Abstract
The carding process plays a key role in determining sliver quality in fibrous material production. However, the dynamic aspects of the process, particularly the influence of time delays and internal positive feedback loops on the unevenness of the carded sliver, remain insufficiently studied, which hinders the development of effective control systems. To address this limitation, the aim of this work is to develop a theoretical mathematical model that establishes a quantitative relationship between design and operational parameters (such as doffing ratio and draft) and unevenness indicators. The study examines a dynamic model of fibrous mass motion that accounts for the interaction between the main cylinder and the doffer cylinder using methods from control theory to derive transfer functions. The analysis reveals that the system dynamics, described by a delay equation, exhibit stepwise exponential transient responses where the settling time is dependent on the doffing ratio. Furthermore, frequency analysis demonstrates the machine's selective leveling properties: the maximum leveling effect is achieved for unevenness wavelengths equal to half the cylinder circumference or a multiple thereof, while low- frequency (long-wave) variations are practically uncorrected. These findings allow for a quantitative assessment of the influence of key parameters on sliver unevenness and provide a foundation to optimize process settings and develop automatic control systems that compensate for undesirable dynamic effects.