G E A R S

What is a gear? Toothed wheel Transmits rotary motion and power

What do they do? Change the direction of motion Change the output speed

Most common gear? SPUR gear

SIMPLE GEAR TRAINS

What is a simple gear train?

Meshed (interlocking gears) Two or more gears in series

Input gear = DRIVER Output gear = DRIVEN

What effect does this have on the output (DRIVEN)

Reverses motion Changes speed/ power

Movement- multiplier Ratios (Gear Ratio)

What is this?

Ratio of the movement between the gears Divide number of teeth on DRIVEN by the number on the

DRIVER

Practice!

A simple gear train is shown. The driver gear A has 20 teeth, while gear B has 40 teeth.

What is the movement multiplier ratio of the system?

If shaft A rotates anti-clockwise, in which direction does shaft B rotate?

Solutions

Driver = 20 teethDriven = 40 teeth

M.R. = Driven / Driver = 40/20 = 2

Gear movement ratio is 2 : 1

A rotates anti- clockwise B rotates clockwise

Speed Ratio

What is this?

Ratio of the speed between the input and output gears

Divide number of teeth on DRIVER by the number on the DRIVEN

Practice!

A simple gear train is shown. The driver gear A has 20 teeth, while gear B has 40 teeth.

Calculate the Speed Ratio

Solutions

Driver = 20 teethDriven = 40 teeth

S.R. = Driver / Driven = 20/40 = 1/2

Gear speed ratio is 1 : 2

Calculating Output Speed

We know from previous work that the SR for the gear train shown is:

Driver = 20 teethDriven = 40 teeth S.R. = Driver / Driven

= 20/40 = 1/2

If the driver has a speed of 200rpm, what is the driven speed?

Output speed = SR x input speed

= ½ x 200 = 100rpm

Idler Gears

What is an IDLER gear?

A third gear inserted between Driver and Driven Allows Driver and Driven to rotate in same direction No effect on Speed or Gear Ratio of the system Usually a small gear (takes up less space)

More Gears!! Calculate the multiplier ratio for the simple gear train below and then

find the speed ratio. If gear A rotates at 250 rpm in a clockwise direction, calculate the output speed. Show all your working.

A = 20 teethB = 5 teethC = 30 teeth

For the simple gear train shown below, find the following. The gear that rotates in the same direction as A. The multiplier ratios of A to B, A to C and A to D. The speed of B, C and D if A rotates at 500 rpm.

A = 50 teeth B = 10 teeth C = 25 teeth D = 100 teeth

Compound Gears

What are compound gears?

A gear system with pairs of gears mounted on the same shaft

Produce large speed changes (100 : 1) Provide multiple outputs with different speeds and

directions

Compound Gear Example Gear Ratio/ MR

The multiplier ratio (Gear Ratio) for the first pair of meshing teeth is

The multiplier ratio for the second pair of meshing teeth is

The total multiplier ratio is calculated by multiplying both ratios:

1:610

60

driver

drivenCD of Ratio

Ratio = 4 : 1 x 6 : 1 = 24 : 1Total

Short cut

For a compound gear train the following is true:

Gear movement ratio = product of number of teeth on driven divided by the product of

number of teeth on driver

From previous example:

Gear Ratio = 80 x 60 = 4800 = 24 = 24 : 1

20 x 10 200 1

Compound Example SR

The speed ratio for the first pair of meshing teeth is

The speed ratio for the second pair of meshing teeth is

The total speed ratio is calculated by multiplying both ratios:

Driver/Driven = 20/80 = 1:4

Driver/Driven = 10/60 = 1:6

1/4 x 1/6 = 1:24

Note: The same short cut can be taken with movement ratio, can be taken with the speed ratio

Practice

 

 

A

B

C D

  In the compound train shown below wheel A is rotating at 100 rpm. If the numbers of teeth in the gear wheels A, B, C and D are 25, 50, 25, and 50 respectively, determine the SR, the GR and the speed of rotation of wheel D,

Worm and Wheel

What is a Worm and Wheel?

A worm looks like a screw thread It is attached to a drive shaft (the worm can only drive

a worm wheel, not the other way about!) It meshes with the worm wheel (fixed to driven shaft) Driven shaft runs at 90 degrees to the driver shaft

Why is it used?

Another way of making large speed reductions Can be used as a safety device, (the worm can only

turn in 1 direction. Thus it will not run back if lifting loads.)

Example:

Think of worm as 1 toothed spur gear The multiplier ratio between the gears shown is  

This would mean that for a motor rotating at 100 rpm, the output driven gear would rotate at only 3.33 rpm.

 

1:301

30

driver

drivenratioMultiplier

Bevel Gears

What is a Bevel Gear?

Two meshed gears at 90 degrees Gears are angled at 45 degrees Different sized gears give different output rotation speeds

Tasks

Produce the greatest possible speed within a compound gear train using spur gears with 8t, 16t, 24t and 40t. The driver motor is set at 1 rpm.

