13 11 Ball Bearing Motor

Transcription

1 11 Ball Bearing Motor

2 11. Ball Bearing Motor uses electrical energy to create rotational motion. On what parameters do the motor efficiency and the velocity of the rotation depend? 2

3 INTRODUCTION 3

4 What is a Bearing Motor? 4

5 What is a Bearing Motor? 5

6 What is a Bearing Motor? 6

7 What is a Bearing Motor? 7

8 What is a Bearing Motor? 8

9 It Works! 9

10 EXPERIMENTS 10

11 Experimental apparatus 11

12 Experimental apparatus 12

13 Experimental apparatus M V V 13

14 Experimental Results 14

15 Max Speed Measurement 15

16 max speed [RPM] 13 Max Speed Measurement 400 disconnected push time [s] 16

17 max speed [RPM] 13 Max Speed vs. Current current [A] current was changing in time during experiments (battery discharging etc.) 17

18 Efficiency Measurement efficiency output power η = P o P i input power Δ rotational energy Δ time Δ work of electric current Δ time 18

19 Efficiency Measurement efficiency output power η = P o P i input power = Δ 1 2 Jω2 Δt Δ rotational energy Δ time J = kg m 2 (see Appendix) Δ work of electric current Δ time 19

20 Efficiency Measurement efficiency output power η = P o P i input power = Δ 1 2 Jω2 Δt Δ rotational energy Δ time Δ work of electric current Δ time 20

21 Efficiency Measurement efficiency output power I η = P o P i input power = Δ 1 2 Jω2 Δt U e I Δ rotational energy Δ time Δ work of electric current Δ time M V Ue V too large to be measured directly 21

22 Efficiency Measurement efficiency output power I η = P o P i input power R w = Δ 1 2 Jω2 Δt U e I Δ rotational energy Δ time Δ work of electric current Δ time M V Ue V U d too large to be measured directly drop on wire! I = U d R w 22

23 Efficiency Measurement efficiency output power η = P o P i = Δ 1 2 Jω2 Δt input power U e I R w U d R w Δ rotational energy Δ time Δ work of electric current Δ time M V Ue V U d R w (t): R w = R α T 23

24 Efficiency Measurement efficiency output power η = P o P i = Δ 1 2 Jω2 Δt input power U e I R w U d R w (t) Δ rotational energy Δ time Δ work of electric current Δ time M V Ue V U d 24

25 efficiency [%] 13 Efficiency Measurement time [s] 25

26 efficiency [%] 13 Efficiency Measurement 1 0,8 0,6 0,4 0, time [s] 26

27 input power voltage current internal resistance of source maximal current resistance battery heat capacity temperature running time 28

28 output power number of bearings inner friction moment of inertia amount of lubricant coaxiality rolling resistance axle type of bearings 29

29 EXISTING THEORIES 13

30 #1: Magnetic Theory explanation of rotation: eddy currents in rollers/axle (several variations) Kirk T. McDonald. Ball-Bearing Motor, Joseph Henry Laboratories, Princeton University, Princeton 31

31 #2: Thermal Theory explanation of rotation: local deformations of surface caused by heating due to extreme current density 32

32 #2: Thermal Theory 33

33 Which one is valid in our case? 34

34 Experiment #1: Cylindrical Bearings 13 should be qualitatively the same could be different (different shape different deformation) 35

35 Experiment #1: Cylindrical Bearings 13 36

36 Which one is valid in our case? experiments: #1: cylindrical bearings the same different 37

37 Experiment #2: Strong External Magnetic Field ( > 1T) 13 could be different should be the same 38

38 Experiment #2: Strong External Magnetic Field ( > 1T) 13 39

39 Which one is valid in our case? experiments: #1: cylindrical bearings #2: external magnetic field the same possibly different different the same 40

40 Experiment #3: Deforming the Bearing 13 power decrease (greater friction) power might increase (greater normal forces) 41

41 peak output power [W] Experiment #3: Deforming the Bearing ,5 1 1,5 deformation [mm] 42

42 Which one is valid in our case? experiments: #1: cylindrical bearings #2: external magnetic field #3: deforming the bearing the same possibly different power decrease different the same power increase 43

43 Which one is valid in our case? experiments: #1: cylindrical bearings #2: external magnetic field #3: deforming the bearing the same possibly different power decrease different the same power increase 44

44 Conclusion DETERMINED RELEVANT PARAMETERS Thank you for your attention! ILLUSTRATED CONSTRUCTION & BUILT APPARATUS EXPLORED EXISTING THEORIES (THERMAL, MAGNETIC) M I V Ue R w V U d + SHOWED VALIDITY OF THERMAL FOR OUR CASE η 13 t MEASURED EFFICIENCY P i P o U I c N f J T R R s I max t r amount of lubricant coaxiality R r axle 45 type of bearings

45 Conclusion DETERMINED RELEVANT PARAMETERS Thank you for your attention! ILLUSTRATED CONSTRUCTION & BUILT APPARATUS EXPLORED EXISTING THEORIES (THERMAL, MAGNETIC) M I V Ue R w V U d + SHOWED VALIDITY OF THERMAL FOR OUR CASE η 13 t MEASURED EFFICIENCY P i P o U I c N f J T R R s I max t r amount of lubricant coaxiality R r axle 46 type of bearings

46 Appendices 48

47 Measuring Current current very large (> 100 A) directly solution: voltage drop on wire 1.25 V drop on thick copper wire! but: wire resistance R unknown too small to be measured directly calculation prone to errors cannot measure I = U d M R w I V U e 49 R w V U d

48 Measuring Current current very large (> 100 A) directly solution: voltage drop on wire 1.25 V drop on thick copper wire! but: wire resistance R unknown too small to be measured directly calculation prone to errors cannot measure I = U d M R w I V U e 50 R w V U d

49 Measuring Current solution: voltage drop on wire 1.25 V drop on thick copper wire! M I = U d R w I V U e R w V U d R: 1. discharge the battery so it sources measurable current ( 2. measure current & voltage drop simultaneously 3. calculate the resistance R w = U d I = Ω 51

50 Importance of temperature change T = UI dt mc T 80 but it is also cooled by air from R w = R α T : α Cu = K 1 20% resistance change 52

51 Determining Wire Temperature R w = R α T Q = mcδt = P w t dt P w = U d 2 R R w t = R α U d 2 Δt R prev mc 53

52 Our Bearings Type: 6206 Type: 6303 Type: NJ206EC welded together with our currents braked (will come back to later) d D B mm mm mm d D B mm mm mm d D B mm mm mm 54

53 Calculation of moment of inertia Inner race 1 - Main inner race 2 - Bearing holder 3 - Flyback wheel holder 4 - Outer race 5 - Flyback wheel 5 J = J 3.2 = 10 2 kg J n m2 n=1 J 1,2,3 = 1 2 mr2 J 4,5 = 1 2 m(r 2 2 r 1 2 ) 55

54 Small ball bearings 56