# Basic knowledge of thread gauge

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What ia s thread gauge?

Table of Contents

- What ia s thread gauge?
- Special taper gauge for gas cylinder
- Metric trapezoidal thread Tr
- Calculation formula of thread
- Pitch diameter calculation and tolerance of external thread with 60 ° profile (national standard GB197/196)
- Calculation and tolerance of major diameter of external thread (GB197/196)
- Calculation and tolerance of internal thread small diameter
- Calculation of dividing head by single dividing method
- Calculation of inscribed hexagon in circle
- Calculation of hexagonal opposite sides and diagonals in cold heading process
- Calculation of inscribed square in circle
- Calculation of square opposite sides and diagonals in cold heading process
- Calculation of hexagonal volume
- Volume calculation of circular platform (cone)
- Volume calculation of spherical missing body (such as semicircular head)
- Machining dimension calculation of tap for internal thread
- Calculation of material length for cold heading of various shapes
- Calculation of change gear of gear hobbing machine

Thread gauge is a gauge to check whether the thread meets the requirements. Thread plug gauge is used to inspect internal thread and thread ring gauge is used to inspect external thread.

Thread is an important and commonly used structural element. Thread is mainly used for structural connection, sealing connection, transmission, reading and bearing. From general service conditions to harsh conditions (high temperature, high pressure, severe corrosion), from rough level to very quiet, in short, it is widely used.

- 1. Ordinary thread (also known as American thread or metric thread) m;
- 2. American standard unified thread, which is also UNC, UNF, UNEF, UN, UNS series;
- 3. Pipe thread without thread seal (old nominal cylindrical pipe thread);
- 4. Trapezoidal thread;
- 5. Other threads.

NPSM-American standard straight pipe threads for mechanical connection: these internal and external threads are used for free mechanical connection without internal pressure, and the products are inspected with straight pipe through-stop ring plug gauge.

NPSL-straight pipe threads for American Standard lock nuts: these internal and external threads are used for mechanical fit of anti delivery threads.

NH-American standard fire hydrant threads: these internal and external threads are used for fire hydrants, garden hoses, chemicals and elevators.

NPSH American standard hose connection threads: these internal and external threads are used for steam, air, water and other standard pipe connection threads.

Npsc American standard straight pipe thread for pipe connection: the thread shape of pipe joint is the same as that of inner straight pipe thread. When the outer conical thread NPT is used for sealing packing assembly, it can usually form a sealing connection after being tightened by a wrench, which is mostly used in low-pressure pipeline system.

NPSF-American standard oil way dry sealing threads: these internal threads are used on soft materials or nodular iron castings without sealing and are assembled with NPTF external threads.

NPSI American standard dry seal intermediate threads: these internal threads are used for assembly of hard or brittle materials with ptf-sae short external threads, but can also be used for full-length assembly of NPTF external threads.

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Special taper gauge for gas cylinder

The special taper thread for gas cylinder is used to connect the cylinder body and valve of various steel cylinders (such as oxygen cylinder, gas tank, acetylene cylinder, etc.). The reliability of locking and sealing of threaded connection is the main factor to ensure safety in the process of production and use.

Available for pz19.2, pz19.8, pz27.8, pz39 taper thread ring gauge, plug gauge and tap.

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Metric trapezoidal thread Tr

Trapezoidal thread is mainly used in transmission (feeding and lifting) and position adjustment devices, and is widely used in the machinery industry. The tolerance system of metric common thread is adopted for the tolerance of general purpose metric trapezoidal thread, and there is no separate tolerance value for single parameters such as thread lead (pitch) and sub measuring angle. Therefore, this trapezoidal thread is not suitable for precision transmission threads with high requirements for transmission accuracy. Precision transmission trapezoidal thread needs to supplement the tolerance of single parameter of thread on the basis of general trapezoidal thread standard.

Trapezoidal thread can also be used for fastening connection. Available for acme thread and metric serrated thread gauges.

American inspection system for fastening threads (UN, unr, unj, m and MJ).

