The relevant calculation formula used in the production of fasteners.

The relevant calculation formula used in the production of fasteners.

The fastener is a general-purpose basic component, and its manufacturing materials include steel, non-ferrous metals, stainless steel, titanium alloys and other engineering materials. At present, in order to improve product accuracy, improve quality, and improve production efficiency, 90% of the fasteners are cold heading processing. Therefore, it is very important for fastener enterprises to better master the cold heading technology of fasteners and apply it to manufacturing.

Calculation and Tolerance of External Thread Pin Diameter of 1. 60 ° Tooth (GB 197/196)

A. basic dimension calculation of pitch diameter: basic dimension of thread pitch diameter = thread major diameter-pitch × coefficient value formula: d/D-P × 0.6495 examples: calculation of pitch diameter of external thread M8 8-1.25 × 0.6495=8-0.8119 ≈ 7.188 B. the commonly used 6-h external thread pitch tolerance (based on pitch) upper limit value is "0" lower limit value 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 P2.5-0.17 upper limit calculation formula, I .e. basic dimension, the calculation formula of the lower limit value d2-hes-Td2 that is, the 6h grade pitch diameter tolerance value of pitch diameter basic dimension-deviation-tolerance M8: the upper limit value 7.188 the lower limit value: 7.188-118=7.07 C. the commonly used 6g grade external thread pitch diameter basic deviation: (based on pitch) P 0.80-0.024 P 1.00-0.026 P1.25-0.028 P1.5-0.032 P1.75-0.034 P2-0.038 P2.5-0.042 upper limit calculation formula d2-ges, that is, basic dimension-deviation lower limit calculation formula d2-ges-Td2, that is, basic dimension-deviation-tolerance example M8 6g pitch diameter tolerance value: 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 tolerance is subject to coarse teeth, and the thread tolerance of fine teeth changes accordingly, but the tolerance is only larger, so it will not exceed the standard limit according to this control, therefore, it is not marked out one by one in the above. ② The diameter of the threaded rod blank is increased by 0.04-0.08 in the actual production according to the accuracy of the design requirements and the different extrusion pressure of the thread processing equipment, which is the diameter value of the threaded rod blank, for example, the blank diameter of our company's M8 external thread 6g grade threaded smooth rod is in the range of 7.08-7.13. ③ Considering the needs of the production process, the lower limit of the pitch diameter control of external thread in the actual production without heat treatment and surface treatment should be kept at 6h grade as far as possible.

II. Calculation and Tolerance of Pitch Diameter of 60 Internal Thread (GB 197/196) Upper Limit Value of Pitch Tolerance of Class A. 6H Thread (Based on Pitch): 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 Lower Limit Value is "0", Calculation Formula 2 TD2, Basic Dimension Tolerance Example M8-6H Internal Thread Pitch Diameter: 7.188 0.160=7.348 Upper Limit Value: 7.188 is the lower limit B. the calculation formula for the basic pitch diameter dimension of the internal thread is the same as that of the external thread, I .e. D2 = D-P × 0.6495, I .e. the major pitch diameter of the internal thread-pitch × coefficient value c. 6G grade thread basic pitch diameter deviation E1 (based on 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: M8 6G internal thread pitch diameter upper limit value: 7.188 0.026 0.16=7.374 lower limit value: 7.188 0.026=7.214 upper limit value formula 2 GE1 TD2 is pitch diameter basic dimension deviation tolerance lower limit value formula 2 GE1 is pitch diameter dimension deviation

Calculation and Tolerance of 3. External Threads (GB 197/196)

A. the 6h large diameter upper limit value of external thread, I .e. thread diameter value example M8 is Φ 8.00 upper limit value tolerance is "0" B. the 6h large diameter lower limit value tolerance of external thread (based on thread 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 large diameter lower limit calculation formula: d-Td is thread large diameter basic dimension-tolerance example: M8 6h large diameter dimension: external thread upper limit is Φ 8, the lower limit is φ 8-0.212 = φ 7.788 c. the calculation of the major diameter of the external thread of grade 6g and the reference deviation (based on the pitch) of the tolerance grade 6g external thread P0.8-0.024 the upper limit calculation formula of the P1.25-0.028 P1.5-0.032 P1.25-0.024 P1.75 -0.034 P2.0-0.038 P2.5-0.042 d-ges is the basic dimension of the major diameter of the thread-the lower limit calculation formula d-ges-Td is the basic dimension of the major diameter of the thread-the reference deviation-the tolerance

