The difficulty of mapping cylindrical helical gears is to map the indexing circle helix angle. For the displacement cylindrical helical gear, it is more complicated, because the helix angle and the displacement coefficient can compensate each other, if the two wheels are replaced at the same time. It brings flexibility to the surveyor, but in many cases requires a single match, which brings a lot of inconvenience to the surveying and mapping work. Combining years of practical experience, I have summed up a set of normal normals to calculate the normal modulus, and then use the common normal length and the tip diameter to calculate the indexing circle helix angle and the displacement coefficient. The hobbing machine verifies the circular helix angle of the indexing, so as to calculate the accurate parameter mapping method, the obtained various errors are small, and the accuracy requirement of the helical gear single matching is satisfied.

11 Surveying principle To accurately measure cylindrical helical gears, it is necessary to first understand the manufacturing country or region of the original helical gear that needs to be matched, so as to determine whether the standard of the gear is modular or radial, and determine the pressure angle A of the indexing circle.

The method described in this paper is based on the modulus system for calculation and measurement. The steps are as follows:

(1) Count the number of teeth of the original helical gear z.

(2) Try to measure the diameter of the tip circle and the diameter df of the root circle, and then calculate the full height of the tooth according to the following formula.

h=(da-df)/2(3)Understand the production site, preliminary estimate the height coefficient h*an, radial clearance coefficient c*n, indexing normal pressure angle An, gear backlash type and manufacturing Accuracy level.

(4) Calculate the length of the common normal line and calculate the number of teeth across the k.

k=Anz/180b 015(1) Take the number of teeth greater than or equal to k and test its common normal line, select the appropriate number of teeth k, accurately measure the length of the common normal line, and then measure the number of teeth across the path is k 1 or k-1 The length of the public law line is calculated and the extremely immigrated norm modulus is calculated.

Mn=(Wk 1-Wk)/PcosAn or mn=(Wk-Wk-1)/PcosAn(2) Since the normal modulus is a standard value, the normal modulus can be determined by looking up the table.

(5) The initial tooth tip displacement coefficient is calculated by the tooth full height formula yn.

h=(2h*an c*n- yn)mn(3)(6) Estimate the helix angle B Assuming the displacement coefficient x1=0, calculate the helix angle B1.

Da=mnz/cosB 2(h*an x- yn)mn(4)(7) Estimating the end face pressure angle At is calculated At1tanAt=tanAn/cosB(5)(8) The estimated displacement coefficient x is recalculated from the common normal length formula The displacement coefficient x2, but the manufacturing normal tolerance (including the backlash) due to the length of the common normal line, the common normal length should be the value calculated by the formula (7).

Wk=mncosAn[P(k-015) zinvAt 2xtanAn](6)Wk=Wk Measure ESWm 015TWm(7) where ESWm))) the average length of the common normal line is TWm))) The average length tolerance of the common normal line (9) The displacement coefficient x2 calculated above is substituted into the formula (4), and a new helix angle B3 is calculated; At3 is calculated by the formula (5); the displacement coefficient is further derived by the formula (6); and the calculation is repeated until the obtained x and The crest circle diameter da and the common normal line length Wk calculated by B are close to the measured values.

(10) Calculate the impending circle diameter d from the last obtained B value.

d=mnz/cosB(8)(11) Surveying and verifying the accuracy of using the hobbing machine to check B.

1Adjust the hobbing machine to disengage the split tooth movement so that the table has only additional motion, the hob shaft does not rotate, and the hob holder moves vertically.

o Mount the measured helical gear on the table of the hobbing machine according to the hobbing method. Fix the dial indicator on the hob holder so that the probe touches the index circle d and is perpendicular to the tooth surface. The tooth surface of the dial gauge is as shown in the figure. ? Start the machine tool, let the tool holder observe the vertical motion and record the change of the reading of the dial indicator and its direction of change. If the dial gauge pointer reading does not change, the differential hanging gear ratio is consistent with the helix angle B of the gear. When measuring, pay attention to the dial gauge probe can not be loose, when the hob is raised and lowered, the probe can not touch the adjacent tooth tip, otherwise the dial gauge reading is not allowed. The helix angle is corrected and then re-matched with the hanging wheel according to the correction value. The measurement is performed in the same way as above until the dial gauge reading does not change.

