**Emmanuil Kushnir**Finite-Element Analyst

Horseheads, N.Y.

Vertical-machining centers are often used for high-precision applications such as moldmaking and graphite machining, and VMC builders typically rely on portal structures to satisfy strict requirements for accuracy and productivity. Most machines on the market tend to have similar portal designs with stationary, rigid double columns for stability.

Where they differ is in the mounting positions for the Y-axis slide. The slide may be vertical, at 45 or 60° angles, or horizontal, and this can impact overall performance. The static and dynamic stiffnesses of a machine-tool structure, to a large degree, determine the machine's accuracy and productivity. Static stiffness affects displacement between tool and workpiece when cutting. Dynamic stiffness affects chatter and maximum material removal rate. Thus, comparing tooling and workpiece movements and machine-tool frequency response for different structures lets designers predict machine-tool cutting performance.

**COMPLIANCE DISTRIBUTION**To compare various VMC structures, simplified designs were developed of three bridge-type milling machines. All three designs have similar base and column dimensions, the same ram, and the same linear guides that support the ram and slide. The only difference is in the position of the Y-axis joint, which defines slide movement relative to the bridge. Dimensions of the slant-60° bridge were modified so its torsional stiffness matched that of the horizontal and vertical bridges.

Finite-element models of all three structures permit static analysis and the creation of a compliance (stiffness) matrix for each machine. The matrices help designers evaluate displacement between tool and workpiece when cutting and compare accuracies.

Compliance in the cutting zone for each machine was calculated with opposing loads acting on the tool and workpiece. (Absolute and relative (percent) matrix values are shown in the Compliance matrices tables.) The data indicate the machine with a vertical Y-axis joint has substantially less compliance than a horizontal-joint machine and is 5 to 13% better than a slant-joint machine.

The contribution of every major component in compliance was analyzed, with some components defined as rigid. Results show the portal's contribution to compliance is nearly the same for all three designs. But for the machine with a horizontal joint, the portal makes a larger contribution in the Y direction. This is because the center of the horizontal joint is farther from the cutting zone than in the other two models.

The position of the Y-axis joint has the most effect on the slide and ram contribution to compliance when cutting. In the slide, the distance from the center of joint to the load point affects its contribution. In the ram, its length — at least as presented in these models — defines compliance, especially for the horizontal-joint machine.

**STATIC STIFFNESS**Vertical-machining centers are most-often used for milling. Displacement perpendicular to the machined surface usually defines machine accuracy and, when milling, the machined surface may be in any orientation and different designs must be compared spatially

Designers usually tackle face and end milling separately. Face-milling accuracy can be analyzed by considering the slope, or maximum displacement away from ideal, as the cutting point moves relative to the milling plane. For example, take the case of plane milling in the X direction with a 3.25-in.-diameter-mill. The side cutting edge angle is 45° and the cutting force has three components: in-feed rate direction = 100 lb, in-plane direction = 60 lb, and normal to the machined surface = 50 lb.

Displacement in the Z direction at the center of the mill need not be considered because it can be compensated for and does not affect the machined surface profile. The slope of the mill is a function of the distance from the cutting plane to the center of the Y-axis slide, rotational stiffness, and displacement of the mill center in the Y direction. The distance to the center of rotation — the point where resultant displacements are negligible — may be found from an FE model. Calculating displacement in Y direction from the previous compliance matrices and defined cutting forces show the surface machined by the VMC with a horizontal Y-axis joint has a slope approximately 40% larger than in the other two machines. (Results are shown in the Angular deflection table.)

Displacement under a cutting load perpendicular to the machined surface in the X-Y plane determines end-milling accuracy. Because it is difficult to predict cutting forces in different types of milling, consider a case where the cutting force in the X-Y plane is 1 lb and 0.5 lb in Z direction. To simplify analysis, assume forces act perpendicular to the machined surface, as is the case when machining a round workpiece at a constant width and cutting depth. Radial displacement represents machine compliance at different angles. Because the models are symmetrical relative to the X-Z plane, considering only stiffnesses-from 0 to 180° relative to the positive X axis is sufficient. (Results for all three machines are presented in VMC compliance.) As in the previous case, the machine with a horizontal Y-axis joint has a lot less stiffness than the other two. All else being equal, milling machines with a horizontal Y-axis joint will be less accurate than those using the other two layouts.

**DYNAMIC STIFFNESS**Chatter can limit machine-tool productivity. In general, productivity is proportional to the maximum possible depth of cut without chatter. This depth is inversely proportional to the negative real portion of the machine-tool frequency response function (FRF). Its value, obtained from FE structural models, can be used as a measure of the maximum depth of cut without chatter at all spindle speeds.

Using the three VMC models, we performed dynamic analysis and FRF calculations under the following conditions:

- 12 natural modes taken into consideration
- Damping ratio at all modes = 0.05
- Frequency step = 2 Hz
- Analyzed frequency range = 10 to 250 Hz
- Load force direction vector = (0.47; 0.84; 0.28)
- Displacement vector = (0.86; 0; 0.5)
- Cutting with 3.25-in.-diameter face mill, side cutting edge angle = 60°.

Frequency response data show the machine structure with a horizontal Y-axis joint will have a maximum depth of cut without chatter about 30% that of machines with vertical or 60° slant Y-axis joints. (See Frequency response chart.) The effect of structural layout on the dynamic characteristics of bridge-type vertical-machining centers is, therefore, a lot more pronounced than the effects generated by their static characteristics.

Thus, designs with horizontal Y-axis joints must be improved to compete with the static and dynamic stiffness of the other two. For example, one possibility would be to lower the position of the horizontal joint (requiring a lower bridge) and increase the width of the bridge and column size to compensate for the bridge's reduced torsional stiffness.

Such a model was developed that satisfies these requirements. Bridge height decreased almost half. Width of the bridge increased to compensate for torsional stiffness of a bridge with half the original height. Column size had to increase to support the new bridge, and the distance between rails grew to take advantage of the wider bridge.

These changes in portal dimensions are estimated to increase machine weight from 11,476 to 12,933 lb, a 12.7% increase. Comparing stiffness of the wide-bridge machine with the original, it increased dramatically (30%) only in the X direction. Greater distance between the linear guides increased stiffness in the new horizontal joint around the Y axis. But stiffness in the X direction still cannot match that of the other two machines. It means the design with horizontal Y-axis joint has to be further improved to be competitive.

**MAKE CONTACT**Emmanuil Kushnir

(607) 796-0003