POLYTHECNIC OF TURIN
Department of Mechanical and Aerospace Engineering Master of Science in AUTOMOTIVE ENGINEERING
Thesis Project
Design and Validation of the Unsprung Masses of a Formula SAE vehicle
Supervisor Candidate
Prof. Andrea Tonoli Luis Daniel Medina Querecuto
April 2020
ABSTRACT
ACKNOWLEDGEMENTS
TABLE OF FIGURES
“ ”
LIST OF TABLES
INTRODUCTION
i. Context and motivation
“ ”
5
ii. Problem Statement
iii. Aim and Objectives
iv. Delimitation
v. Method and processes
Sep-17 Oct-17 Nov-17 Dec-17 Jan-18 Feb-18 Mar-18 Apr-18 May-18 Jun-18 Jul-18 Aug-18
1- 2017 season outcome 2- 2018 target setting 3- Recruitment 4- Budget and partners definition 5- PRELIMINARY DESIGN 5.1- Veichle dynamics 5.2- Battery pack 5.3- Packaging 6- DESIGN 6.1- System-level analyses 6.2- CAD modelling and simulation 7- PROTOTYPING, TESTING AND VALIDATION 8- COLLABORATIVE DEVELOPMENT 9- PRODUCTION 9.1- Components sourcing 9.2- Lamination 9.3- Machining 9.4- PCB production 9.5- Wiring 10- CAR ASSEMBLY 11- BENCH TEST AND DEBUGGING 12- TRACK TESTS 12.0- Track tests on SC17 12.1- Reliability tests 12.2- Installation laps 12.3- Dynamic events simulation 13- FSAE Italy
14- Tack tests 15- FSS Spain
vi. Background and literature review
𝜇𝑥 =𝐹𝑥
𝐹𝑧
𝜇𝑦=𝐹𝑦
𝐹𝑧
𝑆𝑅 =𝛺−𝛺0
𝛺0
𝛺 𝛺0
α
vii. Unsprung Mass
viii. Role of the unsprung mass in vehicle performance
Road holding
𝜔𝑢𝑠= √𝐾𝑚𝑠+𝐾𝑡
𝑢𝑠
Suspension geometry
ix. Yaw inertia
𝐼𝑍𝑍= 𝐼𝑧𝑧+ 𝑚 𝑑2
𝑀𝑧 = 𝐽𝑧𝜓̈ = 𝐹𝑦𝑓𝑎 − 𝐹𝑦𝑟𝑏 +1
2𝐶𝑀𝑧𝑆𝜌𝑉2