Because there are many misunderstandings, certain risks and economic requirements in the field of thread detection, it brings a lot of trouble to the acceptance of thread products and buries many hidden dangers to the quality of mechanical products. In order to fundamentally reverse this passive situation, the United States has carried out a lot of technical research in thread inspection, and put forward the standard of fastening thread inspection system (ASME standard) and the uncertainty data of 60 º thread gauge measurement (ASME technical report). The thread processing and testing technology of the United States is the world leader. In the future, other countries in the world will learn from the experience of the United States and formulate their own thread testing system standards to improve the product quality of their own threads. If our technicians can learn and master this set of thread detection system technology as soon as possible, the quality of thread products in our country will be improved rapidly and get rid of the situation of rough thread production.

From the American thread inspection system, you can also learn some advanced thread processing technologies in the United States. For example, the use of differential indicator gauge detection technology can improve the adjustment accuracy of machine tools and tools and process threads close to the theoretical correct size. At the same time, the service life of the tool will also be increased.

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Calculation formula of thread

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Pitch diameter calculation and tolerance of external thread with 60 ° profile (national standard GB197/196)

a. Calculation of pitch diameter basic dimension: basic dimension of pitch diameter of thread=major diameter of thread-pitch x Coefficient value.

Formula: D/D-P x 0.6495

Example: Calculation of pitch diameter of external thread M8 thread.

- 8-1.25 x 0.6495=8-0.8119≈7.188

b. Common pitch diameter tolerance of 6h external thread (based on pitch).

The upper limit is “0”, and the lower limit is p0.8-0.095, p1.00-0.112, p1.25-0.118, p1.5-0.132, p1.75-0.150, p2.0-0.16 and p2.5-0.17.

The upper limit calculation formula is the basic dimension, and the lower limit calculation formula d2-hes-td2 is the basic dimension deviation tolerance of pitch diameter.

6h pitch diameter tolerance of M8: upper limit 7.188; Lower limit: 7.188-0.118=7.07.

C. Basic pitch diameter deviation of common 6G external thread: (based on pitch).

P0.80-0.024、P1.00-0.026、P1.25-0.028、P1.5-0.032、P1.75-0.034、P2-0.038、P2.5-0.042

Upper limit value calculation formula d2-ges i.e. basic dimension-deviation.

The lower limit value is calculated by the formula d2-ges-Td2, i.e. basic dimension deviation tolerance

For example, the tolerance value of grade 6G pitch diameter of M8: upper limit value: 7.188-0.028=7.16, lower limit value: 7.188-0.028-0.118=7.042.

**Note**:

- ① the above thread tolerances are subject to coarse teeth, and the thread tolerances of fine teeth change accordingly, but they are only larger, so the control will not exceed the specification limit, so they are not marked1 by1 in the above.
- ② In the actual production, according to the accuracy required by the design and the extrusion force of the thread processing equipment, the polished rod diameter of the thread is correspondingly increased by 0.04-0.08 compared with the designed pitch diameter of the thread, which is the polished rod diameter value of the thread. For example, the polished rod diameter of grade 6G M8 external thread of the company is 7.08-7.13.
- ③ Considering the needs of the production process, the lower limit of pitch diameter control of external thread without heat treatment and surface treatment in actual production shall be kept at level 6h as far as possible.

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Pitch diameter calculation and tolerance of 60 ° internal thread (GB197/196).

a. Pitch diameter tolerance of grade 6h thread (based on pitch).

Upper limit value:

- P0.8+0.125P1.00+0.150P1.25+0.16P1.5+0.180
- P1.25+0.00P2.0+0.212P2.5+0.224

The lower limit value is “0”, and the upper limit value is calculated by formula 2+TD2, i.e. basic dimension+tolerance.

For example, the pitch diameter of M8-6h internal thread is 7.188+0.160=7.348, and the upper limit value is 7.188, which is the lower limit value.

b. The calculation formula of pitch diameter basic dimension of internal thread is the same as that of external thread.

