Modeling the Dynamic Drafting Process Based on
Discrete-Event Simulation
MA Bao-long(麻宝龙)1, WANG Jun(汪 军)1, 2*, ZENG Yong-chun(曾泳春)1, 2
【摘 要】Abstract：The goal of this paper is to provide an approach to investigate the variation of fiber quantity in a certain cross-section of the drafting zone. This model with discrete-event simulation (DES) method was presented to simulate the dynamic drafting process. This model described the behavior of individual fibers, which was divided into four phases and simulated by corresponding modules. Three sets of processing conditions in industry were simulated and demonstrated the applications of this model. The comparison between experiments and simulation results could also validate this model. This model could be used to simulate various drafting process with appropriate drafting settings.
【期刊名称】东华大学学报（英文版）【年(卷),期】2016(033)004【总页数】5
【关键词】Key words：drafting process; irregularity; discrete-event simulation (DES); dynamic behavior
Introduction
Roller-drafting is the process of attenuating the count of a strand using a combination of pairs of rollers rotating at different speeds. Researchers have been studying how to improve the sliver regularity by optimizing the drafting apparatus and configuring the drafting process for many years. A serial of theoretical and experimental researches on theintrinsic factor of sliver irregularity have been done by Martin dale[1], Rao[2], Korkmaz and Behery[3], Grosberg[4], Zhang and Yu[5] and Lin et al.[6] However, the discussion cannot describe the dynamic characteristics of the drafting process. Further researches have focused on simulation and optimization of the dynamic drafting process by establishing mathematical models to simulate the behavior of strands. The fiber motion was firstly given in the form of mathematical equation by Foster[7]. Johnson[8] simulated the roller-drafting of staple fibers and Djiev[9] presented a model of double-zone drafter as transfer functions. Huh and Kim[10] set up a model to describe the dynamic behavior of a fiber bundle based on mass balance and momentum balance. Komori and Itoh[11]
formulated the dynamics of a fiber bundle based on the scheme of the fluid mechanics. Nevertheless, these models are continuous simulation models. The strand is treated as a continuous flow, and the motion of individual fibers in drafting process is neglected.The drafting process is a typical stochastic process within all kinds of random factors and conforms to the syste mcharacteristics of discrete-event simulation (DES). Therefore, it is feasible that a DES model is established to trace the motion of each separate fiber during the drafting process. Cherkassky[12-13] first demonstrated a model of one-dimensional fibrous materials based on DES, and then obtained results were used for neural network meta-model of roll-drafting process. However, the parameters were not enough to simulate the drafting process and the movement time of fibers in the drafting zone could not be calculated. Thus, it had to use movement distance of fibers (length) instead of the simulation time (i.e., 1 mm=1 s). In addition, some parameters (i.e., the front end of fibers) were changed artificially and the effect of input unevenness on the simulation results was not taken into account. Consequently, the results obtained by modeling have an academic interest only and couldn’t correspond to roll-drafting process in practice.
To simulate and investigate the dynamic performance of drafting process more accurately, a drafting model in a time domain is developed on the basis of calculated movement time of individual fibers in DES. This is a basic model to provide an approach of statistics about the variation of the fiber quantity in a certain cross-section of the drafting zone. In this model, the drafting process is divided into four phases and the movement time of each fiber passing through the drafting zone is calculated and emulated by different modules. System performance, namely the drafting effect, is investigated by statistical information on the number of fibers at each cross-section of the drafting zone. Therefore, in this paper a basic model was elaborated to simulate the dynamic drafting process and validated by experimental data.
1 Model Development
In a drafting zone, all fibers would move at the back roller velocity until each fiber is accelerated to the front roller velocity at a certain position near the nip of the front rollers, leading to an increased distance between the fibers. The strand is stretched and the number of the fibers in the strand cross-section is decreased. Consequently, the drafting process may be regarded as a process of the rearrangement of the distances among fibers along the axis of the strand. The schematic diagram of the simulation process of a single fiber passing through a drafting zone is illustrated in Fig.1. The drafting process of individual fibers has been divided into four phases in this drafting model: (A) the leading
end of a fiber is nipped by back rollers (back beard) and enters into the drafting zone; (B) the leading end of this fiber arrives at the accelerated point (floating fiber) and changes its velocity to the front roller velocity instantaneously; (C) the leading end of this fiber arrives at the front nip line and is nipped by the front rollers (front beard); and (D) the trailing end of this fiber exits from the drafting zone.
