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Planetary Gear Train …• In this train, the blue gear has six times the diameter of the yellow gear • The size of the red gear is not important because it is just there to reverse the di

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10

30

: Hệ số hình dạng bề mặt tiếp xúc

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70

80

location where it is applied to performing useful work

to another gear or device

c Non-intersecting and Non-parallel

worm and worm gears

SPUR GEAR

parallel shaft

sprinkler, windup alarm clock, washing

machine and clothes dryer

External and Internal spur Gear…

Helical Gear

quietly than spur gears

correct, they can be mounted on perpendicular shafts, adjusting the rotation

angle by 90 degrees

Helical Gear…

Herringbone gears

• To avoid axial thrust, two helical gears of

opposite hand can be mounted side by side, to

cancel resulting thrust forces

• Herringbone gears are mostly used on heavy

machinery

Rack and pinion

• Rack and pinion gears are used to convert

rotation (From the pinion) into linear

motion (of the rack)

system on many cars

Bevel gears

• They are usually mounted on shafts that are 90 degrees apart, but can be designed to work

at other angles as well

• The teeth on bevel gears can be straight, spiral or hypoid

• locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines, etc.

Straight and Spiral Bevel Gears

WORM AND WORM GEAR

to have reductions of 20:1, and even up to 300:1 or greater

• Many worm gears have an interesting property that no other gear set has: the worm can easily turn the gear, but the gear cannot turn the worm

• Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc

WORM AND WORM GEAR

NOMENCLATURE OF SPUR GEARS

• Pitch surface: The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be

considered to replace

• Pitch circle: A right section of the pitch surface

• Addendum circle: A circle bounding the ends of the teeth, in a right section of the gear

• Root (or dedendum) circle: The circle bounding the spaces between the teeth, in a right section of the gear

• Addendum: The radial distance between the pitch circle and the addendum circle

• Dedendum: The radial distance between the pitch circle and the root circle

• Clearance: The difference between the dedendum of one gear and the addendum of the mating gear

• Face of a tooth: That part of the tooth surface lying outside the pitch surface

• Flank of a tooth: The part of the tooth surface lying inside the pitch surface

• Circular thickness (also called the tooth thickness): The thickness of the tooth measured on the pitch

circle It is the length of an arc and not the length of a straight line

• Tooth space: pitch diameter The distance between adjacent teeth measured on the pitch circle

• Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear

• Circular pitch (Pc) : The width of a tooth and a space, measured on the pitch circle

N

D P

c

π

• Diametral pitch (Pd): The number of teeth of a gear unit pitch diameter The diametral pitch is, by

definition, the number of teeth divided by the pitch diameter That is,

Where

Pd = diametral pitch

N = number of teeth

D = pitch diameter

• Module (m): Pitch diameter divided by number of teeth The pitch diameter is usually specified in inches or

millimeters; in the former case the module is the inverse of diametral pitch.

m = D/N

D N

VELOCITY RATIO OF GEAR DRIVE

d = Diameter of the wheel

N =Speed of the wheel

ω = Angular speed

velocity ratio (n) =

2

1 1

2 1

2

d

d N

N

=

=

ω ω

GEAR TRAINS

turning each other in a system to generate power and speed

the torque

Types of Gear Trains

• Simple gear train

• Compound gear train

• Planetary gear train

Simple Gear 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

• Only one gear may rotate about a single axis

Simple Gear Train

Compound Gear Train

• For large velocities, compound

arrangement is preferred

• Two or more gears may rotate about

a single axis

Planetary Gear Train (Epicyclic Gear Train)

Planetary Gear Train …

• In this train, the blue gear has six times the diameter of the yellow gear

• The size of the red gear is not important because it is just there to reverse the direction of rotation

• In this gear system, the yellow gear (the sun) engages all three red gears (the planets) simultaneously

• All three are attached to a plate (the planet carrier), and they engage the inside of the blue gear (the ring) instead of the outside

Planetary Gear Train…

rugged

which gear you use as the input, which gear you use as the output, and which one you hold still

Planetary Gear Train…

manually

electric motor

Short Quetions

• Why gear drives are called positively driven?

• What is backlash in gears?

• What are the types of gears available?

• What is gear train? Why gear trains are used?

• Why intermediate gear in simple gear train is called idler?

• What is the advantage of using helical gear over spur gear?

• List out the applications of gears

• Define the term ‘module’ in gear tooth

• What is herringbone gear?

Essay type questions

Gears and Transmissions

Why Is a Transmission Necessary?

moving (torque converter & clutch)

What Does a Transmission Do?

