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[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 1
Machine Design & CAD - II POWER TRANSMISSION SYSTEM DESIGN
PROJECT
Power Transmission System Design Project:
Rack & Pinion Gear Design
Supervisor:
Respected Sir, Prof. Dr. Abdul Hameed Memon Sahab
GROUP MEMBERS:
Khalil Raza Bhatti 07ME40 Waqas Ali Tunio 07ME34 Ayaz Ali Soomro 07ME31 Waqar Ahmed Bhutto 07ME36 Muhammad Farooque Pirzado 07ME56 Zain-ul-Abideen Qureshi 07ME57
Department of Mechanical Engineering, Quaid-e-Awam University of Engineering, Science & Technology, Nawabshah, Pakistan
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 2
Contents Page
1 Introduction 3
2 Problem Definition 4
3 Project Objectives 4
4 Design Methodology 5
5 Problem Solution Alternatives 20
6 Working Drawing 21
7 Conclusion 22
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
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Introduction: Rack and Pinion Gear: A rack and pinion gears system is composed of two gears. The normal round gear is the pinion gear and the straight or flat gear is the rack. The rack has teeth cut into it and they mesh with the teeth of the pinion gear.
Basic Mechanism Rack and pinion gears provide a greater feedback and steering sensation. A rack and pinion gear gives a positive motion especially compared to the friction drive of a wheel in tarmac. In a rack and pinion railway, a central rack between the two rails engages with a pinion on the engine allowing a train to be pulled up very steep slopes. A well designed mechanism such as the rack and pinion gears save effort and time. The rack and pinion is used to convert between rotary and linear motion. Rack and pinion can convert from rotary to linear of from linear to rotary. The diameter of the gear determines the speed that the rack moves as the pinion turns. Rack and pinions are commonly used in the steering system of cars to convert the rotary motion of the steering wheel to the side to side motion in the wheels.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 4
Problem Definition/ Statement
Determine the various forces, parameters & Specifications to design the Rack and Pinion Gear mechanism and incorporate those forces to develop a Railway Crossing Sliding Gate.
Need is to develop a system for closing and opening of railway crossing gate with rack and pinion mechanism.
In order to design that we will have to assume some data as shown:
Gate is to slide on a rail by rail and wheel mechanism.
Sliding path is frictionless.
Two rack and pinion gears are used to slide gate on rail as load will uniformly be distributed mounted on its ends.
Project Objectives Understand rack and pinion gear mechanism.
Develop a direct design method for gear design in an efficient way.
Come up with an innovative solution for building that design as a standard one.
Determine the various forces that are meshed within gears.
In context of all the gear parameters referring to right selection of material for rack and as well as for pinion.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 5
Design Methodology Designing Rack and Pinion
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
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Spur Gear Design and Selection
Objectives
• Calculate forces on teeth of spur gears, including impact forces associated with
velocity and clearances.
• Determine allowable force on gear teeth, including the factors necessary due to angle
of involute of tooth shape and materials selected for gears.
• Design actual gear systems, including specifying materials, manufacturing accuracy,
and other factors necessary for complete spur gear design.
• Understand and determine necessary surface hardness of gears to minimize or
prevent surface wear.
• Understand how lubrication can cushion the impact on gearing systems and cool
them.
• Select standard gears available from stocking manufacturers or distributors.
Design Requirements
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
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Preliminary Design For spur gear design, pinion and rack both have straight teeth or spur geometry of teeth. So for we will first consider the design of pinion as spur gear.
