EGH166 Hands-on Lab

## Lab 3: Gears

#### Introduction

##### Background

Gears can be found in just about everything with moving parts.  Music boxes, toys, clocks, cars and tape players all have gears.  The typical type of gear is a pinion gear however there are many other types of gears each of which meet the needs of certain applications.

##### Purpose

The purpose of this lab is to familiarize you with the properties of torque and speed, and to introduce you to the application of various types of gears.

##### Basic Principles

In this lab write-up, we will cover some basic principles behind:

1.      Torque and speed, and

2.      Types of gears.

##### Lab Experience

The lab experience will encompass:

1.      Applications of Worm Gears,

1. Application of Bevel gears and Rack & Pinion, and
2. Application of Spur gears and Sprockets.

#### TORQUE AND SPEED

##### Introduction

Gears are used to perform mechanical work.  A common application of gears is to convert from one rotational speed to another through a gear train (or gear box or speed reducer).  A clock has two or three hands, each of which spin at different speeds but there is only one motor or power source turning the hands.  The clock takes the speed of the input motor, gears it down and drives the second hand, gears it down again to drive the minute hand and down further to drive the hour hand.  Several gears allow one power source to drive a variety of objects.

##### Torque

When rotational speed is changed through gearing, the rotational force that can be applied also changes.  Consider a car traveling on a highway, the car is in high gear traveling fast but with low acceleration ability.  When the car approaches a steep incline it down shifts, putting the car in a lower gear, which produces more torque but the car can not go as fast (the engine must turn much faster to maintain speed).

The transmission in a car transfers power from the engine to the drive train and moves the car.  Power (or energy) is always conserved in any system, so this must also be true for a car's power train.  Power, in a rotational system is represented by rotational speed and rotational force (or torque).

##### Interplay of Torque and Speed

In linear motion the relationship of Power, Force, Work and Speed are as follows:

In rotational motion the formulas are identical, we just have some different terms.  Rotational force is called Torque and rotational distance is measured in radians or degrees.

Power = Torque * (Rotational Speed)

A car is equipped with an engine capable of delivering a certain horsepower; the gear that the car is in determines how the power is converted into speed and torque.  For a fixed power, if you need more torque the speed must go down or if more speed is needed then the torque available will decrease.

A bicycle is another perfect example of how gearing controls toque and speed.  Shifting gears on a bicycle is done to make the rider as efficient as possible.  Low gear is for going up hills, high gear is used to go fast on smooth flat land.

#### TYPES OF GEARS

##### Spur Gears

A pinion or spur gear is a simple gear used to mesh with another gear in the same plane.

Spur Gear Terminology

 Terminology Definition Pitch Circle determines the gear ratio Tooth size diametral pitch Pinion smaller of two gears Gear larger of two gears Gear ratio m = N1 / N2

##### Bevel Gears

Bevel gears are designed to mesh with each other at 90° angles.  This type of drive is used to change the axis of rotation.  A differential (which is discussed later in this lab) uses bevel gears to control its motion.

##### Rack and Pinion

A pinion turns and moves a rack in order to convert rotational motion into linear motion.  Rack and pinion steering is just one of many applications of this gear set.

##### Worm gears

This type of gear, like the bevel gears, converts the axis of rotation by 90°.  A worm gear is used for high ratio speed reduction.  When a worm rotates, it moves just one tooth on its meshing gear.  (Some double helix worms move two teeth.)  Because of the shape of worm gear, the driven gear must be specially made in order to mesh properly.

#### LAB EXPERIENCE

Make sketches of equipment used in class; include them in your lab write-up.

Applications of Worm Gears

##### Automobile Windshield Wiper Motor

Observe the motion of the given gear head motor unit. Take

the gear assembly apart.

Determine the gear ratio.  # of teeth on the output gear : #

of worm gears.

##### Using Legos

Observe the motion of the Lego™ robot gripper that is

given.

Use the robot gripper to grab items.  Notice

how the worm gear is used to provide holding power

without energizing the motor.

##### Questions

1.      What is the gear ratio of the windshield wiper motor?

How did you determine this?

2.      How does the Lego™ worm gear robot gripper still

hold objects without a continuously applied force?

Compare this mechanism to a crescent wrench.  Use

Bevel Gears and Racks

A differential is used to transfer power from the drive shaft to the wheels of the car.  When a car turns a corner the wheels move at different speeds, and so travel different distances.  Move the Lego™ differential unit provided and prove this to yourself.  A differential provides equal force to each wheel while allowing different speeds at each wheel.

##### Questions

Understanding a differential, explain what happens if one

tire is sitting on ice and the other tire is on clean pavement

and the drive shaft is spinning?  Will the car move?

##### Bicycle Gearing

A bicycle demonstrates the trade off of speed and torque.

Experiment with the speed and force attainable at

different gear ratios.  Since a bicycle uses a chain the

direction of rotation of the output shaft (sprocket) is

not reversed as it is with a pair of gears.

For the given bicycle, find the gear ratio

(sprocket combination) for:

a) Max Torque

b) Max Speed

c) Redundant combinations

For this experiment, create a table that shows all

the possible gear combinations.  Show which ones are

redundant. (Measure wheel diameter and length of pedal

arm).

##### Gear Boxes

Using the Legos™ set provided build a simple gear box

that has a gear ratio of 1:75.

##### Questions

1.      Draw the gearbox you made for the 1:75 gear ratio.  Be

sure you could reproduce the gearbox from this sketch.

2.      If a rider can pedal no faster than 5 revolutions per

second, what is the fastest he/she can make the bicycle

in the lab go.

(hint: determine the diameter of the rear tire and the

length of the pedal).

3.      A biker weighs 175 lbs and his bike weighs 25 lbs.

What is the steepest hill the rider can climb?  (Assume

the rider can put all of his/her weight on the pedal.)

4.      Would a wrench driven by an electric motor have a very high or a very low gear ratio?

#### LAB REPORT

##### Format

·   Lab reports must be done as a TEAM lab report

·   Follow given lab report format.

·   Maximum 4-5 pages (including figures and tables)

##### General Guidelines

1)      Cover Page

2)      Introduction/Background

3)      Description of lab experiments. Include sketches of the equipment you used

4)      Solutions to questions.  Follow order presented in lab handout