That is, D2=D-P x 0.6495 i.e. pitch diameter of internal thread major diameter pitch x Coefficient value.

c. Basic pitch diameter deviation E1 of 6G thread (based on pitch).

- P0.8+0.024P1.00+0.026P1.25+0.028P1.5+0.032
- P1.75+0.034P1.00+0.026P2.5+0.042

Example: upper limit of pitch diameter of M86g internal thread: 7.188+0.026+0.16=7.374

Lower limit: 7.188+0.026=7.214

Upper limit value formula 2+GE1+TD2, i.e. pitch diameter basic dimension+deviation+tolerance

Lower limit formula 2+GE1, i.e. pitch diameter+deviation

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Calculation and tolerance of major diameter of external thread (GB197/196)

a. The upper limit value of 6h major diameter of external thread is the thread diameter value.

For example, M8 is φ8.00 upper limit tolerance is “0”.

b. Tolerance of lower limit value of 6h large diameter of external thread (based on pitch).

- P0.8-0.15P1.00-0.18P1.25-0.212P1.5-0.236P1.75-0.265
- P2.0-0.28P2.5-0.335

Calculation formula of lower limit of major diameter: d-td is the basic dimension tolerance of major diameter of thread.

Example: M8 external thread 6h major diameter size: the upper limit is φ8. The lower limit is φ8-0.212= φ7.788

c. Calculation and tolerance of external thread grade 6G major diameter.

Reference deviation of 6G external thread (based on pitch)

- P0.8-0.024P1.00-0.026P1.25-0.028P1.5-0.032P1.25-0.024P1.75–0.034
- P2.0-0.038P2.5-0.042

The upper limit calculation formula d-ges is the basic dimension of thread major diameter-datum deviation

The lower limit calculation formula d-ges － TD is the basic dimension of thread major diameter datum deviation tolerance.

Example: M8 external thread 6G large diameter upper limit value φ8-0.028= φ7.972.

Lower limit value φ8-0.028-0.212= φ7.76

**Note**:

- ① the major diameter of the thread is determined by the blank diameter of the thread polished rod and the tooth wear degree of the thread take-up plate/thread roller, and its value is inversely proportional to the pitch diameter of the thread on the basis of the same blank and thread processing tools, that is, if the pitch diameter is small, the major diameter is large, otherwise, if the pitch diameter is large, the major diameter is small.
- ② For the parts to be processed by heat treatment and surface treatment, considering the relationship between the processing process, the major diameter of the thread shall be controlled at the lower limit of 6h level plus more than 0.04mm in actual production. For example, the major diameter of M8 external thread in rolling (rolling) thread shall be kept at above φ7.83 and below φ7.95.

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Calculation and tolerance of internal thread small diameter

a. Basic dimension calculation of internal thread small diameter (D1).

Basic dimension of thread small diameter=basic dimension of internal thread-pitch x coefficient

Example: the basic size of small diameter of internal thread M8 is 8-1.25 x 1.0825=6.646875≈6.647

b. Calculation of small diameter tolerance (based on pitch) and small diameter value of internal thread grade 6h.

- P0.8+0.2P1.0+0.236P1.25+0.265P1.5+0.3P1.75+0.335
- P2.0+0.375P2.5+0.48

The lower limit deviation formula D1+HE1 of internal thread grade 6h is the basic dimension+deviation of internal thread small diameter.

**Note**: the lower deviation value of level 6h is “0”.

The upper limit value calculation formula of internal thread grade 6h=D1+HE1+TD1, that is, the basic dimension of internal thread small diameter+deviation+tolerance.

Example: the upper limit of small diameter of grade 6h M8 internal thread is 6.647+0=6.647

Lower limit of small diameter of grade 6h M8 internal thread 6.647+0+0.265=6.912

c. Calculation of basic deviation (based on pitch) and small diameter value of internal thread grade 6G.

- P0.8+0.024P1.0+0.026P1.25+0.028P1.5+0.032P1.75+0.034
- P2.0+0.038P2.5+0.042

The formula for the lower limit of small diameter of internal thread grade 6G=D1+GE1, that is, the basic size of internal thread+deviation.

