Basic knowledge of thread gauges and a collection of calculation formulas for various types of threads

Thread Content

Basic knowledge of thread gauges – Thread gauges are tools used to check whether threads meet the specified requirements. Thread plug gauges are used to inspect internal threads, while thread ring gauges are used to inspect external threads. - Threads are an important and commonly used structural element. Threads are mainly used in applications such as structural joining, sealing connections, transmission, reading, and load bearing. From normal operating conditions to harsh ones (high temperature, high pressure, severe corrosion), and from a rough level of noise to very quiet operation – in short, they have a wide range of applications. - 1. Ordinary threads (also known as American threads or metric threads) M – 2. Unified American threads, which include the UNC, UNF, UNEF, UN, and UNS series – 3. Pipe threads without threaded seals (old designation for cylindrical pipe threads) – 4. Tapered threads – 5. Other types of threads – NPSM: American standard for straight pipe threads used in mechanical connections; these internal and external threads are used for free mechanical connections where there is no pressure inside, and they are inspected using straight plug gauges. - NPSL – American standard lock nuts with straight pipe threads: These internal and external threads are used for the mechanical engagement that prevents thread backfeeding. - NH-American standard fire hydrant threads: These internal and external threads are used for fire hydrants, garden hoses, chemical equipment, and elevators. - NPSH – American standard threads for hose connections: These internal and external threads are used for steam, air, water, and in other applications where standard pipe threading is employed. - NPSC – American standard straight pipe threads for pipe fittings: The thread pattern of these pipe fittings is the same as that of internal straight pipe threads; when their external tapered threads NPT are tightened with a wrench after sealing filler is applied, a sealed connection is achieved, and they are commonly used in low-pressure piping systems. - NPSF–American standard dry-sealed male threads: These internal threads are used on soft materials or ductile iron parts where sealing is not required, for mating with NPTF female threads. - NPSI-American standard dry-sealed intermediate threads: These internal threads are used for the assembly of hard or brittle materials with PTF-SAE short external threads, but they can also be used for the full-length assembly of NPTF external threads. - Taper gauge for gas cylinders – The tapered threads specific to gas cylinders are used for connecting the cylinder bodies with valves in various types of steel cylinders, such as oxygen cylinders, gas cylinders, acetylene cylinders, etc. The reliability of the locking and sealing in threaded connections is a key factor in ensuring safety during production and use. - Suitable for PZ19.2, PZ19.8, PZ27.8, and PZ39 tapered thread ring gauges, plug gauges, and taps – Metric trapezoidal threads. Trapezoidal threads are primarily used in drive (feed and lifting) and position adjustment mechanisms, and they are widely utilized in the machinery industry. The tolerances for general-purpose metric trapezoidal threads adopt those of standard metric threads; no separate tolerance values are specified for individual parameters such as the thread lead and the helix angle. Therefore, this trapezoidal thread is not suitable for precision transmission threads that require high transmission accuracy. Precision transmission trapezoidal threads require additional specifications for the tolerances of individual thread parameters on top of the standard trapezoidal thread standards. - Trapezoidal threads can also be used in fastening applications. Available for ACME threads and metric serrated threads – the American testing system for fastening threads (UN, UNR, UNJ, M, and MJ) – Due to numerous misconceptions in the field of thread inspection, as well as certain risks and economic considerations, this situation poses many difficulties in the acceptance of threaded products, thereby creating potential issues with the quality of mechanical products. To fundamentally reverse this passive situation, the United States conducted extensive technical research on thread inspection, establishing standards for fastener