the noise level. The frequency range from 30 Hz to 2 kHz is specified and thus explicitly differentiates itself from the driveability range as defined in Schmidt et al.⁶ In addition, Lucas et al.¹⁶ extend this method to virtual test vehicles. The majority of the publications focus on the vibrations throughout the entire vehicle resulting from the rotational vibration of the powertrain. Andersson and Abrahamsson,¹⁷ Nickmehr et al.,¹⁸ Sorniotti¹⁹ and Wang et al.²⁰ consider the deformation and vibration modes of the powertrain and highlight the main factors influencing the level of natural frequencies. Sorniotti¹⁹ specifies the properties of the tires and side shafts as the main influencing factors. The investigations by Yamada et al.²¹ on wheel hub motors as unsprung masses and by Andert et al.²² on the coupling of an engine and a transmission test rig are to be regarded as special cases.

Regarding the influence on the natural frequency of the powertrain, the publication by Hoang et al.²³ should be emphasised. By using a rheological bearing as a tunable vibration absorber on the test rig, the frequencies of the test specimen are shifted away from the resonance frequency. The steady-state vibrations can be reduced, but the structure of the test rig must be actively influenced.

An important component in analysing the driveability of vehicles is considering human perception of vibrations. List and Schoeggl²⁴ and Machmudi Isa et al.²⁵ describe a method for taking into account driveability (gear shift, engine start behaviour) and early tuning of the control units on the vehicle to reduce the time required for calibration, in particular. Albers et al.²⁶ show a general framework in the development process that is also suitable for analysing driveability.

Fan⁵ and Hagerodt²⁷ investigate characteristic parameters of the vehicle, using vehicles with combustion engines and manual transmissions, and evaluate their influence on the perceptible vibrations in the longitudinal direction. Through their research into various possible phenomena, Schmidt et al.⁶ formulate the frequency range relevant for powertrain driveability at frequencies below 30 Hz.

Methodical evaluation of the powertrain in the XiL complex

The idea of integrating a test object into a cyber-physical test network is more than 100 years old² and has evolved in recent decades from a platform for validating control units or control mechanisms to a tool for system synthesis and optimisation.²⁸

In doing so, Brayanov and Stoynova² present the historical development of this tool, from its origins as an application for simple flight simulators to its current complexity, with a particular focus on the various architectures and definitions that have emerged during this period. Fathy et al.²⁸ name the most important prerequisites for the integration and operation of a HiL network. These relate to the hardware used for the test object and the test environment, as well as the real-time capable communication of the systems involved. For example, the sensors/signal acquisition, processing of the signals (decoding, pre-filtering and measurement noise), the demands on the computing technology used, the causality of the connected components (master-slave) and the modelling quality of the residual vehicle simulation used should be mentioned here in particular. Using the example of an electronic control unit test rig, Khan²⁹ describes a HiL system that enables adaptation for various test objects without requiring changes to the test rig.

For the comparison of the measured data recorded in the ‘ideal’ HiL and in the ‘real’ field test, dos Santos et al.⁴ describe a methodology to compare these results and to describe the representativeness of the data from the test rig. The factors to be considered here are precision (random errors), accuracy (combination of random and systematic errors), reliability (dependence on the test to be run) and representativeness itself (a few test points describe the overall system just as well as if a large number of test points had been run). The key message is that the informative value of the measurement data depends on both the system, which consists of the test rig environment and the test specimen, and the type of test performed. To quantify the uncertainty of the result, the accuracy of the signals that pass through a modelled subsystem is multiplied by its accuracy. If two or more signals are added together, the accuracy of the resulting signal is determined by the average of the individual accuracies. For a more detailed explanation, refer to dos Santos et al.⁴ Forrier et al.³⁰ and Klein et al.³¹ compare the data from HiL applications with real data from the field, for example. Olofsson and Pettersson³² also compare data from real driving with data from an all-wheel drive powertrain test rig, but focus on modelling the driver, who is linked to the test rig through a complete vehicle simulation. Powell et al.³³ describe the possibilities and differences resulting from the investigations in the test field, such as the positioning of sensors.