Example: M8 external thread 6g grade large diameter upper limit Φ 8-0.028 = Φ 7.972 lower limit Φ 8-0.028-0.212 = Φ 7.76

Note: ① The large diameter of the thread is determined by the blank diameter of the thread rod and the wear degree of the thread profile of the washboard/thread roller, and its value is inversely proportional to the thread middle diameter on the basis of the same blank and thread processing tools, I .e. the small middle diameter leads to the large diameter, otherwise the large middle diameter leads to the small diameter. ② For the parts that need heat treatment and surface treatment, considering the relationship between the processing process, the thread diameter should be controlled at the lower limit of 6h level plus 0.04mm or more in actual production. For example, the thread diameter of M8 external thread in rolling (rolling) wire should be guaranteed to be above φ7.83 and below 7.95. Calculation and tolerance of 4. internal thread diameter A. Basic dimension calculation of internal thread diameter (D1) Basic dimension of thread diameter = Basic dimension of internal thread-pitch × coefficient Example: the minor diameter basic dimension of internal thread M8 is 8-1.25 × 1.0825=6.646875 ≈ 6.647 B. the minor diameter tolerance of internal thread 6H grade (based on pitch) and the minor diameter value calculation 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 lower limit deviation formula D1 HE1 of internal thread 6H grade note: the downward deviation value of grade 6H is "0". The upper limit value calculation formula of grade 6H of internal thread = D1 HE1 TD1 is the basic dimension deviation tolerance example of internal thread small diameter: the upper limit value 6.647 of the minor diameter of 6H M8 internal thread is 0=6.647 the lower limit value 6.647 of the minor diameter of 6H M8 internal thread is 0 0.265=6.912 c. the basic deviation of the minor diameter of 6G internal thread (based on pitch) and the calculation of the minor diameter value 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 lower limit value formula of the minor diameter of 6G internal thread is D1 = D1, I .e: the lower limit value of the minor diameter of 6G grade M8 internal thread 6.647 0.028=6.675 the upper limit value formula of the minor diameter of 6G grade M8 internal thread D1 GE1 TD1 is the basic dimension deviation tolerance of internal thread

For example, the upper limit value of the minor diameter of 6G M8 internal thread is 6.647 0.028 0.265=6.94

Note: ① The tooth height of the internal thread is directly related to the bearing torque of the internal thread, so it should be within the upper limit value of 6H as far as possible in the production of the blank. ② During the processing of the internal thread, the smaller the diameter of the internal thread, the more tools will be added-the use benefit of the tap will be affected. From the point of view of use, the smaller the diameter, the better. However, when considering comprehensively, the diameter is generally between the middle limit and the upper limit. If it is cast iron or aluminum, the diameter between the lower limit and the middle limit of the diameter should be used. ③ The diameter of grade 6G for internal thread can be implemented as grade 6H in blank production. The precision grade mainly considers the coating of thread diameter, therefore, only the diameter size of the tap is considered during thread processing without considering the small diameter of the light hole.

5. dividing head single dividing method calculation formula of single dividing method: n = 40/Z n: is the number of revolutions that the dividing head should turn z: equal fraction of workpiece 40: dividing head fixed number example: calculation of milling hexagon is substituted into formula: n = 40/6 calculation: ① simplified fraction: find the minimum divisor 2 for dividing, I .e. divide the numerator and denominator by 2 to obtain 20/3. At the same time, the fraction is reduced and its equal fraction remains unchanged. ② Calculate the fraction: at this time, it depends on the value of the numerator and denominator. If the denominator of the numerator is large, the calculation is carried out. 20 ÷ 3=6(2/3) is the N value, that is, the dividing head should be turned by 6(2/3) turns. At this time, the fraction has become a band fraction. The integer part with fraction 6 is that the dividing head should turn 6 full circles. The score 2/3 with score can only be 2/3 of one turn. At this time, it is necessary to recalculate the selection and calculation of ③ indexing plate: the calculation of less than one turn must be realized by means of the indexing plate of the indexing head. The first step in the calculation is to expand the score by 2/3 at the same time. For example, if the score is 28/42 when it is expanded 14 times at the same time; If it is expanded 10 times at the same time, the score is 20/30; If it is expanded 13 times at the same time, the score is 26/39... the number of expanded split-gate multiples should be selected according to the number of holes in the index plate.