thread inspection systems (ASME standards) as well as uncertainty data for measurements using 60° thread gauges (ASME technical reports). The United States leads the world in thread processing and testing technologies. In the future, other countries around the world will draw on American experience to establish their own standards for thread testing, in order to improve the quality of threads produced in their own countries. If our country’s numerous technical personnel can promptly learn and master the technology of this thread inspection system, the quality of threaded products in China will be significantly improved, thereby putting an end to the production of poorly made threads. - The U.S. thread inspection system also allows one to learn some advanced U.S. thread processing techniques. For example, by using differential indicator gauge detection technology, the adjustment accuracy of machine tools and cutting tools can be improved, allowing for the production of threads that are close to the theoretically correct dimensions. At the same time, the tool life will also increase. Mobile calculation formulas for threads -- I. Calculation and tolerances of the pitch diameter for external threads with a 60° thread profile (National Standard GB 197/196) a. Calculation of the basic pitch diameter: The basic value of the thread pitch diameter = major diameter of the thread – pitch × coefficient value. The formula is: d/D – P × 0.6495. Example: Calculation of the pitch diameter for an external M8 thread: 8 – 1.25 × 0.6495 = 8 – 0.8119 ≈ 7.188. b. The common tolerance for the pitch diameter of 6h external threads (based on the pitch). The upper limit value is “0”, while the lower limit values are 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 formula for calculating the upper limit is the basic dimension; the formula for calculating the lower limit is d2-hes-Td2, which represents the basic diameter dimension minus the deviation plus the tolerance. Mid-diameter tolerance value for grade 6 of M8: upper limit value is 7.188 ； Lower limit: 7.188-0.118=7.07. C. Basic deviation of the pitch diameter for commonly used 6g-grade external threads: (based on the pitch). For P0.80-0.024, P1.00-0.026, P1.25-0.028, P1.5-0.032, P1.75-0.034, P2-0.038, and P2.5-0.042, the formula for calculating the upper limit is d2-ges, which refers to the basic dimension minus the tolerance. The formula for calculating the lower limit is d2-ges-Td2, which refers to the basic dimension minus the tolerance minus the allowance. For example, for an M8 bolt with a 6g grade of middle diameter tolerance: the upper limit is 7.188-0.028=7.16, while the lower limit is 7.188-0.028-0.118=7.042. Note: ① The thread tolerances mentioned above are based on coarse threads; the tolerances for fine threads vary slightly, but they only increase. Therefore, adhering to these values will ensure that the specifications are not exceeded, which is why they are not listed individually above. ②In practical manufacturing, the diameter of the bare shaft for threads is increased by 0.04–0.08 compared to the designed pitch diameter, depending on the required precision per the design specifications and the extrusion force of the thread processing equipment; this increased value represents the diameter of the bare shaft for threads. For example, for the M8 external threads of grade 6g in this company, the diameter of their bare shafts ranges from 7.08 to 7.13, falling within this range. ③Considering the requirements of the production process, for externally threaded parts produced without heat treatment or surface treatment, the lower limit for mid-diameter control should preferably be maintained at the 6H grade. II. Calculation and tolerances of the pitch diameter for 60° internal threads (GB 197/196). a. Tolerances for the pitch diameter of 6H grade threads (based on the pitch). Upper limit values: P0.8+0.125, P1.00+0.150, P1.25+0.16, P1.5+0.180, P1.25+0.00, P2.0+0.212, P2.5+0.224. The lower limit value is “0”. The formula for calculating the upper limit value is 2 + TD2, that is, the basic dimension plus the tolerance. In example M8-6H, the inner thread pitch diameter is: 7.188 + 0.160 = 7.348; the upper limit value is 7.188, which serves as the lower limit value. b. The formula for calculating the basic dimension of the pitch diameter for internal threads is the same as that for external threads. That is, D2 = D – P × 0.6495; in other