𝜓̈
𝛽
𝛼𝑖 𝑟
𝑚𝑉(𝛽̇ + 𝑟) + 𝑚𝑉̇𝛽 = 𝑌𝛽𝛽 + 𝑌𝑟𝑟 + 𝑌𝛿𝛿 + 𝐹𝑦𝑒 𝐽𝑧𝑟̇ = 𝑁𝛽𝛽 + 𝑁𝑟𝑟 + 𝑁𝛿𝛿 + 𝑀𝑧𝑒
𝑌𝛽 𝑌𝑟 𝑌𝛿 𝑁𝛽 𝑁𝑟 𝑁𝛿 𝐹𝑦𝑒
𝑀𝑧𝑒
𝑃𝑟̈ + 𝑄𝑟̇ + 𝑈𝑟 = 𝑆′′𝛿 + 𝑇′′𝛿̇+ 𝑁𝛽𝐹𝑦𝑒− 𝑌𝛽𝑀𝑧𝑒+ 𝑚𝑉𝑀̇𝑧𝑒 9
𝑃 = 𝐽𝑧𝑚𝑉 𝑆′′= 𝑌𝛿𝑁𝛽− 𝑁𝛿𝑌𝛽
𝑄 = −𝐽𝑧𝑌𝑏− 𝑚𝑉𝑁𝑟 𝑇′′= 𝑚𝑉𝑎𝐶1 𝑈 = 𝑁β(𝑚𝑉 − 𝑌𝑟) + 𝑁𝑟𝑌𝛽
x. Thermal capacity of brake rotors and calipers
Δ𝐸𝑏 =𝑚2(𝑉12− 𝑉22) +𝐼
2(𝜔12− 𝜔22) − 𝐹𝑑𝑟𝑎𝑔𝑑𝑏𝑟𝑎𝑘𝑒
𝑚 𝐼 𝑉
𝜔
𝛥 𝑇 =
𝐸𝑏𝑖𝑝𝑚𝑑𝑖𝑠𝑐𝐶𝑝 𝐸𝑏𝑖
𝑖 𝑚𝑑𝑖𝑠𝑐 𝐶𝑝
𝑝
𝐵𝑖 =
ℎ𝐿𝑐𝑘
≪ 0.1
ℎ 𝑘
𝐿𝑐
𝐹𝑜 =
𝛼𝑡𝐿𝑐2
𝛼 𝑡
𝑇−𝑇∞
𝑇𝑖−𝑇∞
= 𝑒
−𝐵𝑖⋅𝐹𝑜𝑖
xi. PoliTo Racing 2018
CHAPTER 1. PROJECT DEFINITION
End of 2017 season
1.1 Evaluation of the 2017 season
PROS CONS Good mechanical reliability
Adequate battery pack capacity Flexibility in suspension configuration Adjustable aerodynamic package
Excessive weight and inertia Sub-optimal use of the tire forces
Low downforce compared to competitors Excessive steering compliance
Difficult maintenance
1.2 Top-Level Concept definition and target setting
1.2.1 Requirements and targets for systems involving unsprung components
𝑁𝑚 𝑟𝑎𝑑
Additional competition regulations
Tilt test
Brake test procedure
1.2.2 Results from the preliminary analyses
1.2.2.1 Suspension geometry and loads•
•
•
•
1.2.2.2 Transmission envelope
•
•
•
1.2.2.3 SC17 brakes performance
1.2.2.4 Steering system
CHAPTER 2. DESIGN PHASE
2.1 Brakes system design
2.1.1 Possibilities for weight saving on the brake calipers
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2.1.2 Brake caliper selection
𝐹𝑧1𝑏𝑟𝑎𝑘𝑒𝑑 = 𝐹𝑧1𝑠𝑡𝑎𝑡𝑖𝑐+ Δ𝐹𝑧 𝐹𝑧2𝑏𝑟𝑎𝑘𝑒𝑑 = 𝐹𝑧2𝑠𝑡𝑎𝑡𝑖𝑐− Δ𝐹𝑧
