急急急！ 机械英语外文翻译Let us consider a belt conveyor with the number

急急急！ 机械英语外文翻译
Let us consider a belt conveyor with the number of its rollers tending to infinity. The optimal point for installing the
weighing support roller must be determined and so must the minimum number of support rollers that determine the zone of
influence on the BW readings,i.e.,the number that must meet regulation requirements as to the accuracy of the assembly (the
level of the device,the span length,the trough profile,the allowable roller wobble,etc.
The criterion for the optimal BW installation point must be taken to be the reaction of the weighing support roller
to the linear load of material and the belt,multiplied by the length of the weighing segment (Fig. 1),i.e
Let us consider a belt in the form of a beam on pivoting supports with zero bending moments at the outermost sup-
ports. The number of supports in the computational diagram varies from five to nine. We adopt computational diagrams with
an odd number of supports to simplify the analysis by using symmetry properties. Figure 1 shows a segment with a uniformly
distributed load q. Support roller 1at the center of symmetry is the weighing support roller.
The support rollers 2limit the theoretical BW influence zone when the belt is represented as a split beam [8].
Support rollers Aand Blimit the presumable actual BW influence zone because of the belt stiffness. Representing the rollers
by pivoting supports and replacing supports 1and 2by their reactions X2,X1,X2,we form canonical strain equations of the
method of forces:
In Eq. (1),the coefficient δikfor an unknown force factor Xiis equal to the displacement in the direction of that fac-
tor by a unit force factor Xk. In accordance with the theorem of correlation of displacements,σik= σki.
The free term ∆ipdenotes the displacement in the direction of the factor Xi,caused by the action of the load P= 4ql.
For calculation of the coefficients δik,Fig. 1 shows the curves of the bending moments plotted against the force factors X1
and X2(MIand MII) and against the given load q(Mq) [8].
To determine δikand δip,taking the equivalent belt stiffness EJ[8],where Eis the elastic modulus of the belt and J
is the moment of inertia of its cross section,we find a system of equations that replace system (1):
Figure 2ashows the curves of the deviations of the support reactions Xifrom the calculated value of qlalong the
zone of influence,changing sign and amplitude on passing from support to support. The minimum of the error δ5= –7% cor-
responds to support 1,where the LD is to be installed.
The BW error δI= –7% obtained is an error of method that is due to an incorrect way of setting the force acting on
the outermost supports Aand B,since by convention any large number of identical support rollers is placed to the right and
left of them. This explains why the Xi(l) have such sharp bends.
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