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### AGMA WormGear Equations For Rating Factors

**Gear Engineering and Design **

**Mechanics and Machine Design and Engineering**

Related:

AGMA Worm and Spur Gear Design Equations and Calculators

AGMA Wormgear Equations For Rating Factors

Values for the ratio correction factor, the velocity factor, and materials factors can be found from tables provided in the ANSI/AGMA 6034-B92 standard. The following equations for the ratio correction factor, the velocity factor, and materials factors provide approximations to the values given in the tables.

**The ratio correction factor C _{m} is a function of the gear ratio, m_{G}**.

For 3 ≤ m_{G} ≤ 20

C_{m} = 0.02 ( -m^{2}_{G} + 40m_{G} - 76)^{0.5} + 0.46

For 20 < m_{G} ≤ 76

C_{m} = 0.0107 ( -m^{2}_{G} + 56m_{G} + 5145)^{0.5}

For m_{G} > 76

C_{m} = 1.1483 - 0.0065m
_{G}^{2}

**Velocity correction factor C _{v} is a function of the sliding velocity at the mean worm diameter, V_{t}**.

For 0 < V_{t} ≤ 3.556 m/s

C_{v} = 0.659 e^{-0.2165Vt}

For 3.556 < V_{t} ≤ 15.24 m/s

C_{v} = 0.652 V_{t}^{-0.571}

For V_{t} > 15.24 m/s

C_{v} = 1.098 V_{t}^{-0.774}

Note: (V_{t} m/s ) x 196.5 = ( V_{t} ft/min )

**Friction, µ is a function of the sliding velocity at the mean worm diameter, V _{t}**.

For V_{t} = 0,

µ = 0.15

For 0 < V_{t} ≤ 0.0508 m/s

µ* *= 0.124 e^{( -2.233z )}

where: z = V_{t}^{0.645}

V_{t} > 0.0508 m/s

µ = 0.103 e^{( -1.185z )}

where: z = V_{t}^{0.45}

**The materials factor C _{s} depends on the method of casting.**

**For Sand Casting**

For center distance (Radius) C ≤ 76.2 mm, an initial estimate for the materials factor can be obtained from:

C_{s} = 720 + 0.000633C^{3}

This value can be compared to the values obtained for the relevant means of casting, as indicated by the following relationships and the smaller value used.

**For sand cast gears then:**

for d_{m} ≤ 63.5 mm

C_{s} = 1000

for d_{m} > 63.5 mm

C_{s} = 1856.104 - 476.5454 log_{10} d_{m}

**For chill cast bronze gears:**

For center distance (Radius) C ≤ 76.2 mm, an initial estimate for the materials factor can be obtained from:

C_{s} = 720 + 0.000633C^{3}

for d_{m} ≤ 203.2 mm

C_{s} = 1000

for d_{m} > 203.2 mm

C_{s} = 2052.011 - 455.8259 log_{10} d_{m}

**For centrifugally cast gears:**

For center distance (Radius) C ≤ 76.2 mm, an initial estimate for the materials factor can be obtained from:

C_{s} = 720 + 0.000633C^{3}

for dm ≤ 635 mm

C_{s} = 1000

for dm > 635 mm,

C_{s} = 1503.811 - 179.7503 log_{10} d_{m}

References:

ANSI/AGMA 6034-B92, Practice for Enclosed Cylindrical Wormgear Speed Reducers and Gearmotors, Annex C Fomulas for rating factors.

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