By E. F. Codd, Robert L. Ashenhurst

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2). Another solution would be to employ an electric level fixed to the headstock and to use its signal to control the gaps in the guideways of the column. These solutions must be compared with that for a design of the bed, its levelling pads and of the base slide of the column with corresponding sufficiently high stiffness. The case of a heavy vertical lathe shown in Fig. 12(d) is analogous to some extent to the case of the piano-milling machine. There is one differing point in this case. The deformation of the cross-rail causes not only the deviation of planeness of the surface turned by the horizontal movement of the slide but also an error of cylindricity if turning by vertical feed of the ram.

In Fig. 27b forces and reactions in plane 1 are shown for the position of the driving p pin above the workpiece centre. a are acting. These may be replaced by the action of the force Pl = — acting at right angles to the radius 2a. The force Pi is resolved into the force P[ loading the driving pin and the force Ρ[' loading the centre. The load on the centre is resolved into its vertical P"2 and horizontal P['y components. It may be seen that the direction of STATIC AND DYNAMIC STIFFNESS 57 the P'ly component is opposite to the direction of the horizontal component of the origiP nal force Py and the value of P"y is four times the reaction ~- which comes on the tailstock centre.

Therefore, the conclusion which may be drawn from the preceding discussion emphasizes the importance of the analysis of the MTS 4 42 MACHINE TOOL STRUCTURES static stiffness of the frame. If the analysis of the resulting static stiffnesses K and K' is carried out and on the basis of it the "weak links" are discovered and their stiffness is increased, an improvement of the dynamic behaviour of the machine tool according to criteria 3 and 4 will also be achieved. Some examples may now be quoted. The static analysis of the resulting stiffness K' of the centre lathe will discover the following important springs: the spindle with its mount­ ing, the centre and sleeve of the tailstock, the tool post and carriage and, with long lathes, the twist of the bed.

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