Example: the lower limit of small diameter of grade 6G M8 internal thread is 6.647+0.028=6.675

The upper limit formula D1+GE1+TD1 for the small diameter of grade 6G M8 internal thread is the basic dimension of internal thread+deviation+tolerance.

For example, the upper limit of small diameter of grade 6G M8 internal thread is 6.647+0.028+0.265=6.94

**Note**:

- ① The tooth h8of the internal thread is directly related to the bearing torque of the internal thread, so it should be within its 6h upper limit as far as possible in the blank production.
- ② In the process of internal thread processing, the smaller the internal thread small diameter will affect the use efficiency of the tool tap. From the perspective of use, the smaller the small diameter is, the better. However, when considering comprehensively, the small diameter is generally between the middle limit and the upper limit. In case of cast iron or aluminum parts, the lower limit and the middle limit of the small diameter should be used.
- ③ The small diameter of internal thread grade 6G can be implemented according to grade 6h in blank production, and its accuracy grade mainly considers the coating of thread pitch diameter. Therefore, only the pitch diameter of tap is considered during thread processing, and the small diameter of smooth hole does not need to be considered.

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Calculation of dividing head by single dividing method

Calculation formula of single division method: n=40/Z

n: Is the number of revolutions that the indexing head should turn; Z: Equal fraction of workpiece; 40: fixed number of dividing head.

Example: the calculation of milling hexagonal is substituted into the formula: n=40/6

**Calculation**:

① reduce the score: find out the minimum divisor 2 to reduce the score, that is, divide the numerator and denominator by 2 at the same time to get 20/3, reduce the score and keep its equal score unchanged.

② Calculate fraction: it depends on the numerator and denominator values; If the numerator denominator is large, it shall be calculated.

20÷3=6(2/3), i.e. n value, i.e. the dividing head shall rotate for 6(2/3) revolutions. At this time, the score has become with score; The integer part 6 with fraction is the dividing head, which should turn 6 whole turns. The fraction 2/3 with fraction can only be 2/3 of1 turn. At this time, it must be recalculated.

③ Selection and calculation of dividing plate: the calculation of less than1 circle must be realized with the help of the dividing plate of the dividing head. When calculating, the first step is to expand the score by 2/3 at the same time. For example, if it is expanded by 14 times at the same time, the score is 28/42; If it is expanded 10 times at the same time, the score is 20/30; If the score is 26/39 when expanding 13 times at the same time. The number of times to expand the door should be selected according to the number of holes on the dividing plate.

**Note at this time**:

① The number of holes in the selected dividing plate must be divisible by the denominator 3. As in the previous example, 42holes are 14 times that of 3, 30 holes are 10 times that of 3, and 39holes are 13 times that of 3.

② The expansion of the fraction must be the expansion of the numerator and denominator, and its equal division remains unchanged, as in the example:

- 28/42=2/3 x 14=(2 x 14)/(3 x 14); 20/30=2/3 x 10=(2 x 10)/(3 x 10)；
- 26/39=2/3 x 13=(2 x 13)/(3 x 13)

28/42 denominator 42, that is, 42holes of division number are used for division; Molecule 28 turns forward on the positioning hole of the upper wheel, and hole 28, that is, hole 29, is the positioning hole of the current wheel; 20/30 is the positioning hole of the wheel when the 30 hole indexing plate rotates forward 10 holes, i.e. 11holes, and 26/39 is the positioning hole of the wheel when the 39hole indexing plate rotates forward 26holes, i.e. 27holes.

When milling hexagonal (bisection), 42holes, 30 holes, 39holes and other holes divided by 3 can be used as indexing: the operation is to turn the handle for 6 turns, and then turn 28+1/10+1/26+forward on the positioning hole of the upper wheel! Hole 29/11/27 of the hole is used as the positioning hole of the wheel.

Example 2: Calculation of gear milling 15 teeth.

