I, J Factor Reference Charts and Rules for Stronger Spur Gear Designs
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Pitting Resistance I Factor, Bending Resistance J Factor Reference Charts and Underlying Rules for Stronger Spur Gear Designs Shuo Will Zhang Oerlikon Fairfield 6/7/2015 1
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Transcript of I, J Factor Reference Charts and Rules for Stronger Spur Gear Designs
Pitting Resistance I Factor,Bending Resistance J Factor
Reference Charts and Underlying Rules for Stronger Spur Gear Designs
Shuo Will Zhang
Oerlikon Fairfield
6/7/2015
1
From I, J Factors to Stresses
β’ πΆπππ‘πππ‘ π π‘πππ π =π‘ππππ’π
ππππ. πππ‘πβ ππππππ‘ππ2 Γ ππππ π€πππ‘β Γ πΌ ππππ‘ππ
1 2Γ ππ‘βππ ππππ‘πππ
β’ π΅ππππππ π π‘πππ π =π‘ππππ’π
ππππ. πππ‘πβ ππππππ‘ππ Γ ππππ π€πππ‘β Γπ½ ππππ‘ππ
ππππππ‘πππ πππ‘πβ
Γ ππ‘βππ ππππ‘πππ
2
Contact stress Bending stress
Most of the times, torque, ratio, center distance, operating pitch diameters, face widths are fixed, or fully utilized already. βOther factorsβ are out of designersβ control. The only elements that can be optimized are:I factor, and J factor/diametral pitch.
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
I Factor: 20PA, 1.00-1.35 Add./Ded. Index
106.54.232.421.61.31
Gear ratio
Pitting Resistance I factor
β’ For example: Find I factor for 25T pinion, 40T gear, 20PA
Step 1: find the right chart to use
Step 2: find pinion tooth number
Step 3: find gear ratio (40/25=1.6), i.e. which curve to use
Step 4: read I factor from chart: 0.093
3
I Factor:20PA, 1.00-1.25 Add./Ded. Index
4
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
10
6.5
4.2
3
2.4
2
1.6
1.3
1
Gear ratio
I Factor:20PA, 1.00-1.35 Add./Ded. Index
5
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
10
6.5
4.2
3
2.4
2
1.6
1.3
1
Gear ratio
I Factor:20PA, 1.15-1.35 Add./Ded. Index
6
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
10
6.5
4.2
3
2.4
2
1.6
1.3
1
Gear ratio
I Factor:25PA, 1.00-1.35 Add./Ded. Index
7
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
10
6.5
4.2
3
2.4
2
1.6
1.3
1
Gear ratio
I Factor:28PA, 1.00-1.35 Add./Ded. Index
8
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
10
6.5
4.2
3
2.4
2
1.6
1.3
1
Gear ratio
I Factor:30PA, 1.00-1.35 Add./Ded. Index
9
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I fac
tor
Tooth number
10
6.5
4.2
3
2.4
2
1.6
1.3
1
Gear ratio
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
J Factor: 25PA, 1.00-1.35 Add./Ded. Index
1000
200
100
60
40
28
20
16
13
Bending Resistance J factor
β’ For example: Find J factor for 28T pinion, 60T gear, 25PAStep 1: find the right chart to use
Step 2: find pinion tooth number
Step 3: find gear tooth number, i.e. which curve to use
Step 4: read J factor for pinion from chart: 0.457
10
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
J Factor: 25PA, 1.00-1.35 Add./Ded. Index
1000
200
100
60
40
28
20
16
13
Bending Resistance J factor
β’ Example contβd: Find J factor for 30T pinion, 60T gear, 25PA
Step 5: find gear tooth number
Step 6: find pinion tooth number, i.e. which curve to use
Step 7: read J factor for gear from chart: 0.507
11
J Factor:20PA, 1.00-1.25 Add./Ded. Index
12Assumptions of full-tip-radius hob and zero backlash apply to all J factor charts
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
1000200100604032252017
J Factor:20PA, 1.00-1.35 Add./Ded. Index
13
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
1000200100604032252017
Assumptions of full-tip-radius hob and zero backlash apply to all J factor charts
J Factor:20PA, 1.15-1.35 Add./Ded. Index
14
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
1000
200
100
60
40
32
25
20
17
Assumptions of full-tip-radius hob and zero backlash apply to all J factor charts
J Factor:25PA, 1.00-1.35 Add./Ded. Index
15
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
1000200100604028201613
Assumptions of full-tip-radius hob and zero backlash apply to all J factor charts
J Factor:28PA, 1.00-1.35 Add./Ded. Index
16
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
1000200100604028201613
Assumptions of full-tip-radius hob and zero backlash apply to all J factor charts
J Factor:30PA, 1.00-1.35 Add./Ded. Index
17
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
10 20 30 40 50 60 70 80 90 100
J fa
cto
r
Tooth number
1000200100604028201613
Assumptions of full-tip-radius hob and zero backlash apply to all J factor charts
J Factor/diametral pitch20PA, 1.00-1.25 Add./Ded. Index
18
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80 90 100
J fa
cto
r /
dia
met
ral p
itch
Tooth number
0.5
0.65
0.8
1
1.2
1.5
2
3
5
Gear ratio
Charts for βJ Factor/diametral pitchβ (page 18~23) are case studies for a fixed center distance, so the numbers are NOT directly usable for various center distances. The significance is the comparison among all input parameters.
