A new method to accurately determine the helix angle of helical gears
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Figure 1 Indentation method is to paint the tooth on the top of the gear to be measured, so that it rolls on a piece of paper, this paper will leave a trace of the top roll, according to the indentation to make the extension of the top line The line and the auxiliary line, then the angle measuring device measures the tooth angle, which is the helix angle at the gear tooth tip (see Figure 1), and then calculate the helix angle at the gear index circle according to the other geometric parameters of the gear. Since the width of the gear is generally not large, the extension line and the auxiliary line made have a certain width error. When measuring with a protractor, it is inevitable that there will be an error, and the scale of the protractor is a unit of “degrees†for those accurate to “minutesâ€. The measurement of the "second" angle is powerless. 3 The new measurement method uses a universal angle ruler or indentation method to first make a rough measurement of the helix angle of the tooth top of the tested gear, and measures the approximate angle of the tooth top hate and rotation angle, and then uses the points on the universal milling machine. The method of measuring the head with a hanging wheel or measuring on a gear hobbing machine to determine the helix angle at the gear tooth tip. Then the calculation determines the helix angle of the gear at the index circle. The method for determining the helix angle of the addendum is as follows: Measure the approximate value b' of the helix angle of the gear under test on a universal milling machine, and then roughly calculate the normal modulus mn of the gear based on other measured data (according to the standard Value selection). Mn≈dn/[(Z/cosba+2ha]
Where: Z - the number of teeth of the gear to be measured da - the diameter of the top circle of the gear under test ha - the height coefficient of the gear top will be installed on the workbench of the universal milling machine, and then will be The measuring gear spindle is mounted on the tip of the indexing head and tailstock and the following wheel is selected: a × c = 1 × pmnZ bd 40 t·sinba
In the formula: a, b, c, d - the number of teeth of the selected hanging wheel 1/40 - the transmission ratio of the dividing head t - the pitch of the screw of the milling machine table (mm), t = nk n - milling machine The number of squares rotated on the worktable dial k - the ergonomic worktable of the sipping bed. After the matching of the egg hanging wheels, the handle of the dividing head is shaken, and the dividing head and the worktable are coordinated. 
1. Hanging wheel 2. Indexing head
3. Dial indicator 4. Gear 5. Tailstock
Figure 2 Determination of helix angle ba": In the selection of the hanging wheel according to the above formula, often encountered more complex calculations, some data is difficult to decompose the situation, in order to simplify the calculation, some data can be properly selected, so that the selected out The indexing head of the hanging wheel—the helix angle formed during the movement of the milling machine worktable system—is not the helix angle ba′ at the time of roughing, but the (heel top) helix angle baâ€. Ba"=arcsin(pmnZ/40ti)
In the formula i=(a/b)x(c/d)——The transmission ratio of the hanging wheel mechanism determines the measurement error compensation angle g. We set the actual helix angle ba of the measured gear tooth tip and the calculated helix angle heave ba' The difference between the g is called the measurement error compensation angle, measurement error compensation angle g measurement method is to use hundred (thousand) points of contact with the top of the top of the measured gear tooth at the tooth surface (see Figure 2). Shake the indexing head handle to rotate the gear and move the table at the same time. The moving distance L of the table can be read from the scale on the dial of the table (L=nk), and can be read on the hundred (thousand) minutes table The amount of displacement d in the vertical direction of the helix of the table head is shown in FIG. 3 after the helix is ​​unfolded. 
image 3 
Fig. 4 tgg=d/s=d/Lcosba" g=arctg[(dcosba")/L] Where: S - Determination of the actual helix angle at the tip of the measuring gear after the helix is ​​unrolled: 3 It can be seen that the actual helix angle at the tip of the gear ba=ba"±g=ba"±arctg[(dcosba")/L] (d>0 takes the "+" sign; d<0 takes the "-" No.) Determination of the helix angle at the gear index circle: According to the geometric parameters of the gear, the helix angle of the gear at the index circle can be derived. According to Figure 4, there is tgb=Rtgba/Ra.
