Practical calculation method of thread chain hanging wheel in hob machining

Shovel teeth and shovel teeth are the two main processes in hob machining. Both processes are performed on a shovel tooth lathe. The toothed lathe used is usually a C8955 model with a lead lead of 12.7mm. References [1], [2] introduced how to calculate the threading wheel of a hob in use, given that the literature [1] has errors in the interpretation of the principle, and literature [2] does not give a practical method, so the author proposes Some specific schemes are for operator's reference.

1. The basic method of hanging wheel calculation

　　 First of all, the required transmission ratio i is calculated and represented by approximate fractional values. The numerator and denominator are then decomposed into the hanging wheels that the machine tool has. Common formulae at this time are as follows:

i=nPx/12.7 (1:1) (1)

i=nPx/203.2 (1:16) (2)

In the formula, n—the number of hob heads Px—the actual calculation of the hob axial pitch has the following problems:
(1) In order to express i as a fraction, it is necessary to perform factorization and other calculations. The calculator must be equipped with a "Choose Table" and other data.
(2) Sometimes the calculation of the hanging wheel machine does not have, but the replacement of a set of hanging wheels can not meet the accuracy requirements. In order to find a suitable hanging wheel, it often takes a long time.
(3) The obtained transmission ratio i cannot find the corresponding score value in the table, and substituting the adjacent score value can not reach the accuracy requirement.
The author proposes some practical methods below.

2. Scaffolding process thread chain hanging wheel calculation

This process is an intermediate process (finishing process) of hob machining. The tooth pitch tolerance is large, which allows greater flexibility when calculating the caster. Taking into account the effect of heat treatment on the hob pitch, the scraping process requires some correction of the finished tooth pitch. The commonly used empirical formula is

P′x=0.998Px (3)

In the formula, P′x—the axial tooth pitch of the hob scraping process, proposes three practical calculation methods for the deficiencies of [1] and [2].
(1) Replace only one drive wheel by equations (1), (3): i=nPx/12.7, when n=1, i=0.998Px/12.7=0.998 (mnπ/cosλ)/ 12.7. General single-head hob λ ≤ 5°, so cosλ ≈ 0.998, ie

(4)

In the formula mn - hob normal modulus λ - hob sub-cylindrical thread angle (4) means that there are three hanging wheels are fixed, ie 95, 80, 96, according to different modules, as long as To replace a driving wheel, the value is 20 multiplied by the normal modulo value (usually the gear hob flag and the m on the drawing are mn), which is very convenient for calculation.
For example, the processing of m = 3mm gear hob, the four of the four hanging wheels a, b, c, d are known, according to type (4) available

The applicable conditions of formula (4) are: 1 single head gear hob; 2 shovel bed with 1:1 gear.
(2) A passive wheel is a constant 100, and the other passive wheel can be selectively selected according to P'i to calculate i, and then select a passive wheel b (the machine has) to get b×i; take b× The first four digits of i (the fifth digit is rounded off) are treated as an integer and the integer is decomposed into the product of the two driving wheels. All four hanging wheels are thus determined, of which the passive wheels are artificially selected b and constant 100.
If the product of the two driving wheels cannot be found in the "Integer Factor Table", or the decomposed hanging wheel machine does not have one, the original selected passive wheel b can be replaced and then calculated again according to the above method until it is satisfied. .
For example, a hob shoveled on a C8955 shovel tooth lathe has a P′x=18.924mm and a 1:16 gear position on a shovel bed, then i=P′x/203.2=18.924/203.2= 0.09312921; Take b = 144, then i × 144 = 13.40770866, take the first four integers to 1341, its factorization, and 1341 in the factor table can not be found, it can not be used. At this point, if b=120 is selected again, then i×120=11.17559055. Take the first four digits to obtain 1118, and perform factorization to obtain 1118=2×13×43=26×43. According to this, the hanging wheel can be written as follows: . Experience calculations, ΔP'x=0.007. Under normal circumstances, when the scraper process error ΔP′x is about 0.01mm, it can meet the requirements, and the current ΔPx′=0.007mm. Therefore, the hitch is fully applicable.
(3) Among the four hanging wheels used in the pre-determined method, there are three persons who are pre-determined. From the predetermined hanging wheel, the fourth hanging wheel can be calculated, and whether the fourth hanging wheel is applicable can be determined in time. This method does not require the use of the "wheel ratio table", "integer factor table" and other data, but requires a pocket calculator that can store formulas, simple operation, limited space, intends to introduce another article.

