• PHISHING SCAM attempt TARGETING HOBBY-MACHINIST members. It has been brought to our attention that a pop-up survey is soliciting userfeedback from H-M members. In exchange for survey information, the user is given an opportunity to win a prize if they pay for shipping charges. This is NOT a Hobby Machinist program, survey or contest. DO NOT click through the links. Close your browser immediately and restart your computer. Clear cookies, cache and log back into Hobby Machinist. Again, this is NOT a Hobby Machinist contest or survey - IT IS a PHISHING SCAM attempt to get your credit card information.To close this notification, click the "X" in the top right corner of this box.

calculating effective gear diameter

dansawyer

H-M Supporter - Silver Member
H-M Supporter - Silver Member
Joined
Jun 13, 2018
Messages
107
The project is to make a worm gear set to drive an instrument, a telescope. I have settled on a worm gear design. I have a piece of Acme rod for the worm drive and am planning on cutting the gear with a tap. I am ready to cut the first test gear and after watching several videos I realized the effective diameter of the gear is not the raw outside diameter of the blank, but rather the resulting diameter after the tap as removed material sufficient to seat the threads. I am using a 1/2 inch drive and tap. The gear is 1/4 inch thick. I believe the tap will reduce the effective diameter of the gear blank as it cuts teeth. Does anyone have experience with designing this? Is there a reference?
 

P. Waller

Brass
Former Member
Joined
Mar 10, 2018
Messages
921
Worm gear set dimensions are available for FREE on the interweb

Table 4.22 presents the relationships among worm and worm wheel with regard to axial plane, transverse plane, normalplane, module, pressure angle, pitch and lead.
Fig. 4.16 Cylindrical worm (Right hand)

Fig. 4.16 Cylindrical worm (Right-hand)
Table 4.22 The relations of cross sections of worm gear pairs
Worm
Axial planeNormal planeTransverse plane
Table 4.22 The relations of cross sections of worm gear pairs 1
Table 4.22 The relations of cross sections of worm gear pairs 2
Table 4.22 The relations of cross sections of worm gear pairs 3
Transverse planeNormal planeAxial plane
Worm wheel

Reference to Figure 4.16 can help the understanding of the relationships in Table 4.22. They are similar to the relationsin Formulas (4.16) and (4.17) in that the helix angle β be substituted by (90 deg – γ). We can consider thata worm with lead angle γ is almost the same as a helical gear with helix angle (90 deg – γ).
(1) Axial Module Worm Gear Pair
Table 4.23 presents the equations, for dimensions shown in Figure 4.16, for worm gears with axial module, mx, andnormal pressure angle αn=20°.
Fig. 4.17 Dimentions of cylindrical worm gear pair

Fig. 4.17 Dimentions of cylindrical worm gear pair
Table 4.23 The calculations for an axial module system worm gear pair
No.ItemSymbolFormulaExample
Worm (1)Wheel (2)
1Axial modulemxSet Value3
2Normal pressure angle( αn )( 20 deg )
3No. of threads,
no. of teeth
zDouble Thread (R)30 (R)
4Coefficient of Profile shiftzt20
5Reference diameterd1
d2
( Qmx) NOTE1
z2mx
44.00090.000
6Reference cylinder lead
angle
γ
Table 4.23 The calculations for an axial module system worm gear pair 6
7.76517 deg
7Center distancea
Table 4.23 The calculations for an axial module system worm gear pair 7
67.000
8Addendumha1
ha2
1.00 mx
( 1.00 + xt2 ) mx
3.0003.000
9Tooth depthh2.25 mx6.750
10Tip diameterda1
da2
d1 + 2ha1
d2 + 2ha2 + mx NOTE2
50.00099.000
11Throat diameterdtd2 + 2ha296.000
12Throat surface radiusri
Table 4.23 The calculations for an axial module system worm gear pair 12
19.000
13Root diameterdf1
df2
da1 – 2h
dt – 2h
36.50082.500
NOTE 1.
Diameter factor, Q, means reference diameter of worm, d1, over axial module, mx.
Q=d1 / mx
NOTE 2.
There are several calculation methods of worm wheel tip diameter da2 besides those in Table 4.25.
NOTE 3.
The facewidth of worm, b1, would be sufficient if: b1=πmx (4.5 + 0.02z2)
NOTE 4.
Effective facewidth of worm wheel bw=
Table 4.23 NOTE 4

