ENGI 128 INTRODUCTION TO ENGINEERING SYSTEMS. Lecture 4: Torque, Gears & Torque, Transmissions & Torque, Bicycles & Torque

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1 ENGI 128 INTRODUCTION TO ENGINEERING SYSTEMS Lecture 4: Torque, Gears & Torque, Transmissions & Torque, Bicycles & Torque Understand Your Technical World 1

2 Outline Goal: Add rigor to the concepts of gears and torque that you learned last time. Gears are in almost every modern vehicle, so we ll use different vehicles as our systems du jour. 2

3 Torque 3

4 Speed and Force, Translation and Rotational speed force power linear motion speed s force f p = s f rotational motion angular speed w twisting force t p = w t 4

5 Torque always makes people unhappy Torque is simple: It is a force that makes anything rotate It s just that simple. Any time anything rotates, there is a torque involved. It s also called a rotational force or a twisting force You can feel torque if you try 5

6 The power of radius: The equation for torque is simple: But that r is what causes all the mental problems Imagine these two cranes: r 1 = 2m r 1 = 1m 10n 10n f 1 = 10n Which weight is harder to lift? t 1 =? t 2 =? f 2 = 10n 6

7 The power of radius: The equation for torque is simple: But that r is what causes all the mental problems Imagine these two cranes: r 1 = 2m r 2 = 1m 10n 10n f 1 = 10n t 1 = 20nm f 2 = 10n Which weight is harder to lift? t 2 = 10nm 7

8 Gears & Torque 8

9 LEGO Gears The red gear has 8 teeth, yellow gear has 24 teeth. How far will the yellow gear turn per revolution of the red gear? 9

10 The Gear Ratio The gear ratio is the ratio of input turns to output turns Ratios can be written as fractions, or with a colon g = 3:1 Is usually written with the right hand side normalized (set to) 1 How do we compute the gear ratio? 10

11 Gear Ratio 11

12 LEGO Gear reduction The red gear has 8 teeth, yellow gear has 24 teeth 12

13 Gear Ratio 13

14 The no slip condition Gears can t slip. They have teeth. 14

15 Gear Ratio Basic equation for distance around a circle 15

16 Gear Ratio We want to compute in terms of and Definition: The gear ratio is the ratio of input turns to output turns: Constants: 16

17 Gears & Speed 17

18 Rotational (angular) Speed First think: Should the output gear be going faster or slower? By how much? Output Input 18

19 Rotational (angular) Speed Definition of angular speed: 19

20 Angular Speed We want to compute in terms of and 20

21 Gears & Torque 21

22 Torque and gears First think: Should the output gear have more or less torque? By how much? Output Input 22

23 Gears and torque Let s start with our torque equation: 23

24 Gears and torque We want to compute in terms of and 24

25 Summary No free lunch: If you want more torque, you have to give up speed (and vice versa) When trading torque for speed, something is conserved 25

26 Transmissions 26

27 Transmissions What is a transmission? Where can you find them? 27

28 Car Transmission 28

29 2010 Ford Mustang 29

30 2010 Ford Mustang 30

31 2004 Ford F

32 2009 Ford F

33 Automatic Transmission Different sets of gears trade torque for speed Most cars have 4-6 gear ratios + reverse 33

34 Automatic Transmission They re ridiculously complicated, but look, they have gears! 34

35 Final Drive A set of bevel gears rotate the power 90 degrees, And a differential splits it between the two rear wheels 35

36 2009 Honda CBR 600RR Where is the transmission? How many gears? Why? 36

37 2009 Honda CBR 600RR Where is the transmission? How many gears? Why? 37

38 2014 Specalized Stumpjumper FSR Comp Evo Where is the transmission? How many gears? Why? 39

39 40

40 Other types of transmissions? Or maybe just things that use the word transmission? 41

41 [Hoover Dam] 42

42 Transmission Lines 43

43 Critical for Green Energy Green power sources are often far from people 44

44 Abstraction 45

45 Transmissions in Block Diagrams What do all these transmission have in common? What is a transmission block diagram element? What is its interface? 46

46 Transmissions in Block Diagrams What do all these transmission have in common? What is a transmission block diagram element? What is its interface? electrical power mechanical power mechanical power energy storage: battery energy conversion: motor power transmission: gears physical force: rotor blade 47

47 Transmissions in Block Diagrams What do all these transmission have in common? What is a transmission block diagram element? What is its interface? mechanical power mechanical power power transmission: gears 48

48 Transmissions in Block Diagrams What do all these transmission have in common? What is a transmission block diagram element? What is its interface? power power power transmission: distance 49

49 Wait a minute Power in and power out [wait for the realization from previous no free lunch comment] power power power transmission: distance 50

50 Conservation of Energy Power in = power out! How do you compute power in a system of gears? power power power transmission: distance 51

51 Summary, part II No free lunch: If you want more torque, you have to give up speed (and vice versa) When trading torque for speed, something is conserved 52

52 Summary, part II No free lunch: If you want more torque, you have to give up speed (and vice versa) When trading torque for speed, power is conserved! 53

53 Speed and force and power speed force power linear motion speed s force f p = s f rotational motion angular speed w twisting force t p = w t 54

54 Fun with Torque: Physics of Two-Wheeled Vehicles 55

55 The Brakie r 1 + mg r 2 mgr 1 - mnr 2 = 0 mn 56

56 2014 Specalized Stumpjumper FSR Comp Evo What is this bike designed for? 58

57 Slickrock Trail, Moab, UT 59

58 [slidewhow] 60

59 Question 1: Torque and Brakes Which has more stopping power? A. Front brakes B. Rear brakes C. Both are equal 61

60 Braking Torque [todo: finish slide: add torque arrows] nfront ffront frear nrear 62

61 Braking Torque Application of brakes creates a torque This torque increases the normal force on the front wheel With more normal force, the front wheel can generate more friction Almost ¾ of braking force comes from the front wheels! 63

62 2009 Honda CBR 600RR 64

63 Question 2: Torque and Steering What makes a bicycle go straight? A. Rider balance B. Gyroscopic force C. Torque around front wheel axis 65

64 Caster 66

65 Caster angle in Bicycles 67

66 Caster angle in cars 68

67 Question 3: Torque and Bunny Hops How does a bunny hop work? A. Toe clips B. Torque around the center of mass C. Bouncing off of the tires 69

68 The Bunny Hop 70

69 Try This: Shopping Cart Bunnyhops! 71

70 72

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