Relevant calculation formulas used in fastener production:
1. Calculation and tolerance of external thread pitch diameter of 60° profile (National Standard GB 197/196)
a. Calculation of basic dimensions of pitch diameter
The basic size of thread pitch diameter = thread major diameter – pitch × coefficient value.
Formula expression: d/D-P×0.6495
Example: Calculation of pitch diameter of M8 external thread
8-1.25×0.6495=8-0.8119≈7.188
b. Commonly used 6h external thread pitch diameter tolerance (based on pitch)
The upper limit value is “0″
The 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
The upper limit calculation formula is the basic size, and the lower limit calculation formula d2-hes-Td2 is the basic diameter diameter-deviation-tolerance.
M8′s 6h grade pitch diameter tolerance value: upper limit value 7.188 lower limit value: 7.188-0.118=7.07.
C. The basic deviation of the pitch diameter of commonly used 6g-level external threads: (based on the 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
The upper limit value calculation formula d2-ges is the basic size-deviation
The lower limit value calculation formula d2-ges-Td2 is basic size-deviation-tolerance
For example, the 6g grade pitch diameter tolerance value of M8: upper limit value: 7.188-0.028=7.16 and lower limit value: 7.188-0.028-0.118=7.042.
Note: ① The above thread tolerances are based on coarse threads, and there are some changes in the thread tolerances of fine threads, but they are just larger tolerances, so the control according to this will not exceed the specification limit, so they are not marked one by one in the above. out.
② In actual production, the diameter of the threaded polished rod is 0.04-0.08 larger than the designed thread pitch diameter according to the accuracy of the design requirements and the extrusion force of the thread processing equipment. This is the value of the diameter of the threaded polished rod. For example The diameter of our company’s M8 external thread 6g grade threaded polished rod is actually 7.08-7.13, which is within this range.
③ Considering the needs of the production process, the lower limit of the pitch diameter control limit of the actual production of external threads without heat treatment and surface treatment should be kept at level 6h as much as possible.
2. Calculation and tolerance of pitch diameter of 60° internal thread (GB 197/196)
a. Class 6H thread pitch diameter tolerance (based on pitch)
Upper limit:
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 upper limit value calculation formula 2+TD2 is basic size + tolerance.
For example, the pitch diameter of M8-6H internal thread is: 7.188+0.160=7.348. The upper limit value: 7.188 is the lower limit value.
b. The calculation formula for the basic pitch diameter of internal threads is the same as that of external threads.
That is, D2 = D-P × 0.6495, that is, the pitch diameter of the internal thread is equal to the major diameter of the thread – pitch × coefficient value.
c. Basic deviation of pitch diameter of 6G grade thread 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 grade internal thread pitch diameter upper limit: 7.188+0.026+0.16=7.374
Lower limit value:7.188+0.026=7.214
The upper limit value formula 2+GE1+TD2 is the basic size of the pitch diameter+deviation+tolerance
The lower limit value formula 2+GE1 is the pitch diameter size + deviation
3. Calculation and tolerance of external thread major diameter (GB 197/196)
a. The upper limit of 6h major diameter of external thread
That is, the thread diameter value. For example, M8 is φ8.00 and the upper limit tolerance is “0″.
b. The lower limit tolerance of the 6h major diameter of the external thread (based on the 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 calculation formula for the lower limit of the major diameter is: d-Td, which is the basic size-tolerance of the major diameter of the thread.
Example: M8 external thread 6h large diameter size: upper limit is φ8, lower limit is φ8-0.212=φ7.788
c. Calculation and tolerance of 6g grade major diameter of external thread
Reference deviation of grade 6g external thread (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
The upper limit calculation formula d-ges is the basic size of the thread’s major diameter – the reference deviation
The lower limit calculation formula d-ges-Td is the basic size of the thread’s major diameter – the datum deviation – the tolerance.
Example: M8 external thread 6g grade major diameter upper limit value φ8-0.028=φ7.972.
Lower limit valueφ8-0.028-0.212=φ7.76
Note: ① The major diameter of the thread is determined by the diameter of the threaded polished rod and the degree of tooth profile wear of the thread rolling plate/roller, and its value is inversely proportional to the pitch diameter of the thread based on the same blank and thread processing tools. That is, if the middle diameter is small, the major diameter will be large, and conversely if the middle diameter is large, the major diameter will be small.
② For parts that require heat treatment and surface treatment, taking into account the processing process, the thread diameter should be controlled to be above the lower limit of grade 6h plus 0.04mm during actual production. For example, the external thread of M8 is rubbing (rolling) The major diameter of the wire should be above φ7.83 and below 7.95.