Then b=arctg[(Ra-mnha)tgba]/Ra
In the formula: R—the gear dividing circle radius Ra—the radius of the gear tooth tip circle. Since the indexing circle diameter of the displacing gear is equal to the index circle diameter of the non-variable gear, whether the gear displaces the helical gear helically The angle has no effect, so the method of measuring the helix angle also applies. Measuring on a gear hobbing machine The gear to be tested is mounted on a table of a gear hobbing machine. The hundred (thousand) points of the magnetic table seat sticky sucker on the hob, 100 (thousands) of the contact points on the top of the tooth surface measured gear tooth at the top, according to the rough measured helix angle helix 'Select the hanging wheel. When selecting the hanging wheel, the used switching formula is different because of the different type of gear hobbing machine used. On the Y3150 gear hobbing machine, the differential gear is selected as follows: a2 × c2 = 9sinba' b2 d2 mnk Select the differential gear a2 × c2 = 7.9577sinba' b2 d2 mnk on the Y38 gear hobbing machine on the Y3180 gear hobbing machine. The following selects the differential suspension wheel: a2 × c2 = 6sinba' b2 d2 mnk Where: a2, b2, c2, d2 Matching the number of teeth of the hanging wheel mn - the normal modulus k of the gear under test - Suppose When the number of hobs (k=1 or k=2) is installed, the hobbing machine is turned on after installation, and the displacement amount of the tool rest is measured. The displacement amount, d, of the tooth surface of the extension head is measured and then the tooth is calculated. The helix angle ba at the top and the helix angle b at the index circle. Ba=ba"±arctg[(dcosba')/LJ] b=arctg[(Ra-mnha)tgba/Ra]
In the formula, ba"——the calculated helix angle of the measurement (calculated according to the model of the selected hobbing machine from the transposed formula.) 4 Example In a machine, a diagonal cylindrical gear is damaged (some gear teeth are broken) and the gear is measured. The number of teeth Z = 26, the diameter of the tip circle da = 86.87, the helix angle ba' = 16deg & gt; and the root circle diameter d1 = 73.37, in order to more accurately determine the helix angle b of the gear, used in the X62W horizontal universal milling machine With the method of dividing the head to measure, determine the normal modulus of the gear based on the measured parameters mnmn=da/[(Z/cosba')+2ha=86.8786.87/[(26/cos16°)+2×1) =2.99≈3 Optional hanging wheels are obtained from the formula: a × c = pmnZ = p × 3 × 26 = 370 = 74 × 100 = 3.7042 ≈ 3.7 bd 40tsinba' 40 × 6 × sin16° 100 100 20 X62W Milling Table The pitch of the lead screw is t = 6mm, and the amount of movement per cell is k = 0.05mm. It is determined to calculate the helix angle ba" = arcsin (pmnZ/40ti) = arcsin (p × 3 × 26/40 × 6 × 3.7) = 16.06187° L=35mm; d=+0.236mm Calculating error compensation angle gg=arctg(dcosba"/L)=arctg(0.236×cos16.0187°/35)=0.3713° Determination of the actual helix angle ba at the tooth tip of the gear ba =ba"t±g=16.0187°+0.3713°=16.39° Gear Determination of helix angle b (index circle) b=arctg[(Ra-mnha)tgba/Ra]=arc[(86.87/2-3x1)/(86.87/2)]/tg16.39°= 15.313°=15°8'47" Verification calculation: diameter of gear tip circle da=mnZ/cosb+2mnha=3×26/cos15.313°+2×3×1=86.87 gear root circle diameter df=( mnZ)/cosb-2mn(ha+c)=(3x26)/cos15.313°-2x3x(1+0.25)=73.371 The calculated results are in accordance with the measured dimensions.