Gear Mesh - see Terminology above

oExternal

OR

oInternal

Read-only

Gear Center-Distance

See also center-distance calculation in Adjustments tab

Number-of-Teeth, z1 (Minimum =5)

The number of-teeth on the input-gear - usually the Driving-Gear

Number-of-Teeth, z2 (Minimum = 5)

The number of-teeth on the output gear - usually the Driven-Gear

Notes:

A Gear-Segment must not rotate fully. It must oscillate.

Gear # Segmentation

◉Complete Gear - a normal, or full gear

◉Gear Segment - a gear that is not complete, it has fewer teeth.

Gear 1 and/or Gear 2 can be a Gear-Segment

To reduce the number-of-teeth of Gear 1 and/or Gear 2:

Gear-Slip (degrees)

These parameters rotate Gear 1 and Gear 2 around at the Pin-Joint.

This parameter rotates the gear teeth. It does NOT rotate the Part. I have never used this parameter.

Top-Tip:

If you add a Gear-Slip to one Gear, then, to keep the gears in mesh:

Gear-Slip 2 = – (# Teeth,z1 / # Teeth, z2) × Gear-Slip 1

E.g.: Gear-Slip 1 = 2 degrees, # Teeth, z1 = 120, # Teeth, z2 = 40.

Gear-Slip 2 = –(120/40)*2 = –6 degrees.

Clearance (move gears apart)

This parameter changes the length of the Line-of-Centers, the center-distance, between the Gears.

Usually, Clearance is a +ve value for External Gears, and a –ve value for Internal Gears. See Notes on recommended backlash.

An alternative way to change the clearance is to reduce (by machining) the size of the gear-teeth and not to change the center-distance. We do not include for you a parameter with this deign option. However, it is the standard method to provide backlash in commercial gear-boxes. Talk with the gear supplier, machinist.

Center-Distance Calculation

If External Mesh, then center-Distance = Clearance + (Module×(Number-of-Teeth Gear1+Number-of-Teeth Gear2)÷2)

If Internal Mesh, then center-Distance = Clearance + (Module×(Number-of-Teeth Gear1-Number-of-Teeth Gear2)÷2)

Notes:

Recommend Backlash / Clearance.

•Minimum: 0.006 × (center-distance)0.5

•Maximum: 0.024 × (center-distance)0.5

Also, I have read that:

•Minimum normal backlash = 0.03 × module + 0.05 mm

If the torque reverses each machine cycle, then you should aim for the minimum recommended backlash.

Module , m

Module, m = P.C.D (in mm) ∕ Number-of-Teeth.

If you increase module, the diameter of the Gears increases.

The module of the gears in the Gear-Pair are equal.

Pressure-Angle α - default = 20º

Standard gears are 20º.

Other standards are:

•14º, 17.5º (weaker, quieter),

•22.5º and 25º (stronger, noisier).

Addendum, ha - default = m.

The radial height of the gear tooth from the Pitch Circle to the top of the tooth.

Dedendum, hf - default = m × 1.25.

The radial depth of the gear tooth below the Pitch Circle to the root of the tooth.

The Dedendum is usually larger than the Addendum to give a working-clearance for the teeth.

If 0.25<m<1, Dedendum is usually = m × 1.4

If m>1, Dedendum is usually = m × 1.25

Root-Radius, rf - Default is 0.3 × m

The small fillet between the Flank and the Root of the Gear Tooth.

Note: In reality, if the gear is manufactured from a Hob/Rack Cutter, then the root of the gear is a Trochoid.

# Points along Profile

The number of facets and points along the gear tooth flank (and around the two Root Radii).

To display Gears more accurately, increase the number of points. Generally, do not increase the number of Points along the Profiles without a good reason.

4 is OK. 10 is accurate, but not usually needed.

For information:

Working Clearance = Dedendum - Addendum

Working Depth = Addendum × 2

Total Depth = Addendum + Dedendum

ALL READ-ONLY

Contact-Ratio:

Contact-Ratio should not be less than 1.1. Contact-Ratio should be a minimum of 1.2 for working gears.

Working Clearance = Dedendum - Addendum

[Note: the units should be [m] not [mm], or let Working-Clearance[mm] = Working-Clearance × 1000]

The distance between the top land of a gear tooth and the bottom land of the gear with which is meshed.

Gear 1 PCD and Gear 2 PCD

PCD = Pitch Circle Diameter.

PCD = Module × Number-of-Teeth, (m×z)

Normal Backlash (mm)

This is the gap (backlash) between the gear-flanks you can measure with a 'feeler gauge'.

Normal Backlash is a function of the center Distance Adjustment parameter ONLY.

Angular Backlash - Gear 1 (deg) jΘ1

This parameter gives the maximum rotation of Gear 1 if you do not move Gear 2.

Angular Backlash is a function of the center Distance Adjustment parameter ONLY.

Angular Backlash - Gear 2 (deg)

This parameter gives the maximum rotation of Gear 2 if you do not move Gear 1.

Angular Backlash is a function of the center Distance Adjustment parameter ONLY.

