1. Calculation and tolerance of the pitch diameter of the external thread of the 60° profile (national standard GB 197/196)

a. Calculation of the basic size of the pitch diameter: the basic size of the pitch diameter of the thread = the major diameter of the thread – the pitch × the coefficient value.

Formula: d/D-P×0.6495

Example: Calculation of pitch diameter of external thread M8

8-1.25×0.6495=8-0.8119≈7.188

b. Commonly used 6h external thread pitch diameter tolerance (based on thread 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, P2. 5-0.17

The upper limit calculation formula is the basic size, and the lower limit calculation formula d2-hes-Td2 is the pitch diameter basic size-deviation-tolerance.

The 6h-level pitch diameter tolerance value of M8: the upper limit value is 7.188; the lower limit value: 7.188-0.118=7.07.

C. Commonly used 6g grade external thread pitch diameter basic deviation: (based on the pitch).

P0.80-0.024, 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 the basic size-deviation-tolerance

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

Note: ①The above thread tolerances are based on the coarse thread, and the thread tolerance for the fine thread is changed accordingly, but the tolerances are only increased, so the control will not exceed the standard limit, so the above are not one by one. out.

②The diameter of the polished rod blank of the thread is 0.04-0.08 larger than the diameter of the designed thread according to the accuracy of the design requirements and the extrusion force of the thread processing equipment in actual production, which is the diameter of the polished rod blank of the thread, such as The company’s M8 external thread 6g level threaded rod blank diameter is actually 7.08-7.13 in this range.

③ Considering the needs of the production process, the lower limit of the pitch diameter control of the actual production of the external thread without heat treatment and surface treatment should be kept at the 6h level as much as possible.
2. Calculation and tolerance of pitch diameter of 60° internal thread (GB 197/196)

a. 6H thread pitch diameter tolerance (based on thread 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 is “0”,

The upper limit value calculation formula 2+TD2 is the basic dimension + tolerance.

For example, the pitch diameter of M8-6H internal thread is: 7.188+0.160=7.348 Upper limit: 7.188 is the lower limit.

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

That is, D2=D-P×0.6495, that is, the inner thread medium diameter thread major diameter-thread pitch×coefficient value.

c. The basic deviation E1 of the pitch diameter of the 6G-grade thread (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: M8 6G-level internal thread pitch diameter upper limit: 7.188+0.026+0.16=7.374

Lower limit: 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 diameter size + deviation

3. Calculation and tolerance of major diameter of external thread (GB 197/196)

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

Example M8 is φ8.00 upper limit tolerance is “0”.

b. Tolerance of the lower limit value of the 6h-class major diameter of the external thread (based on the 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

The formula for calculating the lower limit of the major diameter: d-Td is the basic dimension-tolerance of the major diameter of the thread.

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

c. Calculation and tolerance of 6g major diameter of external thread.

Benchmark deviation of 6g-grade 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 major diameter of the thread – the reference deviation

The lower limit calculation formula d-ges-Td is the basic size of the major diameter of the thread – the reference deviation – the tolerance

Example: M8 male thread 6g class major diameter upper limit φ8-0.028=φ7.972.

Lower limit φ8-0.028-0.212=φ7.76

Note: ①The major diameter of the thread is determined by the diameter of the thread polished rod and the tooth profile wear degree of the thread rolling plate/roller, and its value appears inversely proportional to the pitch diameter of the thread on the basis of the same blank and thread processing tools That is, if the middle diameter is small, the major diameter is large, and if the middle diameter is large, the major diameter is small.

② For parts that need to be processed such as heat treatment and surface treatment, considering the relationship between the processing process, the major diameter of the thread should be controlled at the lower limit of the 6h class plus 0.04mm or more in actual production. For example, the M8 external thread is rubbing (rolling) The major diameter of the wire should be guaranteed to be above φ7.83 and below 7.95.

4. Calculation and Tolerance of Internal Thread Small Diameter

a. Basic dimension calculation (D1) of the minor diameter of the female thread.

Basic size of small diameter of thread = basic size of internal thread – thread pitch × coefficient

Example: Small diameter basic size of female thread M8 8-1.25×1.0825=6.646875≈6.647

b. Minor diameter tolerance (based on thread pitch) and minor 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 D1+HE1 of the internal thread 6H grade is the basic size of the internal thread small diameter + deviation.

Note: The down bias value of 6H class is “0”

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

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

The lower limit of the small diameter of the 6H grade M8 internal thread 6.647+0+0.265=6.912

c. The basic deviation of the small diameter (based on the thread pitch) and the small diameter value of the 6G level of the female 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 lower limit value of the small diameter of the female thread 6G class = D1 + GE1 is the basic size of the female thread + deviation.

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

The formula D1+GE1+TD1 for the upper limit value of the small diameter of the 6G-grade M8 internal thread is the basic size of the 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: ①The tooth height of the internal thread is directly related to the bearing moment of the internal thread, so it should be within the upper limit of its 6H level as far as possible in the production of blanks.