J Factor/diametral pitch20PA, 1.00-1.35 Add./Ded. Index
19
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80 90 100
J fa
cto
r /
dia
met
ral p
itch
Tooth number
0.5
0.65
0.8
1
1.2
1.5
2
3
5
Gear ratio
Charts for βJ Factor/diametral pitchβ (page 18~23) are case studies for a fixed center distance, so the numbers are NOT directly usable for various center distances. The significance is the comparison among all input parameters.
J Factor/diametral pitch20PA, 1.15-1.35 Add./Ded. Index
20
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80 90 100
J fa
cto
r /
dia
met
ral p
itch
Tooth number
0.5
0.65
0.8
1
1.2
1.5
2
3
5
Gear ratio
Charts for βJ Factor/diametral pitchβ (page 18~23) are case studies for a fixed center distance, so the numbers are NOT directly usable for various center distances. The significance is the comparison among all input parameters.
J Factor/diametral pitch25PA, 1.00-1.35 Add./Ded. Index
21
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80 90 100
J fa
cto
r /
dia
met
ral p
itch
Tooth number
0.5
0.65
0.8
1
1.2
1.5
2
3
5
Gear ratio
Charts for βJ Factor/diametral pitchβ (page 18~23) are case studies for a fixed center distance, so the numbers are NOT directly usable for various center distances. The significance is the comparison among all input parameters.
J Factor/diametral pitch28PA, 1.00-1.35 Add./Ded. Index
22
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80 90 100
J fa
cto
r /
dia
met
ral p
itch
Tooth number
0.5
0.65
0.8
1
1.2
1.5
2
3
5
Gear ratio
Charts for βJ Factor/diametral pitchβ (page 18~23) are case studies for a fixed center distance, so the numbers are NOT directly usable for various center distances. The significance is the comparison among all input parameters.
J Factor/diametral pitch30PA, 1.00-1.35 Add./Ded. Index
23
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80 90 100
J fa
cto
r /
dia
met
ral p
itch
Tooth number
0.5
0.65
0.8
1
1.2
1.5
2
3
5
Gear ratio
Charts for βJ Factor/diametral pitchβ (page 18~23) are case studies for a fixed center distance, so the numbers are NOT directly usable for various center distances. The significance is the comparison among all input parameters.
J Factor vs. Tooth Thickness (General trend)
0.309
0.314
0.319
0.324
0.329
0.334
0.339
0.344
0.144 0.149 0.154 0.159 0.164
J fa
cto
r
Tooth thickness
24
Conclusions: How to Decrease Stresses
β’ Contact Stressβ Longer addendum on pinion (page 5,6)β dedendum has no effect (page 4,5)β More teeth, finer pitch (any of page 4~9)β Higher pressure angle (page 7~9)
β’ Bending Stressβ Longer addendum on mating member (page 19,20)β Reduce dedendum index (page 18,19)β Fewer teeth, coarser pitch (any of page 18~23)β Higher pressure angle (page 21~23)β Thicker tooth (page 24)
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