So the actual facewidth of b2 ≧ bw + 1.5mx would be enough.
(2) Normal Module System Worm Gear Pair
The equations for normal module system worm gears are based on a normal module, mn, and normal pressure angle, αn=20°. See Table 4.24.
Table 4.24 The calculations for a normal module system worm gear pair
No.ItemSymbolFormulaExample
Worm (1)Wheel (2)
1Normal modulemnSet Value3
2Normal pressure angleαn( 20 deg )
3No. of threads,
No. of teeth
zDouble (R)30 (R)
4Reference diameter of wormd144.000
5Normal profile shift coefficientxn2– 0.1414
6Reference cylinder lead
angle
γ
Table 4.24 The calculations for a normal module system worm gear pair 6
7.83748 deg
7Reference diameter of
worm wheel
d2
Table 4.24 The calculations for a normal module system worm gear pair 7
90.8486
8Center distancea
Table 4.24 The calculations for a normal module system worm gear pair 8
67.000
9Addendumha1
ha2
1.00 mn
( 1.00 + xn2 ) mn
3.0002.5758
10Tooth depthh2.25 mn6.75
11Tip diameterda1
da2
d1 + 2ha1
dt2 + 2ha1 + mn
50.00099.000
12Throat diameterdtd2 + 2ha296.000
13Throat surface radiusri
Table 4.24 The calculations for a normal module system worm gear pair 13
19.000
14Root diameterdf1
df2
da1 – 2h
dt – 2h
36.50082.500
NOTE : All notes are the same as those of Table 4.23.
(3) Crowning of the Tooth
Crowning is critically important to worm gears. Not only can it eliminate abnormal tooth contact due to incorrectassembly, but it also provides for the forming of an oil film, which enhances the lubrication effect of the mesh. Thiscan favorably impact endurance and transmission efficiency of the worm mesh. There are four methods of crowning wormgear pair :
(a) Cut Worm Wheel with a Hob Cutter of Greater Reference Diameter than the Worm.
A crownless worm wheel results when it is made by using a hob that has an identical pitch diameter as that of theworm. This crownless worm wheel is very difficult to assemble correctly. Proper tooth contact and a complete oil filmare usually not possible.
However, it is relatively easy to obtain a crowned worm wheel by cutting it with a hob whose reference diameter isslightly larger than that of the worm.
This is shown in Figure 4.18. This creates teeth contact in the center region with space for oil film formation.
Fig.4.18 The method of using a greater diameter hob

Fig.4.18 The method of using a greater diameter hob
(b) Recut With Hob Center Position Adjustment.
The first step is to cut the worm wheel at standard center distance. This results in no crowning. Then the worm wheelis finished with the same hob by recutting with the hob axis shifted parallel to the worm wheel axis by ±Δh. This resultsin a crowning effect, shown in Figure 4.19.
Fig.4.19 Offsetting up or down

Fig.4.19 Offsetting up or down
(c) Hob Axis Inclining Δθ From Standard Position.
In standard cutting, the hob axis is oriented at the proper angle to the worm wheel axis. After that, the hob axisis shifted slightly left and then right, Δθ, in a plane parallel to the worm wheel axis, to cut a crown effect on theworm wheel tooth.
This is shown in Figure 4.20. Only method (a) is popular. Methods (b) and (c) are seldom used.
Fig. 4.20 Inclining right or left

Fig. 4.20 Inclining right or left
(d) Use a Worm with a Larger Pressure Angle than the Worm Wheel.
This is a very complex method, both theoretically and practically. Usually, the crowning is done to the worm wheel,but in this method the modification is on the worm. That is, to change the pressure angle and pitch of the worm withoutchanging base pitch, in accordance with the relationships shown in Equations 4.25 :
formula 4.25

In order to raise the pressure angle from before change, αwx, to after change, αx , it is necessary to increase theaxial pitch, pwx, to a new value, px, per Equation (4.25). The amount of crowning is represented as the space betweenthe worm and worm wheel at the meshing point A in Figure 4.22. This amount may be approximated by the following equation:
formula 4.26

Where
d1 : Reference diameter of worm
k : Factor from Table 4.25 and Figure 4.21
Table 4.25 The value of factor k
Table 4.25 The value of factor k

Fig. 4.21 The value of factor (k)

Axial pressure angle αx
Fig. 4.21 The value of factor (k)
 

RJSakowski

H-M Supporter - Gold Member
H-M Supporter Gold Member
Joined
Feb 1, 2015
Messages
5,180
Here is a previous post.
 
It can take up to an hour for ads to appear on the page. See our code implementation guide for more details. If you already have Auto ad code on your pages there's no need to replace it with this code
Top
AdBlock Detected

We get it, advertisements are annoying!

Sure, ad-blocking software does a great job at blocking ads, but it also blocks useful features of our website. For the best site experience please disable your AdBlocker.

I've Disabled AdBlock