Fourth International Conference on Material and Component Performance under Variable Amplitude Loading
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Load Spectra (2)

Session chair: Kepka, Miloslav, Professor (University of West Bohemia, Regional Technological Institute - research center of Faculty od Mechanical Engineering, Pilsen, Czech Republic)
Shortcut: E
Date: Monday, 30. March 2020, 15:50
Room: Hall A
Session type: Oral


15:50 E-01

Categorization of customer usage due to road quality (#119)

M. Städele1, B. Mundl1, R. Großkopf2, M. Streicher2

1 monalysis GmbH, Kempten, Bavaria, Germany
2 MAN Truck & Bus AG, München, Bavaria, Germany

As the load and stress conditions on the many components of a vehicle are significantly influenced by operational parameters such as e.g. the road quality, the road type or the topology, specific customer requirements for the distribution of vehicles are to be reliably taken into account.
The prerequisite for this is a suitable query of these operational parameters at the customer as well as an expedient translation into the loading and stress conditions which are relevant in terms of fatigue strength.
In this article a method is presented that enables to analyze traveled routes in order to evaluate and classify the essential operational parameters e.g. road quality, road category as well as longitudinal and lateral dynamics in terms of load and stress conditions. In addition this important information about the load and stress conditions are translated into a language which is understandable to the customer and can hence be queried by sales at the customer in an appropriate way.
Recorded accelerations are processed to reflect the load and stress conditions in terms of fatigue strength by height and frequency independently of vehicle conditions such as type of suspension, wheelbase, type of body, etc. Depending on the detected accelerations reliable conclusions can be made about the load and stress conditions on the vehicle. Moreover roads can on the one hand be categorized according to their conditions and on the other hand assigned to street quality classes which are described in words and pictures.
This method can for example be used to assess and categorize individual road sections as well as entire customer missions in relation to vehicle loads. Different regions can be compared in terms of road quality and regional trends can be identified.
With little effort this method can be integrated into mass-production vehicles. Thus each vehicle can serve as a measurement vehicle. Moreover service intervals can be adjusted individually to the specific usage.
The application of the method is illustrated by the example of load measurements with e-trucks in different countries. First, the procedure for determining the road quality is explained. Afterwards it is shown how the vehicle`s load conditions can be assessed, categorized depending on the road quality and compared to existing validation standards.

Keywords: road quality, customer usage, load and stress conditions
16:10 E-02

Fatigue load spectra: model and identification proposals for the automotive. (#120)

M. L. Facchinetti1, C. Doudard2, E. Bellec2, 1, M. Paz Silvestri2, 1

1 PSA Groupe, Chassis System Engineering, Voujeaucourt, France
2 ENSTA Bretagne, IRDL - UMR CNRS 6027, Brest, France

Variable Amplitude Loads (VAL) are of prior concern for fatigue design applied to the automotive industry. Road Load Data (RLD) coming from proving grounds or customer measurements, but also virtual RLD provided by numerical computations, are nothing but variable amplitude time series signals input for the fatigue assessment of the chassis system, the powertrain and the carbody. Within this framework, it is worth nothing that almost no homologation requirements or international standards do exist, leaving automotive carmakers free to tune their own reference proving grounds and relevant design load cases. The only constraint is to ensure the structural durability of the car safety parts, hence achieved under a self-certification process. As far as automotive carmakers are more and more connected themselves and cooperate in a fast changing market, the comparison of different frameworks are of major interest.

This paper is devoted to the concept of load spectra as a key feature able to provide such a comparison. Following some previous papers of the authors [1,2], the model proposed by [3] is considered as a pragmatic and flexible tool. It is based on elementary hypothesis (Basquin, Palmgren-Miner), calls for a minium number of parameters and leads to some useful analytical insights. Here, the identification of the model parameters are deeply examined, before any further inference. Several RLD sets dealing with passenger cars are analyzed, focusing on the load applied at the wheel center of front and rear axles, on different directions. According to [3], the shape of the spectrum is supposed to be the key feature to comment. Nevertheless, prior to that it is necessary to assess its characteristic length and the maximum load amplitude, both of these values being responsible of any relevant dimensionless reduction. Moreover, the effective maximum load amplitude may be submitted to special cut-off procedure, if the overall shape of the spectrum leads to the evidence of overload outliers, belonging to misuse.


[1] M.L. Facchinetti, Fatigue damage of materials and structures assessed by Wöhler and Gassner frameworks: recent insights about load spectra for the automotive, Procedia Engineering (2017) 213, 217-225

[2] M.L. Facchinetti, Load spectra and fatigue damage: applications to the automotive industry, MATEC Web of Conferences 165, 17008 (2018)

[3] P. Heuler, H. Klätschke, Generation and use of standardised load spectra and load-time histories, International Journal of Fatigue (2005) 27, 974-99


Keywords: fatigue, load spectrum, analytical model, parameter identification, automotive
16:30 E-03

Decomposition of random vibration loading into Gaussian portions using the trispectrum (#53)

A. Trapp1, P. Wolfsteiner1

1 University of Applied Sciences, Department of Mechanical, Automotive and Aeronautical Engineering, Munich, Bavaria, Germany

Designing reliable structures under the aspects of optimal dimensioning, a verified design and the saving of costs and time requires a comprehensive but efficient description of in-service loading. If the in-service loading is of random nature, such as road, railway, and aerospace vehicle excitation, a load description is rather accessible by measured realizations of existing structures than by establishing exhaustive numerical models.   