Substitute into formula: n=40/15

Calculation n=2 (2/3)

Turn 2 full turns, and then select the dividing holes divided by 3, such as 24, 30, 39, 42, 51, 54, 57, 66, and then turn forward 16, 20, 26, 28, 34, 36, 38, 44 plus 1hole, i.e. 17, 21, 27, 29, 35, 37, 39, 45, as the positioning hole of this wheel.

Example 3: graduation calculation of milling 82 teeth.

Substitution formula: n=40/82

Calculation n=20/41

That is, as long as the dividing plate with 41 holes is selected, turn 20+1, that is, 21 holes on the positioning hole of the upper wheel as the positioning hole of the current wheel.

Example 4: graduation calculation of milling 51 teeth

Substitute the formula n=40/51. Since the score cannot be calculated at this time, you can only directly select the hole, that is, select the dividing plate with 51holes, and turn 51+1, that is, 52holes on the positioning hole of the upper wheel as the positioning hole of the current wheel.

Example 5: graduation calculation of milling 100 teeth.

Substitute into formula n=40/100

Calculation n=4/10=12/30

That is, select the indexing plate with 30 holes and turn 12+1, i.e. 13holes on the positioning hole of the upper wheel as the positioning hole of this wheel.

If all indexing plates do not have the number of holes required for calculation, the compound indexing method shall be used for calculation, which is not included in this calculation method. Gear hobbing is generally used in actual production, because the actual operation after compound indexing calculation is very inconvenient.

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Calculation of inscribed hexagon in circle

Formula:

① find the hexagonal opposite side (s-plane) of circle D; S=0.866d, i.e. diameter x 0.866 (coefficient)

② Find the diameter of circle (d) with hexagonal opposite side (s surface); D=1.1547s, i.e. opposite side x 1.1547 (coefficient).

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Calculation of hexagonal opposite sides and diagonals in cold heading process

Formula:

- ① Find the diagonal e from the opposite side of the outer hexagon (s); E=1.13s, i.e. opposite side x 1.13
- ② Find the diagonal (E) of the opposite side (s) of the inner hexagon; E=1.14s, i.e. opposite side x 1.14 (coefficient).
- ③ To calculate the head material diameter of the diagonal (d) from the opposite side (s) of the outer hexagon, calculate the circle (d) diameter according to the opposite side (s) of the hexagon (formula 6.2), and appropriately increase its offset center value, that is, D ≥ 1.1547s. The offset center can only be estimated.

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Calculation of inscribed square in circle

Formula:

① find the opposite side (s-plane) of a square with a circle (d); S=0.7071d, i.e. diameter x 0.7071

② Square opposite side (s plane) to find circle (d); D=1.414s, i.e. opposite side x 1.414

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Calculation of square opposite sides and diagonals in cold heading process

Formula:

① find the diagonal (E) from the opposite side (s) of the outer square; E=1.4s, i.e. opposite side (s) x 1.4 parameters

② Find the diagonal (E) of the opposite side (s) of the inner square; E=1.45s, i.e. opposite side (s) x 1.45 coefficient

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Calculation of hexagonal volume

Formula:

① S20.866 x H/M/K is the opposite side x Opposite side x 0.866 x H8 or thickness.

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Volume calculation of circular platform (cone)

Formula 0.262h (D2+D2+D) x d) I.e. 0.262 x h8×( Big head diameter x Big head diameter+small head diameter x Small head diameter+large head diameter x Small head diameter).

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Volume calculation of spherical missing body (such as semicircular head)

Formula 3.1416h2 (R-H/3), i.e. 3.1416 x h8 x h8×( Radius-h8÷ 3).

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Machining dimension calculation of tap for internal thread

1. Calculation of major diameter d0 of tap.

Formula d0=D+(0.866025p/8) ×( 0.5 ~ 1.3), i.e. basic size of tap large diameter thread+0.866025 pitch÷8 x 0.5 to 1.3.

**Note**: the selection of 0.5 to 1.3 should be confirmed according to the pitch. The larger the pitch value, the smaller the coefficient should be used. On the contrary, the smaller the pitch value, the larger the coefficient should be used accordingly.

