http://www.ziddu.com/download/3418863/MachineDesign-Gear.pdf.html
http://www.ziddu.com/download/3418864/SpurGearDesign.pdf.html
http://www.ziddu.com/download/3418865/PrecisionEngineering.pdf.html
http://www.ziddu.com/download/3418866/MaterialAnalysis.pdf.html
http://www.ziddu.com/download/3418867/GearDesign.pdf.html
http://www.ziddu.com/download/3418868/Springs.ppt.html
http://www.ziddu.com/download/3418869/X-RayDiffraction.ppt.html
http://www.ziddu.com/download/3418870/Joining.pdf.html
http://www.ziddu.com/download/3418871/BevelGears.ppt.html
http://www.ziddu.com/download/3418872/MaterialScience.pdf.html
Thursday, February 5, 2009
Wednesday, February 4, 2009
Gear Design
Design - DSGN 215, 221 Gear Design Home Page.
Introduction.
When mating gear teeth are designed to produce a constant angular velocity ratio during meshing they are said to have 'conjugate action'. To provide this an 'involute' type profile is almost universally used for tooth forms.
There are two modes that are important causes of gear failures. Bending stresses (leading to tooth breakage) which are a maximum at the tooth root and compressive stresses (leading to pitting) that are a maximum on the tooth face. Because tooth loading is cyclic, both of these mechanisms are of a fatigue nature. The design of gears needs to counter both of these potential failure modes. An important part of providing the resistance to the high contact stresses is to use gears of appropriate hardness. The lower the levels of impurities in a material, the better it is normally able to resist fatigue.
Link to page showing some gear nomenclature.
Quite a bit of information is available about gears on the following sites:
DR Gears site.
Quality Transmission Components site, go to QTC Technical Library.
Loads on Teeth
The tangential force on the teeth can be found from:
Wt = 60H/(3.14159.d.n) where:
Wt = transmitted load, N
H = power, W
d = gear diameter, m
n = speed, rev/min.
Bending Stresses - The Lewis Formula
Although this was published in 1893, it is still very widely used for assessing bending stresses when designing gears. The method involves moving the tangential force and applying it to the tooth tip and assuming the load is uniformly distributed accross the tooth width with the tooth acting as a simple cantilever of constant rectangular cross section, the beam depth being put equal to the thickness of the tooth root (t) and the beam width being put equal to the tooth, or gear, width (bw).
The section modulus is I/c = bwt2/6 so the bending stress is given by:
sigmabending = M/(I/c) = 6WtL/(bwt2) eqn.1.
Assuming that the maximum bending stress is at point 'a'.
By similar triangles: 
Rearranging eqn.1 gives:
Substitute the value for 'x' from eqn.2 and multiply the numerator and denominator by the circular pitch, 'p' gives:
This is the original Lewis equation and 'y' is called the Lewis form factor which may be determined graphically or by computation.
Engineers often now work with the 'diametral pitch', 'P', 
Then 
Written in terms of the module:
The Lewis form factor considers only static loading, it is dimensionless, independent of tooth size and is a only a function of tooth shape. It does not take into account the stress concentration that exists in the tooth fillet.
The Lewis formula is generally limited to pitch line velocities up to 7.6 m/s and based on tests (in the 19th Century) on cast iron gears with cast teeth, C G Barth suggested a modification involving a velocity factor, KV.
For cut or milled teeth the Barth equation (in SI units) is often modified to:
sigmabending, allowable = Wt/bwmYKV
NB Recent Changes in Barth Equation
In about 2000 the AGMA (see below) re-defined the dynamic factor, KV, as the inverse of that originally proposed by Barth, above. Consequently it is greater than 1 (and called KV' here) and the expression for the allowable bending stress becomes:
sigmabending, allowable = WtKV'/bwmY
For a full depth tooth with a 20o pressure angle, Y varies between 0.245 for a gear with 12 teeth to 0.471 for a gear with 300 teeth. (0.485 for a rack).
It is common for spur gears to be designed with a face width of between 3 and 5 times the circular pitch.
American Gear Manufacturers Association (AGMA) Code
Some key points from the AGMA approach to gear design are shown below.