At this time, it should be noted that: ① the number of holes selected for the indexing plate must be divisible by the denominator 3. For example, hole 42 in the previous example is 14 times of 3, hole 30 is 10 times of 3, and hole 39 is 13 times of 3... ② The expansion of the fraction must be the same as the expansion of the numerator and denominator, for example, 28/42=2/3 × 14 =(2 × 14)/(3 × 14) in the example; 20/30=2/3 × 10 =(2 × 10)/(3 × 10); 26/39=2/3 × 13 =(2 × 13)/(3 × 13) 28/42 denominator 42 is indexed by 42 holes of indexing number; Molecule 28 is the positioning hole of the upper wheel and then turns forward through hole 28, that is, hole 29 is the positioning hole of the current wheel, 20/30 is the positioning hole for this round when the 30-hole indexing plate is turned forward by 10 holes, I .e. 11 holes. 26/39 is the positioning hole for this round when the 39-hole indexing plate is turned forward by 26 holes, I .e. 27 holes. when milling hexagonal (six equal parts), 42 holes, 30 holes, 39 holes and other holes divided by 3 can be used as indexing: the operation is that after the handle is turned for 6 times, then turn forward 28 1/ 10 1/26 on the positioning hole of the upper wheel respectively! The 29/11/27 hole of the hole is used as the positioning hole of this round. Example 2: The gear calculation for milling 15 teeth is substituted into the formula: n = 40/15 calculation n = 2(2/3) is to rotate 2 full turns and then select the indexing holes divided by 3, such as 24,30,39,42.51.54.57,66, etc., and then rotate 16,20,26,28,34,36,38 forward, 44 plus 1 hole, that is, 17,21,27,29,35,37,39,45 holes as the positioning hole of this round.

Example 3: Substituting the indexing calculation of milling 82 teeth into the formula: n = 40/82 calculating n = 20/41, that is, as long as the indexing plate with 41 holes is selected, and 21 holes are turned on the positioning hole of the upper wheel as the positioning hole of this round.

Example 4: The indexing calculation of milling 51 teeth is substituted into the formula n = 40/51. Since the score cannot be calculated at this time, the hole can only be directly selected, that is, the indexing plate of 51 holes is selected, and 51 1 or 52 holes are turned on the positioning hole of the upper wheel as the positioning hole of this round, that is

Example 5 The indexing calculation of milling 100 teeth is substituted into the formula n = 40/100 to calculate n = 4/10=12/30, that is, a 30-hole indexing plate is selected, and 121 or 13 holes are turned on the upper wheel positioning hole as the positioning hole of this round, that is, if all indexing plates do not have the number of holes required for calculation, the compound indexing method should be adopted for calculation, which is not included in this calculation method, hobbing is generally used in actual production, because the actual operation after the calculation of compound indexing is extremely inconvenient.

The calculation formula of 6. circle inscribed with hexagonal square: ① circle d to find the hexagonal opposite side (s-plane) S = 0.866D, I .e. diameter × 0.866 (coefficient); ② hexagonal opposite side (s-plane) to find the circle (d) diameter D = 1.1547S, I .e. opposite side × 1.1547 (coefficient)

Seven, cold heading process of the hexagonal opposite side and diagonal calculation formula ① external hexagonal opposite side (s) find the diagonal angle e e = 1.13s that is opposite side x 1.13 ② internal hexagonal opposite side (s) find the diagonal angle (e) e = 1.14s that is opposite side x 1.14 (coefficient) ③ external hexagonal opposite side (s) find the head material diameter of diagonal angle (d), the diameter of the circle (d) shall be calculated according to the (6.2 formula) hexagonal opposite side (s-plane) and its offset center value shall be appropriately increased, I .e. D≥ 1.1547s offset center value can only be estimated

The calculation formula of 8. circle inscribed with square: ① circle (d) to find the opposite side (s-face) of square S = 0.7071D, I .e. diameter × 0.7071; ② square opposite side (s-face) to find the circle (D) D = 1.414S, I .e. opposite side × 1.414

The calculation formula of the four opposite sides and the opposite angle of the 9. cold heading process ① the outer four opposite sides (s) find the opposite angle (e) e = 1. the 4S is the opposite side (s)× 1.4 parameter ② the inner four opposite sides (s) find the opposite angle (e) e = 1.45s is the opposite side (s)× 1.45 coefficient

The formula for calculating the volume of 10. hexagonal body ① s20.866 ×H/m/k is opposite side × opposite side × 0.866 × height or thickness