Design Process To select gears from a stock gear catalogue or do a first approximation for a gear design select the gear material and obtain a safe working stress e.g Yield stress / Factor of Safety. /Safe fatigue stress
Determine the input speed, output speed, ratio, torque to be transmitted Select materials for the gears (pinion is more highly loaded than gear) Determine safe working stresses (uts /factor of safety or yield stress/factor of
safety or Fatigue strength / Factor of safety ) Determine Allowable endurance Stress Se Select a module value and determine the resulting geometry of the gear Use the lewis formula and the endurance formula to establish the resulting face
width If the gear proportions are reasonable then - proceed to more detailed
evaluations If the resulting face width is excessive - change the module or material or both
and start again
The gear face width should be selected in the range 9-15 x module or for straight spur gears-up to 60% of the pinion diameter Specifications for standard Gear Teeth
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 8
Standards AGMA 2001-C95 or AGMA-2101-C95 Fundamental Rating factors and Calculation
Methods for involute Spur Gear and Helical Gear Teeth BS 436-4:1996, ISO 1328-1:1995..Spur and helical gears. Definitions and allowable
values of deviations relevant to corresponding flanks of gear teeth BS 436-5:1997, ISO 1328-2:1997..Spur and helical gears. Definitions and allowable
values of deviations relevant to radial composite deviations and runout information BS ISO 6336-1:1996 ..Calculation of load capacity of spur and helical gears. Basic
principles, introduction and general influence factors BS ISO 6336-2:1996..Calculation of load capacity of spur and helical gears.
Calculation of surface durability (pitting) BS ISO 6336-3:1996..Calculation of load capacity of spur and helical gears.
Calculation of tooth bending strength BS ISO 6336-5:2003..Calculation of load capacity of spur and helical gears. Strength
and quality of materials
If it is necessary to design a gearbox from scratch the design process in selecting the gear size is not complicated - the various design formulea have all been developed over time and are available in the relevant standards. However significant effort, judgement and expertise is required in designing the whole system including the gears, shafts , bearings, gearbox, lubrication. For the same duty many different gear options are available for the type of gear , the materials and the quality. It is always preferable to procure gearboxes from specialised gearbox manufacturers
Spur Gear Design
The spur gear is is simplest type of gear manufactured and is generally used for transmission of rotary motion between parallel shafts. The spur gear is the first choice option for gears except when high speeds, loads, and ratios direct towards other options. Other gear types may also be preferred to provide more silent low-vibration operation. A single spur gear is generally selected to have a ratio range of between 1:1 and 1:6 with a pitch line velocity up to 25 m/s. The spur gear has an operating efficiency of 98-99%. The pinion is made from a harder material than the wheel. A gear pair should be selected to have the highest number of teeth consistent with a suitable safety margin in strength and wear. The minimum number of teeth on a gear with a normal pressure angle of 20 desgrees is 18. The preferred number of teeth are as follows
12 13 14 15 16 18 20 22 24 25 28 30 32 34 38 40 45 50 54 60 64 70 72 75 80 84 90 96 100 120 140 150 180 200 220 250
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
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Materials used for gears
Mild steel is a poor material for gears as it has poor resistance to surface loading. The carbon content for unhardened gears is generally 0.4%(min) with 0.55%(min) carbon for the pinions. Dissimilar materials should be used for the meshing gears - this particularly applies to alloy steels. Alloy steels have superior fatigue properties compared to carbon steels for comparable strengths. For extremely high gear loading case hardened steels are used the surface hardening method employed should be such to provide sufficient case depth for the final grinding process used.