words, it is the inner thread pitch diameter equal to the thread major diameter minus the pitch multiplied by a coefficient value. c. Basic deviation E1 for the pitch diameter of 6G class threads (based on the pitch). P0.8+0.024 P1.00+0.026 P1.25+0.028 P1.5+0.032 P1.75+0.034 P1.00+0.026 P2.5+0.042 Example: For M8 6G grade internal threads, the upper limit of the pitch diameter is: 7.188+0.026+0.16=7.374; the lower limit is: 7.188+0.026=7.214. The formula for the upper limit is 2+GE1+TD2, that is, the basic pitch diameter value plus deviations and tolerances. The formula for the lower limit is 2+GE1, that is, the pitch diameter value plus deviation. III. Calculation and tolerances of the major diameter of external threads (GB 197/196): a. The upper limit of the 6h major diameter of external threads corresponds to the thread diameter value. For example, in M8, the upper limit value is φ8.00 with a tolerance of “0”. b. Tolerance for the lower limit of the major diameter of external threads at grade 6h (based on pitch). P0.8-0.15 P1.00-0.18 P1.25-0.212 P1.5-0.236 P1.75-0.265 P2.0-0.28 P2.5-0.335 The formula for calculating the lower limit of the major diameter is: d-Td, that is, the basic dimension of the thread major diameter minus the tolerance. Example: For M8 external threads of grade 6h, the maximum diameter is φ8, while the minimum diameter is φ8 – 0.212 = φ7.788. c. Calculation and tolerances for the outer diameter of external threads of grade 6g. Base deviation for 6g grade external threads (based on pitch): P0.8–0.024, P1.00–0.026, P1.25–0.028, P1.5–0.032, P1.25–0.024, P1.75–0.034, P2.0–0.038, P2.5–0.042. Formula for the upper limit: d-ges, which is the basic diameter of the thread minus the base deviation. Formula for the lower limit: d-ges – Td, which is the basic diameter of the thread minus the base deviation minus the tolerance. Example: For an M8 external thread of 6g grade, the upper limit value is φ8–0.028 = φ7.972. The lower limit value is φ8 – 0.028 – 0.212 = φ7.76. Note: ① The major diameter of the thread is determined by the diameter of the bare shaft from which the thread is formed, as well as the degree of wear on the die/screw wheel used for thread formation. This value varies inversely with the pitch diameter of the thread; that is, a smaller pitch diameter results in a larger major diameter, while a larger pitch diameter leads to a smaller major diameter. ②For parts that require heat treatment and surface treatment, taking into account the processing steps, the major diameter of the threads should in actual production be kept at a value above the lower limit of grade 6h plus 0.04 mm; for example, for the external threads of M8, the major diameter after thread rolling should be maintained between φ7.83 and 7.95. IV. Calculation and tolerances of the minor diameter of internal threads a. Basic dimension calculation of the minor diameter of internal threads (D1). Basic diameter dimension of the thread = Basic diameter dimension of the internal thread – Pitch × Coefficient. Example: The basic diameter dimension for an internal thread of size M8 is 8 – 1.25 × 1.0825 = 6.646875 ≈ 6.647. b. The tolerance for the diameter of internal threads of grade 6H (based on the pitch) and the corresponding diameter values are calculated as follows. P0.8 +0.2 P1.0 +0.236 P1.25 +0.265 P1.5 +0.3 P1.75 +0.335 P2.0 +0.375 P2.5 +0.48 The formula for the lower limit deviation of internal threads of grade 6H is D1+HE1, that is, the basic dimension of the inner thread diameter plus the deviation. Note: The lower deviation value for grade 6H is “0”. The formula for calculating the upper limit value of grade 6H for internal threads is D1 + HE1 + TD1, that is, the basic diameter dimension of the internal thread plus the deviation and the tolerance. Example: The upper limit value of the minor diameter for a 6H grade M8 internal thread is 6.647 + 0 = 6.647. The lower limit value of the minor diameter for a 6H grade M8 internal thread is 6.647 + 0 + 0.265 = 6.912. c. Calculation of the basic deviation of the minor diameter (based on the pitch) and the actual minor diameter value for a 6G grade internal thread. P0.8 +0.024 P1.0 +0.026 P1.25 +0.028 P1.5 +0.032 P1.75 +0.034 P2.0 +0.038 P2.5 +0.042 The formula for the minimum minor diameter of 6G grade internal threads is D1+GE1, that is, the basic dimension of the internal thread plus the tolerance. Example: The lower limit for the minor