Gears:
Toothed cylindrical (or occasionally conical) wheels for the transmission of mechanical power from one rotating shaft to another.
Typically used where the distance between the shafts is not large.
Torque:
πππππ’π = πππ€ππ/π΄πππ’πππ πππππππ‘y
The speed of the pinion is higher than the speed of the gear, the output torque is higher than the input torque.
Conservation of energy (assuming no energy losses in the system)
πΌπππ’π‘ π βπππ‘ πππ€ππ = ππ’π‘ππ’π‘ π βπππ‘ πππ€πr
Functions and typical applications of gears:
- Transmit power from one location to another.
- Match the torque and speed of a
driving and a driven machine component. - Change the direction of a rotating component.
- Synchronise the motion of one rotating component with another.
Roller Drive:
Change in angular velocity and torque (inversely proportional).
Power transmission limited by friction at roller contact point.
Primitive Gears:
Primitive gear trains consisted of teeth or pegs located on discs.
Velocity ratio not constant, changing through meshing cycle.
Classification of gears by relation of shafts:
Parallel Axes
Non-parallel co-planar (intersecting axes)
Non-parallel non coplanar (non-intersecting axes)
Gear Parameters:
Pitch circle diameter (d)
Circular pitch (p)
Addendum (a)
Dedendum (b)
Base circle
Centre distance (D)
*π·= (π·π+π·πΊ)/2
Module (m)
*Pitch dia./ no of teeth
- π=π/N
Pitch diameter:
*π = ππ
Circular pitch:
*π = ππ = ππ/N
Pressure Angle (Ο)
Pressure Angle (Ο):
The angle through which forces are transmitted between meshing gears.
Radial component of force pushes shafts apart.
Typical angles 25Β°,20Β°, and (now rather rare)
14.5Β°.
Involute Profile:
Involute profile maintains constant velocity ratio between meshed gears.
Procedure to determine geometry of meshing gears (pinion and gear):
1.For given module (m) and number of teeth: draw the pitch diameters.
- For given pressure angle: draw pressure line.
- Draw perpendicular lines OgB and OpA.
- Draw base circles.
- Divide base circles into equal parts.
- Construct radial lines OgA0 , OgA1 ,…
- Construct perpendiculars to radial lines with length equal to A0A1 , A0A2 , A0A3.
- Curve constructed through these points is the involute of the gear, involute of the pinion is constructed in the same way.
- Then, calculate circular pitch p= Ο m.
- Width of teeth and spaces are Β½ the circular pitch.
- Draw addendum and dedendum.
- Mirror involute profile.
Straight Cut Gears:
Also referred to as βspur gearsβ.
For parallel shafts.
Simplest, cheapest, most common.
Produce noise and are less compact than helical cut gears of the same capacity.
Helical-Cut Gears:
They can be designed for both parallel shafts, but also non-parallel, non-coplanar shafts.
Generally, more expensive than straight cut gears.
Typically, quieter than straight-cut gears.
Smaller than straight cut for same capacity.
Produce (generally unwanted) axial force.
Crossed Helical Gears:
Helical gears can be used with crossed axis shafts, (non-parallel, non-intersecting).
Worm Gears:
Transmit drive between non-parallel non-coplanar shafts.
Very high reduction ratio.
90Β° configuration most common.
High friction losses compared to other gears.
Straight Bevel Gears:
Non-parallel, co planar shaft axes.
Straight teeth, they can be made in smaller sizes (module of as small as 0.5)
Potential tolerancing difficulties to ensure correct engagement.
Spiral Bevel Gears:
Spiral bevel gears offer similar advantages to helical gears.
Strength and noise level advantage over straight bevel gears.
Applications that require high
speed and high torque.
Reduced risk of overheating.
However, they produce an axial
thrust load.
Hypoid Gears:
Hypoid gears similar to spiral bevel gears but allow non-coplanar shafts.
Stronger as load is applied to multiple teeth simultaneously.
Very low noise levels.
Gear Failure Causes:
- Bending stress fatigue in the teeth
- Number of teeth
- Pressure angle
- Bearing fatigue on tooth surfaces
Gear Trains:
One or more pairs of gears operating together to transmit power.
Types of Gear Trains:
Simple
Compound
Reverted
Epicyclic (Planetary)
Reverted Gear Train:
In a reverted gear train, the axes of the first
gear (i.e. first driver) and the last gear (i.e.
last driven or follower) are co axial.
A Reverted Gear Train has:
-Two gear pairs
-Two shafts
-The input and output shafts are co axial.
Clearly, at least one gear must not be keyed to the shaft.
Gear Design: Number of Teeth:
For a given diameter, the greater the number of teeth, the finer the pitch and
hence the weaker they are.
-In general, choose the maximum number of teeth consistent resistance to failure.
Integer ratios mean that the same teeth engage on each revolution, (a bad thingβ¦).
Use of βhuntingβ tooth for wear equalisation. (Only possible where change in speed is acceptable).
Tooth systems are standards that define the geometric proportions of gear teeth.
Epicyclic or planetary gears:
A system of gears consisting of a central sun gear, planet gears (on a carrier) and outer ring or annulus.
Without holding one element stationary the system has two degrees of freedom.
A variety of ratios can be achieved dependent on which element is held stationary.
Spur, helical or bevel gears typically.
Often used in automobiles for automatic
transmission.
For equispaced planetary gears:
*(ππ +ππ )/ππ.ππ ππππππ‘π = ππ πππ‘πππr
Summary - General design considerations:
- Gears offer a compact, high efficiency, and (where required) high speed drive.
- Gears also offer a wide range of configurations (depending on the position of their axes), to meet a variety of design requirements and constraints.
- A gear train consists of one or more pairs of gears operating together to transmit power.
