INTRODUCTION TO THE GEARS, NEED FOR GEAR BOX ANDRESISTANCE TO VEHICLE MOTION
Gear Trains A gear train is two or more gear working together by meshing their teeth and turning each other in a system to generate power and speed. It reduces speed and increases torque. To create large gear ratio, gears are connected together to form gear trains. They often consist of multiple gears in the train. The most common of the gear train is the gear pair connecting parallel shafts. The teeth of this type can be spur, helical or herringbone. The angular velocity is simply the reverse of the tooth ratio. 2
Gear TrainsAny combination of gearwheels employed to transmitmotion from one shaft to theother is called a gear train.The meshing of two gearsmay be idealized as twosmooth discs with theiredges touching and no slipbetween them. This idealdiameter is called the PitchCircle Diameter (PCD) ofthe gear. 3
Simple Gear Trains 4
Simple Gear TrainsThe typical spur vgears as shown in vdiagram. Thedirection of rotation ωA ωBis reversed from one ωCgear to another. The only function ofthe idler gear is tochange the direction GEAR A GEAR B GEAR Cof rotation. (Idler gear) 5
vIt has no affect on vthe gear ratio. Theteeth on the gears ωA ωB ωCmust all be thesame size so ifgear A advancesone tooth, so doesB and C. GEAR A GEAR B GEAR C (Idler gear) 6
t = number of teeth on the gear,D = Pitch circle diameter, N = speed in rpm Dm = module = tandmodule must be the same for allgears otherwise they would not mesh. 7
DA DB DCm= = = tA tB tCDA = m t A; DB = m t B and DC = m t Cω = angular velocity. Dv = linear velocity on the circle. v = ω = ω r 2The velocity v of any point on the circle must be thesame for all the gears, otherwise they would be slipping. 8
DA DB DCv = ωA = ωB = ωC 2 2 2 ω A DA = ω B DB = ωC DC ω A m t A = ω B m t B = ωC m t C ω A t A = ω B t B = ωC t Cor in terms of rev / min N A t A = N B t B = N C tC 9
DA DB DCv = ωA = ωB = ωC 2 2 2 ω A DA = ω B DB = ωC DC ω A m t A = ω B m t B = ωC m t C ω A t A = ω B t B = ωC t Cor in terms of rev / min N A t A = N B t B = N C tC 10
Input speedThe gear ratio is defined as GR = Output speedIf gear A is the input and gear C is the output; N A tCGR = = also called as Speed ratio/Speed value NC t A N C Speed of driven gearIf = is called the Train value N A Speed of driver gear 11
Simple Gear Trains Application: a) to connect gears where a large center distance is required b) to obtain desired direction of motion of the driven gear ( CW or CCW) c) to obtain high speed ratio 12
Compound Gear train INPUT B F D E A OUTPUT C GEAR B Compound Gears GEAR A GEAR D GEAR C GEAR F GEAR E 13
Compound gears are Inputsimply a chain of simplegear trains with the input B Dof the second being theoutput of the first. A chain A Outputof two pairs is shown Cbelow. Gear B is the output Compound Gearsof the first pair and gear C GEAR Bis the input of the secondpair. Gears B and C are GEAR A GEAR Dlocked to the same shaftand revolve at the same GEAR Cspeed. 14
For large velocitiesratios, compound gear Inputtrain arrangement ispreferred. B DThe velocity of each tooth A Outputon A and B are the same so: C Compound Gears GEAR BωA tA = ωB tB-as they are simple gears. GEAR A GEAR DLikewise for C and D, GEAR CωC tC = ωD tD. 15
ω A ωB ωC ω D = and =tB tA tD tC tB × ωB tD × ωDωA = and ωC = tA TC tB × ωB tD × ωDω A × ωC = × tA tCω A × ωC t B t D = ×ω B × ω D t A tC 16
Compound Gear train Since gear B and C are on the same shaft Input ω B = ωC ω A tB tD B D = × = GR ω D t A tC A Output Since ω = 2 × π × N C Compound Gears The gear ratio may be GEAR B written as : N ( In ) t B t D GEAR A GEAR D = × = GR N ( Out ) t A tC GEAR C 17
The driver and driven axeslies on the same line. These Bare used in speed reducers,clocks and machine tools. A C N A tB × tD INPUT GR = = Compound Gears GEAR A N D t A × tC GEAR BIf R and T=Pitch circle radius GEAR D GEAR C& number of teeth of the gear RA + RB = RC + RD OUTPUTand tA + tB = tC + tD 19
Epicyclic Gear train Epicyclic means one gear revolving upon and around another. The design involves planet and sun gears as one orbits the other like a planet around the sun. Here is a picture of a typical gear box. This design can produce large gear ratios in a small space and are used on a wide range of applications from marine gearboxes to electric screw drivers. 20
A small gear atthe centercalled the sun,several mediumsized gearscalled theplanets and alarge externalgear called thering gear. 21
It is the system of epicyclic gears in which at leastone wheel axis itself revolves around anotherfixed axis. 22
Planet wheelBasic Theory B BThe diagram showsa gear B on the end Armof an arm. Gear B Arm Ameshes with gear Cand revolvesaround it when the Carm is rotated. B is Ccalled the planet Sun wheelgear and C the sun. 23
