STRIKING THE RIGHT CHORD FOR PARTIAL DIAMETERS
STRIKING THE RIGHT CHORD FOR PARTIAL DIAMETERS
Measuring the diameter of a hole is one of the most common measuring tasks in a production environment. In addition, given the kind and number of tolerances for diameters, there are many different gauging techniques available to do these checks. From calipers to air gauging and everything in between, there is an appropriate gauge for the application.
However, what if the hole you need to measure is not a complete circle rather it is a partial circle or a combination of partial circles with less than 180 degrees of the arc available? In some hydraulic pump configurations, there are such holes (Figure 1) that are not measurable with a conventional bore gauge, as most bore gauges measure strictly on the diameter.
The solution is to use a gauge that measures chordal drop rather than diameter. We have written before about bench ID/OD gauges that come in “T” and “V” plate configurations. In the “T” plate version, part diameter reads directly across the diameter.
However, the “V” plate design incorporates two reference stops one at the top of each arm of the “V” in addition to a sensitive contact. These reference contacts must be adjust symmetrically to assure that the part is stage on the center plane of the “V.” This double stop has a locating effect similar to that of a vee block, and provides positive and precise location of the part on the gauge. As a result, the gauge does not directly measure diameter. It measures chord height, which distanced between the sensitive contact and the chord formed by the two reference contacts.
There are a couple of things to bear in mind about chordal measurements. The first is that since the sensitive and reference contacts are not in a direct line, there is not a one-to-one relationship between sensitive contact movement and the diameter to measure. Rather, the measurement is determine by a multiplier, which varies with the angle between the references. The sensitive contacts just like the multiplier used when measuring a diameter on a vee block. The angle chosen depends on the size and portion of the hole available to measure and the ease of using a multiplier to get the correct results.
Some chordal gauges use an angle of 53° that produces a requirement for a 4:5 ratio or a 1.25 multiplier to get the correct result. This means, for every four units of chord height measured by the gauge, the indicator shows five units. This style of bench gauge is great for small bearings or parts brought to the gauge.
However, pump housings are a little too large and heavy to reach the bench gauge. For these applications, portable chordal gauges are available to take measurements on the part. In these gauges two reference contacts, one on each side of the sensitive contact set up the vee to make the chordal drop measurement. Often the reference contacts span much less than the partial arc available and thus there is some room available to “explore” the measured diameter. Depending on the size of the part, the reference contacts can be set to various angles. This changes the multiplier needed to produce the correct result but is finish with electronic readout devices.
The other thing to keep in mind about this chordal measurement is that these configurations work only for comparative readings and cannot be stretch into the “absolute measurement” world. This is because there is a rather tight “window” of accuracy wrapped around the angle setup for the reference contacts. Moving the sensitive contact significantly away from or toward the reference contacts as would normally happen in an absolute measurement scenario changes the angle relationship. This changes the multiplier needed to get correct results. A scaling multiplier applied based on the measurement size and the location of the contact but that is complicated for a bench fixture gauge.
Fortunately, for most applications the user need not worry about all these angles, ratios and chordal measurements. The gauges consider the details and have been for a long time with proven success. However, there are number of things you need to keep in mind when using chordal gauges:
- Make sure the parts to be measured are clean and free from oil/cooling fluid and measurable debris.
- Make sure the gauge is seated on both references: most chordal gauges have the two reference contacts plus a reference surface almost like a stop collar that sits on the face of the hole to square up the gauge.
- Don’t force the gauge too much when seating. Depending on the gauge design, this can distort the reference contacts and influence the diameter reading.
- Master the gauges with span masters to help verify operation and improve accuracy.
George Schuetz, Mahr.