Unified Embodiment Description for functional evaluation of used components in circular manufacturing systems

Circular manufacturing systems require functional evaluation of used components based on their physical state. Existing approaches describe this state from separate perspectives, such as design, manufacturing, and degradation, resulting in fragmented and incompatible representations. As a consequence, the physical state cannot be reliably linked to the functional behavior of the corresponding subsystem, which is a prerequisite for informed R-strategy decisions. This paper introduces the Unified Embodiment Description (UED), a state-dependent representation of mechanical components structured into two coupled layers. The first layer is a unified characteristic space, which adapts and extends as new lifecycle effects emerge. The second layer consists of functionally derived tolerance regions that link these embodiment characteristics to the functional behavior of the surrounding subsystem. A supporting UED method guides the systematic development of both layers. The UED is demonstrated in a case study on the spindle shaft of an angle grinder, in which manufacturing variations and degradation patterns such as polishing wear and scratches are quantified. These embodiment changes are embedded into the unified characteristic space and translated into functionally derived tolerance regions through experimental testing of the spindle-bearing subsystem. The results show that embodiment changes induced over the lifecycle can be consistently integrated within the unified characteristic space and that the relations between embodiment and functional behavior can be quantified to support R-strategy decisions. Overall, the UED provides a foundation for a state-dependent embodiment description and supports decision-making based on the functional evaluation of used components in circular manufacturing systems.