This week’s gauging category takes a step back and focus on Thread Taper as a whole. This week we will define thread taper, discuss the importance of taper, how to properly measure taper on the various connection types, the effect taper error has on standoff and lastly we will touch on the differences between different manufacturers gauges.

### What is Taper?

First we must define some common taper nomenclature.

- API Definition Taper– the increase in pitch diameter of the thread, measured in inches per inch of thread.
- Physical Description of Taper – the increase of diameter within a specified length along the pipe. Typically measured over 1” intervals.
- TPF – Taper per foot, the standard callout for a taper measurement.
- Taper tolerances are expressed in terms of “inch per inch of thread” and taper deviation shall be determined accordingly. The measurements are made for the specific interval lengths and the observed deviation shall be calculated to the “in/in thread” basis.

When measuring Thread Taper, you are measuring the pitch diameter of a thread in two locations a known distance apart and comparing them.

Despite the the standard callout being a TPF measurement there are very few instances where there exists a full foot of thread to measure taper over. Because of this the measurement is taken as a deviation of pitch diameter over an inch.

Contact point size is calculated to ensure that the contact point contacts the flanks of the thread at the pitch line.

- The pitch line of a thread is an imaginary line that runs through the center of the thread. at a location that the distance of the thread is the same distance as between the threads.
- The inspector must make sure the contact points are the correct size using a caliper or a micrometer to verify before inspection. Incorrect Contact Points will cause error in measurement.

## Why is is Thread Taper Important?

Although it is possible to create a gas tight seal with the combination of a well manufactured thread and a sealant (Teflon Tape/Pipe dope). Taper connections have a distinct advantage because they are able to engage maximum number of threads in fewer rotations allowing the threads to be engaged faster. In the Oil and gas industry this is very important to keep maximum efficiency for the rig.

However, an improper taper can cause catastrophic failure for a well downhole.

**How does Thread Taper effect Standoff**** and
functional diameter?**

For decades the only API approved method for checking API Threads has been to use a ring or plug gauge. Despite changes to the API spec many companies still use ring or plug gauges to measure standoff or functional diameter. These gauges will give you a general idea on how the connections will fit together, but they do not give you the full scope of what is affecting the standoff reading. Using ring or plug gauges cannot give you specifics about any one individual thread element, because it is a measurement of diameter, taper, lead, flank angle and form error all at once. It is possible for a ring or plug gauge to show bad standoff measurements, when the actual individual thread elements are all within tolerance, this could cause re-manufacturing of a good part.

**Standoff (API Definition) – **the distance between faces of gauges or gauges and product reference planes when mated.

**Physical Description –** the distance between the ring or plug gauge face and the connection face or shoulder.

Now that we have defined taper and standoff, let’s examine how they correlate to each other. In order to properly calculate the effect of taper error on standoff. First we must collect the Taper measurement in TPF and the Pitch diameter deviation from nominal. We need this information because standoff is a function of taper and pitch diameter. Once you have these dimensions, we can find the deviation needed to locate standoff with the following formula:

**(12/TPF) X PD (deviation) = Standoff**

Ex: (12/.75) x (+.003) = +0.048”

First you divide 12 by the TPF of the part and then multiply the result by the pitch diameter deviation value. In the above example, we used the TPF of ¾” and a pitch diameter deviation of +.003”. Based off these dimensions, we calculated the standoff at +.048”. For standard API ¾” TPF 8 round connections, the tolerance for your standoff is +/- one turn or +/-0.125”. So, based off our calculated value, any calibrated ring gauge should achieve the correct standoff. This of course is not accounting for the other individual thread elements, which could further affect the standoff reading. This calculated value is also the amount of material needed to be removed in order to bring the part to the proper standoff tolerance.

Another important aspect to remember is: the less steep the taper, the greater effect that a change in pitch diameter will have on the standoff. After seeing how the standoff is effected by ¾” TPF on Tubing & Casing connections, let’s see the effect is has on Rotary Shouldered Connections with steeper taper degrees.

**(12/TPF) X PD (deviation) = Standoff**

Ex: (12/2) x (+.003) = +0.018”

As you can see in the two examples above, the RSC connection has a much larger degree of taper, yet the resulting effect on standoff is less than that of the T&C connection example. You can see that the resulting effect on standoff is significantly higher when the taper is less steep.

**Understanding Taper ratio and degree callouts**

Depending on the company you work for or the procedure you follow, you may see taper written as an expression in taper per foot (TPF), a ratio or even a degree. In either case, you must be able to understand what each means and how to convert between the different callouts. So, lets investigate how to properly covert between the three.

First, you want to take you taper callout and convert it to a ratio. Taper is commonly called out in Taper per Foot (TPF) but you need to use equivalent units when converting to a ratio. For example, 3” taper per foot is the same as 3 inches of change for every 12 inches. This could be called out as a 3 to 12 or 1 to 4 ratio. If your taper callout has fractions, such as 1 ½ inch taper per foot, you must convert the fractions to decimals for the ratio. So this example would be 1.5 to 12 ratio. Now, fundamentally you have a right triangle problem to solve. Let the length be the base and the adjacent side to the angle of interest of a right triangle, that is 1 ft or 12 inches. The opposite side of the right triangle is 1/2 of the diameter change or 3/2 = 1.5 or 1.5/2 = 0.75.

**3” TPF/2 = 1.5 = 1.5 to 12 ratio **

**1.5” TPF/2 = 0.75 = 0.75 to 12 ratio**

Next, you want to divide the first number in the ratio by the second number in the ratio. The result of this calculation is the tangent of the taper expressed in degrees. Using the above example, the ratio of 1.5 to 12 becomes 0.125 or the ratio of 0.75 to 12 becomes 0.0625.

**1.5 to 12 ratio = 1.5/12 = 0.125**

0**.75 to 12 ratio = .75/12 = 0.0625**

Finally, you then determine the arctangent of the result from step 2 above. On scientific calculators, this is “tan-1” function. After you take the arctangent of the divided ratio, the result is the angle of the taper now expressed in degrees. For our above examples, the arctangent of 0.125 is 7.125 degrees while the arctangent of 0.75 is 7.125. So for a taper of 3 inches per foot, the equivalent is 7.125 degrees. For a taper of 1.5 inches per foot, the equivalent is 3.576 degrees.

**1.5/12 = 0.125 = tan ^{-1}**

**(0.125) = 7.125 degrees**

**0.75/12 = 0.0625 = tan ^{-1}(0.0625) = 3.576 degrees**

**Common causes of Taper
Error**

- Hardness of the material
- Thickness of the material
- Speed of the threading
- Tool push off
- Chuck not level

*There are many factors that can affect the threading of the part while in the machine. Aside from common causes of deviation, such as tool push off and speed of threading, another big factor is the hardness or thickness of the material being threaded requiring multiple passes.*

**Preventative Actions**

- Check you taper on parts in the machine
- Measure taper independently
- Always check you program information
- Chuck not level

In conclusion, you can see how taper error can exponentially affect standoff as well as pitch diameter across the various connections. Taper error is a huge problem for companies using ring and plugs to quantify functional diameter. What most people don’t realize is that ring and plug gauges aren’t taking a true pitch diameter measurement, they are taking a cumulative measurement of diameter, lead, taper, flank angle and form error. Each of these dimensions will have a profound effect on the standoff measurement, which is why taper should always be checked separately. Just like all the individual thread elements called out in the various API specs. With the equations shown here, you can now calculate the affect your taper error is having on your standoff to ensure your connection will accept the mated part.