diameter of a 6G grade M8 internal thread is 6.647 + 0.028 = 6.675. The upper limit for the minor diameter of a 6G grade M8 internal thread is given by the formula D1 + GE1 + TD1, which represents the basic dimension of the internal thread plus the deviations and tolerances. Example: The upper limit value for the minor diameter of an M8 internal thread of grade 6G is 6.647 + 0.028 + 0.265 = 6.94. Note: ① The thread height of an internal thread is directly related to the magnitude of the torque it can withstand; therefore, during blank production, it should be kept within the upper limit value corresponding to grade 6H as much as possible. ②During the machining of internal threads, the smaller the minor diameter of the thread, the greater the impact on the efficiency of the cutting tool used – the tap. From a practical standpoint, a smaller minor diameter is preferable, but in general, a value within the middle to upper range of this diameter is chosen. For cast iron or aluminum components, a value within the lower to middle range of the minor diameter should be used. ③The minor diameter of internal threads of grade 6G can be manufactured according to grade 6H during the production of the blank. The precision grade is primarily determined by the coating on the major diameter of the thread; therefore, only the major diameter of the tap is taken into account during thread machining, while there is no need to consider the minor diameter of the bare hole. V. Calculation for the single-indexing method of the dividing head
Formula for the single-indexing method: n = 40/Z
n: The number of revolutions the dividing head should make ； Z: Equal division number of the workpiece ； 40: Index head constant. Example: For calculating the milling of a hexagonal shape, substitute this value into the formula: n=40/6. Calculation: ① Simplify the fraction: Find the greatest common divisor, which is 2, and divide both the numerator and denominator by 2 to get 20/3; the fraction remains equivalent after this simplification. ②Calculate the fraction: At this point, the value is determined by looking at the numerator and denominator ； Calculations are performed when the denominator is larger than the numerator. 20÷3=6(2/3), which is the value of n; in other words, the dividing head must make 6(2/3) revolutions. At this point, the fraction has become a mixed number ； The integer part 6 of the mixed number indicates that the dividing head must make 6 full rotations; the fractional part 2/3 means it should rotate only 2/3 of one full rotation. In this case, recalculation is necessary. ③Selection and calculation of index plates: Calculations involving less than one full revolution must be carried out using the index plate of an indexing head. In the calculation, the first step is to simultaneously expand the fraction 2/3. Example: If the fraction when expanded by 14 times at the same time is 28/42 ； When expanded by 10 times at the same time, the fraction is 20/30 ； When expanded by 13 times, the fraction is 26/39... The number of times to expand it depends on the number of holes in the scale. It should be noted at this time that: ① the number of holes on the scale plate must be divisible by the denominator 3. As in the examples given earlier, 42 is 14 times 3, 30 is 10 times 3, and 39 is 13 times 3... ② To increase a fraction, both the numerator and denominator must be increased by the same amount, so that the value of the fraction remains unchanged. For example, 28/42 = 2/3 × 14 = (2 × 14)/(3 × 14); 20/30 = 2/3 × 10 = (2 × 10)/(3 × 10) ； 26/39 = 2/3 × 13 = (2 × 13)/(3 × 13). For 28/42, the denominator is 42; thus, division is carried out using 42 divisions ； Molecule 28 is the positioning hole from the previous round; by moving forward another 28 holes, i.e., to hole 29, that becomes the positioning hole for this round ； For 20/30, the positioning hole for this round is at hole 11, which is 10 holes further forward on the 30-hole index plate; for 26/39, the positioning hole for this round is at hole 27, which is 26 holes further forward on the 39-hole index plate. When milling a hexagon (divided into six equal parts), holes that are divisible by 3, such as 42, 30, and 39, can be used as indexing points. The procedure involves turning the handle by a full 6 rounds, after which the positioning holes on the upper wheel are adjusted by turning an additional 28 + 1/10 + 1/26 + ! turns, so that the 29/11/27th