– Ability to alter shaft RPM

– Ability to multiply torque

– Ability to reverse the direction of shaft rotation

How Does the Transmission Produce Torque Multiplication

through the transmission as well as the direction of rotation

Types of Gears

• Spur

– Simplest gear design

– Straight cut teeth

• Helical

– Spiral cut teeth

– At least two teeth are in mesh at any time

• Distributes the tooth load

• Quieter operation

• Planetary

– Used in almost all automatic transmissions

– Contains three parts

• Sun gear

• Planet gears

• Internal gear (ring gear)

Power Vs Torque

– Power is dependent on torque and RPM

Gear Ratios

• When two gears are in mesh, a gear ratio exists

• Driven Gear = Ratio

• Example:

– Drive gear has 14 teeth

– Driven gear has 28 teeth

– 28 ÷ 14 = 2:1 ratio (two to one ratio)

– The drive gear must rotate twice to make the driven gear rotate once Drive Gear

How Stuff Works

Reversal of Direction

Speed Change

proportional to the gear ratio

– Input gear turns at 900 RPM

– Output gear turns at 300 RPM

Torque Multiplication

proportional to the gear ratio

– Engine turns input gear at 900 RPM with 50 lb/ft of force

– Output gear turns driveshaft at 300 RPM with 150 lb/ft of force

Torque Multiplication

1 inch 3 inches

Multiple Gear Ratios

– Example: Chevy caprice with a TH-350 transmission and a 305 engine

• By removing the differential cover and inspecting the gearset you are able to count 10 teeth on the input gear and 41 teeth on the output gear

• 41 ÷ 10 = 4.1:1

• You are able to find the 1st gear ratio of the TH-350 in a manual which is listed as 2.52:1

Multiple Gear Ratios

• Rear end ratio x 1st gear ratio = total gear ratio

• 4.1 x 2.52 = 10.33:1

– This tells us that the engine turns 10.33 revolutions for every 1 revolution of the tires (speed

reduction)

• Torque multiplication can also be calculated

– The 305 engine produces 245 lb/ft of torque at 3200 RPM

– @ 3200 RPM in 1st gear the torque acting on the rear tires = 230 lb/ft x 10.33 = 2375.9 lb/ft torque !!!

Gear Engine Output

Torque

Engine Speed Gear Ratio Transmission Output

Torque

Transmission Output Speed

Automatic Transmission I.D.

– Look at the shift indicator to determine if the transmission is a 3-speed, 4-speed etc.

Automatic Transmission I.D.

1 Aluminum Powerglide 14 bolts

Planetary Gearsets

• Simple planetary gearsets contain three components

– Internal (ring) gear / (annulus gear)

– Planet gears (and carrier)

Planetary Action

– Any two of the components are driven

– 1:1 Ratio

Sun Carrier Internal Speed Torque Direction

Reduction

Maximum Increase Same as Input

Reduction

Minimum Increase Same as Input

Calculating Planetary Gear Ratios

– Carrier is output

# of sun gear teeth + #of ring gear teeth

# of teeth on the driving member

= Ratio

Calculating Planetary Gear Ratios

– Carrier is input

# of teeth on the driven member .

# of sun gear teeth + #of ring gear teeth

= Ratio

Calculating Planetary Gear Ratios

Ken Youssefi Mechanical Engineering Dept 139

Gears

Ken Youssefi Mechanical Engineering Dept 140

Applications of Gears

• Control gears– long life, low noise, precision gears

kinematic & stress analysis

• Aerospace gears– light weight, moderate to high load

kinematic & stress analysis

• Power transmission– long life, high load and speed

kinematic & stress analysis

• Appliance gears– long life, low noise & cost, low to moderate load

kinematic & some stress analysis

• Toys and Small Mechanisms– small, low load, low cost

kinematic analysis

Ken Youssefi Mechanical Engineering Dept 141

Types of Gears

Spur gears– tooth profile is parallel to the axis of rotation, transmits

motion between parallel shafts.

Pinion (small gear)

Gear (large gear)

Internal gears

– teeth are inclined to the axis of rotation, the angle

provides more gradual engagement of the teeth during meshing,

transmits motion between parallel shafts.

Helical gears

Ken Youssefi Mechanical Engineering Dept 142

Types of Gears

Bevel gears– teeth are formed on a conical surface, used to transfer

motion between non-parallel and intersecting shafts

Straight bevel gear

Spiral bevel gear

Ken Youssefi Mechanical Engineering Dept 143

Types of Gears

Worm gear sets– consists of a helical gear and a power screw

(worm), used to transfer motion between parallel and

non-intersecting shafts.

Rack and Pinion sets– a special case of spur gears with the gear

having an infinitely large diameter, the teeth are laid flat.

Rack Pinion

Ken Youssefi Mechanical Engineering Dept 144

Gear Design and Analysis

• Force analysis

• Design based on tooth surface strength.

Ken Youssefi Mechanical Engineering Dept 145

Nomenclature of Spur Gear Teeth

= (tooth spacing)driven gear – (tooth thickness)driver , measured on the pitch circle.

Backlash

Pitch circle gear diam.

