Modelling textile processes continuous models

Modelling the processes of textile technology is perhaps the most difficult and complex area of textile research. Models of this type involve an additional layer of complexity associated with the difficulties in describing a direct link between the properties of the input product, the parameters of the process, and the properties of the output product. 

One of the methods applied for modelling a continuous transformation of an input product to the output product by a processing unit, where both are characterized by a variation in their properties, is based on the application of control theory and signal processing theory. The processing unit, e.g. carding machine, can be modelled as a linear time-invariant system where the transformation process is described by a dynamic characteristic called a transfer function  

The one-to-one correspondence between many typical functions and their images can be found in mathematical handbooks (Korn and Korn, 1968). 

ITirough the knowledge of the transfer function it is possible to model the process s response to the periodic, random, and step variations in the properties of the input product and to predict the resultant variations in the output product. The modelling can be done in three steps as follows  

Apply the inverse Laplace transform gout(0= Ml2out( S) to find the response as a function of time. 

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Using a predictive model developed from mesothelioma data from studies of asbestos insulation workers (Peto et al. 1982), asbestos textile workers (Peto 1980), amosite factory workers (Seidman 1984), and asbestos-cement workers (Finkelstein 1983), EPA (1986a) estimated that continuous lifetime exposure to air containing 0.0001 f/mL of asbestos would result in about 2-3 cases of mesothelioma per 100,000 persons. The corresponding cumulative lifetime exposures associated with excess risks of 10 " -10 are shown in Figure 3-1. Cumulative exposure levels of 0.031, 0.0031, 0.00031, and 0.000031 f-yr/mL represent excess mesothelioma risks of 10" , 10 , 10, and 10 ", respectively. Appendix D provides further details on the derivation of these risk estimates. Currently (in 2001), EPA is in the process of reviewing their cancer risk estimates for asbestos fibers. 

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