3. Scaffold grinding process thread chain hanging wheel calculation

This process is the finishing process of the hob. The precision of the tooth pitch produced is the precision of the finished product. It must meet the requirements of the corresponding standards. Generally, it is calculated in μm. It is difficult for the method used in the above scooping process to meet such a high precision requirement. Therefore, other calculation methods should be considered.
The gear ratio i of the shovel grinding process is calculated according to (1) or (2). However, it should be noted that due to the difference in performance of each machine (sometimes due to operator performance differences), although in theory the Px should be used to calculate the hanging wheel, in practice it is often necessary to make minor corrections to Px, increasing or decreasing Μm, the corrected Px value is called the specific required value. For example, a machine tool processing m4 hob, Px = 12.573, according to this calculation used by the wheel hob scraped off the hob tooth pitch is unqualified, need to increase 2μm, that is calculated by 12.585 qualified, 12.585 That is, it is a specific requirement value. It is not acceptable to be greater or less than this value. It can only be calculated as 12.585, and it cannot be calculated according to the theoretical value or other values.
Due to the high precision of the process, the problems pointed out in the aforementioned "basic method" are often encountered. For example, the specific required value of a hob is Px=17.778mm, and the hanging wheel is requested with a 1:16 grade, and the error ΔPx<1 μm is required for the hanging round. According to equation (2), the gear ratio i=Px/203.2=17.778/203.2=0.08749. Check the “hook wheel ratio table” without this value, can only be replaced with adjacent values, ie 0.08748=58/663, empirical calculation Px=17.776, ΔΡx=-2 μm; another alternative table value 0.08750=7 /80, The empirical calculation is Px=17.780, and ΔPx=+2μm. Both results do not meet the requirements. At this point, the following method can be used to solve:
(1) seeking gear ratio i;
(2) artificially selected a passive round d, get i′=d×i;
(3) Find the corresponding score value as A/b according to the mantissa after the decimal point of i′ (when checking the table, it is not necessary to strictly correspond, and it can be checked in a few lines or even a dozen or so lines. This is the maximum of this method. Advantages and features, check denominator b should be the number of rounds the machine has;);
(4) from the above order i' = integral part + A / b, through points after i' = F / b;
(5) Check "integer factor table" to get F = a × c;
(6) Write the hanging wheel: (a×c is the value determined in step 5, b is the value determined in step 3, and d is the value determined in step 2).
(7) Proofreading accuracy.
The following problems should be paid attention to in the calculation process: 1 Sometimes there is no corresponding value when checking the table according to step 5. At this time, you should return to step 3 again. After another group of A/b values, check the table again. 2 If the accuracy still cannot meet the requirements, or if there are other inconveniences, you can return to step 2, and then select the d value before performing operations.
The above example is calculated according to the method proposed in this paper, available:
(1) i=Px/203.2=17.778/203.2=0.08749;
(2) take d = 135, i' = 135 × i = 11.81117;
(3) The score value corresponding to the mantissa 0.81117 in the “Scrolled Wheel Ratio Chart” is 494/609. Since the denominator 609 is not the number of wheels that the machine tool has, it is not necessary. Therefore, finding the denominator in the neighboring table is a simple number of the hanging wheel b that the machine tool has, find 0.81102 → 103/127, so take A/b = 103/127;
(4) then
(5) Lookup table 1500 = 2 × 2 × 3 × 5 × 5 × 5 = 30 × 50 (a × c);
(6) Write the hanging wheel:
(7) Checking: , ΔPx→0, meets requirements.

4. summary

　　 The general principle of the hanging wheel calculation is to use the “basic method”. The calculation of the thread chain when machining a hob on a shovel bed has various methods depending on the process. The rough machining process is more flexible, and the calculation requirements of most single-head gear hobs can be satisfied by using (4) type, and usually ΔΡx is about 0.01 mm. The precision machining process should be calculated accurately. Using the method described in this paper can guarantee that any set of Px (ΔPx <1μm) hanging wheels, and a larger range of numerical values ​​when looking up the table; where the passive wheel is artificially determined, the calculation is simple and convenient Without complicated derivation process.