Thursday, September 27, 2012

Gear

GEARS - are toothed cylindrical wheels used in transmitting motion and power from one rotating shaft to another.

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= N/ 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 = D+ 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 = D– 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 = P/ 2

b.      For Backlash is not  zero

T = P - 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 = Dcosф

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:
        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:





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

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 / Ptan δ
Where:
                P = 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:



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