Schmidt et al.⁶ examines the use of in-the-loop approaches in various stages of vehicle development and emphasises that for even more time- and thus cost-efficient methods, the application is necessary at the overall vehicle maturity level. The state of the art in analysing driving behaviour is still time-consuming and costly, relying on real driving tests. For the early investigation of driveability in the development process, this is primarily due to the powertrain subsystem. The residual vehicle simulation for integration into the HiL approach and understanding the influence of the test rig on the test specimen are cited as major challenges. Depending on the application, the characteristic properties of the powertrain may differ from those of the overall vehicle.⁶

As a consequence, Schmidt et al.⁶ emphasise that the consistent comparison of a test specimen in the HiL and the complete vehicle must be made. This should be carried out following the explanations in dos Santos et al.⁴ for special characteristic variables, and thus depending on the corresponding test manoeuvres. The accuracy of the results must be evaluated by analysing the complete combination of test specimen, test rig and test scenario.

In his work, Düser¹ describes a framework for categorising the validation of increasingly complex driving functions in the vehicle development process and ensuring it is holistic. This is explained using driving assistance functions and their interaction with the vehicle powertrain as an example.

Finally, the main findings from the literature review will be summarised, and the defined questions will be addressed.

Question 1

– To date, there are no publications that deal adequately with the consideration of longitudinal vehicle shuffle at the subsystem level. The property that characterises driveability at the overall vehicle level is not validated based on the subsystem in the HiL network, as far as the research investigated is concerned. It should be emphasised in particular that the investigations for electric drives are hardly present concerning the increasing electromobility, see Düser.¹

– The frequency range of the driveability to be analysed can be limited to 30 Hz.⁶

Question 2

– The main factors influencing the position of the frequency of the longitudinal vehicle shuffle and the decay of the vibration are the properties of the side shafts and the tire slip, which is proportional to the damping.^5,19 Pillas³⁴ indicates this as the main influencing factor of damping. This also illustrates the need for exact representation on the test rig, whereby the level of detail must be selected accordingly and non-linear properties must be taken into account.⁶

– The main factors influencing operation can be summarised as signal acquisition and processing, the computer technology concerning real-time requirements and the simulation models linked to the test rig. These must be tailored to meet the specific application’s requirements.²⁸

– Both the test specimen itself and the test rig have a significant influence on the measurement result. The influence of the test rig comprises several components. These are, for example, the mechanical adaptations of the test specimen to the test rig, whereby additional components introduce additional masses, stiffness, and damping, which can significantly influence the vibrating system. Schmidt and Prokop³⁵ show an example of the influence on the vibration properties of the test rig (Figure 3) used in the following. On the other hand, the scenarios applied in the coupled overall vehicle simulation result in different requirements for the dynamics of the HiL. For example, a manoeuvre with a step function in load demand requires high gradients for torque and speed and can be significantly influenced by the controller or the dead times.^22,36

Question 3

– A step function in the set-point specification is suitable for characterising the first natural frequency of the powertrain in the HiL system. This allows conclusions to be drawn about the step response, the frequency response and the first torsional natural frequency.³⁶

Current system status and challenges

The challenge is to adapt the characteristic properties of the specimen in the HiL to the target values of the DUT, as applied in the complete vehicle. In the context of driveability, this also concerns the dynamic properties. The primary goal is to map the results of the HiL approach with real-world driving tests at the full vehicle level. For this consideration, Schmidt et al.⁶ specify that the property adaptation on the test rig should be model-based in the co-simulation.

A subsequent methodical search campaign was conducted to identify adaptation options reported in the literature. A particular focus was placed on customisation options in the HiL network. The results presented in Table A3 resp. Figure 2 shows that no method exists for analysing vehicle shuffle. The adjustments made to the powertrain are aimed at optimising energy management and performance by varying the parameters of the digital twins.