Δ𝐹𝑧
Δ𝐹𝑧 = 𝑚𝑎𝑥(ℎ𝐶𝐺
𝑙 )
𝑎𝑥 ℎ𝐶𝐺
𝑙
Δ𝐹𝑧 𝐹𝑧1𝑏𝑟𝑎𝑘𝑒𝑑 𝐹𝑧2𝑏𝑟𝑎𝑘𝑒𝑑 𝐹𝑥1 𝐹𝑥2
𝑖
𝑇
𝑏𝑟𝑎𝑘𝑒𝑖=
𝐹𝑥𝑖2
𝑅
𝑙𝑖 𝑅𝑙𝑝𝑙𝑖𝑛𝑒𝑖=𝑇𝑏𝑟𝑎𝑘𝑒𝑖 𝑟𝑝𝑎𝑑𝑖
⋅
𝐴 1𝑐𝑖𝜇𝑝𝑎𝑑𝑠𝑖 𝑟𝑝𝑎𝑑
𝑟𝑝𝑎𝑑
𝐴𝑐
𝜇𝑝𝑎𝑑𝑠
0 200 400 600 800 1000 1200
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0
P4 32/26 P4 30/34 P4 26/28 P4 24 P2 24 P4-24 P2-24
Front Axle Rear Axle
Mass [g]
Pressure [bar ]
Mass Pressure (best case) [bar] Pressure (worst case) [bar]
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 50 100 150 200 250 300 350 400 450
Friction Coefficient
Temperature [°C]
Z04 CC SA LA RC SC
2.1.3 Load distribution study
𝐹
𝑝𝑒𝑑𝑎𝑙𝐾
𝑏=
𝑇brake1𝑇brake2
=
𝐹pedal 𝐴MC1× 𝑙2
𝐿bar×𝑟pad1×𝐴𝐶1×𝜇𝑝𝑎𝑑𝑖 𝐹pedal
𝐴MC2× 𝑙1
𝐿bar×𝑟pad2×𝐴𝐶2×𝜇𝑝𝑎𝑑𝑖 𝐴𝑀𝐶1 𝐴𝑀𝐶2
𝐿𝑏𝑎𝑟
𝑙1 𝑙2
𝐾
𝑏= (
𝑙2𝑙1
) (
𝐴MC2×𝑟pad1×𝐴𝐶1𝐴MC1×𝑟pad2×𝐴𝐶2
)
%𝐹𝑟𝑜𝑛𝑡 𝐵𝑖𝑎𝑠 =
𝑙2𝐿𝑏𝑎𝑟
× 100
𝐹𝑥
2𝑟𝑒𝑎𝑙=
𝐹𝑥1𝑖𝑛𝑝𝑢𝑡𝐾𝑏
(𝐹𝑥1𝑖𝑛𝑝𝑢𝑡− 𝐹𝑥2𝑖𝑑𝑒𝑎𝑙) = 𝜇𝑥(𝑚 𝑔
𝑙 (𝑏 − 𝑎 + 𝜇𝑥 2 ℎ𝑐𝑔) + (𝐹𝑧𝑎𝑒𝑟𝑜1− 𝐹𝑧𝑎𝑒𝑟𝑜2) −2 𝐹𝑑𝑟𝑎𝑔 ℎ𝑐𝑔
𝑙 +2𝜇𝑥(𝐹𝑧𝑎𝑒𝑟𝑜1+ 𝐹𝑧𝑎𝑒𝑟𝑜2) ℎ𝑐𝑔
𝑙 )
𝜇𝑥 = 𝐹𝑥1𝑖𝑛𝑝𝑢𝑡 +𝐹𝑥2𝑖𝑑𝑒𝑎𝑙
𝑚𝑔+𝐹𝑧𝑎𝑒𝑟𝑜1+𝐹𝑧𝑎𝑒𝑟𝑜2
𝐹𝑧𝑎𝑒𝑟𝑜𝑖 =1
2𝜌𝑎𝑖𝑟𝐶𝑧𝑖𝑆𝑉2 𝐶𝑧1𝑆 𝐶𝑧2𝑆 𝐹𝑥2𝑖𝑑𝑒𝑎𝑙
𝐾𝑏
2.1.3.1 Proportional valve
•
•
•
2.1.3.2 Effects of Regenerative Braking
2.1.4 Brake rotors design
2.1.4.1 Determining the energy converted into heat by the brake rotors
Φ =
𝐹𝑥2𝐹𝑥2+𝐹𝑥1
𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑓𝑖𝑛𝑎𝑙
Δ𝐸
𝑏1= (1 − Φ) (
𝑚2
(𝑉
𝑖𝑛𝑖𝑡𝑖𝑎𝑙2− 𝑉
𝑓𝑖𝑛𝑎𝑙2) − 𝐹
𝑑𝑟𝑎𝑔𝑑
𝑏𝑟𝑎𝑘𝑒) +
𝐼12
(
𝜔𝑖𝑛𝑖𝑡𝑖𝑎𝑙2 − 𝜔𝑓𝑖𝑛𝑎𝑙2)
Δ𝐸
𝑏2= Φ (
𝑚2
(𝑉
𝑖𝑛𝑖𝑡𝑖𝑎𝑙2− 𝑉
𝑓𝑖𝑛𝑎𝑙2) − 𝐹
𝑑𝑟𝑎𝑔𝑑
𝑏𝑟𝑎𝑘𝑒) +
𝐼12
(
𝜔𝑖𝑛𝑖𝑡𝑖𝑎𝑙2 − 𝜔𝑓𝑖𝑛𝑎𝑙2)
𝑑𝑏𝑟𝑎𝑘𝑒 𝑎𝑥
𝑑
𝑏𝑟𝑎𝑘𝑒=