②In the process of processing the internal thread, the smaller the diameter of the internal thread will affect the use efficiency of the tool-tap. From the point of view of use, the smaller the diameter, the better. Between the lower limit and the upper limit, if it is cast iron or aluminum parts, the lower limit to the middle limit of the small diameter should be used.

③The small diameter of the internal thread 6G can be implemented according to the 6H level in the production of the blank. The accuracy level mainly considers the coating of the pitch diameter of the thread, so only the pitch diameter of the tap is considered in the thread processing without considering the small diameter of the light hole.

Five, the indexing head single indexing method calculation

Single-division calculation formula: n=40/Z

n: the number of revolutions that the indexing head should turn; Z: equal parts of the workpiece; 40: the fixed number of the indexing head

Example: Calculation of milling hexagon, 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 to get 20/3, and reduce the fraction while reducing its equal fraction.

②Calculate the fraction: At this time, it depends on the value of the numerator and denominator; if the numerator and the denominator are larger, the calculation is performed.

20÷3=6(2/3) is the n value, that is, the indexing head should turn 6(2/3) turns. At this time, the fraction has become a fraction; the integer part 6 with a fraction means that the indexing head should turn 6 full circles, and the fraction 2/3 with a fraction can only be 2/3 of one circle. must be recalculated.

③ Selection and calculation of the indexing plate: The calculation of less than one circle must be realized by the indexing plate of the indexing head. The first step in the calculation is to expand the fraction 2/3 at the same time. Example: If the score is 28/42 when it is expanded by 14 times at the same time; if it is expanded by 10 times at the same time, the score is 20/30; if it is expanded by 13 times at the same time, the score is 26/39… How much to expand the division multiple depends on The number of holes in the indexing plate can be selected.

At this point it should be noted:

①Select the number of holes of the indexing plate must be divisible by the denominator 3. For example, in the previous example, 42 holes are 14 times of 3, 30 holes are 10 times of 3, and 39 is 13 times of 3…

②The expansion of the fraction must be that the numerator and denominator are expanded at the same time and its 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)

28/42 The denominator 42 is the 42 hole of the index number for indexing; the numerator 28 is the positioning hole of the upper wheel and then turns forward and then passes through the 28 hole, that is, the 29 hole is the positioning hole of the current wheel; 20/30 is the positioning hole of the current wheel; The hole indexing plate is rotated forward through 10 holes, that is, the 11 hole is the positioning hole of the current wheel, and the 26/39 is the positioning hole of the current wheel when the 39-hole indexing plate is rotated forward and then 26 holes, that is, the 27 hole.

When milling hexagonal (six equal parts), 42 holes, 30 holes, 39 holes and other holes that are divisible by 3 can be used as the index: the operation is to rotate the handle 6 circles, and then move forward on the positioning holes of the upper wheel respectively. Then turn the 29/11/27 holes of the 28+1/ 10+1 / 26+! holes as the positioning holes of the current wheel.

Example 2: Calculation of milling a 15-tooth gear.

Substitute into the formula: n=40/15

Calculate n=2(2/3)

It is to turn 2 full circles and then select the indexing holes that are divisible by 3, such as 24, 30, 39, 42, 51, 54, 57, 66, etc. on the orifice plate and then turn forward 16, 20, 26, 28, 34, 36 , 38, 44 plus 1 hole that is 17, 21, 27, 29, 35, 37, 39, 45 holes as the positioning hole of the current wheel.

Example 3: Index calculation for milling 82 teeth.

Substitute into the formula: n=40/82

Calculate n=20/41

That is, as long as the 41-hole indexing plate is selected, 20+1 or 21 holes are rotated on the positioning hole of the upper wheel as the positioning hole of the current wheel.

Example 4: Index calculation for milling 51 teeth

Substitute into the formula n=40/51, because 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 positioning hole of the upper wheel as the positioning hole of the current wheel That is.

Example 5: Index calculation for milling 100 teeth.

Substitute into the formula n=40/100

Calculate n=4/10=12/30

That is, select a 30-hole indexing plate, and then turn 12+1 or 13 holes on the positioning hole of the upper wheel as the positioning hole of the current wheel.

If all the indexing plates do not have the number of holes required for the calculation, the double indexing method should 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 the double indexing calculation is extremely inconvenient.

6. Calculation of a circle inscribed in a hexagon

Formula: ① circle D to find the opposite side of the hexagon (S surface); S=0.866D, that is, diameter × 0.866 (coefficient)

② Find the diameter of the circle (D) on the opposite side (S face) of the hexagon; D=1.1547S is the opposite side × 1.1547 (coefficient)

7. Calculation of hexagonal opposite sides and diagonals of cold heading process

Formula: ① The opposite side (S) of the outer hexagon is to find the diagonal e; e=1.13s, that is, the opposite side × 1.13

②The opposite side (s) of the inner hexagon is to find the opposite angle (e); e=1.14s is the opposite side × 1.14 (coefficient)

③ To find the diameter of the head material of the diagonal (D) on the opposite side (s) of the outer hexagon, the diameter of the circle (D) should be obtained according to the (6.2 formula) on the opposite side (s surface) of the hexagon, and the offset center value should be appropriately increased, i.e. D≥1.1547s offset center amount can only be estimated.