Figure 2.

Distribution within the groups, 1 frontloading, 2 hardware-optimisation, 3 vehicle control, 4 energy management, 5 software-optimisation, 6 vehicle performance.

The current system status is analysed using suitable driving manoeuvres, and the challenges for validating driveability at the subsystem level are derived.

Status quo – HiL application for driveability research

Figure 3 shows the schematic structure of the HiL on the test rig used. An EDU, consisting of an inverter, motor control unit, permanent magnet synchronous machine, gear stages and side shafts, represents the DUT. The power supply is provided by a battery emulator, which replaces the real vehicle battery. The high-voltage (HV) box represents the transfer point between the test rig peripherals and the DUT concerning the power supply.

Figure 3.

Powertrain test rig at Technical University Dresden (TUD) with applied electric drive unit (EDU) and coupled full vehicle simulation.

The load machines are each supplied and controlled by a frequency converter, which enables operation in four quadrants and thus both motorised and regenerative operation.

The coupled overall vehicle simulation is executed on a real-time computer and connected to the test rig at a rate of 1 kHz via user datagram protocol (UDP). CarMaker Testbed is used to specify the engine torque demand and wheel speed demands for the individual operation of the three machines. Note that the load machines are in a closed control loop, while the test object is only controlled in an open control loop due to the lack of feedback sensors. An Audi Q4 e-tron with rear-wheel drive was parametrised as a virtual test vehicle.

The main specifications of the test rig are summarised in Table A1.

To analyse the system response concerning the dynamic properties of the powertrain in the HiL, a step function in the form of a pedal jump is specified in the CarMaker Testbed environment. The road surface is defined as a plane with a dry surface. The individual steps of the manoeuvre are:

Acceleration to a constant initial velocity $v$ . The target values are varied here ( $v$ = 0, 10, 20, 30, 40, 50, 60, 70, 80 km/h) to evaluate the influence of the speed on the results. The duration of the first step is 30 s.

Removal of a pedal request and 1 s coast down.

Tip-in from 0% to 50% pedal position in 20 ms and holding the set-point for 4 s.

Tip-out from 50% to 0% pedal position in 20 ms and holding the set-point for 5 s.

Deceleration of the vehicle to a standstill with a deceleration of 2.5 m/s².

The Figure 4 in the upper diagram shows the pedal jump in the simulation (ideal) as well as the realisation on the test rig for each initial velocity. The connection to the DUT is made via a controller area network (CAN) interface with a 100 Hz communication frequency, which is shown in the detailed view and only affects the torque demand signal. The differences that can be seen in the theoretically always identical signal are due to the application status of the prototype DUT. This shifts the test on the time axis and illustrates the influence of signal processing in the real-time system. The influence on the determined data is random and therefore not directly reproducible.

Figure 4.

Tip-in of the cyberphysical vehicle (CarMaker Testbed) – Characteristics of the coupled vehicle simulation depending on the initial velocity in km/h.

The evaluation of the resulting frequency of the vehicle shuffle is in Table 1. An average frequency of 8.8 Hz is obtained over the 27 measurements, with a standard deviation of approximately ±0.27 Hz taking into account the relative probabilities. The middle diagram shows the resulting acceleration signals of the rigid vehicle body in the longitudinal direction (longitudinal shuffle of the vehicle). The lower diagram shows the longitudinal slip condition of one tire of the virtual full vehicle. This is represented by an IPG RealTime Tire (dimension: R19). The curves of slip and longitudinal acceleration are qualitatively the same, as the rolling tire results in a translational movement of the vehicle, and no non-linear properties are reached. The relationship is illustrated in equation (4). The graphs show a decaying oscillation with one period to a stationary end value for the duration of the constant accelerator pedal.

