QUALITYCharles Wang, Optodyne, Inc. Compton, CA email: Optodyne@aol.com However, conventional volumetric positioning error is still defined as the root-mean-square of linear displacement errors on three axes. This definition is not adequate to keep up with progress in manufacturing technology, because the other positioning errors, such as straightness and squareness errors, are not included. Here, 3-D volumetric positioning accuracy is defined as the root-mean-square of the sum of all errors in the X, Y, and Z directions. This definition includes all the positioning errors, such as the straightness errors and squareness errors, and also the effect of angular errors. It truthfully represents the 3-D volumetric positioning accuracy, and has good correlation with geometric errors, body diagonal displacement errors, and parts accuracy. Although the linear positioning accuracies of many HMCs are similar, volumetric positioning accuracies vary significantly. For a three-axis machine, the positioning error in each axis direction,Dx(x,y,z), Dy(x,y,z),and Dz(x,y,z),is the sum of displacement error and straightness errors. That is, Dx(x,y,z)= Dx(x) + Dx(y) + Dx(z),Dy(x,y,z)= DY(x) + DY(y) +DY(z),Dz(x,y,z)= Dz(x) + Dz(y) + Dz(z), whereD is the linear error, the subscript is the error direction, and the position coordinate is inside the parenthesis. The conventional definition assumes that Dx(x) > Dx(y), Dx(z); DY(y) > Dy(x), Dy(z); and Dz(z) > Dz(x), Dz(y). However, these assumptions are no longer true for most CNC machines. Hence, it is necessary to add the three vertical and three horizontal straightness errors in the formulae. Machinists know that calibrating and compensating just the displacement error is not enough, because it will not catch all the errors. By calibrating and compensating volumetrically, you get a much more accurate machine. However, the measurement of these volumetric errors is very complex, time consuming, and costly. The AS ME B5.54 body diagonal displacement tests have been used by Boeing Aircraft and many others for many years with very good results and success in determining the volumetric positioning accuracy. Hence, it is a quick check on the volumetric positioning accuracy. If the machine is not accurate, however, there's not enough information on where the errors are and how to compensate these errors. We recently surveyed seven different HMCs with similar working volumes of about 24 x 22 x 20" (610 x 559 x 208 mm). All seven specified linear positioning accuracy, but only one specified straightness and squareness.These HMCs range from the low end to the high end in terms of cost, and the linear positioning accuracies of the machines are similar. Therefore it's very difficult for a user to determine which HMC has the volumetric positioning accuracy necessary for the machine to be used to cut higher-precision parts. We find that, although the linear positioning accuracies of many HMCs are similar, volumetric positioning accuracies vary significantly. For example, the linear positioning accuracy is typically around 0.0001 to 0.0002" (0.003-0.005 mm), but the volumetric positioning accuracy varies from 0.0005 to 0.010" (0.013-0.25 mm) -a factor of 20. Typically, managers are aware of displacement errors, but there are considerably more errors that can affect the accuracy of parts. With volumetric calibration and compensation, better quality, higher-precision parts can be cut. 16 www.sme.org/manufacturingengineering • February 2004
