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					              ENTC 463
• HW#5 Helical Gears
• Chapter 8 – 44
• Chapter 10 – 2 (change helix angle to 25
  degree), 6.
                ENTC 463
• Exam #1, 2/14/2008
  – Chapter 7 – Belt and Chain
  – Wire rope
  – Chapter 8 – Spur gears and helical gear
    geometry
  – Chapter 9 – Spur gear design and analysis,
    gear materials
  – Chapter 10 – Helical gear design and analysis
       Helical Gears

          ENTC 463
Mechanical Design Applications II
                Helical Gears
•One left hand and one right hand
• Parallel shafts




                     • Crossed helical gears
                     • Both right hand or both left hand
                     • Non-parallel, non-coplanar shafts
              Helical Gears
• Read textbook
  – Chapter 8, geometry and material
  – Chapter 10, forces and stress
• Advantage
  – Smooth engagement
  – Smaller package
• Disadvantage
  – Axial thrust ?
Helical Gear Geometry




           Helical angle ψ –
           between the red and
           blue lines
Gear Geometry
       • Circular pitch
               πD
            p=
                N
       • Normal circular pitch
            pn = p cosψ

       • Axial pitch

                   p
            px =
                 tanψ
              Gear Geometry
                          • Diametral pitch
                            (transverse)
                                     N
                                Pd =
                                     D
                          • Normal duametral
                            pitch
                                         pd
                                  pnd =
                                        cosψ
       π             π
pd =       , pnd =        Where are they in the figure?
       p             pn
Forces Acting on Helical Gear
Forces Acting on Helical Gear



                  Wn : normal force

                  Wt : tangential force

                  Wr : radial force

                  Wx : axial force
Tangential Plane (top view)
                           Wt : tangential force




                             Wx : axial force

                              Wx = Wt tanψ
Bottom of the cheesecake
Transverse Plane (front view)




                                      φt : transverse pressure angle


                                         Wr = Wt tan φt

                                           Wr : radial force
Front shear plane of the cheesecake
Normal Plane (front view rotate ψ)




                     φn : normal pressure angle
                     used as φ

                           ⎛ Wt      ⎞
                      Wr = ⎜
                           ⎜ cosψ    ⎟ tan φn
                                     ⎟
                           ⎝         ⎠
           Wt
          cosψ         Wr : radial force
       Geometry Parameters
  Wr = Wt tan φt                      φt : transverse pressure angle
                                      φn : normal pressure angle
      ⎛ Wt      ⎞
 Wr = ⎜
      ⎜ cosψ    ⎟ tan φn
                ⎟                     ψ : helical angle
      ⎝         ⎠

               Spur gear : pressure angle φ

                 ⎛ Wt      ⎞
Wr = Wt tan φt = ⎜
                 ⎜ cosψ    ⎟ tan φn
                           ⎟
                 ⎝         ⎠
           tan φn                       use φn as φ
⇒ tan φt =
           cosψ                         the only added parameter is ψ
      True Normal Force, Wn
• True normal force Wn, can be calculated
  (but not used)
          Wt cosψ       Wt
     Wn =         =
           cos φn   cosψ cos φn

• Use other components: Wt, Wr, Wx
  – Tables and Figures
  – Shafts, bearings, etc.
             Power - Force

     D
Wt × = T
     2                      ⎛ Wt     ⎞
                       Wr = ⎜
                            ⎜ cosψ   ⎟ tan φn
                                     ⎟
    63000 × hp              ⎝        ⎠
T=
        n
     126000 × hp       Wx = Wt tanψ
Wt =
         nD
       Helical Gear Example
• Normal diametrial pitch pnd=8, normal
  pressure angle φn = 20 degree, N = 32,
  F = 3.0”, ψ = 15 degree. What are the
  forces acting on the gear tooth while the
  gear is rotating at 650 rpm and
  transmitting 7.5 hp
         Stress in Helical Gears
• Bending stress number, st
  –   Geometry factor J (Figure 10.5 to 7)
  –   Overload factor
  –   Size factor                     Use chart/Table from Chapter 9
  –   Load distribution factor
  –   Rim thickness factor
  –   Dynamic factor

                    Wt pd
               st =       Ko K s Km K B Kv
                     FJ
              Geometry Factor, J
   Assume 75 teeth meshing gear/pinion initially




          4
J’=0.49

                                          3


                  2

                            1
 Geometry Factor Multiplier, K

 K=1.035




N P = 30
N G = 150
            J = J ′ × K = 0.49 ×1.035
      Surface Stress Number
                        Wt K o K s K m K v
             sc = C p
                            FDP I

• Geometry factor, I
Bending Stress Consideration
               Wt pd                                         Wt pd
Stress:   σt =           Bending stress number:         st =
                FJ                                            FJ
                                           Wt pd
   Modified bending stress number:    st =       Ko K s Km K B Kv
                                            FJ


                                                                     Compare
    Allowable bending stress (strength):   sat
                                                        ′           YN
  Adjusted allowable bending stress (strength):   sat       = sat
                                                                  SF ⋅ K R
Contact Stress Consideration
                                           Wt
 Contact stress number:     σc = Cp
                                          FDP I

                                                Wt K o K s K m K v
 Modified contact stress number:     sc = C p
                                                    FDP I


                                                                    Compare
  Allowable contact stress (strength):   sac
                                                        ′          Z N CH
Adjusted allowable contact stress (strength):     sac       = sac
                                                                  SF ⋅ K R

				
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