Opportunities and limits of the working space model in product development

Status quo

Modeling the behavior of working spaces and the interactions of working spaces across volume interfaces is an open question in product development that will be addressed in this project. With the help of a phenomenological modeling of interactions between working spaces in technical products, expert knowledge shall become usable across domains early in the development process. At the moment, a description of the function of media-filled working spaces in the analysis and synthesis of product development has failed due to:

  • the lack of applicability of expert knowledge in the form of phenomenological models for the working spaces, or
  • due to the limited usability of product models for more complex issues, or
  • due to the acceptance of such models.

Figure 1 shows an example of a comparison of model elements of the existing, qualitative working space model and the C&C² approach. A significant difference can be found in the content of the working spaces. The working space model describes it as a media-filled space, to which state variables such as temperature or pressure can be assigned accordingly. The C&C² approach describes a channel and support structure, which conducts forces or material flows from one working surface pair to another.

Figure 1: Comparison of working models describing the behavior of working spaces. Left following Beetz (1), right following Matthiesen (2)

(1) Beetz, J.-P.: Modelle und Methoden zur systematischen Entwicklung hygienegerechter Produkte. Dissertation Darmstadt; Technische Universität Darmstadt, 2018

(2) Matthiesen, S.: Ein Beitrag zur Basisdefinition des Elementmodells zum Zusammenhang von Funktion und Gestalt technischer Systeme. IPEK, Karlsruhe, 2002

Project aim

The aim of this research project is to extend the working space model for quasi-static and transient modeling of technical systems in product development. The goal of such an working space model must therefore be the quantitative description of the functions of working spaces, which enables a physically meaningful evaluation of fundamental issues with data available at an early stage. The models must be compatible with the tools used by the specialists for the later elaboration process and provide plausible results as a basis for decision-making with the maturity level of early development. Therefore, these sub-goals are pursued:

  • Processes in media-filled working spaces (matter, charge, …) as important representative functions can be described quasi-statically and transiently with empirical models, the risk of malfunctions and non-functions can be evaluated and thus a decision support for product development can be provided.
  • The coupling of balance equations (energy, matter, charge, …) and equations of state (ideal gas equation, …) of the working spaces is enabled and thus expert knowledge is made available at an early stage in product development.
  • The physical limits of exemplary effects become describable by characteristic parameters of the individual impact areas and allow the comparative evaluation of variants within the conceptual process.


Due to the necessary focus, gaseous and liquid (Newtonian) media are initially considered in the working spaces under the assumption of static states and laminar flows. Doing so, the model developed should support the product developer in evaluating the risks of undesirable functions and the functional performance of desirable functions. For this purpose, an overview of first examples of different working space classes for the description of functions in technical systems on the one hand and the limits of the effects on the other hand is worked out. Furthermore, a procedure model for the mathematical-quantitative analysis of critical processes and operating conditions of the technical system with the working space model is proposed and tested in order to subsequently develop an algorithm for the description and analysis of real systems and dynamic processes for the product development.

Figure 2: Working model of the monotube damper for deriving the damper's equation of motion. Working spaces of restrictor orifice (light blue), oil spaces (orange) and air space as elastic air spring (red) as well as working body piston (green) and separating piston (dark blue) (Following Beetz; image source ZF Friedrichshafen).