Steps In Worm Gear Design

Worm gears are generally used to connect skew shafts usually at 90°. Worm gears are offer high velocity ratios and higher load capacity than point contact crossed helical gears.

The axial pitch of the worm and the circular pitch of the gear must be same for a mating worm and gear. The module of the worm and gear must be equal for correct mating of worm and gear.

Assuming there is a 5:1 speed ratio between worm and gear, we have to find out:

• Module

• Number of Threads of Worm

• Number of Teeth of Gear

• Pitch circle diameter of Worm

• Pitch circle diameter of Gear

• Centre to centre distance

Selection of an appropriate module is beyond the scope of this guide but a larger module will have the capacity to transmit more power. The following module sizes are specified by AGMA (American Gear Manufacturers Association).

Say, we are going ahead with the Module as 2 and the Pitch as 6.238.

Use the following gear design equation:

N1/N2 = T2/T1

And, we will get:

T2 = 5 * T1……………….Eqn.1

Now use the following AGMA empirical formula:

T1 + T2 > 40………………Eqn.2

By using the two equations (Eqn.1 & Eqn.2), we will get the approximate values of

T1 = 7 and T2 = 35

Calculate the pitch circle diameter of the worm (D1) by using the below AGMA empirical formula:

D1 = 2.4 P + 1.1 = 16.0712 mm

The following AGMA empirical formula to be used for calculating the pitch circle diameter of the gear (D2): D2 = T2*P/3.14 = 69.53185 mm

Now, we can calculate the centre to centre distance (C) by the following equation: C = (D1 + D2)/2 = 42.80152 mm

The below empirical formula is the cross check for the correctness of the whole design calculation: (C^0.875)/2 <= D1 >= (C^0.875)/1.07

Observe that our D1 value is falling in the range.

Worm and WormGear Design Equations and Calculator

Gears Engineering and Design

Equations for American Standard Fine Pitch Worms and Wormgears Per. ANSI B6.9

This standard is intended as a design procedure for fine-pitch worms and wormgears having axes at right angles. It covers cylindrical worms with helical threads, and wormgears hobbed for fully conjugate tooth surfaces. It does not cover helical gears used as wormgears.

Hobs: The hob for producing the gear is a duplicate of the mating worm with regard to tooth profile, number of threads, and lead. The hob differs from the worm principally in that the outside diameter of the hob is larger to allow for resharpening and to provide bottom clearance in the wormgear.

Pitches: Eight standard axial pitches have been established to provide adequate coverage of the pitch range normally required: 0.030, 0.040, 0.050, 0.065, 0.080, 0.100, 0.130, and 0.160 inch.

Axial pitch is used as a basis for this design standard because: 1) Axial pitch establishes lead which is a basic dimension in the production and inspection of worms; 2) the axial pitch of the worm is equal to the circular pitch of the gear in the central plane; and 3) only one set of change gears or one master lead cam is required for a given lead, regardless of lead angle, on commonly-used worm-producing equipment.

Lead Angles: Fifteen standard lead angles have been established to provide adequate coverage: 0.5, 1, 1.5, 2, 3, 4, 5, 7, 9, 11, 14, 17, 21, 25, and 30 degrees.

This series of lead angles has been standardized to: 1) Minimize tooling; 2) permit obtaining geometric similarity between worms of different axial pitch by keeping the same lead angle; and 3) take into account the production distribution found in fine-pitch worm gearing applications.

For example, most fine-pitch worms have either one or two threads. This requires smaller increments at the low end of the lead angle series. For the less frequently used thread numbers, proportionately greater increments at the high end of the lead angle series are sufficient.

Pressure Angle of Worm: A pressure angle of 20 degrees has been selected as standard for cutters and grinding wheels used to produce worms within the scope of this Standard because it avoids objectionable undercutting regardless of lead angle.

1) Axial pitch establisheslead which is a basic dimension in the production and inspection of worms; 2) The axialpitch of the worm is equal to the circular pitch of the gear in the central plane; and 3) Only one set of change gears or one master lead cam is required for a given lead, regardless oflead angle, on commonly-used worm-producing equipment.

