A control element is a one-dimensional element with two active nodes (pinion-side node I and chord-side node J ) and one control node (dummy node K)。 It has spring-damper capability as shown in Fig。 4。 The degree of freedom (DOF) for the active nodes and control node is set to be displacement UY  in vertical  direction。

The action of the control element in the structure is based upon the value of the control parameter Pcontrol, which is defined as the displacement of control node K, and parameters defining element switch-on range, i。e。, Pupper   ~ Plower。

At time step i, the control node K is driven up by

displacement control uK , which is computed from ve- locity vK ,

where, D is the nominal diameter of a pinion, T the torsion generated by motor, R the gearbox ratio, g1 the gearbox  efficiency,  g2   is  the  bearing  efficiency  and S

the motor speed (in  rpm)。

As a result, the relation between vertical reaction force and moving-up speed is shown in Fig。 3。 During simulation, the pinions are driven up with displacement control。 The displacement of each pinion for the next time step is determined by the vertical reaction force of the pinion based on the relation   curve。

in which, vK  is obtained from the curve of pinion vertical

reaction force versus moving-up speed with consider- ation of the pinion’s vertical reaction force at  active node I。

An element will be active if uK is within its switch-on range。 The applied force Fapp  will then be   calculated,

Fapp  ¼ kuK  þ CvK ð4Þ

where, k and C are stiffness and damping of the control element, respectively。

0 1 2 3 4 5 6 7 8 9

Moving up velocity (mm/s)

Fig。 3。 Relation between vertical force and moving-up velocity of a pinion。

Fig。  4。 Schematic configuration of control  element。

The applied force will generate the same displace- ment as uK between active nodes I and J in vertical di- rection。 Once Fapp   is obtained, it will be applied on    the

The friction is then imposed on both nodes (node I and node J ) of the closed GAP element as displayed in Fig。 5(b)。 The friction on the chord node   is

active control element。

For  each  pinion,  control  elements  are  created  be-

Fup

¼ Ffriction

ð7Þ

tween the node for the pinion and all the nodes on the chord within the jacking region。 The switch-on ranges for these elements are determined by the elevation level of adjacent nodes on the   chord。

4。Interaction between guide/wear plate and    chord

In practical design, allowances are catered for the tolerances between the guides/wear plates and the chords。 Gap elements are proposed for these tolerances in the FE model。 As shown in Fig。 5(a), gap element is a one-dimensional combination of a spring and damper in parallel being coupled to a gap in series。 The DOF for each node is set to be displacement UZ of the corre- sponding local coordinate system, ZX plane of which is horizontal。 When a gap is closed (uJ — uI þ GAP < 0), gap force is generated and can be described   as

FGAP  ¼ jk · ½uJ  — uI  þ GAP]j þ jC · ðvJ  — vI Þj