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### AGMA Worm and Spur Gear Design Equations and Calculators

**Gear Engineering and Design **

**Mechanics and Machine Design and Engineering**

AGMA Worm and Spur Gear Design Equations and Calculators

Worm gear sets are generally rated by their capacity to handle a particular level of input power, output power, or allowable torque at a particular speed for the input or output shaft. The AGMA power rating is based on pitting and wear resistance, as this is the usual failure mode for worm sets. The AGMA rating (ANSI/AGMA 6034-B92) is based on 10 h of continuous operation under a uniform load.

**Worm gear ratio**:

m_{G} = N_{G} / N_{w}

where

m_{G} = gear ratio,

N_{G} = number of teeth in the worm gear

N_{w} = number of threads in the worm.

**The mean worm gear diameter, d _{m} , is within the following limits:**

d_{m max} = C^{0.875} / 1.07

d_{m min} = C ^{0.875} / 2.0

Where:

C = center distance (Radius) (mm)

**Maximum radial deflection of worm gear at pitch point is limited by**:

Δw_{max} = 0.025 ( p_{x} )^{0.5}

Where:

Δw = deflection of the worm gear (mm)

p_{x} = Axial pitch, (mm)

**Wormgear Calculations **

Preview Wormgear Calculator, torque, output power, power lost, tangential load

**Torque at Wormgear:**

T_{G} = ( W_{t} d_{m} ) / 2000 (N-mm)

W_{t} = Tangential load on wormgear in (N)

d_{m} = Mean gear diameter (mm)

**Output Torque**:

T_{q} = ( W_{t} * d_{g}) / 2000

where T_{q} is in (N-mm)

The input-power rating, P_{input}, is given by:

P_{input} = P_{output} + P_{loss}

where P_{loss} is the power lost due to friction in the mesh (kW).

**The output power is given by**:

P_{output} = ( n W_{t} d_{g} ) / ( 1.91 x 10^{6} m_{G} )

where:

n = rotational speed of the worm (rpm),

W_{t} = worm gear tangential force (N),

P_{output} = output power (kW),

m_{G} = gear ratio

d_{g} = mean gear diameter (mm).

**The power lost is given by**:

P_{loss} = ( V_{t} W_{f} ) / 1000

where

P_{loss} = lost power (kW),

V_{t} = sliding velocity at the mean worm diameter (m/s)

W_{f} = friction force (N).

**The AGMA tangential load on a worm gear is given by**:

W_{t} = ( C_{s} C_{m} C_{v} d_{g}^{0.8} F ) / 75.948

where

C_{s} = materials factor, based on manufacturing process

d_{g} = mean diameter of the gear (mm),

F = effective face width (mm),

C_{m} = ratio correction factor

C_{v} = velocity factor.

Values for the ratio correction factor (C_{m}), the velocity factor (C_{v}), and materials factors ( C_{s}) can be found from tables provided in the ANSI/AGMA 6034-B92 standard ot here:

**AGMA Wormgear Equations For Rating Factors **

**The friction force can be determined by**:

W_{f} = ( µ W_{t} ) / (cosλ cosΦ_{n} )

where

µ = friction, (Based on sliding velocity)

W_{t} = tangential load on the worm gear tooth (N),

λ = lead angle (°),

Φ_{n} = normal pressure angle of the worm thread at the mean diameter (°)

**The sliding velocity at the mean worm diameter can be determined by**:

V_{t} = ( n d_{m} ) / ( 19,098 cosλ )

where

n = rotational speed of the worm (rpm), and

d_{m} = mean worm diameter (mm).

λ = lead angle (°)

**The efficiency, in percent, for worm gearing is given by**:

η = ( P_{outout} / P_{input} ) x 100%

**Substituting for the output power**:

η = ( n W_{t} d_{m} ) / ( 1.91 x 10^{7} m_{G} P_{input} ) x 100%

where

P_{outout} = rated output power (kW),

P_{input} = rated input power (kW),

n = rotational speed of the worm (rpm),

W_{t} = tangential load on the worm gear (N),

d_{m} = mean diameter of the gear (mm),

m_{G} = gear ratio.

An outline design procedure for a worm and wheel gear set using the AGMA equations is:

1. Define the number of starts.

2. Define the center distance, C.

3. Determine a suitable worm gear diameter.

4. Determine the lead.

5. Determine the lead angle.

6. Determine the maximum recommended face width, F.

7. Determine the material factor, Cs.

8. Determine the ratio correction factor, Cm.

9. Determine the tangential velocity, Vt.

10. Determine the velocity factor, Cv.

11. Determine the tangential load, Wt.

12. Determine the coefficient of friction, f.

13. Determine the friction force, Wf.

14. Determine the output power, Poutput.

15. Determine the power lost in mesh, Ploss.

16. Determine the rated input power, Pinput.

17. Estimate the efficiency of the gear set, h.

18. Determine the output torque, Tq.

19. Establish whether the power rating and output torque are sufficient for the application.

20. If not, alter the number of starts, worm diameter, center distance, etc. to provide suitable power rating and output torque.

References and Related:

AGMA Design manual for cylindrical wormgearing. ANSI/AGMA Standard 6022-C93.

AGMA Practice for enclosed cylindrical wormgear speed reducers and gearmotors. ANSI/AGMA Standard 6034-B92.

BS 721-1:1963. Specification for worm gearing. Imperial units.

BS 721-2:1983. Specification for worm gearing. Metric units.

BS ISO TR 10828:1997. Worm gears. Geometry of worm profiles.

PD ISO/TR 14521:2010. Gears. Calculation of load capacity of wormgears.