AGMA have published graphs of allowable bending stresses and allowable surface contact stresses as a function of the Brinell hardness for some grades of through hardened steel.
Grade 2 steels, that have higher allowable stresses, are more closely specified than grade 1 steels.
This is commonly used and contains further refinements compared to the approach above, it also includes detailed guidance about materials.
A number of modifying factors are normally included in the AGMA code:
Ka = application factor - depends on the type of power source
Ks = size factor - increases above 1 for a module, m, of 6 mm or greater.
Km = load distribution factor - depends mainly on face width.
Kv = dynamic factor - depending upon tooth accuracy, loads greater than the transmitted load may be generated.
Contact Stresses
These are determined by Hertzian contact stress analysis. The maximum pressure in the (rectangular) contact zone when two parallel cylinders are pressed together is given by:
w' is the load per unit width = normal load/gear width and
1/Rx = 2((1/pinion dia)+(1/gear dia))/sin(pressure angle)
The same modifying factors are again used with the contact stresses that were used with the bending stresses.
sigmacompressive = pH(Ka Ks Km/Kv)0.5
Link to example gear tooth strength calculation, note file size: 214 kB.
Forces on Helical Gear Teeth
As the teeth on helical gears are inclined to the axis of the gear, the tooth force generates an axial or thrust load in addition to the radial force and the tangential force (which is the only one that does useful work). The tooth load can be resolved in the three directions as shown in this diagram.
The forces and resulting bending moments on the shaft carrying a helical gear are illustrated in this note.
Stresses in helical gear teeth
When calculating the stresses in helical gear teeth, the Lewis form factor for the 'virtual number of teeth' needs to be used rather than that for the actual number of teeth. This is because on looking along a tooth on a helical gear the apparent radius of the gear is greater than that of the gear blank (the cross section is an ellipse). The 'virtual number of teeth' is found by:
Supplementary note on Stresses in Gears
It should be noted that using the simplified version of these methods (including only Kv) on gears in automotive gear boxes gives high stresses, particularly for 1st gear. Gears for car gear boxes are probably manufactured to a high degree of accuracy, to keep noise levels low. The velocity correction factor, Kv, from the Barth equation, is over 100 years old and probably gives a conservative factor compared to that appropriate for modern high quality gears. Using all the AGMA factors - and noting that 'Y' the Lewis form factor is NOT used but the geometry factors J or I, (for bending and compressive stresses) are included, should give a more useful answer.
Note that 1st gear may be designed for a limited life as it so rarely operates under maximum load.
Link to example on helical gear tooth strength calculation, 85kB file size.
Torque Acting on a Gearbox
As the input and output torques associated with a gearbox are normally not the same, some 'holding' torque will be needed to prevent the gearbox rotating. This can be determined as shown in this diagram
Lubrication
During operation the teeth are sliding against one another, so to prevent wear lubrication is normally essential for heavily loaded gears. Even though a gearbox may have an efficiency of 97%, where considerable power is being transmitted, 3% loss as heat generated within the gearbox, may necessitate the provision of some type of forced cooling.
Acceleration of a Geared System
- link to notes.
- example on a geared hoist, 56 kB file size
More detailed information about gears and some helpful animations can be seen in the chapter on 'Gears' at Mechanical Engineering Department pages at the University of Western Australia.
Useful information (albeit in imperial units) can be found on the 'Boston Gear' web site: click here
Further Reading: Shigley and Mischke, chapters 13, 14 and 15.
David J Grieve, 24th November 2005.
Spur Gear Design
The notes below relate to spur gears. Notes specific to helical gears are included on a separate page Helical Gears
Gears are machine elements used to transmit rotary motion between two shafts, normally with a constant ratio. The pinion is the smallest gear and the larger gear is called the gear wheel.. A rack is a rectangular prism with gear teeth machined along one side- it is in effect a gear wheel with an infinite pitch circle diameter. In practice the action of gears in transmitting motion is a cam action each pair of mating teeth acting as cams. Gear design has evolved to such a level that throughout the motion of each contacting pair of teeth the velocity ratio of the gears is maintained fixed and the velocity ratio is still fixed as each subsequent pair of teeth come into contact. When the teeth action is such that the driving tooth moving at constant angular velocity produces a proportional constant velocity of the driven tooth the action is termed a conjugate action. The teeth shape universally selected for the gear teeth is the involute profile.