Table 1.

Shuffle frequency from vehicle simulation for signals in Figure 4, mean values for three measurements.

Initial velocity in km/h	0	10	20	30	40	50	60	70	80
Frequency in Hz	9.0	8.9	8.7	8.7	8.8	8.6	8.8	9.0	8.7

The relationship between the physical load machine/virtual wheel speed and longitudinal acceleration of the virtual vehicle body can be explained in a simplified way using the representation in Figure 5, the equations of motion can be found in equation (1)–(5), (cf. Fan⁵), taking into account the slip definition:

F_{x} \cdot r_{stat} = F_{w} \cdot r_{stat} + m_{vehicle} \cdot \overset{\cdot\cdot}{x} \cdot r_{stat}

(1)

F_{x} \cdot r_{stat} = J_{R} \cdot \underset{R}{\overset{\cdot\cdot}{φ}} + F_{w} \cdot r_{stat} + c (φ_{R} - φ_{F})

(2)

M_{shaft, virt} = J_{F} \cdot \underset{F}{\overset{\cdot\cdot}{φ}} + c (φ_{F} - φ_{R})

(3)

\overset{\cdot\cdot}{X} = {\overset{\cdot}{ω}}_{tire} \cdot r_{dynamic} \cdot (1 - s)

(4)

The balance for the simplified model of the load machine on the test rig side is as follows:

M_{shaft, real} = J_{dyno} \cdot \underset{dyno}{\overset{\cdot\cdot}{φ}} + M_{dyno}

(5)

With F_x as the driving tire force, r_{stat, dynamic} as the static or dynamic tire radius, F_w as the force of the driving resistances (air, gradient and rolling resistance), m_vehicle as the vehicle body mass, x as the translational coordinate in the longitudinal direction of the vehicle, $ω$ _tire as the tire angular velocity and s as slip. The torque transmitted from the DUT via the side shafts to the load machines is labelled M_shaft,real, the equivalent torque taken into account for the simulation is labelled M_shaft,virt. Figure 6 shows the demand values (wheel speed) calculated in the vehicle simulation because of the pedal jump as driver input. Additionally, the actual values for the speed of the right load machine are shown, which are measured via the speed sensor. The measurements are taken from the manoeuvre with an initial velocity v₀ = 20 km/h as an example.

Figure 5.

Transition of cyberphysical system test rig, dynamometer – left, tire in vehicle simulation – right, based on Fan.⁵

Figure 6.

Tip-in of the cyberphysical vehicle (CarMaker Testbed) – measured values of test rig dyno (act) and demands of vehicle simulation (DMD) for three measurements.

At the time of the load step, a deflection of the wheel speed in the direction of the target value can be recognised. The amplitude of the deviation is approximately constant over the load points, respectively, independent of the engine or load machine speed, and is approximately 40 rpm. For the Tip-out, there is also a deflection at the time of the load jump, which also acts in the direction of the target value and is approximately constant in amplitude for the various load points. The deviation of demand and feedback speed is independent of the initial speed, but dependent on the applied load.³⁷ The test rig was designed as a transmission test rig, which utilises a PID controller with feed-forward control. The Load machine, operating in single control mode, cannot compensate instantly for the load step in the prime mover and therefore accelerates unexpectedly. After a certain amount of time, the machine is capable of reaching the desired speed demand.

The deviations in the interval shown (Figure 6) between the demand and actual values of the respective test are noted in Table 2. The normalised root mean square error (NRMSE) was selected as the comparison criterion (equation (6)), with k_meas as the measured values and k_sim as the demand values of the overall vehicle simulation.