A system could be defined to be a collection of entities[14]. A drafting zone can be regarded as a system with each fiber as an entity. The process of an entity from generating to terminating in DES is analogous to the process that a fiber passes through the drafting zone. The number of entities during simulation equals the number of fibers in the drafting zone. The state variables of an entity change instantaneously at separate points in time. These points in time are the ones at which an event occurs, where an event is defined as an instantaneous occurrence that may change the state of the system [14]. For an entity in the simulation system, it represents a single fiber in the strand. In this model, four events occur for each entity, and the horizontal axis in Fig.1 gives the points in time that the discrete event occurs during simulation. The time intervals for the occurrence of the events are calculated till the entity is terminated. The four points in time from t0 to t3 correspond to the four phases above of the drafting process. The moment that an entity generates at t0 corresponds to phase (A), indicating the beginning of the simulation. The moment that the entity arrives at its accelerated time at t1 corresponds to phase (B), indicating the state variable of the entity to the front roller velocity. The moment that one event occurs at t2 corresponds to phase (C), indicating the type of this entity to the type of front beards. The moment that the entity terminates at t3 corresponds to phase (D), indicating the end of the simulation process.
There are six inputp arameters for the basic model: L is the fiber length, P is the distance between the accelerated point and the front nip line, S is the strand linear density, R is the ratch (distance between rollers), V1 is the velocity of the back rollers, and V2 is the velocity of the front rollers. The statistical outputs of this basic model are the numbers of the fibers at some certain cross-section of drafting zone and the coefficient of variation (CV). This model is programmed in DES language GPSSWorld and a flow chart for implementing the algorithm is presented in Fig.2. This flow chart illustrates the simulation principle of this basic model. The entities are generated by the system at different time. This is
implemented by module “Generate”. The time interval T between the generations of the two adjacent entities could be calculated based on some assumptions. If the linear density of input strand could be expressed as
,(1)
where F is the linear density of fibers. Then the average time interval that the next entity is generated can be deduced as.(2)
If an entity is generated at t0, the drafting process is simulated by each module as follows. Module “Advance 1” is used to emulate the time interval for an entity from t0 to t1. The delay time is given as.(3)
Module“Advance 2” calculates the time that this fiber travels from accelerated point to front nip line and the delay time is.(4)
A consecutive module “Advance 3” emulates the phase of this fiber passing through the front roller and the delay time is up to the length of this fiber, which is.(5)
Therefore, the distribution of average delay time of this module absolutely conforms to the distribution of average fiber length. Finally, module “Terminate” is used to terminate this entity, namely, this entity finishes its journey of simulation.Fig.2 Flow chart of simulating in GPSSWorld
The goal of this model established in DES is not only to trace the motion of a single fiber, but also to investigate the variation of the number of fibers in a certain cross-section of the drafting zone. So statistic modules should be added into the model for counting the number of fibers (Fig. 3). Module“TAB 1” to module “TAB n” are used to write out the statistical information in different cross-sections of the drafting zone, and the number of statistic modules is chosen as required. Module “Generate” is used to control its
measuring points of time in a fixed cross-section of the drafting zone.…
Fig.3 Flow chart of statistic modules
This basic model is free of limitations and simplifications which are inherent in the known models of the drafting process and can trace each fiber within the drafting zone. Due to this feature, this model enables investigation of a wide range of drafting cases (i.e., drawing, roving and spinning) and representations in the light of diverse drafting settings. Some optional parameters are as follows: different fiber lengths and distributions for simulating different types of fibers; different linear densities of strands for simulating different thicknesses of input strands; different accelerated point distributions for simulating different accelerated processes of fibers; different numbers of input strands or different types of strands for blending; other technological parameters (draft ratio, roller speed, ratch and so on).
2 Simulation
In order to demonstrate some applications of this drafting model and illustrate the dynamic behavior of this drafting process, three series of simulations with different sets of parameter settings are carried out. The three kinds of drafting conditions [15] and distributions of P based on published literatures [16-17] are listed in Table 1 as the input parameters of simulations.
2.1 Attenuation curves in the drafting zone
Figure 4 illustrates the changes in the total number of fibers in the cross-section along the drafting zone from the back to the front roller nip lines. The results demonstrate that this model simulates a dynamic drafting process that the fiber quantity in the cross-section of the strand is decreased gradually and the strand is stretched in the drafting zone.The attenuation curves with different distributions of P are shown in Fig.5. From the comparison, it can be pointed out that three kinds of distributions of P have almost the same trend with the variation of fiber quantity, while the log-normal distribution is the middle one among them.
2.2 Distributions and number of diverse types of fibers
For the attenuation curve of 1#, the profile of the number of fibers in the cross section at intervals along the length of the input strand within the drafting zone is shown in Figs. 6
Modeling the Dynamic Drafting Process Based on Discrete-Event Simulation