4. Calculation and tolerance of internal thread diameter
a. Basic size calculation of internal thread small diameter (D1)
Basic thread size = basic size of internal thread – pitch × coefficient
Example: The basic diameter of the internal thread M8 is 8-1.25×1.0825=6.646875≈6.647
b. Calculation of small diameter tolerance (based on pitch) and small diameter value of 6H internal thread
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 of 6H grade internal thread D1+HE1 is the basic size of internal thread small diameter + deviation.
Note: The downward bias value of level 6H is “0″
The calculation formula for the upper limit value of grade 6H internal thread is =D1+HE1+TD1, which is the basic size of the small diameter of the internal thread + deviation + tolerance.
Example: The upper limit of the small diameter of 6H grade M8 internal thread is 6.647+0=6.647
The lower limit of the small diameter of 6H grade M8 internal thread is 6.647+0+0.265=6.912
c. Calculation of the basic deviation of the small diameter of the internal thread 6G grade (based on the pitch) and the small 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 formula for the lower limit of the small diameter of 6G grade internal thread = D1 + GE1, which is the basic size of the internal thread + deviation.
Example: The lower limit of the small diameter of 6G grade M8 internal thread is 6.647+0.028=6.675
The upper limit value formula of 6G grade M8 internal thread diameter D1+GE1+TD1 is the basic size of internal thread + deviation + tolerance.
Example: The upper limit of the small diameter of 6G grade M8 internal thread is 6.647+0.028+0.265=6.94
Note: ① The pitch height of the internal thread is directly related to the load-bearing moment of the internal thread, so it should be within the upper limit of grade 6H during blank production.
② During the processing of internal threads, the smaller the diameter of the internal thread will have an impact on the use efficiency of the machining tool – the tap. From the perspective of use, the smaller the diameter, the better, but when considering comprehensively, the smaller diameter is generally used. If it is a cast iron or aluminum part, the lower limit to the middle limit of the small diameter should be used.
③ The small diameter of internal thread 6G can be implemented as 6H in blank production. The accuracy level mainly considers the coating of the thread’s pitch diameter. Therefore, only the pitch diameter of the tap is considered during thread processing without considering the small diameter of the light hole.
5. Calculation formula of single indexing method of indexing head
Calculation formula of single indexing method: n=40/Z
n: is the number of revolutions that the dividing head should turn
Z: equal fraction of the workpiece
40: Fixed number of dividing head
Example: Calculation of hexagonal milling
Substitute into the formula: n=40/6
Calculation: ① Simplify the fraction: Find the smallest divisor 2 and divide it, that is, divide the numerator and denominator by 2 at the same time to get 20/3. While reducing the fraction, its equal parts remain unchanged.
② Calculate the fraction: At this time, it depends on the values of the numerator and denominator; if the numerator and denominator are large, calculate.
20÷3=6(2/3) is the n value, that is, the dividing head should be turned 6(2/3) times. At this time, the fraction has become a mixed number; the integer part of the mixed number, 6, is the dividing number The head should turn 6 full turns. The fraction 2/3 with a fraction can only be 2/3 of one turn, and must be recalculated at this time.
③ Calculation of the selection of the indexing plate: The calculation of less than one circle must be realized with the help of the indexing plate of the indexing head. The first step in the calculation is to expand the fraction 2/3 at the same time. For example: if the fraction is expanded 14 times at the same time, the fraction is 28/42; 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 expansion multiple of the dividing gate should be selected according to the number of holes in the indexing plate.
At this time you should pay attention to:
①The number of holes selected for the indexing plate must be divisible by the denominator 3. For example, in the previous example, 42 holes is 14 times 3, 30 holes is 10 times 3, 39 is 13 times 3…
② The expansion of a fraction must be such that the numerator and denominator are simultaneously expanded and their equal parts remain unchanged, as in the 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)
The denominator 42 of 28/42 is indexed using the 42 holes of the index number; the numerator 28 is forward on the positioning hole of the upper wheel and then rotates through the 28 hole, that is, the 29 hole is the positioning hole of the current wheel, and 20/30 is at 30 The hole indexing plate is turned forward and the 10th hole or the 11th hole is the positioning hole of the epicycle. The 26/39 is the positioning hole of the epicycle after the 39-hole indexing plate is turned forward and the 26th hole is the 27th hole.
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When milling six squares (six equal parts), you can use 42 holes, 30 holes, 39 holes and other holes that are evenly divided by 3 as indexes: the operation is to turn the handle 6 times, and then move forward on the positioning holes of the upper wheel. Then turn the 28+1/ 10+1 / 26+! hole to the 29/11/27 hole as the positioning hole of the epicycle.
Example 2: Calculation for milling a 15-tooth gear.