NRMSE = \frac{\sqrt{\frac{\sum_{i = 1}^{n} {(k_{meas} - k_{sim})}^{2}}{n}}}{\max (k_{sim}) - \min (k_{sim})}

(6)

The results in Table 2 clearly show that the curves must be evaluated differently depending on the interval under consideration. The deviations between target and actual values are minimal concerning the entire test (NRMSE < 2.5%). Concerning the manoeuvre (Tip-in and Tip-out with decay time, t = [31 s, 37 s]), the deviations with values less than 5% are also to be regarded as small. However, the consideration of the error concerning the interval of the longitudinal oscillation due to the Tip-in (t = [31 s, 31.5 s], comparison detailed plot in Figure 4) is at least 70%.

Table 2.

NRMSE in % for speed demand values (for rear right tire) from vehicle simulation and measured speed from test rig (right dyno), mean values for three measurements.

Initial velocity in km/h	0	10	20	30	40	50	60	70	80
NRMSE, t = [0 s, 50 s]	2.4	1.9	1.6	1.4	1.2	1.1	1.1	1.0	0.9
NRMSE, t = [31 s, 37 s]	5.0	5.1	5.0	4.9	5.0	5.0	5.0	5.0	5.0
NRMSE, t = [31 s, 31.5 s]	87.7	99.6	87.0	84.0	91.5	83.9	80.1	81.6	73.4

The Rotor speed is transmitted back to the coupled vehicle simulation, where it is interpreted as wheel speed. The overshoot causes large wheel slip values due to the rapid increase in wheel speed compared to the vehicle’s velocity. This directly influences the calculated acceleration curves or the longitudinal vehicle shuffle of the vehicle, as shown in Table 1 and equation (1).

It can therefore be concluded that the loads applied by the load machines, which the DUT experiences, do not correspond to those that would be expected during real driving, particularly when focusing on the Tip-In/Out regarding driveability. The longitudinal accelerations determined in Figure 4 are therefore not directly transferable, and consequently, it follows that no valid consideration of driveability is currently possible for this specimen using the example of longitudinal vehicle shuffle on the subsystem test rig. Examining the minor deviations over the entire test period can be misleading when it comes to specific features, such as vehicle shuffle. Another significant cause for the discrepancy between demand and actual values resulting from the step function can be attributed to the dead times of the electric machines. Table 3 shows the dead times of the three machines used. For reasons of confidentiality, the display is standardised to the dead time of the load machines.

Table 3.

Comparison of the experimentally determined dead times of the permanent magnet synchronous machines used, normalised to load machines.

Parameter	Device under test	Load machines (identical)
Dead time ( $t_{dead, i} / t_{dead, load}$ ) in [−]	6.25	1

The ratio of the times (factor > 6) shows that the DUT sets the demand values with a significant delay compared to the load machines. The synchronously sent signals of the demand values are therefore applied highly asynchronously. Taking equation (5) into account, the non-synchronised torques can change in the rotational speed of the rotor shaft.

Challenges for the validation of driveability at subsystem level

The system shown, consisting of a test rig, test specimen, and residual vehicle simulation, will be analysed in more detail by the authors in further investigations to make the test rig suitable for considering driveability at the subsystem level. Further adaptations are required for the use case presented.

This results in the following main areas of investigation and challenges, which are to be presented in the future:

The significant influence of the side shafts and the tire properties on the position and the vibration behaviour of the vehicle longitudinal shuffle are known from the literature and refer primarily to results from the simulation or tests with complete vehicles or powertrains with real tire-road contact.^{5,19,34,38–40} Since the genuine side shafts are used in the test rig application, as shown in Figure 3, their influence is recorded and taken as given. However, the road contact or slip is represented by the coupled simulation models and applied by the load machines. The influence of the used tire model on the resulting vehicle longitudinal acceleration is to be investigated by analysing the sensitivity. A real-time capable short wavelength intermediate frequency tire (SWIFT) model will be used here. This tire model enables the modelling of tire dynamics up to 60 Hz and thus covers the complete relevant frequency range of driveability. In contrast, the less complex magic formula tire (MF-Tire) model only maps frequencies below 10 Hz.⁴¹

New control concepts are being developed to reduce the influence of the test rig on the dynamics of the test specimen and thus on the coupled closed-loop overall vehicle simulation for highly dynamic manoeuvres such as Tip-ins and Tip-outs. Among other things, these should enable dead time compensation in the time domain, improve sensitivity to load jumps and ultimately reflect the behaviour observed in real-world driving tests → Road Matching. Concepts need to be developed and implemented for this. In particular, the transferability of using other test specimens in the HiL and the parametrisation of the concept must be developed.