Eleven, the frustum (cone) body volume calculation formula 0.262H(D2 d2 D x d) is 0.262 x height x (big head diameter x big head diameter small head diameter x small head diameter big head diameter x small head diameter)

Twelve, the ball missing body (such as semicircular head) volume calculation formula 3.1416 h2(R-h/3) that is 3.1416 x height x height x (radius-height 3)

Thirteen, internal thread with tap processing size calculation 1. tap diameter D0 calculation formula D0 = D +(0.866025P/8)×(0.5~1.3) that is, tap diameter thread basic size 0.866025 pitch ÷ 8 × 0.5 to 1.3 note: the number of 0.5 to 1.3 should be confirmed according to the size of the pitch, the larger the pitch value, should use a smaller coefficient, on the contrary, the smaller the pitch value, the larger the coefficient 2. The calculation formula of tap diameter (D2) is D2 =(3 × 0.866025P)/8, that is, tap diameter = 3 × 0.866025 × pitch ÷ 83. The calculation formula of tap diameter (D1) is D1 =(5 × 0.866025P)/8, that is, tap diameter = 5 × 0.866025 × pitch ÷ 8

Fourteen, various shapes of cold heading forming material length calculation known: the volume formula of a circle is diameter x diameter x 0.7854 x length or radius x radius x 3.1416 x length, that is, d2 x 0.7854 x L or R2 x 3.1416 x L. when calculating, the volume x ÷ diameter ÷ diameter ÷ 0.7854 or x ÷ radius ÷ radius ÷ 3.1416 is the length formula = X/(3.1416R2) or x/0.7854d2, x indicates the volume of material required. The value L represents the length of the actual feed. The value R/d represents the radius or diameter of the actual feed.

Fifteen, hobbing machine roller gear hanging wheel calculation a. roller gear spindle number 24 B. roller gear hanging wheel calculation is based on the data decomposition, I .e. at the same time to expand or reduce its equal division to achieve the same B1 and b2 schematic diagram for compound speed change, b3 and b4 schematic diagram for direct speed change c. spindle parameter 24 decomposition c1 direct decomposition can be 2 × 12=24; 3 × 8=24; 4 × 6=24c2 decomposition after expansion: if the expansion is 5 times 24 × 5=120, the 120 can be decomposed into 20 × 6; 3 × 40; 4 × 30; 6 × 20 If the expansion is 8 times 24 × 8=192, the 192 is decomposed into 2 × 91; 91 × 2; 48 × 4; 4 × 48; 3 × 64; 64 × 3; 8 × 24; 24 × 8; 32 × 6; When expanding the multiple of 6 × 32, the number of teeth of the processed parts shall be expanded at the same time until it is easy to decompose. D. calculation case decomposition d.1 calculation formula when the processed part is 15 teeth: 24/15 is expanded 10 times at the same time and then 240/150; decomposition and removal of common multiple 3 (3 × 80)/(3 × 50)= 80/50 At this time, B .4 schematic diagram can be used to install an arbitrary intermediate wheel in the middle, I .e. 80-tooth gear at ① and 50-tooth gear at ②. d.2 The calculation formula when the processed part is 77 teeth: 24/77 is expanded by 90 times at the same time and 2160/6930; decomposition (40 × 54)/(70/99) At this time, the assembly gear of B .1 schematic diagram can be used. Considering the convenient assembly of gears, the numbers 1 and 3 can be changed at will, 2 and 4 can also be exchanged at will, but the positions of 1 and 2 or 4 and 3 and 2 or 4 are not suitable for exchange, whereas 4 and 1 or 3 and 2 and 1 or 3 cannot be exchanged with d.3 when the processed part is 32 teeth, the calculation formula is: 24/32 is expanded by 5 times at the same time and 120/160; decompose into (4 × 30)/(4 × 40) and remove the common multiple 4 to obtain 30/40. At this time, B .3 schematic diagram can be used to install any intermediate wheel in the middle, I .e. 30 gears at ① and 40 gears at ②. The calculation formula for gear d.4 when the processed parts are 13 teeth: 24/13 is expanded by 100 times at the same time and 2400/1300; the decomposition force (30 × 80)/(20 × 65) can be assembled by using B .2 schematic diagram at this time. Note: Why can the decomposition be 30 × 80 or 40 × 60 at 2400 time? At this time, it depends on the coincidence of the assembled gears. As long as the coincidence is good, the number of teeth of this gear can also be 2400 decomposed into 20 × 120 to be assembled with the schematic diagram of the 6.4,