Consider one end of a piece of string is fastened to the OD of one cylinder and the other end of the string is fastened to the OD of another cylinder parallel to the first and both cylinders are rotated in the opposite directions to tension the string(see figure below). The point on the string midway between the cylinder P is marked. As the left hand cylinder rotates CCW the point moves towards this cylinder as it wraps on . The point moves away from the right hand cylinder as the string unwraps. The point traces the involute form of the gear teeth.
The lines normal to the point of contact of the gears always intersects the centre line joining the gear centres at one point called the pitch point. For each gear the circle passing through the pitch point is called the pitch circle. The gear ratio is proportional to the diameters of the two pitch circles. For metric gears (as adopted by most of the worlds nations) the gear proportions are based on the module.
m = (Pitch Circle Diameter(mm)) / (Number of teeth on gear).
In the USA the module is not used and instead the Diametric Pitch d pis used
d p = (Number of Teeth) / Diametrical Pitch (inches)
Profile of a standard 1mm module gear teeth for a gear with Infinite radius (Rack ).
Other module teeth profiles are directly proportion . e.g. 2mm module teeth are 2 x this profile
Many gears trains are very low power applications with an object of transmitting motion with minium torque e.g. watch and clock mechanisms, instruments, toys, music boxes etc. These applications do not require detailed strength calculations.
Standards
|
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
Terminology - spur gears
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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 |
Materials used for gears
Mild steel is a poor material for gears as 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 machinability | low cost commercial quality gears. Quality up to medium precision |
| 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 |
Equations for basic gear relationships
It is acceptable to marginally modify these relationships e.g to modify the addendum /dedendum to allow Centre Distance adjustments. Any changes modifications will affect the gear performance in good and bad ways...
| Addendum | h a = m = 0.3183 p |
| Base Circle diameter | Db = d.cos α |
| Centre distance | a = ( d g + d p) / 2 |
| Circular pitch | p = m.π |
| Circular tooth thickness | ctt = p/2 |
| Dedendum | h f = h - a = 1,25m = 0,3979 p |
| Module | m = d /n |
| Number of teeth | z = d / m |
| Outside diameter | D o = (z + 2) x m |
| Pitch circle diameter | d = n . m ... (d g = gear & d p = pinion ) |
| Whole depth(min) | h = 2.25 . m |
| Top land width(min) | t o = 0,25 . m |
Module (m)
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
0,5 0,8 1 1,25 1,5 2,5 3 4 5 6 8 10 12 16 20 25 32 40 50
Normal Pressure angle α
An important variable affecting the geometry of the gear teeth is the normal pressure angle. This is generally standardised at 20o. Other pressure angles should be used only for special reasons and using considered judgment. The following changes result from increasing the pressure angle
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Contact Ratio
The gear design is such that when in mesh the rotating gears have more than one gear in contact and transferring the torque for some of the time. This property is called the contact ratio. This is a ratio of the length of the line-of-action to the base pitch. The higher the contact ratio the more the load is shared between teeth. It is good practice to maintain a contact ratio of 1.2 or greater. Under no circumstances should the ratio drop below 1.1.
A contact ratio between 1 and 2 means that part of the time two pairs of teeth are in contact and during the remaining time one pair is in contact. A ratio between 2 and 3 means 2 or 3 pairs of teeth are always in contact. Such as high contact ratio generally is not obtained with external spur gears, but can be developed in the meshing of an internal and external spur gear pair or specially designed non-standard external spur gears.
(Rgo2 - Rgb2 )1/2 + (Rpo2 - Rpb2 )1/2 - a sin α
contact ratio m =
p cos α R go = D go / 2..Radius of Outside Dia of Gear
R gb = D gb / 2..Radius of Base Dia of Gear
R po = D po / 2..Radius of Outside Dia of Pinion
R pb = D pb / 2..Radius of Base Dia of Pinion
p = circular pitch.
a = ( d g+ d p )/2 = center distance.
