204 



CHAPTER XI 



The duty of the trash turner in sugar mills is to direct the crushed cane 

 from the first cylinder pair (one and two) to the second (two and three). 

 The crushed cane must be so guided that cylinder 3 can take the feed without 



stopping the working of the plant. 



Let Ti represent the speed with 

 which the crushed cane leaves the 

 first cylinder pair and Tg that of the 

 bagasse leaving the second C5dinder 

 pair (see Fig. 102) ; then must always 

 Tj = Tg, and it hence follows that 

 the passage of the bagasse over the 

 trash turner must be uniform. 



Consider the movement of a point 

 p {Fig. 103) ; using a system of polar 

 co-ordinates the point p will reach A in 

 time ^ with a velocity V ; this velocity 

 can be divided into two components 

 c and w, of which c is in the direction 

 of the radius vector and i& is perpen- 

 dicular to it. The crushed cane must move over the trash turner in such a 

 way that these components are constant, a result to be obtained by the 

 following conditions : — - 



If r and « are the polar co-ordinates of the point p, then 



dr = c dt. 



^ _dr 



^~~dt 



or 



Now, since C is constant, one obtains by integration 



r = ct + Ci- 

 The value of C^ is obtained by considering that when t = 0, r must be equal 

 Using these equalities it follows that 



C, = R 

 r=ct + R . . . . . . (i) 



r-du 



to R. 



Further 



w =- 



dt 



or w.dt = r.du. 



The value of r can be obtained by substitution from (i) whence it follows that 



w.dt = (ct + R) du 

 or w.dt 



ct + R 



= du. 



On integration 



w 



u = —log{R + ct) + Co- 



The constant C„ can be obtained by putting t - and u = 0, whence 



Co 



loe: R. 



Substituting this value of Co it follows that 



w w 



u =— log {R + ct)- — log R 



or 



u = 



log- 



R + ct 



R 



{2} 