Suppose the arm isheld stationary andgear C is rotated once. Planet wheelB spins about its own B Bcenter and the number Armof revolutions it makes Arm Ais the ratio: tC tB CB will rotate by this Cnumber for every Sun wheelcomplete revolution ofC. 24
Now consider the sun gear Cis restricted to rotate and thearm A is revolved once. Gear Planet wheelB will revolve B Bbecause of the orbit. It is thisextra rotation that causes Armconfusion. One way to get Arm Around this is to imagine thatthe whole system is revolvedonce. C C tC Sun wheel 1+ tB 25
Planet wheelThen identify the gear B Bthat is fixed andrevolve it back one Arm Arm Arevolution. Work outthe revolutions of theother gears and addthem up. The following Ctabular method makesit easy. C Sun wheel 26
Automotive Gears: Gears play an important role in trucks,car, buses, motor bikes and even geared cycles. These gearscontrol speed and include gears like ring and pinion, spiralgear, hypoid gear, hydraulic gears, reduction gearbox. 37
Depending on the size ofthe vehicles, the size of thegears also varies. There arelow gears covering ashorter distance and areuseful when speed is low.There are high gears alsowith larger number ofteeth. 38
Conveyor Systems:Conveyor is a mechanicalapparatus for carrying bulkmaterial from place to placeat a controlled rate; forexample an endless movingbelt or a chain ofreceptacles. There arevarious types of conveyorsthat are used for differentmaterial handling needs.
Agro Industry: All agro machinery consists of differenttypes of gears depending upon their function andproperty. Different gears are used differently in theindustry.Wind Turbine: When the rotor rotates, the load on themain shaft is very heavy. It runs with approximate 22revolutions per minute but generator has to go a lot faster.It cannot use the turning force to increase the number ofrevolutions and that is why wind turbine uses gear toincrease the speed.
Power Station:Helical gears - Are used tominimize noise and power losses.Bevel gears - Used to change theaxis of rotational motion.Spur gears - Passes power fromidler gears to the wheels.Planetary gears - Used betweeninternal combustion engine and anelectric motor to transmit power.
Marine Gears: Marine gears meet awide variety of marine applicationsin a variety of configurations andinstallations to meet the mostcritical applications.Specific marine applicationsinclude main propulsion,centrifuges, deck machinery suchas winches, windlasses, cranes,turning gears, pumps, elevators,and rudder carriers.
Mining Gears: Mining is a processof extracting ores or minerals fromthe earths surface. The gears areused for increasing the torqueapplied on the tool used for mining.They are used for commercial goldproduction, and coal mining.
Differential Gear Box
Throttle pedal , simply regulates the rate at whichthe engine is doing workAt high speeds power output is high but torqueis lowMaximum torque may be available over only avery limited speed range
One need to control power output and speedrange of the engine relative to range of speed overwhich the vehicle is at any time likely to berequired to operateA gear box is necessary , therefore , so that thedriver can regulate torque by selecting theappropriate speed range or in other words , thevehicle speed at which the maximum torque isobtainable.
1. Resistance a. Aerodynamic b. Rolling c. Grade
Main ConceptsResistanceTractive effortVehicle accelerationBrakingStopping distance F = ma + Ra + Rrl + Rg
Resistance is defined as the force impeding vehicle motion 1. What is this force? 2. Aerodynamic resistance 3. Rolling resistance 4. Grade resistance F = ma + Ra + Rrl + Rg
Aerodynamic Resistance RaComposed of: 1. Turbulent air flow around vehicle body (85%) 2. Friction of air over vehicle body (12%) 3. Vehicle component resistance, from radiators and air vents (3%) ρ Ra = C D A f V 2 2 ρ PRa = C D A f V 3 2 ft ⋅ lb 1 hp = 550 from National Research Council Canada sec
Rolling Resistance Rrl Composed primarily of 1. Resistance from tire deformation (∼90%) 2. Tire penetration and surface compression (∼ 4%) 3. Tire slippage and air circulation around wheel (∼ 6%) 4. Wide range of factors affect total rolling resistance 5. Simplifying approximation: Rrl = f rlW V PR rl = f rlWV f rl = 0.011 + ft ⋅ lb 147 1 hp = 550 sec
Grade Resistance RgComposed of Gravitational force acting on the vehicle Rg = W sin θ g θg For small angles, sin θ g ≈ tan θ g Rg = W tan θ g Rg tan θ g = G θg W Rg = WG
Available Tractive Effort The minimum of: 1. Force generated by the engine, Fe 2. Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, Fmax Available tractive effort = min ( Fe , Fmax )