Spur gear Forces, torques, velocities & Powers
|
| Tangential force on gears F t = F cos α |
| Separating force on gears F s = F t tan α |
| Torque on driver gear T 1 = F t d 1 / 2 |
| Torque on driver gear T 2 = F t d 2 / 2 |
| Speed Ratio =ω 1 / ω 2 = d 2 / d 1 = z 2 /z 1 |
| Input Power P 1 = T1 .ω 1 |
| Output Power P 2 =η.T 1 .ω 2 |
Spur gear Strength and durability calculations
Designing spur gears is normally done in accordance with standards the two most popular series are listed under standards above:
The notes below relate to approximate methods for estimating gear strengths. The methods are really only useful for first approximations and/or selection of stock gears (ref links below). — Detailed design of spur and helical gears is best completed using the standards. Books are available providing the necessary guidance. Software is also available making the process very easy. A very reasonably priced and easy to use package is included in the links below (Mitcalc.com)
The determination of the capacity of gears to transfer the required torque for the desired operating life is completed by determining the strength of the gear teeth in bending and also the durability i.e of the teeth ( resistance to wearing/bearing/scuffing loads ) .. The equations below are based on methods used by Buckingham..
Bending
The basic bending stress for gear teeth is obtained by using the Lewis formula
σ = Ft / ( ba. m. Y )
- F t = Tangential force on tooth
- σ = Tooth Bending stress (MPa)
- b a = Face width (mm)
- Y = Lewis Form Factor
- m = Module (mm)
σ = Ft / ( ba. p. y )
Where y = Y/π and p = circular pitch
When a gear wheel is rotating the gear teeth come into contact with some degree of impact. To allow for this a velocity factor is introduced into the equation. This is given by the Barth equation for milled profile gears.
K v = 6,1 / (6,1 +V )
V = the pitch line velocity = d.ω/2
Note: This factor is different for different gear conditions i.e K v = ( 3.05 + V )/3.05 for cast iron, cast profile gears.
The Lewis formula is thus modified as follows
σ = K v.Ft / ( ba. m. Y )
Surface Durability
| This calculation involves determining the contact stress between the gear teeth and uses the Herz Formula σ w = 2.F / ( π .b .l ) σ w = largest surface pressureF = force pressing the two cylinders (gears) together l = length of the cylinders (gear) b = halfwidth = ν 1, ν 2 Poisson ratio for the two gear materials E 1 ,E 2 Are the Young's Modulus Values for the two gears To arrive at the formula used for gear calculations the following changes are made F is replaced by F t/ cos α d is replaced by 2.r l is replaced by W The velocity factor K v as described above is introduced. Also an elastic constant Z E is created
Note: Values for Allowable stress values Se and ZE for some materials are provided at Gear Table r1 = d1 sin α /2 r2 = d2 sin α /2 Important Note: The above equations do not take into account the various factors which are integral to calculations completed using the relevant standards. These equations therefore yield results suitable for first estimate design purposes only... |
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
Internal Gears
Advantages:
- Geometry ideal for epicyclic gear design
- Allows compact design since the center distance is less than for external gears.
- A high contact ratio is possible.
- Good surface endurance due to a convex profile surface working against a concave surface.
- Housing and bearing supports are more complicated, because the external gear nests within the internal gear.
- Low ratios are unsuitable and in many cases impossible because of interferences.
- Fabrication is limited to the shaper generating process, and usually special tooling is required.
Lewis form factor.
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 | | 0,176 | 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 | | 0,289 | 0,092 | 0,326 | 0,104 | 0,399 | 0,127 | 0,377 | 0,12 | 0,49 | 0,156 | 0,553 | 0,176 |
| 22 | | 0,292 | 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 |
| 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 |
Gear
Gear Design
Gears have been around for hundreds of years and are as old as almost any machinery ever invented by mankind. Gears were first used in various construction jobs, water raising devices and for weapons like catapults.
