Grinding Out the Angular Deflection

I was the engineering manager at Charmilles Technology Manufacturing Corp. (CTMC) in Owosso, Mich., where we produced a wide range of electrical discharge machining machine tools that included both wire-cutting and die-sinking models.

The Roboform 40 and 41 series of die-sinking machines had a long-standing problem meeting one of the final quality control checks during machine runoff at the plant. All linear axes of the machine were required to meet pitch, yaw, and roll angular specifications of 8 arc-seconds. The only problem was with the Y-axis pitch, which often required reworking (or "tweaking") to get within the 8 arc-second specification.

The machine was comprised of four basic grey cast-iron machine elements. The L-shaped base incorporated a large work table and mounting surfaces for the X-axis linear rails on the top. The saddle was guided on the X-axis rails, and also mounted linear bearings perpendicular to the X-axis for the Y-axis guide rails.

The Y-axis had the linear rails mounted on the bottom of the box section casting, and the linear bearings for the Z-axis on the front of the casting. The Z-axis was another heavy box section casting with the linear rails mounted to precision ground surfaces on the rear of the axis. At the full 400mm extent of Y-axis travel, a large overhung load was created on the machine base and X-axis saddle.

Preliminary calculations on section modulus and linear bearing stiffness convinced me that we were experiencing a combination of structural bending and bearing deflection, which produced the angular deflection. It didn't appear that redesigning the structure would be cost-effective, and we were already using the stiffest roller-bearing linear guides commercially available. Other ideas to solve the problem, such as counterbalancing the overhung load, would likely also add unwanted cost.

Given the bearing spacing, I calculated that a vertical linear correction of 13 microns at the bearing supports would compensate for the 8 arc-seconds of angular deflection at the full 400mm travel. However, I could not find a practical way of producing this motion, particularly since the full 13 micron correction was only needed at the full extent of Y-axis travel, and the amount of correction would need to be proportional to the extent of axis travel.