2. Calculation of tap pitch diameter (D2).

Formula: D2=(3) x 0.866025p)/8, i.e. tap pitch diameter=3 x 0.866025 x Pitch÷8

3. Calculation of tap small diameter (D1).

Formula: D1=(5) x 0.866025p)/8, i.e. tap small diameter=5 x 0.866025 x Pitch÷8

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Calculation of material length for cold heading of various shapes

It is known that the volume formula of a circle is diameter x diameter x 0.7854 x Length or radius x radius x 3.1416 x Length.

I.e. D2 x 0.7854 x L or R2 x 3.1416 x L

During calculation, the volume of material to be used x÷diameter÷diameter÷0.7854 or X÷radius÷radius÷3.1416 is the length of feeding.

Formula=x/(3.1416r2) or X/0.7854d2; Where X represents the volume of material required; L represents the actual feeding length value; R/D represents the radius or diameter of the actual feeding.

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Calculation of change gear of gear hobbing machine

a. Fixed number of roller gear spindle 24.

b. The calculation of rolling gear change gear is realized by decomposing the data, that is, expanding or reducing its equal division unchanged at the same time. The schematic diagrams of B1 and B2 are composite speed change, and the schematic diagrams of B3 and B4 are direct speed change.

c. Decomposition of spindle parameter 24.

C1 can be directly decomposed into 2 x 12=24；3 x 8=24；4 x 6=24

C2 decomposition after expansion:

- If expanded 5 times 24 x 5=120, then 120 can be decomposed into 20 x 6;3 x 40;4 x 30;6 x 20;
- If expanded 8 times 24 x 8=192, then 192 is decomposed into 2 x 91; 91 x 2; 48 x 4;4 x 48;3 x 64;64 x 3；
- 8 x 24; 24 x 8; 22 x 6;6 x 32 when expanding the multiple, the number of teeth of the processed parts shall be expanded at the same time until it is easy to disassemble.

d. Calculus case decomposition.

d.1 calculation when the machined part is set as 15 teeth.

Formula: 24/15, 240/150 after 10 times of expansion at the same time; Decompose and clear the common multiple 3 at the same time (3 x 80)/(3 x 50)=80/50 at this time, b.4 schematic diagram can be used to install any intermediate wheel in the middle, that is, install 80 teeth gear at ① and 50 teeth gear at ②.

d.2 calculation when the machined part is 77 teeth.

Formula: 2160/6930 after 24/77 is expanded by 90 times at the same time; Disassembly (40 x 54)/(70/99) at this time, the assembly gear shown in B.1 can be used. Considering the convenient assembly of the gear, the numbers 1 and 3 can be exchanged arbitrarily, and 2 and 4 can also be exchanged arbitrarily, but the positions of 1 and 2 or 4 and 3 and 2 or 4 are not suitable for exchange. On the contrary, 4 and 1 or 3 and 2 and 1 or 3 cannot be exchanged.

d.3 calculation when the machined part is set as 32 teeth.

Formula: 24/32, 120/160 after 5-fold expansion at the same time; Decompose into (4 x 30)/(4 x 40) at the same time, 30/40 is obtained after removing the common multiple 4. At this time, any intermediate wheel can be installed in the middle according to the diagram in B.3, that is, 30 gears are installed at ① and 40 gears are installed at ②.

d.4 calculation when the machined part is 13 teeth.

Formula: 2400/1300 after 24/13 is expanded by 100 times at the same time; Decomposition force (30) x 80)/(20 x 65) at this time, B.2 schematic diagram can be used for assembly. Note: why is it decomposed into 30 at 2400 x 80 can also be decomposed 40 x 60. At this time, it depends on the mutual coincidence of the gears after assembly. As long as they are well matched, the number of teeth of this gear can also be decomposed from 2400 to 20 x 120 can be assembled with the schematic diagram in 6.4.

Source: Network Arrangement – China **Pipe Fitting Manufacturer** – Yaang Pipe Industry (www.epowermetals.com)

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)

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