MATRIX REPRESENTATION OF BLOWING PROCESS IN COTTON SPINNING SYSTEM

In this paper calculation of size distribution (by weight) of fiber stocks in Blowing Process is discussed by matrix method*. By using histgram or cumultive frequency, it is easy to decide inqut and output size distribution of the process by measuring the weight of fiber stocks. When the size distribution of input and output are represented by vector form, an element of the vector might be given by the ordinate (either as percentage or fraction) at which a size (abscissa) intercepts the smooth curve drawn from the size analysis, that is, these vector elements are culculated from smooth curve of the histograms or cumultive frequencies by substituting an arbitrary unit to the abscissa. Then, input vector F and output vector F′ can be explained as fallows, where it is suitably chosen enough to show each distributions. When it is considered that F is changed to F′ by the process operation, it is reasonable to introduce a transfer matrix B, which characterizes the process; F′=BF Taking a probability of vector undergone the process action, F must be manipulated by the probability π; F′=B(πF)+(I-π)F Then open circuit breakage system can be stated by the above equation. Since transfer matrix B is introduced to show the state of transition of vector components to each size after a cycle of breakage, column of B must give a discrete probability function, but is so difficult to decide the function either theoretically or experimentally that Poison distribution is supposed. Then an element of B, aij show the probability of transition of fi from size i to j after the breakage. where it is difficult for more than two stocks to combine; then B becomes triangular matrix. Elements remained are derived from Poisen distribution table or the equations; by using two conditions, that is, parameter K is decided from aij=0 i=j x=n-i i=j Eexperiments were done between Hopper Opener and Hopper Feeder with Overflow, and Hooper Feeder and Lattice Feeder. Cumultive frequency curves were completed using more than 500 data, which were smoothed by Least Square Mean Method in order to decide veotors easily. To find the influence of vector's dimensions to the accuracy of culculation by the equation, they were changed and critical weight of fiber stocks, at which the condition of πij becomes πij≤1, were compared with each other.