Ratchet and Pawl

What is a RATCHET?

A wheel with saw- shaped teeth around its rim

What is a PAWL?

A pawl is a small tooth that engages with a ratchet

Ratchet and Pawl

Together they engage and allow rotation in one direction only

Examples: Ratchet and Pawl

Where would you see a ratchet and pawl?

A wheel with saw- shaped teeth around its rim

Torque

Torque (turning force)

The turning force of a lever, e.g. spanner, is larger when the effort is further away from the fulcrum. You can get more torque from a spanner with a long handle, than one with a short one.

Torque = Effort (newtons) x Distance (metres)

Torque

Torque can be increased in a gear or pulley system by changing the size or output speed of the output gears.

If we have a Driver of 40t and a Driven of 80T, this will have a lower output torque than say a Driver of 40T and Driven of 100T.

Torque and Drive Systems

Torque is the amount of turning produced by a force

Torque T = Force x Radius (Units are Nm)

Example

How much torque is required to tighten a nut if the force needed is 45N and the tool radius is 200mm?

T = F x r T = 45N x 200mm T = 45N x 0.2m T = 9Nm

Torque and Drive SystemsThe gearing system shown, can operate with either a 50t or

an 80tDriven gear. The Driver gear has 200t. Calculate the output

torquefor the gear system if the input torque is 20Nm.

Multiplier Ratio 1 = Driven/Driver = 50/200 = ¼ Multiplier Ratio 2 = Driven/Driver = 80/200 = 2/5

Output Torque 1 = MR x Input Torque = ¼ x 20 = 5Nm

Output Torque 2 = MR x Input Torque = 2/5 x 20 = 8Nm

Belt and Chain Drives

Belts and chains transmit rotary motion between parts of a mechanism

This is usually combined with a change of speed

Too many gears in a simple gear train results in a low efficiency

Belt Drives

A belt is wrapped around two or more pulleys

Pulleys are grooved wheels

The belt is tensioned by one of the pulleys

Also common to use a jockey pulleyFor tensioning purposes

Belts are also angled for greater grip (vee- belt)

Belt Drives

Changes in direction achieved by crossing the belt over

Inexpensive to produce (rubber and string) Easy to replace Require little maintenance (no lubrication) Absorb shock loads (can slip to protect engine)

D R IVEN

D R IVER

Multiplier Ratio for belt drives

Pulleys can be used to transmit rotary motion over large distances

Input speed is often fixed speed/ torque (motor)

Speed Ratio (VR) = diameter of driver pulley ------------------------------

diameter of driven pulley

Multiplier Ratio = diameter of driven pulley diameter of driver pulley

Toothed Belts

Slipping belts can be an advantage, why?

Protect against shock loads

Toothed belts are used when non-slip is required

Cars use toothed belts as timing belts

If this slipped the pistons would collide with the valves causing damage

Chain Drives

Used for transmitting large forces with no slip Pulley replaced with sprocket

Require maintenance (oiling) When worn will slip

Tension provided by pair of jockey wheels

M.R = # teeth on driven/ # teeth on driver

Chain Drives

The chain and sprocket is really a form of pulley system that does not allow slippage. (the sprocket is a pulley with teeth, the chain is a metal belt)

Chain Drives Questions:

The bicycle shown has two rear sprockets (50t and 80t). The driver sprocket has 200t. Calculate the output torque for the rear sprockets if the input is 20Nm

Find MR of small sprocket = #teeth on driven = 50 = 1:4 # teeth on driver 200

Find MR of large sprocket = #teeth on driven = 80 = 1:2.5 # teeth on driver 200

Now find o/p torques: T(small) = Input torque x MR = 20Nm x 1:4 = 5Nm

T(large) = Input torque x MR = 20Nm x 1:2.5 = 8Nm

Rack and Pinion

Transforms rotary motion into linear motion (or vice versa)

Spur gear meshes with a ‘rack’

Task 1:

A rack with 100 teeth per metreis meshed to a pinion with 10 teeth.

1. If the pinion rotates once how far does the rack move?

2. How many revolutions does it take to move the rack from one end to the other? The rack is 1m long

Rack and Pinion Solutions

Task 1 (A)

Rack is 1m long with 100T, so each tooth is worth 1000/100 = 10mm

This value is known as the Tooth Pitch of the rack.

If the pinion rotates once, then it moves 10T, so the movement of the rack is 10 x 10 = 100mm

(B) If rack is 1m long then it will take 1000/100 = 10 revolutions to move from one end to the other.

Questions

The compound gear train shown below is driven by a motor that runs at 1000 rpm. Calculate the multiplier ratio of the motor to the output shaft, the speed ratio and then the output speed. Show all your working.  A = 20 teethB = 60 teethC = 40 teethD = 50 teeth M O TO R

A B

CD

O U TPU T

Friction & Effect

Friction between moving parts reduces the efficiency of the system

Ways in which we can reduce friction

These include:

• Lubrication, Oil or grease• Use roller bearings