Substitute into the formula: n=40/15
Calculate n=2(2/3)
Turn 2 full circles and then select the indexing holes divisible by 3, such as 24, 30, 39, 42.51.54.57, 66, etc. Then turn forward on the orifice plate 16, 20, 26, 28, 34, 36, 38, 44 Add 1 hole, namely holes 17, 21, 27, 29, 35, 37, 39, and 45 as the positioning holes of the epicycle.
Example 3: Calculation of indexing for milling 82 teeth.
Substitute into the formula: n=40/82
Calculate n=20/41
That is: just choose a 41-hole indexing plate, and then turn 20+1 or 21 holes on the upper wheel positioning hole as the positioning hole of the current wheel.
Example 4: Index calculation for 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 51-hole indexing plate, and then turn 51+1 or 52 holes on the upper wheel positioning hole as the current wheel positioning hole. That is.
Example 5: Calculation of indexing for milling 100 teeth.
Substitute into the formula n=40/100
Calculate n=4/10=12/30
That is, choose a 30-hole indexing plate, and then turn 12+1 or 13 holes on the upper wheel positioning hole as the positioning hole of the current wheel.
If all indexing plates do not have the number of holes required for calculation, the compound indexing method should be used for calculation, which is not included in this calculation method. In actual production, gear hobbing is generally used, because the actual operation after compound indexing calculation is extremely inconvenient.
6. Calculation formula for a hexagon inscribed in a circle
① Find the six opposite sides of circle D (S surface)
S=0.866D is diameter × 0.866 (coefficient)
② Find the diameter of the circle (D) from the opposite side of the hexagon (S surface)
D=1.1547S is the opposite side × 1.1547 (coefficient)
7. Calculation formulas for six opposite sides and diagonals in the cold heading process
① Find the opposite side (S) of the outer hexagon to find the opposite angle e
e=1.13s is the opposite side × 1.13
② Find the opposite angle (e) of the inner hexagon from the opposite side (s)
e=1.14s is the opposite side × 1.14 (coefficient)
③Calculate the head material diameter of the opposite corner (D) from the opposite side (s) of the outer hexagon
The diameter of the circle (D) should be calculated according to the (second formula in 6) the six opposite sides (s-plane) and its offset center value should be increased appropriately, that is, D≥1.1547s. The offset center amount can only be estimated.
8. Calculation formula for a square inscribed in a circle
① Find the opposite side of the square (S surface) from the circle (D)
S=0.7071D is diameter×0.7071
② Find the circle (D) from the opposite sides of the four squares (S surface)
D=1.414S is the opposite side×1.414
9. Calculation formulas for the four opposite sides and opposite corners of the cold heading process
① Find the opposite angle (e) of the opposite side (S) of the outer square
e=1.4s, that is, the opposite side (s)×1.4 parameter
② Find the opposite angle (e) of the inner four sides (s)
e=1.45s is the opposite side (s)×1.45 coefficient
10. Calculation formula of hexagonal volume
s20.866×H/m/k means opposite side×opposite side×0.866×height or thickness.
11. Calculation formula for the volume of a truncated cone (cone)
0.262H (D2+d2+D×d) is 0.262×height×(large head diameter×large head diameter+small head diameter×small head diameter+large head diameter×small head diameter).
12. Volume calculation formula of spherical missing body (such as semicircular head)
3.1416h2(R-h/3) is 3.1416×height×height×(radius-height÷3).
13. Calculation formula for processing dimensions of taps for internal threads
1. Calculation of tap major diameter D0
D0=D+(0.866025P/8)×(0.5~1.3), that is, the basic size of the large diameter thread of the tap+0.866025 pitch÷8×0.5 to 1.3.
Note: The selection of 0.5 to 1.3 should be confirmed according to the size of the pitch. The larger the pitch value, the smaller the coefficient should be used. On the contrary,
The smaller the pitch value is, the larger the coefficient will be.
2. Calculation of tap pitch diameter (D2)
D2=(3×0.866025P)/8 that is, tap pitch=3×0.866025×thread pitch÷8
3. Calculation of tap diameter (D1)
D1=(5×0.866025P)/8 that is, tap diameter=5×0.866025×thread pitch÷8
14. Calculation formula for length of materials used for cold heading molding of various shapes
Known: 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
When calculating, the volume of material required is X÷diameter÷diameter÷0.7854 or X÷radius÷radius÷3.1416, which is the length of the feed.
Column formula=X/(3.1416R2) or X/0.7854d2
X in the formula represents the required volume of material;
L represents the actual feeding length value;
R/d represents the actual radius or diameter of the material fed.
Post time: Nov-06-2023