Worm Dimensions Equations (All dimensions are in inches unless otherwise specified).

Lead l = nP_x

Pitch Diameter d = 1 / ( π tan λ )

Outside Diameter d_o = d + 2a

F_W = [ D_o² - D²] ^1/2

Wormgear Dimensions Equations

Pitch Diameter D = NP / π = N Π_ε/ π

Outside Diameter D _o = 2C - d / (2a)

Face Width F_Gmin = 1.125 • [ ( d_o + 2c) ² - ( d_o - 4a) ²] ^1/2

Dimensions Worm and Wormgear

Addendum a = 0.3183P_n

Whole Depth h_t = 0.7003P_n + 0.002

Working Depth Clearance c = h_t - h_k

Tooth Thichness t_n = 0.5P_n

Normal Pressure Angle (Approx.) Φ_n = 20°

Center Distance C = 0.5 • (d + D)

All dimensions in inches unless otherwise indicated.

a Current practice for fine-pitch worm gearing does not require the use of throated blanks. This results in the much simpler blank shown in the diagram which is quite similar to that for a spur or helical gear. The slight loss in contact resulting from the use of non-throated blanks has little effect on the load-carrying capacity of fine-pitch worm gears. It is sometimes desirable to use topping hobs for producing wormgears in which the size relation between the outside and pitch diameters must be closely controlled. In such cases the blank is made slightly larger than Do by an amount (usually from 0.010 to 0.020) depending on the pitch. Topped wormgears will appear to have a small throat which is the result of the hobbing operation. For all intents and purposes, the throating is negligible and a blank so made is not to be considered as being a throated blank.

b This formula allows a sufficient length for fine-pitch worms.

c As stated in the text on page 2207, the actual pressure angle will be slightly greater due to the manufacturing process.

Although the pressure angle of the cutter or grinding wheel used to produce the worm is 20 degrees, the normal pressure angle produced in the worm will actually be slightly greater, and will vary with the worm diameter, lead angle, and diameter of cutter or grinding wheel. A method for calculating the pressure angle change is given under the heading Effect of Production Method on Worm Profile and Pressure Angle.

Pitch Diameter Range of Worms: The minimum recommended worm pitch diameter is 0.250 inch and the maximum is 2.000 inches.

Tooth Form of Worm and Wormgear: The shape of the worm thread in the normal plane is defined as that which is produced by a symmetrical double-conical cutter or grinding wheel having straight elements and an included angle of 40 degrees.

Because worms and wormgears are closely related to their method of manufacture, it is impossible to specify clearly the tooth form of the wormgear without referring to the mating worm. For this reason, worm specifications should include the method of manufacture and the diameter of cutter or grinding wheel used. Similarly, for determining the shape of the generating tool, information about the method of producing the worm threads must be given to the manufacturer if the tools are to be designed correctly.

The worm profile will be a curve that departs from a straight line by varying amounts, depending on the worm diameter, lead angle, and the cutter or grinding wheel diameter. A method for calculating this deviation is given in the Standard. The tooth form of the wormgear is understood to be made fully conjugate to the mating worm thread.

Effect of Diameter of Cutting on Profile and Pressure Angle of Worms

FullHD_2.jpg - a few seconds ago Effect of Production Method on Worm Profile and Pressure Angle In worm gearing, tooth bearing is usually used as the means of judging tooth profile accuracy since direct profile measurements on fine-pitch worms or wormgears is not practical. According to AGMA 370.01, Design Manual for Fine-Pitch Gearing, a minimum of 50 percent initial area of contact is suitable for most fine-pitch worm gearing, although in some cases, such as when the load fluctuates widely, a more restricted initial area of contact may be desirable.

Except where single-pointed lathe tools, end mills, or cutters of special shape are used in the manufacture of worms, the pressure angle and profile produced by the cutter are different from those of the cutter itself. The amounts of these differences depend on several factors, namely, diameter and lead angle of the worm, thickness and depth of the worm thread, and diameter of the cutter or grinding wheel. The accompanying diagram shows the curvature and pressure angle effects produced in the worm by cutters and grinding wheels, and how the amount of variation in worm profile and pressure angle is influenced by the diameter of the cutting tool used.