Only when the HiL has been optimised to such an extent that valid road matching can be reliably provided is it even possible to evaluate the individual comfort of the vehicle occupants using objective parameters. With their work, the authors aim to develop a test rig suitable for this purpose. Objectivising ride comfort is a topic in its own right. For a general overview of the perception of whole-body vibrations, please refer to Schmidt et al.⁶ and the VDI.7 Biller et al.⁴² show objective metrics of longitudinal dynamics specifically for electric vehicles.

Conclusion

The literature research has shown that the validation of the overall vehicle characteristic of longitudinal vehicle shuffle frequency has not yet been carried out at the subsystem level. The current state of research in this area consists primarily of investigations into energy management and emissions reduction, as well as the reduction of test time. The demand for an agile development process in vehicle development necessitates further innovations in this area.

The presentation of a modern, highly dynamic powertrain test rig shows that the measurement results must always be evaluated in the context of the manoeuvre performed. For example, when performing transient tests, particularly, there is a high deviation in the measurable results, which is propagated in the calculation of a coupled overall vehicle simulation. This further consideration of vehicle properties is novel and not sufficiently represented in the current state of research.

This finding aligns with the literature research, which suggests that the mechanical adaptation of the test specimen and the periphery of the test rig can have a significant influence on system dynamics. In the current setup, these influences do not yet allow for a systemic consideration of the first natural frequency of the powertrain or the vehicle’s longitudinal shuffle as the response to a step function.

For a valid description of the effective chain from test rig to test specimen, the test rig control system must first be adapted. Suitable approaches must be found here to minimise or compensate for dead times and other disturbance variables in the control loop. To achieve these goals, the authors are taking the following steps:

– Creation of a suitable modelling approach for the test rig shown, which describes the torsional dynamics in the required frequency range.

– Development of a parametrisation method on the test rig to determine the required parameters.

– Creation of the state space model and analysis of the plant, taking into account the existing dead times.

– Design of a suitable controller following the requirements and results of the analysis.

In the second step, the significant influencing variables of the coupled vehicle simulation on the test specimen must be analysed. A balance must be struck between the level of detail in the models and their real-time capability. The modelling of tire-road contact should be particularly emphasised here, due to the impact factor shown on the value of the first torsional natural frequency of the powertrain. For this reason, the authors are investigating the influence of different tire models on the cyberphysical prototype.³⁷

Footnotes

Appendix

Table A3.

Categorisation of the publications included in the review for the second search from 7 November 2023 with the search terms allintitle: (Rig to Road OR in the loop OR powertrain OR drivetrain OR driveline) AND matching– 28 of 71 publications were considered for the evaluation – multiple entries possible.

Group	Description	Publications
Reduction in development time	Reduction of the necessary test times for real components/prototypes or frontloading	^93,100,101
Hardware optimisation	Optimisation of the parameters using a HiL setup	⁹³
Vehicle control	Vehicle control, brake control, torque control, shift control	¹⁰²
Energy management	Energy/performance management, energy consumption, efficiency	^{100 –125}
Software optimisation	Optimisation of powertrain parameters by creating a digital twin	^{100 –126}
Performance	Improving the performance of the powertrain	^{104 –106,109–112,116–126}
Number of publications		28

Acknowledgements

This report was written in German and translated into English. KI (DeepL) was used for this purpose.

Handling Editor: Chenhui Liang

ORCID iD

Carl Hübner

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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