Overview in PDF format - Tallinna Tehnikaülikool

2 2( kl − J p + Aωp )ob M la1= b2=,2 22( kl − J o p + Aωb p − β l ω b )3M l β pb1= −a2=2 22(2.38)( kl − J o p + Aωbp − β l ωb)( k + k ) 2 , M = ( M M )/2k = y z / y + z(2.39)2 *( k2yl− Joω) Fall1c1=2 * 2,2 2 * 2 * 2( k yl− Joω) + ( βlω ) + ( Aωbω)2 *2Aωb( k yl− Joω) Fall1c2=2 2 *2,2 2 * 2 * 2βl[( k yl− Joω) + ( βlω ) + ( Aωbω) ]* 2 2 * 2ω [( β l ) + ( Aωbω) ] Fall1d1=2 2 * 2 2 * 2 * 2β [( ω2(2.40)l k yl− Jo) + ( β l ω ) + ( Aωbω) ]The general solution of Eqs (2.22) is the sum of Eqs (2.36)–(2.37):z = z+ z2= exp( − n1t)( D1cos ω1t− D3sin ω1t)( − n t)( D cos ω t + D sin ω t)1+ expy = y+ exp222*+ a2 cos pt + b2sin pt + c2cos ω t ,1+ y2= exp( − n1t)( D1sin ω1t+ D3cosω1t)( − n t)( − D sin ω t + D cosωt)+2224**+ a1 cos pt + b1sin pt + Frl1/ k yl+ c1cosω t + d1sinωt , (2.41)422++where D 1 , D 2 , D 3 and D 4 are constants of integration to be determined from theinitial conditions, ω 1 and ω 2 are the natural frequencies of vibrations withgyroscopic forces and damping.2.6. Experimental Analysis2.6.1. Preliminary experimental test2.6.1.1. Experimental test of the spring constant of the latheThe accuracy of the accepted models was tested on the lathe 1K62. During thetheoretical analysis, calculation accuracy depends both on the degree of fitness ofthe accepted models of the real system and on how accurately mechanicalcharacteristics of the lathe are determined. One of these characteristics is the spring30