The correction formula for the helix angle B is: B=arctan[(btanB' a)/b] (9) After the helix angle B is measured, the exact index circle diameter d is calculated by the formula (8); calculated by the formula (5) At; the displacement coefficient is calculated by the top circle circle, the root circle diameter and the common normal length. Thereby determining the correct parameters of the gear.

21 Example In a reducer of our factory, the number of helical gears of a helical gear shaft is 16, right-handed, two teeth broken, no spare parts, need to be single. It is understood that the reducer is manufactured in China, and the diameter of the tip circle is measured as da=13416mm, and the diameter of the root circle is df==1031128mm. Therefore, it is estimated that the gear is a modular system, and the pressure angle of the index circle is An=20b. The height of the tip is h*an=1, the radial clearance coefficient is c*n=0125, the type of gear backlash is C, and the manufacturing accuracy level is 7.

Calculate k=2 from formula (1), test the length of the common normal line, and select the most suitable number of teeth to be 3, so as to determine k=3.

According to the number of teeth 3, the length of the common normal line is W3 = 551398mm, W3 = 551502mm after compensation calculation, the number of teeth across the gap is k = 4, the length of the common normal is W4 = 761043mm, and W4 = 761147mm after compensation calculation, according to the formula ( 2) Calculate mn=61993, take the standard value mn=7.

The yn=01002 is calculated from the full height formula (3) of the tooth, because the small value has little effect on the calculation and can be ignored.

According to formula (4), take x1=0, calculate the helix angle B1=21b46c, substitute B1=21b46c into formula (5) and calculate At1=21b24c, then substitute B1=21b46c and At1=21b24c into formula (6) to calculate the displacement coefficient x2. =014.

Then, the displacement coefficient x2=014 is substituted into the formula (4), the spiral angle B2=13b6c is calculated, and At2=20b29c is calculated by the formula (5), and the displacement coefficient x3=0145 is calculated by the formula (6); 11b30c, At3=20b22c; finally calculate x4=0146, B4=11b09c; calculate the graduation circle diameter d=1141155mm according to formula (8).

According to the above mapping method, the workpiece is installed on the former Soviet Union's 5353 gear hobbing machine to check the helix angle. B4=11b09c and mn=7 are substituted into the transmission ratio formula to obtain the transmission ratio i=16sin11b09c/7=01442007388, and the differential ratio is selected according to the transmission ratio. Wheel 30@47/55@58.

When measuring, first let the dial indicator point to the circumference of the tooth surface with a diameter of 1141155mm, press the watch one turn, let the hob move vertically downwards 30mm, then find that the dial indicator is rotated clockwise by 6213, ie b= 30mm, a=-01623mm, calculate the helix angle B5=10b according to formula (9), calculate the diameter of the index circle d=1131728mm according to formula (8), and then calculate the transmission ratio i=0139691012 according to the helix angle B5=10b, Hang the differential hanging wheel 35@55/50@97 and start the hobbing machine in the same way. When b=100mm, the dial indicator does not move, indicating that the helix angle at this time is the indexing circle helix angle of the measured helical gear, that is, B=10b.

Using the tip circle diameter da=mnz/cosB 2(h*an x)mn to calculate the displacement coefficient is x=01491.

Calculate the displacement coefficient with the diameter of the root circle df=mnz/cosB-2(h*an c*nx)mn x=01493.

Calculate the displacement coefficient with the common normal length formula x=01460.

Observing the gear tooth tip and tooth root is better, the tooth surface wear is more serious. Considering x=01493 comprehensively, the geometry of the single helical gear is the normal modulus mn=7, the indexing circle normal pressure angle. An=20b, the indexing circle spiral angle B=10b, the displacement coefficient x=01493, the index circle diameter d=1131728mm, the tip circle diameter da=1341630mm.

31 Conclusion In summary, we have used the above method to map a variety of helical gears, which are satisfactory to users after use.

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