Conical parts, such as machine tool tapers, gas petcocks, and the shanks of modular prosthetic joints, must often be inspected for taper accuracy. This is usually performed with a special air or electronic gage, custom-made for the specific part. The gage is configured as a female counterpart of the conical part, with air jets or electronic probes located inside at two or more known heights. The gage essentially measures two or more diameters on the tapered feature, calculates the difference between them, and expresses the results either in angular units, or as deviation from a specified slope.
Tool holders are of particular interest, because the accuracy of the taper affects the quality of the parts they are used to manufacture. According to ANSI standard B5.10, V-flange tool holders are built with a specified rate of taper of 3 ½ inches per foot, +0.001 inch/-0.000 inch. ISO standard 1947 defines a number of taper grades, and establishes different tolerances depending upon both grade and taper length. Regardless of which standard is followed, it is necessary to master the gage before it can be used to measure parts. The taper master is typically a more precise version of the part, but before it can be used to master the gage, it must be certified.
ANSI's 0.001 inch per foot tolerance seems easy enough to achieve until you look at the complexity of the inspection process. First, most toolholders are much shorter than 1 foot, so most gages actually compare diameters that are just 3 inches or 4 inches apart. Taking 3 inches as an example, the part has to meet a gaged tolerance of 0.001 inch/4 = 0.00025 inch. Using a standard 10:1 ratio, the gage master should be accurate to 25 microinches, and the gage should resolve to the same amount. To certify the master, again at 10:1, will require a ring and disc comparator or a universal measuring machine (UMM) that resolves to 2.5 microinches.
Certifying the master roughly replicates the production measurement process. The diameter of the master is measured at two known heights, and the slope or angle is calculated from the results. The comparator or UMM is fitted with ball or roller contacts, respectively, whose diameters are known. Because straight-sided gage blocks are used to master the gage (both vertically and horizontally) for measurements on a tapered part, trigonometry is required to calculate the differences between the points at which the mastering occurs, and the points at which the gage contacts touch the tapered part.
Using gage blocks, a very precise indicator and a height stand, set the height of the tops of the contacts so that the contacts will touch the master at the same height as the lower contacts in the production gage (TH1 in the diagram). Next, use gage blocks to master the distance between the two contacts, again accounting for the "error" between the mastering points of contact (at D1), and the measuring points of contact (at TD1). Then measure the taper master at TD1.
Using the same procedures, reset contact height and spacing in order to measure the master's diameter at the same height as the upper contacts in the production gage (TH2). Calculate the angle or slope of the master from the data obtained.
Note that the master must be staged absolutely vertical on the comparator or UMM. Prior to certifying the master, a circular geometry gage could be used to check the squareness of the master's end face to its axis.
Certifying taper masters is not for the faint-hearted. Operating within the realm of single-digit microinches, it requires the use of special instrumentation and methods in a lab environment, and a command of trigonometry.
Once the master is certified, however, it can be used to "zero" the production gage, whose use is somewhat easier.