Classification of Gears According to the Nature of Axis
1. Parallel Axis
a. External Spur Gear d. Herringbone Gear
b. Internal Spur Gear e. Rack & Pinion
c. Twisted Spur Gear f. Pin Gearing
2. Intersecting Axis
a. Plain Bevel Gear
b. Crown Bevel Gear
c. Spiral Bevel Gear
3. Non- intersecting or Non-Parallel Axis
a. Hyperboloidal
b. Hypoid
c. Screw Gear
Kinds Of Gears
1. Spur Gear 3. Worm Gear
2. Helical Gear 4. Bevel Gear
1. Spur Gear – are gear having teeth that are straight and arranged parallel to the axis of the shaft carries the gear. The curve shapes of the faces of the spur gear teeth have a special geometry called involute curve.
Spur Gear Formulas:
1. Circular Pitch
Pc = π DP Pc = π Dg Pc = π M
NP Ng
Where:
Pc = circular pitch, mm/tooth or in/tooth
M = module, mm/tooth or in/tooth
Pd = diameter pitch, mm or in.
Dg = Gear diameter, mm or in.
Dp = pinion diameter, mm or in.
Ng = Number of teeth in gear
Np = number of teeth in pinion
2. Diameter Pitch
Pd= Np / Dp Pd = Ng / Dg Pd = π/Pc Pd = 1 / M
Where:
Pc = circular pitch, mm/tooth or in/tooth
M = module, mm/tooth or in/tooth
Pd = diameter pitch, mm or in.
Dg = Gear diameter, mm or in.
Dp = pinion diameter, mm or in.
Ng = Number of teeth in gear
Np = number of teeth in pinion
3. Clearance
C = d – a C = W - Wr
Where:
a = addendum, mm or in.
Pd = diametral pitch, tooth/mm or tooth/in
W = whole depth, mm or in.
Wr = working depth, mm or in.
4. Addendum
a = 1 / Pd
Where:
a = addendum, mm or in.
Pd = diametral pitch, tooth/mm or tooth/in
5. Dedendum
a. For 14 1/2° and 22 1/2°
d = 1.157 / Pd
b. For 20° and 25°
d = 1.25 / Pd
Where:
a = addendum, mm or in.
Pd = diametral pitch, tooth/mm or tooth/in
6. Outside Diameter
a. For Pinion
Dop = Dp + 2a = (Np + 2) / Pd
b. For Gear
Dog = Np + 2 = Dg + 2a
Pd
Where:
Pd = diametral pitch, tooth/mm or tooth/in
Dg = Gear diameter, mm or in.
Dp = pinion diameter, mm or in.
Np = number of teeth in pinion
Dop = outside diameter of pinion, mm or in
7. Root Diameter
a. For Pinion
Drp = Dp – 2a
b. For Gear
Drg = Dg – 2d
Where:
Dg = Gear diameter, mm or in.
Dp = pinion diameter, mm or in.
Drp = root diameter of pinion, mm or in.
Drp = root diameter of pinion, mm or in
d = dedendum
8. Whole depth
W = a + d W = Wr + C
Where:
W = whole depth, mm or in.
c = clearance, mm or in.
Wr = working depth, mm or in.
a = addendum, mm or in.
d = dedendum, mm or in.
9. Working Depth
Wr = 2a Wr = W - C
Where:
W = whole depth, mm or in.
Wr = working depth, mm or in.
a = addendum, mm or in.
d = dedendum, mm or in.
10. Tooth Thickness
a. For Backlash is zero
T = PC / 2
b. For Backlash is not zero
T = PC - B
2
Where:
T = tooth thickness, mm/ tooth or in/tooth
Pc = circular pitch, mm/tooth or in/tooth
B = backlash, mm or in.
11. Tooth Space
S = T + B
Where:
T = tooth thickness, mm/ tooth or in/tooth
B = backlash, mm or in.
S = tooth space or space width, mm or in.
12. Base Circle Diameter
a. For Pinion
Dbp = Dp cosф
b. For Gear
Dbg = Dgcosф
Where:
Dg = gear diameter, mm or in.
Dp = pinion diameter, mm or in.
Dbp = base circle diameter of pinion, mm or in.
Dbg = base circle diameter of gear, mm or in.
Ф = pressure angle, deg
13. Center distance between gear
C = (Dg + Dp) / 2 --- for external contact
C = (Dg - Dp) / 2 --- for internal contact
Where:
C = center distance between gears, mm or in.
Dg = gear diameter, mm or in.
Dp = pinion diameter, mm or in.
14. Backlash
B = S – T
B = 0.03 to 0.04
Pd pd
Where:
Where:
T = tooth thickness, in./tooth
B = backlash, in
S = tooth space or space width, in.
Pd = diametral pitch, or tooth/in.
15. Face Width
2.5Pc < b > 4 Pc
(8 / P) < b > (12.5 / Pd)
Where:
b = face width
Pd = diameter pitch
Pc = circular pitch
SPUR GEAR applications:
SPUR GEAR applications:
2. Helical Gear are gears arranged so that they lie at an angle with respect to the axis of the shaft.
Formulas (Helical Gears)
1. Tangential Force
Ft = Fr
tanф
Where:
Ft = tangential force, N or lb.
Fr = radial force, N or lb.
Ф = pressure angle, deg
2. Radial Force
Fr = Fn sin ф
Where:
Fn = normal force, N or lb.
Fr = radial force, N or lb.
Ф = pressure angle, deg
3. Axial Force
Fa = Ft tan δ
Where:
Fa = axil force, N or lb.
Ft= tangential force, N or lb.
δ = helix angle, deg
4. Normal Pressure Angle
4. Normal Pressure Angle
Фn = tan -1 (tan ф cos δ)
Where:
Ф = pressure angle, deg
Фn = normal pressure angle, deg.
δ = helix angle, deg
5. Axial Pitch
Pa = Pcn / tan δ or π / Pd tan δ
Where:
Pa = axial pitch
Pcn = normal circular pitch
Pd = diametral pitch
δ = helix angle, deg
6. Normal Diametral Pitch
Pdn = Pd / cos δ
Where:
Pdn = normal diametral pitch
Pd = diametral pitch
δ = helix angle, deg
7. Normal Circular Pitch
Pcn = Pc cos δ
Where:
Pcn = normal circular pitch
Pc = circular pitch
δ = helix angle, deg
Helical Gear Applications:
No comments:
Post a Comment