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Chapter 9 Spur Gear Design - PowerPoint PPT Presentation

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Chapter 9 Spur Gear Design. Pinion. Gear. Lecture Steps:. Quick review, gear geometry (Chapter 8) Transmitted loads (overhead) Review bending stress, bending stress number, St, allowable bending stress number, Sat and adjusted allowable bending stress number, S’at .

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lecture steps
Lecture Steps:
  • Quick review, gear geometry (Chapter 8)
  • Transmitted loads (overhead)
  • Review bending stress, bending stress number, St, allowable bending stress number, Sat and adjusted allowable bending stress number, S’at.
  • Review contact stress number, Sc, allowable contact stress number, Sac and adjusted allowable contact stress number S’ac.
  • Overview gear design steps.
  • Example(s) gear design!!



Quick review:

Bending Stress No:

Required Allowable Bending Stress No:

Contact Stress No:

Required Allowable Contact Stress No:

steps for gear drive design
Steps for Gear Drive Design:
  • From design requirements, identify speed of pinion, nP, desired output speed of gear, nG, and power to be transmitted, P.
  • Choose type of material for the gears (steel, cast iron, bronze, etc.)
  • Determine overload factor, Ko, using table 9-5
  • Calculated Pdes = KoP and calculate a trial value for the diametral pitch, Pd (for steel use Figure 9-27). Note diametral pitch must be a standard size (see Table 8-2).
    • Note, as Pd decreases, tooth size increases thus bringing down St and Sc. But….. As Pd increases, # teeth increases and gear train runs smoother and quiter and the drive gets smaller as well!
steps for gear drive design5
Steps for Gear Drive Design:
  • Specify Np and NG to meet VR requirement. Calculate center distance, D, OD to make sure there aren’t any interference issues.
  • Specify face width using recommended range: 8/Pd < F < 16/Pd.
    • Remember, increasing face width reduces St and Sc but consider alignment factor. Face width is normally less than 2X Dp.
  • Compute transmitted load, Wt, pitch line speed, vt, quality number, Qv, and other factors required for calculating bending stress and contact stress.
  • Calculate St and required Sat. Does material in 2 meet Sat #? No – then select new material or define new geometry (step 4). If yes, continue to 9.
  • Calculate Sc and required Sac. Does material in 2 meet Sac? No – then select new material to meet Sac and Sat or define new geometry (step 4). If yes, continue to 10.
  • Summarize design

Problem # 9.61

A gear pair is to be a part of the drive for a milling machine requiring 20 hp with the pinion speed at 550 rpm and the gear speed to be between 180 and 190 rpm.


Driven = Milling Machine

Power = 20 hp

Pinion Speed = 550 rpm

Output Speed = 180 -190 rpm ≈ 185 rpm

Continuous Use = 30,000 hours


Compact Gear Design



Design Power:

Assume: Light Shock Driver and Moderate Shock Driven

Ko = 1.75 (Table 9-5, page 389)

PDesign = (Ko)(PInput)

= (1.75)(20hp)

= 35hp


Trial Size

Pick Sizes

Pd = 5 T/in

Dp = 4.80 in

DG = 14.2 in

Np = 24 teeth

NG = 71 teeth

Check physical size!!


Center Distance

Pitch Line Speed

Tangential Load

Note: Use Input Power Here as Ko is applied Later!

Face Width



Design Decisions

Quality Number, Qv = 6 (Table 9-2, Page 378)

Steel Pinion

Steel Gear

More precision, higher quality number!

Cp = 2300 (Table 9-9, Page 400)

Softer material, more relative deformation, therefore contact area increases and stress decreases


Geometry Factors

Pinion: JP = .36

Gear: JG = .415

Figure 9-17, Page 387


Geometry Factors Cont…

Page 402

I = .108


Load Distribution Factor

Equation 9-16, Page 390; Equation is solved on next slide



Load Distribution Factor Cont…

Size Factor

Page 389

ks = 1.0 since Pd ≥ 5


Rim Thickness Factor


For this problem, specify a solid gear blank KB = 1.00

KB = 1.00 for mB = 1.2 or larger


Rim Thickness Factor Cont…

We are assuming a solid gear blank for this problem, but if not then use:

Min Rim Thickness = (1.2)(.45 in) = .54 in

Min back-up ratio


Safety Factor

SF = 1.25 (Mid-Range)

Hardness Ratio

CH =1.00 for early trials until materials have been specified. Then adjust CH if significant

differences exist in the hardness of the pinion and the gear.


Page 396

KR = 1.5 (for 1 in 10,000 failures)


Dynamic Factor Cont… Kv

Qv comes from Figure 9-21

Kv can be calculated like in above equations or taken from Figure 9-21.

Equations are more accurate.


Design Life

Ncp = (60)(L)(n)(q)

L = 30,000 hours from Table 9-7

n = 550 rpm

q = 1 contacts

Ncp = (60)(30,000 hours)(550 rpm)(1 contact) = 9.9x108 cycles

NcG = (60)(30,000 hours)( 185.92 rpm)(1 contact) = 3.34656x108 cycles


Hardness Numbers BENDING (Grade 1)

Page 379

Pinion Bending

Satp = 34,324.5 psi = HB 270

Gear Bending

These stresses are OK

SatG = 28,741.9 psi = HB 215

Go to appendix A3 or A4 and spec out material that meets this hardness requirement! Example AISI 1040, Temper at 900 F


Hardness Numbers CONTACT (Grade 1)

Page 380

Pinion Contact

Sacp = 261,178 psi

Gear Contact

These Stresses are WAY too HIGH!

Values are off table!

SacG = 245,609 psi


Summary of Problem

Contact stresses are too High. Must iterate until stress are low enough until

a usable material can be found.

NOTE: Contact Stress generally controls. If material cannot be found for bending,

contact stress is too high!

Iterate! Decrease Pdand increase F

Excel is a GREAT tool to use for these Iterations.

This problem solved after third iteration using Excel

guidelines for adjustments in successive iterations
Guidelines for Adjustments in Successive Iterations.
  • Decreasing the numerical value of the diametral pitch results in larger teeth and generally lower stresses. Also, the lower value of the pitch usually means a larger face width, which decreases stress and increases surface durability.
  • Increase the diameter of the pinion decreases the transmitted load, generally lowers the stresses and improves surface durability.
  • Increase the face width lowers the stress and improves surface durability but less impact than either the pitch or pitch diameter.
  • Gears with more and smaller teeth tend to run more smoothly and quietly than gears with fewer and larger teeth.
  • Standard values of diametral pitch should be used for ease of manufacture and lower cost (See table 8-2).
  • Use high alloy steels with high surface hardness – results in the most compact system but the cost is higher.
  • Use gears with high quality number, Qv – adds cost but lowers load distribution factor, Km.
  • The number of teeth in the pinion should be as small as possible to make the system compact. But the possibility of interference is greater with fewer teeth. Check Table 8-6 to ensure no interference will occur.