Introduction.....
Nomenclature.....
Design Parameters.....
Specifications.....
Designation.....
Worm Gear Profiles.....
Materials.....
Backlash/quality.....
Design Process.....

Thermal Design.....
Worm Gear Formulue.....
Friction Factors.....
Efficiency.....
Self Locking.....
Strength Design to BS721.....
Strength Design to AGMA.....

IntroductionA worm gear is used when a large speed reduction ratio is required between
crossed axis shafts which do not intersect. A basic helical gear can be used but the power
which can be transmitted is low. A worm drive consists of a large diameter
worm wheel with a worm screw meshing with teeth on the periphery of the worm wheel.
The worm is similar to a screw and the worm wheel is similar to a section of a nut.
As the worm is rotated the wormwheel is caused to rotate due to the screw like action
of the worm. The size of the worm gearset is generally based on the
centre distance between the worm and the wormwheel.
The double enveloping (double throat/double globoid ) option is the most difficult to manufacture and set up. However this option has the highest load capacity, near zero backlash capability, highest accuracy and extended life capability. A more detailed view showing a cylinderical worm and an enveloping gear. The worm is shown with the worm above the wormwheel. The gearset can also be arranged with the
worm below the wormwheel. Other alignments are used less frequently. NomenclatureAs can be seen in the above view a section through the axis of the worm and the centre
of the gear shows that , at this plane, the meshing teeth and thread section is similar
to a spur gear and has the same features Worm gear design parametersWorm gears provide a normal single reduction range of 5:1 to 75-1. The pitch line
velocity is ideally up to 30 m/s. The efficiency of a worm gear ranges from 98% for
the lowest ratios to 20% for the highest ratios. As the frictional heat generation
is generally high the worm box must be designed disperse heat to the surroundings and lubrication is
an essential requirement. Worm gears are quiet in operation. Worm gears
at the higher ratios are inherently self locking - the worm can drive the gear but the gear cannot
drive the worm. A worm gear can provide a 50:1 speed reduction but not
a 1:50 speed increase....(In practice a worm should not be used a braking device for
safety linked systems e.g hoists. . Some material and operating conditions can result
in a wormgear backsliding ) SpecificationsBS721 Pt2 1983 Specification for worm gearing Metric units. Worm Gear DesignationVery simply a pair of worm gears can be defined by designation of the number of threads in the worm
,the number of teeth on the wormwheel, the diameter factor and the axial module i.e z1,z2, q, m
. Worm teeth ProfileThe sketch below shows the normal (not axial) worm tooth profile as indicated in BS 721-2 for unit axial module (m = 1mm)
other module teeth are in proportion e.g. 2mm module teeth are 2 times larger Typical axial modules values (m) used for worm gears are 0,5 0,6 0,8 1,0 1,25 1,6 2,0 2,5 3,15 4,0 5,0 6,3 8,0 10,0 12,5 16,0 20,0 25,0 32,0 40,0 50,0 Materials used for gears
Backlash / quality Grades A worm gear set normally includes some backlash during normal manufacture to allow for expansion
of the gear wheel when operating at elevated temperaturs. The backlash is controlled by adusting the gear wheel
tooth thickness. AGMA and DIN provide a similar grading system
Design of a Worm GearThe following notes relate to the principles in BS 721-2 Initial sizing of worm gear.. (Mechanical)
1) Initial information generally Torque required (Nm), Input speed(rpm), Output speed (rpm). Initial sizing of worm gear.. (Thermal)Worm gears are often limited not by the strength of the teeth but by the heat generated
by the low efficiency. It is necessary therefore to determine the heat generated by
the gears = (Input power - Output power). The worm gearbox must have lubricant to remove
the heat from the teeth in contact and sufficient area on the external surfaces to distibute
the generated heat to the local environment. This requires completing an approximate heat
transfer calculation. If the heat lost to the environment is insufficient then the gears should
be adjusted (more starts, larger gears) or the box geometry should be adjusted, or the worm shaft
could include a fan to induced forced air flow heat loss. FormulaeThe reduction ratio of a worm gear ( R R eg a 30 tooth wheel meshing with a 2 start worm has a reduction of 15 F
Axial force on worm ( F Output torque ( M M Relationship between the Worm Tangential Force F
Relationship between the output torque M M Separating Force on worm-gearwheel ( F Sliding velocity ( V V Peripheral velocity of wormwheel ( V V Friction CoefficientNote: The values of the coeffient of friction as provided in the table below are based on the use of phosphor bronze wormwheels and case hardended , ground and polished steel worms , lubricated by a mineral oil having a viscosity of between 60cSt, and 130cSt at 60 deg.C . Cast Iron and Phosphor Bronze .. Table x 1,15 Friction coefficients - For Case Hardened Steel Worm / Phos Bros Wheel
Efficiency of Worm Gear The efficiency of the worm gear is determined by dividing the output Torque M2 with friction = μ by the output torque with zero losses i.e μ
= 0
η = [(cos α = [(cos α Graph showing worm gear efficiency related to gear lead angle ( γ ) Self Locking
Referring to the above graph , When the gear wheel is driving the curve points intersecting the
zero efficiency line identify when the worm drive is self locking i.e the gear wheel cannot drive to worm.
It is the moment when gearing cannot be moved using even the highest possible torque acting on the worm gear.
The self-locking limit occurs when the worm lead angle ( γ ) equals atan (μ). (2 Worm Design /Gear Wear / Strength Equations to BS721
Note: For designing worm gears to AGMA codes AGMA method of Designing Worm Gears
Permissible Load for Strength The permissible torque (M in Nm) on the gear teeth is obtained by use of the equation M ( example 87,1 Nm = 0,0018 x 0,48 x 63 x 20 x 80 ) Permissible Torque for Wear The permissible torque (M in Nm) on the gear teeth is obtained by use of the equation M ( example 33,42 Nm = 0,00191 x 0,3234 x 6,7 x 1,5157 x 80 Length of root of worm wheel tooth
Radius of the root = R Speed Factor for Bending This is a metric conversion from an imperial formula.. Table of speed factors for bending
Additional factorsThe formula for the acceptable torque for wear should be modified to allow
additional factors which affect the Allowable torque M M
The torque on the wormwheel as calculated using the duty requirements (M M
Thus Factors used in equations
Lubrication (Z Tables for use with BS 721 equations Speed Factors
X Table of Worm Gear Speed Factors Note -sliding speed = V
Stress Factors Table of Worm Gear Stress Factors
Zone Factor (Z)
If b Table of Basic Zone Factors
Duty FactorDuty - time Factor K _{H}
Worm q value selection
The table below allows selection of q value which provides a reasonably
efficient worm design. The recommended centre distance
value "a" (mm)is listed for
each q value against a range of z
AGMA method of Designing Worm Gears
The AGMA method is provided here because it is relatively easy to use and convenient-
AGMA is all imperial and so I have used conversion values so all calculations can be completed
in metric units.. ( C Metric ( mm) ( C The acceptable tangential load (W (W The formula will result in a life of over 25000 hours with a case hardened alloy steel worm and a phosphor bronze wheel Modified Lewis equation for stress induced in worm gear teeth . σ W
The friction force = W W γ = worm lead angle at mean diameter
The sliding velocity = V V d
The torque generated γ at the worm gear = M T The required friction heat loss from the worm gearbox H η = gear efficiency as above.
C
N _{G} = Number of teeth on worm gear.N _{W} = Number of starts on worm gear.m _{G} = gear ration = N_{G} /N_{W}
C
f (V |