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Minimum Number of Teeth on the Pinion in Order to Avoid Interference
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written 5.7 years ago by |
The phenomenon when the tip of a tooth undercuts the root on its mating gear is known as interference. The minimum number of teeth on the pinion which will mesh with any gear (also rack) without interference is 17 or it may be determined by,
Z1=2(sinα)2 where α is pressure angle of gear and Z1= no. of teeth on the pinion
Design Criteria for Gears (Also refer PSG Design Data Book)
Parameter | Spur Gear | Helical Gear |
---|---|---|
Strength Criteria - Design | m≥1.263√[Mt]y[σb]φm⋅Z1 PSG 8.13A |
mn≥1.15cosβ3√[Mt]yv[σbφm⋅Z1 PSG 8.13A |
Strength Criteria - Checking | Fs=πybm[σb] Fs≥FLD or Fd FLD=Ft×Cv PSG 8.50 OR σb=i±1amby[Mt]≤[σb] PSG 8.13A |
Fs=πybmn[σb] Fs≥FLD or Fd FLD=Ft×Cv PSG 8.50 OR σb=0.7i±1abmnyv[Mt]≤[σb] PSG 8.13A |
Wear Criteria - Design | Find module using Fw=FLD Or d1Qkb=Ft×Cv PSG 8.51 |
Find module using Fw=FLD Or d1Qkbcosβ2=Ft×Cv PSG 8.51 |
Wear Critera - Checking | Fw=d1Qkb Fw≥FLD PSG 8.51 |
Fw=d1Qkbcosβ2,Fw≥FLD PSG 8.51 |
Surface / Contact Stresses - Design | a≥(i±1)3√(0.74[σc])2E[Mt]iφ Find module using a=m2(Z1+Z2) PSG 8.13 |
a≥(i±1)3√(0.7[σc])2E[Mt]iφ Find a. Find module using a=mncosβ(Z1+Z2)2 PSG 8.13 |
Surface / Contact Stresses - Checking | σc=0.74i±1a√i±1ibE[Mt]≤[σc] PSG 8.13 | σc=0.7i±1a√i±1ibE[Mt] ≤[σc], PSG 8.13 |
Parameter | Bevel Gear | Worm Gear |
---|---|---|
Strength Criteria - Design | mav≥1.28 3√[Mt]yv[σb]φm⋅Z1 PSG 8.13A |
mx≥1.243√[Mt]zqyv[σb] PSG 8.44 |
Strength Criteria - Checking | Fs=[σb]bπyv(1−bR)m Fs≥FLD or Fd FLD=CvNsfKmFt PSG 8.52 OR σb=R√i2+1[Mt](R−0.5b)2bmyv1cosα≤[σb] PSG 8.13A |
Fs=πybm[σb] Fs≥FLD or Fd FLD=Ft×Cv,Cv= (6+vmg6) PSG 8.25 OR σb=1.9[Mt]m3xqzyv≤[σb] PSG 8.44 |
Wear - Design | Find module using Fw=FLD Or d1Qkbcosδ1=Ft×Cv PSG 8. 52 |
Find module using Fw=FLD( Fd ) Or Dgbkw=Ft×(6+vmg6) PSG 8.52 |
Wear - Checking | Fw=d1Qkbcosδ1,Fw≥FLD PSG 8.52 |
Fw=Dgbkw Fw≥FLD(Fd) PSG 8.52 |
Surface / Contact Stresses - Design | R≥φy√i2+13√(0.72(φy−0.5)[σc]) Find ′R′. Find module using formulae in Table 31, PSG 8.38 |
a=(zq+1)3√(540q[σc])2[Mt] -- 8.44 Find 'a'. Find module using formulae on PSG 8.43 |
Surface / Contact Stresses - Checking | σC=0.72(R−0.5b)√√(i2±1)3ibE[Mt]≤[σc] PSG 8.13 |
σc=(540zq)√√(zq+1)3a[Mt]≤[σC] PSG 8.44 |