313 Chapter 8 Position Tolerancing Fundamentals Copyright Goodheart-Willcox Co., Inc. diameter measured position variation is less than the .0150″ diameter allowable position tolerance, the hole is in an acceptable location. The Coordinate-to-Diameter Conversion Table in Appendix A1 may be used to convert coordinate val- ues into diameter values. The values in the table are diameters. Using the .006″ X variation and –.001″ Y variation, the table shows a value of .01217″. Paper Gaging The position tolerances for produced features may be checked for compliance using a graphical process commonly known in industry as paper gaging. Paper gaging is a method of illustrating a position tolerance and the actual position of a fea- ture in a graph to determine whether the position is within the tolerance. This method of position toler- ance verifi cation was more commonly used before the widespread use of measurement machines and inspection software. It continues to be of use when manual measurements are made and is also conve- nient for explaining concepts related to verifying position tolerance requirements. Depending on the accuracy needed, mea- surement equipment may be relatively simple or it may be of high precision. Whatever measurement equipment is used, it must be able to make accurate coordinate measurements relative to the datum ref- erence frame that is specifi ed in the position toler- ance. In addition to measuring feature locations, it is important to determine the size of produced features. Figure 8-22 illustrates how paper gaging may be used to verify that a hole pattern meets the required position tolerances. Data for the four holes in Figure 8-20 is used. In that fi gure, the given draw- ing includes a position tolerance of .012″ diameter at MMC, relative to datums A, B, and C. Graph paper may be used for paper gaging. The grid values are assigned a large scale to make any minor plotting errors insignifi cant. In the given fi gure, each grid line represents .001″. A point is selected on the graph paper to serve as the origin, and it represents the true position for the measured holes. The positions for all holes controlled by a sin- gle position tolerance specifi cation are plotted rel- ative to one origin. The delta X and delta Y values (variation values in the table) for the measured hole positions are plotted on the graph paper, and points are drawn to represent the centers of the holes. A series of concentric circles is overlaid on the graph paper with the center of the circles at the ori- gin for the plotted points. The circles and grid are drawn to the same scale. The smallest circle in the given fi gure is drawn to represent a diameter of .012″. Another circle is drawn at every .001″ increase in diameter up to a diameter of .017″. The circles are labeled to show their diameters. The associated hole size based on allowable additional tolerance is shown in parentheses. Although the specifi ed position tolerance is .012″ diameter, the MMC modifi er indicates that any hole produced larger than MMC will be allowed an additional tolerance. The plotted location for hole #1 is at .006″, –.001″. The point falls slightly outside the .012″ diameter circle. Because hole #1 was measured at a diameter of .191″, its allowable position toler- ance is .015″ diameter because of the effect of depar- ture from MMC. Therefore, the location of hole #1 is acceptable. Plotting the location variation of all four holes and comparing the point location to the appli- cable tolerance zone diameter for the produced hole size shows the given part to be good. Functional Gages Functional gages can be produced for verifi - cation of hole positions. When many parts must be inspected, it may be less expensive to fabricate a functional gage than to measure each part and ana- lyze the data. Explanations regarding the usage of functional gages for position tolerances are given in the next chapter. The preceding explanations of methods for veri- fying position tolerances are not intended to indicate that every fabricated part must be inspected. Process control, when appropriately applied, may minimize #1 #3 #2 #4 True position Ø.012 (.188) Ø.013 (.189) Ø.014 (.190) Ø.015 (.191) Ø.016 (.192) Ø.017 (.193) Plotted hole location coordinates and position tolerance zones Goodheart-Willcox Publisher Figure 8-22. Grid paper may be used for plotting coordinate variations for a produced hole pattern. A series of concentric circles may be overlaid on the grid to determine the diameter position variation.