holes become the positioning holes for this round. Example 2: Calculation for milling a gear with 15 teeth. Substitute into the formula: n=40/15. The calculation gives n=2(2/3), which means rotating 2 full turns and then selecting the indexing holes that are divisible by 3, such as 24, 30, 39, 42, 51, 54, 57, 66, etc. From there, rotate an additional 16, 20, 26, 28, 34, 36, 38, or 44 degrees, and add 1 more hole, resulting in the holes 17, 21, 27, 29, 35, 37, 39, 45, which serve as the positioning holes for this round. Example 3: Calculation of indexing for milling 82 teeth. Substitute into the formula: n=40/82; calculating gives n=20/41. Therefore, it is sufficient to use a reticle with 41 holes, and then rotate 20+1, that is, 21 holes, from the positioning holes of the previous round as the positioning holes for this round. Example 4: Calculation of the indexing for milling 51 teeth. Using the formula n=40/51, since this fraction cannot be calculated, it is necessary to choose a hole directly; that is, select an indexing plate with 51 holes. Then, rotate an additional 51+1, or 52 holes, on the positioning hole from the previous round, and use that hole as the positioning hole for this round. Example 5: Calculation of indexing for milling 100 teeth. Substitute the formula n=40/100 to calculate; n=4/10=12/30. Thus, use a division plate with 30 holes. Then, rotate 12+1 more degrees on the positioning holes of the previous round, resulting in 13 holes, which will serve as the positioning holes for this round. If all the index plates do not have the required number of holes for calculation, then the compound indexing method should be used; this is not covered by this calculation method. In actual production, gear hobbing is generally employed, as the practical implementation after using the compound indexing method is extremely inconvenient. VI. Calculation of the hexagon inscribed in a circle: Formula: ① Determine the opposite sides of the hexagon (S face) for circle D ； S=0.866D, that is, diameter × 0.866 (coefficient). ② To find the diameter of the circle (D) for the opposite sides of a hexagon (S face) ； D=1.1547S, that is, the opposite side length multiplied by 1.1547 (the coefficient). VII. Calculation of the hexagonal opposite sides and diagonals in the cold heading process: Formula: ① To find the diagonal e for the outer hexagon’s opposite side length (S) ； e=1.13s, that is, the opposite side multiplied by 1.13. ② To find the diagonal (e) for the opposite side (s) of a hex socket ； e=1.14s, that is, the opposite side length multiplied by 1.14 (the coefficient). ③ For the outer hexagon’s opposite side length (s), to determine the diameter of the diagonal (D) required for the head portion, the formula (6.2) should be used; the diameter of the circle (D) is calculated based on the hexagonal opposite side length (s), with an appropriate increase added to account for the offset from the center – hence D≥1.1547s. The amount of this offset can only be estimated. VIII. Calculation of a square inscribed in a circle. Formula: ① For a circle (D), to find the length of the opposite sides of the square (S-side) ； S=0.7071D, that is, diameter × 0.7071. ② Find the circle (D) for the opposite sides of a square (S face) ； D=1.414S, that is, the opposite side multiplied by 1.414. IX. Calculation of the square opposite sides and diagonals in the cold heading process. Formula ①: To find the diagonal (e) given the outer square opposite side (S) ； e=1.4s, that is, the parameter equal to the opposite side length (s) multiplied by 1.4; ② To find the diagonal (e) for a square with inner sides of length (s) ； e = 1.45 × s, where s is the length of a side; this is essentially multiplying the side length by a factor of 1.45. X. Calculation of the volume of a hexagonal prism: Formula ①: V = s² × 0.866 × H/m/k. In other words, it’s the product of the square of the side length, multiplied by 0.866 and then by the height or thickness. XI. Calculation of the volume of a frustum (cone): The formula is 0.262H(D2+d2+D×d), that is, 0.262 × height × (diameter of the larger end² + diameter of the smaller end² + diameter of the larger end × diameter of the smaller end). XII. Calculation of the volume of a spherical cap (e.g., a semicircular head): The formula is 3.1416h²(R – h/3), that is, 3.1416 × height × height × (radius – height ÷ 3). 