Fillet radius Clearance

Base Circle

Ken Youssefi Mechanical Engineering Dept 146

Fundamental Law and Involute Curve

Generation of the involute curve

Tangent at the point of

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Ken Youssefi Mechanical Engineering Dept 148

Standard Tooth Specifications

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Standard Tooth Specifications

Power transmission, 2 ≤ P ≤ 16

Ken Youssefi Mechanical Engineering Dept 150

Rack and pinion

Velocity of the rack

Displacement of the rack

Δθ is in radians

,

Ken Youssefi Mechanical Engineering Dept 151

Kinematics

Worm Gear Sets

Ng = number of teeth on the helical gear

Nw = number of threads on the worm, usually between 2-6

Speed ratio = Ng / Nw

Large reduction in one step, but lower efficiency due heat generation.

Worm Helical gear

Ken Youssefi Mechanical Engineering Dept 152

Kinematics of Gear Trains

Conventional gear trains

Reverted gear train – output shaft is concentric with the input shaft Center

distances of the stages must be equal.

Ken Youssefi Mechanical Engineering Dept 153

Kinematics of Gear Trains

Planetary gear trains

ωgear = ωarm + ωgear/arm

ωF/arm = ωF - ωarm , ωL/arm = ωL - ωarm

= e (train value)

Ken Youssefi Mechanical Engineering Dept 154

Kinematics of Gear Trains

Determine the speed of the sun gear if the arm rotates at 1 rpm Ring gear is stationary.

2 degrees of freedom, two inputs are needed to control the system

Ken Youssefi Mechanical Engineering Dept 155

Planetary Gear Trains - Example

For the speed reducer shown, the input shaft a is in line with output

shaft b The tooth numbers are N2=24, N3=18, N5=22, and N6=64 Find

the ratio of the output speed to the input speed Will both shafts rotate

in the same direction? Gear 6 is a fixed internal gear.

Ken Youssefi Mechanical Engineering Dept 156

The Flexspline is a thin-walled steel cup with gear teeth on the outer surface near the open end of the cup Flexspline is

usually the output.

Circular Spline

Rigid internal circular gear, meshes with the external teeth on the Flexspline.

Ken Youssefi Mechanical Engineering Dept 157

Harmonic Drive

Teeth on the Flexspline and circular spline

simultaneously mesh at two locations

which are 180o apart.

As the wave generator travels 180o, the flexspline shifts one tooth

with respect to circular spline in the opposite direction.

ω Circular Spline = 0

ω Flexspline= output

ωWave Generator= input

The flexspline has two less teeth than the circular spline.

Gear Ratio = - ( Nflex spline)/ 2

PACE Collaborative Project: Emerging Market Vehicle

Transmission Design

Team member:

Anthony Smith Kevin Scot Decorian Harris Jacque Thornton Advisor: Dr Xiaobo Peng Department of Mechanical Engineering Prairie View A&M University, Prairie View, Texas

Goals and Objectives

• High fatigue safety factor

• Ability to handle high torque and horsepower

GOAL: To develop an efficient transmission/gearbox design to suit the needs of the emerging market

vehicle.

Project Management: Gant Chart

Gear Train: Calculation Equations

Minimum Number of Teeth

Gear Design & FEA Analysis

Shaft Design

Reverse shaft

Input shaft

Output shaft

Botom housing Upper housing

Other Major Components

Synchronizer

Reverse engager shaft

Other Major Components

Bearing gasket

Engager shaft Bearing

Transmission Assembly

Results

Conclusion & Recommendations

Epicyclic Gears 175

Epicyclic Gearset

An epicyclic gear set has some gear or gears whose center

revolves about some point.

Here is a gearset with a stationary ring gear and three planet gears

on a rotating carrier.

The input is at the Sun, and the output is at the planet carrier

The action is epicyclic, because the centers of the planet gears

revolve about the sun gear while the planet gears turn.

Finding the gear ratio is somewhat complicated because the planet

gears revolve while they rotate.

INPUT

CARRIER

Ring Planet

Sun

Epicyclic Gears 176

Epicyclic Gearset

Let’s rearrange things to make it simpler:

1) Redraw the planet carrier to show arms rotating about the center.

2) Remove two of the arms to show only one of the planet arms.

INPUT

OUTPUT

INPUT OUTPUT

Epicyclic Gears 177

INPUT OUTPUT

The Tabular (Superposition) Method

To account for the combined rotation and revolution of the planet gear,

we use a two step process.

First, we lock the whole assembly and rotate it one turn

Counter-Clockwise (Even the Ring, which we know is fixed)

We enter this motion into a table using the convention:

Sun Planet Ring Arm Rotate Whole

Assembly CCW +1 +1 +1 +1

Epicyclic Gears 178

The Tabular (Superposition) Method

Next, we hold the arm fixed, and rotate whichever gear is fixed during

operation one turn clockwise

Here, we will turn the Ring clockwise one turn (-1), holding the arm fixed.

• The Planet will turn NRing / NPlanet turns clockwise.

• Since the Planet drives the Sun, the Sun will turn (NRing / NPlanet) x

(-NPlanet / NSun) = - NRing / NSun turns (counter-clockwise).

• The arm doesn’t move.

We enter these motions into the second row of the table.

Sun Planet Ring Arm Rotate Whole

Hold Arm, Rotate

Ring CW NRing / NSun - NRing / NPlanet -1 0