Material Notes applications Ferrous metals
Cast Iron Low Cost easy to machine with high damping
Large moderate power, commercial gears
Cast Steels Low cost, reasonable strength
Power gears with medium rating to commercial quality
Plain-Carbon Steels Good machining, can be heat treated
Power gears with medium rating to commercial/medium quality
Alloy Steels Heat Treatable to provide highest strength and durability
Highest power requirement. For precision and high precisiont
Stainless Steels (Aust) Good corrosion resistance. Non-magnetic
Corrosion resistance with low power ratings. Up to precision quality
Stainless Steels (Mart) Hardenable, Reasonable corrosion resistance, magnetic
Low to medium power ratings Up to high precision levels of quality
Non-Ferrous metals Aluminium alloys Light weight,
non-corrosive and good machinability
Light duty instrument gears up to high precision quality
Brass alloys Low cost, non-corrosive, excellent
low cost commercial quality gears. Quality up to medium precision
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 10
machinability Bronze alloys Excellent
machinability, low friction and good compatability with steel
For use with steel power gears. Quality up to high precision
Magnesium alloys Light weight with poor corrosion resistance
Ligh weight low load gears. Quality up to medium precision
Nickel alloys Low coefficient of thermal expansion. Poor machinability
Special gears for thermal applications to commercial quality
Titanium alloys High strength, for low weight, good corrosion resistance
Special light weight high strength gears to medium precision
Di-cast alloys Low cost with low precision and strength
High production, low quality gears to commercial quality
Sintered powder alloys Low cost, low quality, moderate strength
High production, low quality to moderate commercial quality
Non metals Acetal (Delrin Wear
resistant, low water absorbtion
Long life , low load bearings to commercial quality
Phenolic laminates Low cost, low quality, moderate strength
High production, low quality to moderate commercial quality
Nylons No lubrication, no lubricant, absorbs water
Long life at low loads to commercial quality
PTFE Low friction and no lubrication
Special low friction gears to commercial quality
Module (m)
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 11
The module is the ratio of the pitch diameter to the number of teeth. The unit of the module is milli-metres.Below is a diagram showing the relative size of teeth machined in a rack with module ranging from module values of 0,5 mm to 6 mm
The preferred module values are
0,5 0,8 1 1,25 1,5 2,5 3 4 5 6 8 10 12 16 20 25 32 40 50
Forces on Spur Gear Teeth
Ft = Transmitted force Fn = Normal force. Fr = Resultant force θ = pressure angle Fn = Ft tan θ Fr = Ft/Cos θ
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 12
Surface Speed
Forces on Gear Tooth Forces acting on individual gear tooth.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 13
Strength of Gear Teeth Lewis form factor method Lewis equation
Fs = Allowable dynamic bending force (lb)
Sn = Allowable stress. Use endurance limit and account for the fillet as the stress concentration factor
b = Face width (in.) Y = Lewis form factor (From Table) Pd = Diametral pitch
Lewis form factors (Y)
Table of lewis form factors for different tooth forms and pressure angles
No Teeth
Load Near Tip of Teeth Load at Near Middle of Teeth
14 1/2 deg 20 deg FD 20 deg Stub 25 deg 14 1/2 deg 20 deg FD Y y Y y Y y Y y Y y Y y 10 0,17
6 0,056
0,201
0,064
0,261
0,083
0,238
0,076
11 0,192
0,061
0,226
0,072
0,289
0,092
0,259
0,082
12 0,21 0,067
0,245
0,078
0,311
0,099
0,277
0,088
0,355
0,113
0,415
0,132
13 0,223
0,071
0,264
0,084
0,324
0,103
0,293
0,093
0,377
0,12 0,443
0,141
14 0,236
0,075
0,276
0,088
0,339
0,108