Eight, the calculation of the square inscribed in the circle

Formula: ①The circle (D) finds the opposite side of the square (S surface); S=0.7071D is the diameter×0.7071

②Find a circle (D) on the opposite side (S face) of the square; D=1.414S, that is, the opposite side × 1.414

9. Calculation of the opposite sides and corners of the four sides of the cold heading process

Formula ① The opposite side (S) of the outer quadrilateral finds the opposite angle (e); e=1.4s is the opposite side (s)×1.4 parameter

② The opposite side (s) of the inner quadrilateral finds the opposite angle (e); e=1.45s is the opposite side (s)×1.45 coefficient

10. Calculation of the volume of the hexagonal

Formula ① s20.866×H/m/k is the opposite side×the opposite side×0.866×height or thickness.

11. Calculation of the volume of a truncated (cone) body

The formula 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. Calculation of the volume of missing spherical bodies (such as semicircular heads)

The formula 3.1416h2(R-h/3) is 3.1416×height×height×(radius-height÷3).

13. Calculation of processing dimensions of taps for internal threads

1. Calculation of the major diameter D0 of the tap.

The formula D0=D+(0.866025P/8)×(0.5~1.3) 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 screw pitch. The larger the screw pitch value is, the smaller the coefficient should be. On the contrary, the smaller the screw pitch value is, the larger the coefficient should be.

2. Calculation of the pitch diameter (D2) of the tap.

Formula: D2=(3×0.866025P)/8, namely the tap diameter=3×0.866025×pitch÷8

3. Calculation of tap diameter (D1).

Formula: D1=(5×0.866025P)/8, namely tap diameter=5×0.866025×thread pitch÷8

14. Calculation of material length for cold heading forming 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 the material to be used X÷diameter÷diameter÷0.7854 or X÷radius÷radius÷3.1416 is the length of the feed.

Column formula=X/(3.1416R2) or X/0.7854d2; X in the formula represents the volume value of the material to be used; L represents the length value of the actual feeding; R/d represents the radius or diameter of the actual feeding.

15. Calculation of the hanging wheel of the hobbing gear of the hobbing machine

a. The hobbing spindle has a fixed number of 24.

b. The calculation of the hobbing gear is realized by decomposing the data, that is, expanding or reducing its equal divisions at the same time. The schematic diagrams of B1 and b2 are compound shifting, and the schematic diagrams of b3 and b4 are direct shifting.

c. Decomposition of spindle parameter 24.

c1 can be directly decomposed into 2×12=24; 3×8=24; 4×6=24

C2 is decomposed after expanding the multiple:

If 24×5=120 is expanded by 5 times, then 120 can be decomposed into 20×6; 3×40; 4×30; 6×20

If 24×8=192 is enlarged by 8 times, then 192 is decomposed into 2×91; 91×2; 48×4; 4×48; 3×64; 64×3;

8×24; 24×8; 32×6; 6×32 When enlarging the multiple, the number of teeth of the machined part should be expanded simultaneously until it is easy to decompose;

d. Calculus case decomposition.

d.1 Calculate when the machined part is 15 teeth.

Column formula: 24/15 is expanded by 10 times at the same time and then 240/150; decompose and clear the common multiple of 3 at the same time to get (3×80)/(3×50)=80/50 At this time, you can use b.4 schematic diagram to install an arbitrary medium in the middle The wheel is to install a 80-tooth gear at ① and a 50-tooth gear at ②.

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

Column type: 24/77 2160/6930 after expanding 90 times at the same time; decomposing (40×54)/(70/99) At this time, the assembly gear shown in b.1 schematic diagram can be used. Considering the convenience of gear assembly, 1 and 3 The numbers 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 cannot be exchanged.

d.3 Calculate when the machined part is 32 teeth.

Column: 24/32 120/160 after being expanded by 5 times at the same time; decomposed into (4×30)/(4×40) and 30/40 after removing the common multiple of 4. At this time, the schematic diagram b.3 can be used to install any medium in the middle. The wheel is equipped with 30 gears at ① and 40 gears at ②.

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

Column: 24/13 is expanded by 100 times at the same time and then 2400/1300; the decomposition force (30×80)/(20×65) can be assembled by using the schematic diagram b.2. Note: why 2400 is decomposed into 30×80 It can be decomposed to 40×60. At this time, it should be determined by the match of the gears after assembly. As long as they match well, the number of teeth of the gear can also be decomposed into 20×120 and assembled with the schematic diagram of 6.4.