13. Calculation of the machining dimensions for tap screws with internal threads 1. Calculation of the major diameter D0 of the tap screw. Formula D0 = D + (0.866025P/8) × (0.5–1.3), which is the basic dimension of the major diameter thread of the tap plus 0.866025 times the pitch divided by 8, multiplied by 0.5 to 1.3. Note: The value to choose between 0.5 and 1.3 should be determined based on the pitch size; the larger the pitch, the smaller coefficient should be used, and conversely, the smaller the pitch, the larger coefficient should be applied. 2. Calculation of the tap diameter (D2). Formula: D2 = (3 × 0.866025P) / 8; that is, the pitch diameter of the tap = 3 × 0.866025 × pitch ÷ 8. 3. Calculation of the minor diameter (D1) of the tap. Formula: D1 = (5 × 0.866025P) / 8; that is, the minor diameter of the tap = 5 × 0.866025 × pitch ÷ 8. XIV. Calculation of material length required for cold heading of various shapes. Given that: the formula for the volume of a circle is diameter × diameter × 0.7854 × length, or radius × radius × 3.1416 × length. That is, d2×0.7854×L or R2×3.1416×L. To calculate this, the volume of material required is X÷diameter÷diameter÷0.7854, or X÷radius÷radius÷3.1416; this value represents the length of material that needs to be used. Formula = X/(3.1416R2) or X/0.7854d2 ； In the formula, X represents the value of the volume of material required ； L represents the actual length value of the material fed in ； R/d represents the actual radius or diameter of the material fed. 15. Calculation of gear ratios for hobbing gears on a gear hobbing machine. a. The fixed number of teeth on the hobbing machine’s main shaft is 24. b. The calculation for the roller gear shift is carried out by breaking down the data, thereby simultaneously enlarging or reducing its equal divisions while keeping them unchanged; the diagrams of B1 and b2 represent compound gear shifting, while those of b3 and b4 represent direct gear shifting. c. Decomposition of spindle parameter 24. c1 can be directly decomposed as 2×12=24 ； 3×8=24 ； 4×6=24. When c2 is increased by a certain factor, it can be factored as follows: If it is increased by 5 times, then 24×5=120, and 120 can be factored into 20×6, 3×40, 4×30, and 6×20. If it is increased by 8 times, then 24×8=192, and 192 can be factored into 2×91, 91×2, 48×4, 4×48, 3×64, and 64×3 ； For 8×24, 24×8, 32×6, and 6×32, when increasing the magnification, the number of teeth on the workpiece must also be increased accordingly until it becomes easy to disassemble ； d. Decomposition of calculation examples. d.1 Calculation when the number of teeth of the machined part is 15. Expression: 24/15; after multiplying both numerator and denominator by 10, we get 240/150 ； By decomposing and eliminating the common multiple of 3, we get (3×80)/(3×50) = 80/50. At this point, the diagram in b.4 can be used: an arbitrary idler gear can be placed in the middle, with a gear having 80 teeth installed at position ① and a gear with 50 teeth installed at position ②. d.2 Calculation when the number of teeth of the machined part is set to 77. Expression: 24/77 expanded by 90 times simultaneously gives 2160/6930 ； To calculate (40×54)/(70/99), one can use the assembled gears shown in the schematic diagram in b.1. For ease of assembly, the numbers 1 and 3 can be swapped with each other, as can the numbers 2 and 4. However, it is not permissible to swap the positions of 1 with 2 or 4, nor those of 3 with 2 or 4. Similarly, 4 cannot be swapped with 1 or 3, nor can 2 be swapped with 1 or 3. d.3 Calculation for when the processed part has 32 teeth. Expression: 24/32; after expanding both values by 5, it becomes 120/160 ； By breaking it down as (4×30)/(4×40) and eliminating the common factor of 4, we get 30/40. At this point, the diagram in b.3 can be used: any idler gear can be placed in the middle; a 30-tooth gear can be installed at position ①, and a 40-tooth gear at position ②. d.4 Calculation for when the processed part has 13 teeth. Expression: Multiplying 24/13 by 100 gives 2400/1300 ； For the resolution ratio of (30×80)/(20×65), the schematic diagram in b.2 can be used for assembly at this point. Note: Although 2400 can be resolved into 30×80, it can also be resolved into 40×60. In such cases, it depends on how well the gears fit together after assembly; as long as they fit properly, it’s acceptable. The number of teeth on this gear allows 2400 to be resolved into 20×120 as well, enabling assembly using the schematic diagram in 6.4.