0,307
0,098
0,399
0,127
0,468
0,149
15 0,245
0,078
0,289
0,092
0,349
0,111
0,32 0,102
0,415
0,132
0,49 0,156
16 0,255
0,081
0,295
0,094
0,36 0,115
0,332
0,106
0,43 0,137
0,503
0,16
17 0,264
0,084
0,302
0,096
0,368
0,117
0,342
0,109
0,446
0,142
0,512
0,163
18 0,27 0,086
0,308
0,098
0,377
0,12 0,352
0,112
0,459
0,146
0,522
0,166
19 0,277
0,088
0,314
0,1 0,386
0,123
0,361
0,115
0,471
0,15 0,534
0,17
20 0,283
0,09 0,32 0,102
0,393
0,125
0,369
0,117
0,481
0,153
0,544
0,173
21 0,28 0,09 0,32 0,10 0,39 0,12 0,37 0,12 0,49 0,15 0,55 0,17
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
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9 2 6 4 9 7 7 6 3 6 22 0,29
2 0,093
0,33 0,105
0,404
0,129
0,384
0,122
0,496
0,158
0,559
0,178
23 0,296
0,094
0,333
0,106
0,408
0,13 0,390
0,124
0,502
0,16 0,565
0,18
24 0,302
0,096
0,337
0,107
0,411
0,131
0,396
0,126
0,509
0,162
0,572
0,182
25 0,305
0,097
0,34 0,108
0,416
0,132
0,402
0,128
0,515
0,164
0,58 0,185
26 0,308
0,098
0,344
0,109
0,421
0,134
0,407
0,13 0,522
0,166
0,584
0,186
27 0,311
0,099
0,348
0,111
0,426
0,136
0,412
0,131
0,528
0,168
0,588
0,187
28 0,314
0,1 0,352
0,112
0,43 0,137
0,417
0,133
0,534
0,17 0,592
0,188
29 0,316
0,101
0,355
0,113
0,434
0,138
0,421
0,134
0,537
0,171
0,599
0,191
30 0,318
0,101
0,358
0,114
0,437
0,139
0,425
0,135
0,54 0,172
0,606
0,193
31 0,32 0,101
0,361
0,115
0,44 0,14 0,429
0,137
0,554
0,176
0,611
0,194
32 0,322
0,101
0,364
0,116
0,443
0,141
0,433
0,138
0,547
0,174
0,617
0,196
33 0,324
0,103
0,367
0,117
0,445
0,142
0,436
0,139
0,55 0,175
0,623
0,198
34 0,326
0,104
0,371
0,118
0,447
0,142
0,44 0,14 0,553
0,176
0,628
0,2
35 0,327
0,104
0,373
0,119
0,449
0,143
0,443
0,141
0,556
0,177
0,633
0,201
36 0,329
0,105
0,377
0,12 0,451
0,144
0,446
0,142
0,559
0,178
0,639
0,203
37 0,33 0,105
0,38 0,121
0,454
0,145
0,449
0,143
0,563
0,179
0,645
0,205
38 0,333
0,106
0,384
0,122
0,455
0,145
0,452
0,144
0,565
0,18 0,65 0,207
39 0,335
0,107
0,386
0,123
0,457
0,145
0,454
0,145
0,568
0,181
0,655
0,208
40 0,336
0,107
0,389
0,124
0,459
0,146
0,457
0,145
0,57 0,181
0,659
0,21
43 0,339
0,108
0,397
0,126
0,467
0,149
0,464
0,148
0,574
0,183
0,668
0,213
45 0,34 0,108
0,399
0,127
0,468
0,149
0,468
0,149
0,579
0,184
0,678
0,216
50 0,346
0,11 0,408
0,13 0,474
0,151
0,477
0,152
0,588
0,187
0,694
0,221
55 0,352
0,112
0,415
0,132
0,48 0,153
0,484
0,154
0,596
0,19 0,704
0,224
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 15
60 0,355
0,113
0,421
0,134
0,484
0,154
0,491
0,156
0,603
0,192
0,713
0,227
65 0,358
0,114
0,425
0,135
0,488
0,155
0,496
0,158
0,607
0,193
0,721
0,23
70 0,36 0,115
0,429
0,137
0,493
0,157
0,501
0,159
0,61 0,194
0,728
0,232
75 0,361
0,115
0,433
0,138
0,496
0,158
0,506
0,161
0,613
0,195
0,735
0,234
80 0,363
0,116
0,436
0,139
0,499
0,159
0,509
0,162
0,615
0,196
0,739
0,235
90 0,366
0,117
0,442
0,141
0,503
0,16 0,516
0,164
0,619
0,197
0,747
0,238
100 0,368
0,117
0,446
0,142
0,506
0,161
0,521
0,166
0,622
0,198
0,755
0,24
150 0,375
0,119
0,458
0,146
0,518
0,165
0,537
0,171
0,635
0,202
0,778
0,248
200 0,378
0,12 0,463
0,147
0,524
0,167
0,545
0,173
0,64 0,204
0,787
0,251
300 0,38 0,122
0,471
0,15 0,534
0,17 0,554
0,176
0,65 0,207
0,801
0,255
Rack
0,39 0,124
0,484
0,154
0,55 0,175
0,566
0,18 0,66 0,21 0,823
0,262
Classes of Gears • Transmitted load depends on the accuracy of the gears • Gear Manufacture – Casting – Machining • Forming • Hobbing • Shaping and Planing Force Transmitted Transmitted load depends on the accuracy of the gears. A dynamic load factor is added to take care of this.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 16
• Ft = Transmitted force • Fd = Dynamic force • Commercial
Classes of Gears
Carefully cut Precision
Hobbed or shaved
Expected Error in Tooth Profiles
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 17