Contact-Ratio

The Contact-Ratio gives the number-of-teeth that are in contact, on average, as they pass through the meshing point. A contact ratio between 1 and 2 means that contact alternates between one and two pairs of teeth. Gears that have a high contact-ratio are smoother and quieter. The contact-ratio of an Internal Gear-Pair is higher than that of a similar External Gear-Pair.

If the Contact-Ratio is too low, then consider these options:

•Decrease the pressure-angle

•Increase the number-of-teeth

•Increase the working-depth

Pitch Diameter

Module, m, number-of-teeth, N

D = mN

Circular Pitch

Module

pc = m.π = D.π ∕ N

Module

Diametrical Pitch, Pd

m = 25.4 ∕ Pd

Number-of-Teeth

Module, m, Pitch Diameter, D

N = D ∕ m

Addendum

Module, m

a = m

Dedendum

Module, m

b = 1.25m

Outside Diameter

Module, m, Pitch Diameter, D, or number-of-teeth, N

Do = D + 2m = m (N + 2)

Root Diameter

Pitch Diameter, D, Module, m

DR = D – 2.5m

Base Circle Diameter

Pitch Diameter and Pressure Angle

Db = D cos μ

Base Pitch

Module, m, and Pressure Angle, μ

pb = m π cos μ

Tooth Thickness at

Standard Pitch Diameter

Module, m

Tstd = π. m ∕ 2

Center Distance

Module, m, number-of-teeth, N

C = m . (N1 + N2) ∕ 2

Contact Ratio for Spur Gears

( 1 < CR < 2 )

Outside Radii, Base Circle Radii, center Distance, Pressure Angle

CR = (√R012 – Rb12 + √R022 – Rb22 – C sin μ) ∕ m π cos μ

Backlash (linear)

Change in center Distance, ΔC

B = 2( ΔC )tan μ

Backlash (linear)

Change in Tooth Thickness, ΔT

B = ΔT

Backlash (linear) along

Line-of-action

Linear Backlash along Pitch Circle, B

BLA = B cos μ

Backlash, Angular

Linear Backlash, D

Ba = 6880 B ∕ D (arc minutes)

Min. No. of Teeth

for No Undercutting

Pressure Angle, μ

Nc = 2 ∕ sin2 μ

Nc (20º) = ~17 Teeth

Addendum:

the height of the gear tooth above the pitch circle diameter

Backlash:

the angle the output-shaft of the gearbox can move without the input-shaft moving

Base Circle:

an imaginary circle used in involute gearing to generate the involute that forms the tooth profiles

Bevel Gears:

used for right-angle applications. There are two types of bevel gears which are straight and spiral

Center-Distance:

distance between the axes of two meshed gears - Length of the Line-of centers

Circular Thickness:

the thickness of the tooth on the pitch circle.

Dedendum:

the depth of the tooth below the diameter of the pitch circle.

Diametrical Pitch:

the teeth per inch of the diameter of the pitch circle

Differential Gear:

a bevel gear which allows two shafts to rotate at a different speed.

Gear:

a wheel with teeth that meshes with another wheel with teeth to translate motion.

Gear center:

the center of the pitch circle.

Gear Train:

two or more gears meshed by their teeth. A gear train generates power speed through the meshed gears rotating

Gear Ratio:

the ratio between the numbers of teeth of meshing gears.

Helical Gear:

gear with the gear teeth cut at angles

Line of Contact:

the line or curve along which two tooth surfaces are tangent to each other

Involute:

the curve which describes a line which is unwound from the circumference of the gear

Pinion:

a small cogwheel which fits into a larger gear or track.

Pitch Circle:

the curve of intersection of a pitch surface of revolution and a plane of rotation

Pitch Diameter:

the diameter of the pitch circle

Pitch Radius:

the radius of the pitch circle

Planetary Gears:

a system that consists of three components: the sun gear, ring gear, and two or more planet gears. The sun gear is in the center, the ring gear is the outermost gear, and the planet gears are the gears surrounding the sun gear inside the ring gear.

Pressure Angle:

the angle between the line-of-action and the normal (90º, perpendicular) to the surface of the tooth

Spiral Bevel Gears:

shafts whose axes are perpendicular (90º) to each other and are used in right-angle applications

Spur Gear:

connect parallel shafts which have involute teeth that are parallel to the shaft

Sun Gear:

a gearwheel that rotates around its own axis and has other gears (planet gears) that rotate around it

Torsional Strength:

the measure of the amount of torque that a radial shaft can sustain during its rotation in a mechanical system

Working Depth:

the max depth a tooth of one gear extends into the tooth gear of a mating gear

Worm Gear:

a gear with one or more teeth with screwed threads

Crowning:

End-Relief

Topping and Semi-Topping

End Radius and Edge Radius/End Relief

Top Round/Semi-topping

Circular Pitch = pitch circle circumference(pi.d) / number of teeth(z) ; p = Π.d / z

Module = Pitch Diameter(d) / Number of Teeth(z) ; m = d/z

Circular Pitch(p) / Module(m) ; p/m = Π

Pitch Diameter(d) = module(m) × number of teeth(z) ; d = m.z