Nowadays gears are used on a daily basis and can be found in most people’s everyday life from clocks to cars rolling mills to marine engines. Gears are the most common means of transmitting power in mechanical engineering.
Gears are used in almost all mechanical devices and they do several important jobs, but most important, they provide a gear reduction. This is vital to ensure that even though there is enough power there is also enough torque(is a movement of force).
This site is a valuable resource about gear and gear design.
Bevel Gears
Bevel gears are useful when the direction of a shaft's rotation needs to be changed. They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well.
A good working example of a bevel gear is the mechanism used in a hand drill. As you turn the handle of the drill in a vertical direction, the bevel gears change the rotation of the chuck to a horizontal rotation. The bevel gear also works to increase the speed of the chuck so that its possible for the drill to work on a range of surfaces.
There are four types of bevel gears:
Straight Bevel Gears: These gears have a conical pitch surface and straight teeth tapering towards an apex.
Zero Bevel Gears: Are very similar to straight bevel gears except the teeth are curved.
Spiral Bevel Gears: The teeth are curved at an angle which then allows the contact to be gradual and smooth.
Hypoid Bevel Gears: These gears are similar to spiral bevel except that the pitch surfaces are hyperboloids
Helical Gears
Helical gears are so called because the angle of the teeth are inclined to the axis of the shafts in the form of a helix.
Helical gears are generally seen and described as high speed gears as they can take higher loads than equally sized spur gears. Also with a helical gear the two teeth start to engage and gradually increase as the gears rotate this gradual movement makes helical gears operate much more smoothly and quietly that spur gears. Its because of this design that helical gears are used in the majority of car transmissions.
Rack & Pinion Gears
Rack and pinion gears are used to convert rotation into linear motion or linear motion into rotation. The rack is the flat toothed part and the pinion is the gear. The diameter of the gear determines the speed that the rack moves as the pinion turns.
A perfect example of a rack and pinion gear system is the steering system on many cars. The driver turns the steering wheel which rotates the gear which then engages the rack so as the gear turns it slides the rack to the right or the left depending on which way the steering wheel is turned.
Spur Gears
Spur gears are the most common type of gear they have straight teeth and are mounted on parallel shafts. The main reason for the popularity of spur gears is their simplicity in design, easy manufacturer and maintenance. However due to their design spur gears create large stress on the gear teeth.
Spur gears are known as slow speed gears. Spur gears are seen as noisy due to their design so if noise is not a problem spur gears can be used at almost any speed. Spur gears are noisy because every time a gear tooth engages a tooth on the other gear, the teeth collide, and this impact makes a noise.
Spur gears can be found in applications like washing machines and electric screwdrivers but due to the noise you will never find them in your car.
Worm Gears
A worm gear is used when there is a requirement to reduce speed. It’s very common to see worm gears with reductions like 20:1 and as high as 300:1 or even greater depending on the situation.
A worm gear consists of a cylinder with a spiral groove mounted on a shaft, this is generally referred to as the worm shaft and a gear which is normally referred to as the worm wheel. The gear then meshes with the spiral groove on the cylinder and so when the cylinder rotates it causes the gear to rotate as well. So for each complete turn of the worm shaft the gear shaft advances only one tooth of the gear. So a gear with 20 teeth will see the speed reduced by a factor of 20:1.
The worm always drives the worm wheel around it is not reversible so the worm wheel can’t drive the worm to increase the speed. If it’s attempted the system will normally jam or lock.
Gear Manufacture
The materials that are used for gear manufacturing depend massively on the conditions that the gears will be operating under, conditions like wear and noise etc. Gear manufacturers use metallic or non-metallic materials.
The Metallic materials used in gear manufacture are normally available in cast iron, steel and bronze. Steel is used when there is a need for a high strength design. But cast iron is mainly used because of its good wearing properties, excellent machineability and the ease that complicated shapes can be created due to the casting method.Castings are created by pouring molten metal into a mould and once the metal as cooled it takes the shape of the mould.
The non metallic, materials used are generally wood, rawhide, compressed paper and synthetic resins like nylon. These types of materials are generally used when there is a need for the reduction in noise from the gears.
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