Design Methods • Strength of gear tooth should be greater than the dynamic force; Fs ≥ Fd • You should also include the factor of safety, Nsf. Service Factors
Face width of Gears Relation between the width of gears and the diametral pitch. Dynamic Beam Strength of the Gear
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 18
To increase the dynamic beam strength of the gear – Increase tooth size by decreasing the diametral pitch – Increase face width upto the pitch diameter of the pinion – Select material of greater endurance limit – Machine tooth profiles more precisely – Mount gears more precisely – Use proper lubricant and reduce contamination Buckingham Method of Gear Design • It offers greater flexibility. • Expected error is based on different-pitch teeth. • More conservative design.
Wear strength (Buckingham)
Fw = tooth wear strength.
Dp = diametral pitch of pinion.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 19
Dg = diametral pitch of gear.
b = face width.
Kg = load stress factor.
Rack and Spur Gear Calculation The following table presents the method for calculating the mesh of a rack and spur gear.
Table presents the calculation of a meshed profile shifted spur gear and rack. If the correction factor x1 is 0, then it is the case of a standard gear meshed with the rack.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 20
The rack displacement, l, is not changed in any way by the profile shifting.
Equation remains applicable for any amount of profile shift.
Problem Solution Alternatives
Our basic purpose of the project is to slide the railway crossing gate by a mechanism that is much mechanical convenient to translate that load uniformly. So for we have been able to do that by using rack and pinion gear mechanism. Since the rack and pinion gear transmit the rotary power into linear and linear into rotary one that is the reason that we have incorporated the pinion and rack gear mechanism for opening and closing of the railway crossing gate.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 21
Working Drawing
This shows the pitch circle of a standard gear and the pitch line of the rack. One rotation of the spur gear will displace the rack l one circumferential length of the gear's pitch circle, per the formula: l = πmz
This shows a profile shifted spur gear, with positive correction xm, meshed with a rack. The spur gear has a larger pitch radius than standard, by the amount xm. Also, the pitch line of the rack has shifted outward by the amount xm.
[RACK & PINION GEAR DESIGN] May 1, 2010
Machine Design & CAD - II | Power Transmission System Design Project
Page | 22
Conclusion We the whole group involved in it can conclude the whole project as a thought processing one. First of all as an engineering student we wanted to design such a thing that has not been commonly considered before. So for this reason we wanted the railway crossing gate to be opened and closed by some electric motor power. But in order to do that we required a mechanism that could be used in it and it could work efficiently. In search of those parameters regarding the power transmission devices that could work feasible in this manner we found the one mechanism that has been discussed in detail above that is rack and pinion gear which is used to transmit power linear to rotary and vice versa. To make this project much practical we went to railway station to sort out all sorts of elements that are covered in driving the railway gate horizontally out and in. Meanwhile we got know how about the safe design of the gears and examined that steps that are taken in the real design of any machine element. It has been a practical approach designing a railway gate on rack and pinion gear. Moreover It has nice task to carry out and we the whole group learnt a lot of things regarding Machine Design.