Unfavorably these realizations generally do not represent efficient descriptions of in-service loading. In order to reproduce real failure mechanism they must be representative for all relevant characteristics of a loading and must account for the randomness, which require them to be very long while carrying redundancies. Processing these realizations in a structural response analysis of complex structures becomes extensively time and resource consuming.

In contrast specifying random loading via the power spectral density (PSD) combines an effective statistical description with the ability to efficiently perform structural response analyses of linear structures and subsequent fatigue analyses using frequency-domain methods (e.g. Dirlik method). Yet the PSD is only a full description for stationary Gaussian processes, which is an assumption that typically conflicts with real loading.  Generally, the further a load deviates from this assumption, the greater errors result in the lifetime estimation. Thus specifying non-stationary or non-Gaussian random vibration loading requires a sophisticated statistical description. In recent research, the description of the PSD has been complement by higher-order statistical moments such as skewness and kurtosis. However, useful information contained in the spectral representation of these moments is neglected. In a preceding published paper we introduced the trispectrum, the spectral decomposition of kurtosis, as a tool to study the nature of non-stationary and non-Gaussian vibration loading. The trispectrum allows to relate kurtosis to frequency and thus to structural response behavior. We were able to show the close tie between trispectrum and fatigue damage and used it to distinguish between different non-Gaussian mechanisms of same kurtosis value.

This motivated us to derive a load description that simplifies complex loading based on PSD and trispectrum. We propose a system of equations that allows decomposing real load series by a set of Gaussian processes that reproduce PSD and trispectrum. This permits to imitate the same fatigue damage in arbitrary vibration systems.

The decomposition into Gaussian portions contributes the following gains, it (i) represent an efficient description of complex in-service loading (ii) allows to be processed efficiently in numerical models (iii) permits to use frequency-domain fatigue estimators to derive load spectra for non-Gaussian loading (iv) allows the derivation of realizations of arbitrary length.

The proposed method proves robust results and the underlying system of equations can efficiently be solved by gradient-descent optimizer.


A. Trapp and P. Wolfsteiner: Characterizing non-Gaussian vibration loading using the trispectrum. Recent Advances in Structural Dynamics 2019.

Keywords: random vibration loading, non-stationary loading, higher-order spectra, decomposition into Gaussian portions
16:50 E-04

Drivers influence on wheel load spectra (#110)

S. Ma2, 1, J. Käsgen1, R. Heim1

1 Fraunhofer - Institut Betriebsfestigkeit und Systemzuverlässigkeit LBF, Darmstadt, Germany
2 Beijing Jiaotong University, School of Mechanical, Electronic and Control Engineering, Beijing, China

The load spectra of vehicles are influenced by different parameters like vehicle weight, road surface quality and driven routes. Those parameters are commonly considered during vehicle layout. But there is another parameter with a strong influence on the spectra which is difficult to assess. This parameter is the driver’s influence which is expressed by the personal speed preferences, cornering speeds, acceleration and deceleration behavior and the capability and or willingness to avoid harsh curbstones or potholes pass overs. A common approach to cover this driver’s influence is the definition of a 1% driver, a virtual person who creates load spectra that cover 99% of the driver’s population. Facing this definition in practice often leads to confusion and ends in a “experienced based” approach. The fact is that in many cases it is unknown which influence the driver has on the load spectra.


To assess this influence a measurement survey was started at Fraunhofer LBF. The participating driver population covers 12 different drivers including men and women as well as skilled and unexperienced drivers. A car (Fig 1) was equipped with 4 wheel force transducers and additional sensors. All drivers were asked to drive a 70km long reference route that included city, country roads and highway passages. The route was driven three times by each driver having a requirement regarding the preferred driving speed.  On the first run they were asked to drive “foresightful”. On the second run “regular” and on the third run “speedy”.


The data were analyzed in order to show the differences in spectra expressed by damage values

  1. of the different road category (city, country and highway)
  2. of the different drivers (Fig. 2)
  3. of the speed requirement


The results give a comprehensive evaluation of the driver influence on wheel load spectra (expressed by damage values) of a passenger car. The variance of the damage values per kilometer is given as distribution function. The suitability of the distribution functions was validated by matching cumulative distribution functions with real values. Even so the results express only one car and routing, the results can be assumed to be representative for numerous passenger car applications.


Haibach, E., Betriebsfestigkeit – Verfahren und Daten zur Bauteilberechnung, 3. Auflage, Springer-Verlag, Berlin, Heidelberg, (2006).

Fig 1: Test vehicle equipped with wheel force transducers
Fig 2: Damage value distribution functions for different drivers
Example for damage value distribution functions of different drivers of the longitudinal wheel load (Fx)
Keywords: Wheel force, distribution function, drivers influence, road category