Materials for Worm Gearing

Worm gearing, especially for power transmission, should have steel worms and phosphor bronze wormgears. This combination is used extensively. The worms should be hardened and ground to obtain accuracy and a smooth finish.

The phosphor bronze wormgears should contain from 10 to 12 percent of tin. The S.A.E. phosphor gear bronze (No. 65) contains 88-90% copper, 10-12% tin, 0.50% lead, 0.50% zinc (but with a maximum total lead, zinc and nickel content of 1.0 percent), phosphorous 0.10-0.30%, aluminum 0.005%. The S.A.E. nickel phosphor gear bronze (No. 65 + Ni) contains 87% copper, 11% tin, 2% nickel and 0.2% phosphorous.

Single-thread Worm Gears

The ratio of the worm speed to the wormgear speed may range from 1.5 or even less up to 100 or more. Worm gearing having high ratios are not very efficient as transmitters of power; nevertheless high as well as low ratios often are required. Since the ratio equals the number of wormgear teeth divided by the number of threads or “starts” on the worm, single-thread worms are used to obtain a high ratio. As a general rule, a ratio of 50 is about the maximum recommended for a single worm and wormgear combination, although ratios up to 100 or higher are possible. When a high ratio is required, it may be preferable to use, in combination, two sets of worm gearing of the multi-thread type in preference to one set of the single-thread type in order to obtain the same total reduction and a higher combined efficiency.

Single-thread worms are comparatively inefficient because of the effect of the low lead angle; consequently, single-thread worms are not used when the primary purpose is to transmit power as efficiently as possible but they may be employed either when a large speed reduction with one set of gearing is necessary, or possibly as a means of adjustment, especially if “mechanical advantage” or self-locking are important factors.

Multi-thread Worm Gears

When worm gearing is designed primarily for transmitting power efficiently, the lead angle of the worm should be as high as is consistent with other requirements and preferably between, say, 25 or 30 and 45 degrees. This means that the worm must be multi-threaded. To obtain a given ratio, some number of wormgear teeth divided by some number of worm threads must equal the ratio. Thus, if the ratio is 6, combinations such as the following might be used:

The numerators represent numbers of wormgear teeth and the denominators, the number of worm threads or “starts.” The number of wormgear teeth may not be an exact multiple of the number of threads on a multi-thread worm in order to obtain a “hunting tooth” action.

Number of Threads or “Starts” on Worm: The number of threads on the worm ordinarily varies from one to six or eight, depending upon the ratio of the gearing. As the ratio is increased, the number of worm threads is reduced, as a general rule. In some cases, however, the higher of two ratios may also have a larger number of threads. For example, a ratio of 6 1⁄5 would have 5 threads whereas a ratio of 6 5⁄6 would have 6 threads. Whenever the ratio is fractional, the number of threads on the worm equals the denominator of the fractional part of the ratio.

Worm-Gear Cutting

The machines used for cutting worm-gears include ordinary milling machines, gear-hobbing machines of the type adapted to cutting either spur, spiral, or worm gearing, and special machines designed expressly for cutting worm-gears. The general methods employed are (1) cutting by using a straight hob and a radial feeding movement between hob and gear blank; (2) cutting by feeding a fly cutter tangentially with relation to the worm gear blank; and (3) cutting by feeding a tapering hob tangentially. The fly-cutter method is slow as compared with hobbing but it has two decided advantages: First, a very simple and inexpensive cutter may be used instead of an expensive hob. This is of great importance when the number of worm-gears is not large enough to warrant making a hob. Second, with the fly-cutter method, it is possible to produce worm-gears having more accurate teeth than are obtainable by the use of a straight hob. Taper hobs are especially adapted for cutting worm-gears that are to mesh with worms having large helix angles; they are also preferable for worm-gears having large face widths in proportion to the worm diameter. Worm-gear teeth are generated more accurately with a taper hob than with a straight hob that is given a radial feeding movement.