tailieunhanh - Dynamical simulation of a vibrating crush machine

In this paper dynamics of a vibrating crush machine is considered. The main subjected of the present work is to build a mechanical model of a vibrating equipement for crushing industrial materials. | Ti!-P chi CO' h9c Journal of Mechanics, NCNST of Vietnam T. XVI, 1994, No 3 (32- 37) DYNAMICAL SIMULATION OF A VIBRATING CRUSH MACHINE Part I DOSANH Hanoi Technology University §1. INTRODUTION In this paper dynamics of a vibrating crush machine is considered. The main subjected of the present work is to build a mechanical model of a vibrating equipement for crushing industrial materials. §2. Mj:i;CHANICAL MODEL Let us consider a vibrating crush machine composed of following parts: A platform is moved in a fixed horizontal plane. The platform can be regarded as a rigid body of mass m 0 and is driven by a rotating eccentric vibrator. The debalanc of mass m rotates uniformly at angular velocity w. A pestle of mass m2 moves on the vibrating platform and is put the inside of a motar of mass m 1 . The motar moves the inside of a cylinder rigidly connected the vibrating platform (fig. 1) The described system may be considered to represent a system of nine degrees of freedom. The generalized coordinates can be .chosen as follows: 91 = x, 9z = 97 = y, sz, q3 =a, 98 q4 = s1, = ,82 + 2s,s2 cos(10 2 - l?t)PtP2). + ~J28~. where Jz is the moment of inertia of the motar about its mass centre. In the next let us concern to the kinetic energy of the vibrating platform, which has the form: where J is the moment of inertia of the vibrating platform about centre. At last, the kinetic of energy of the considered system will be: T=T0 +T,+T2+T3. which is expressed in function of generalized coordinates and generalized velocities as follows: 1( ) . 2 + 1 ( mo+m+m +m )y. 2 +zJ+moe 1( 2) 8+ "2 T=zmo+m+m,+m2x 1 2 2 1 J e·2 1 2 + 2 1 e·21 + 2 2 2 + 2JoW 1J T • - moyox a· + moxoyO . . moewsmwt x+ + m 0 ew coswty + m0ew(y0 sinwt + xo coswt)e + ~(m 1 + m2)si+ 1( ) 2 .2 1 2 .2 1 ·2 ( . ) . +2 ml + mz 81 (P! + 2m2s2z + Z(mr + mz) cos PI .Sr ~- 2mz sin(soz- ;o,)li>zsz = R,,. - \Ol)sz- cos ;:>2 i + m 2 sin ;o 2 y + m 2 cos(so2 - ;o,).S1 + m 2 sin( ;o2