𝑉𝑓𝑖𝑛𝑎𝑙2 −𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙2 2𝑎𝑥
𝐹
𝑑𝑟𝑎𝑔=
12
𝜌
𝑎𝑖𝑟𝐶
𝑥𝑆 (
𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙+𝑉𝑓𝑖𝑛𝑎𝑙2
)
2
𝐸𝑏 Φ 𝑎𝑥 𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑓𝑖𝑛𝑎𝑙 𝐶𝑥𝑆
𝑝
2.1.4.2 Thermal analysis of the brake rotors
𝑝 =
√(𝑘𝑑𝑖𝑠𝑐 𝐶𝑝𝑑𝑖𝑠𝑐 𝜌𝑑𝑖𝑠𝑐) 𝑆𝑑𝑖𝑠𝑐
√(𝑘𝑑𝑖𝑠𝑐 𝐶𝑝𝑑𝑖𝑠𝑐 𝜌𝑑𝑖𝑠𝑐) 𝑆𝑑𝑖𝑠𝑐+ √(𝑘𝑝𝑎𝑑𝑠 𝐶𝑝𝑝𝑎𝑑𝑠 𝜌𝑝𝑎𝑑𝑠) 𝑆𝑝𝑎𝑑𝑠
ρ
𝑑𝑖𝑠𝑐 𝑝𝑎𝑑𝑠
𝑃 =
𝑑(𝐸𝑏𝑖)𝑑𝑡
𝑃𝑖(𝑡)= 𝑇𝑏𝑟𝑎𝑘𝑒⋅ 𝜔𝑖(𝑡)
Δ𝑇 = (𝑇
𝑏𝑟𝑎𝑘𝑒⋅ 𝜔
𝑖(𝑡)⋅ 𝑝 − 𝑄̇
𝑐𝑜𝑛𝑣𝑖− 𝑄̇
𝑟𝑎𝑑𝑖) 𝑡
𝑖𝑚
𝑑𝑖𝑠𝑐𝐶
𝑝𝑑𝑖𝑠𝑐𝑄̇
𝑐𝑜𝑛𝑣𝑖𝑄̇
𝑟𝑎𝑑𝑖𝑄̇
𝑟𝑎𝑑𝑖= 𝜖 ⋅ 𝜎 ⋅ 𝐴
𝑑𝑖𝑠𝑐⋅ 𝑇
𝑑𝑖𝑠𝑐4𝐴
𝑑𝑖𝑠𝑐𝜎 =
5.670 × 10−8 Wm2 K
𝜖
𝑄̇
𝑐𝑜𝑛𝑣= ℎ̅ ⋅ 𝐴
𝑑𝑖𝑠𝑐⋅ (𝑇
∞− 𝑇
𝑑𝑖𝑠𝑐) 𝑇
∞𝑁𝑢 ̅̅̅̅ =
ℎ̅𝐿𝑘𝑎𝑖𝑟
2.1.4.3 Analytical estimation of the average heat transfer coefficient
Cylindrical body
ℎ
𝑐𝑦𝑙̅̅̅̅̅ =
𝐶 𝑅𝑒𝐷𝑚𝑃𝑟𝑓13𝑘𝑎𝑖𝑟𝑓
2 𝑟𝑑𝑖𝑠𝑐
Planar body
ℎ
𝑝𝑙𝑎𝑡𝑒̅̅̅̅̅̅̅̅ =
0.664 𝑅𝑒𝐿1/2 𝑃𝑟𝑓1/3 𝑘𝑎𝑖𝑟𝑓
2 𝑟𝑑𝑖𝑠𝑐 𝑃𝑟 ≥ 0.6
ℎ
𝑝𝑙𝑎𝑡𝑒̅̅̅̅̅̅̅̅ =
0.680 𝑅𝑒𝐿1/2 𝑃𝑟𝑓1/3 𝑘𝑎𝑖𝑟𝑓 2 𝑟𝑑𝑖𝑠𝑐
Rotating thin disc
ℎ
𝑟𝑜𝑡̅̅̅̅̅ =
√(0.036 𝑅𝑒𝑈0.8)2+(0.556 𝑅𝑒𝜔0.5)2 𝑘𝑎𝑖𝑟𝑓
2 𝑟𝑑𝑖𝑠𝑐
𝑅𝑒𝜔
𝑅𝑒𝐿
> 0.18
•
𝐴𝑒𝑑𝑔𝑒= 2𝜋 𝑟𝑜𝑢𝑡𝑒𝑟𝑡𝑑𝑖𝑠𝑐 𝑡𝑑𝑖𝑠𝑐
•
ℎ𝑒𝑞𝑢𝑖𝑣
̅̅̅̅̅̅̅̅ = (ℎ̅̅̅̅̅ + 2 ℎ𝑟𝑜𝑡 ̅̅̅̅̅̅̅̅)𝑅𝑝𝑙𝑎𝑡𝑒 𝑠𝑖𝑑𝑒+ ℎ̅̅̅̅̅ 𝑅𝑐𝑦𝑙 𝑒𝑑𝑔𝑒
𝑅𝑠𝑖𝑑𝑒= 𝐴𝑠𝑖𝑑𝑒
2 𝐴𝑠𝑖𝑑𝑒+ 𝐴ℎ𝑜𝑙𝑒𝑠 + 𝐴𝑒𝑑𝑔𝑒 𝑅𝑒𝑑𝑔𝑒= 𝐴𝑒𝑑𝑔𝑒
2 𝐴𝑠𝑖𝑑𝑒+ 𝐴ℎ𝑜𝑙𝑒𝑠 + 𝐴𝑒𝑑𝑔𝑒
𝑅𝑒𝐿= 𝑅𝑒𝑈= 𝑅𝑒𝐷 𝑅𝑒𝜔
2.1.4.4 Simplified model: temperature response during continuous operation
𝑇𝑑𝑖𝑠𝑐(𝑛)= 𝑇∞+(1 − e(−𝑛 𝐵𝑖 𝐹𝑜))Δ𝑇𝑑𝑖𝑠𝑐(𝑛−1) 1 − e(− 𝐵𝑖 𝐹𝑜)
Φ 𝑎𝑥 𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑓𝑖𝑛𝑎𝑙
𝐶𝑥𝑆
2.1.4.5 Calculation of disc temperatures using telemetry data from SC17
𝑝
𝑟𝑒𝑎𝑟= 𝑝
𝑓𝑟𝑜𝑛𝑡(
100−%𝐹𝑟𝑜𝑛𝑡𝑏𝑖𝑎𝑠%𝐹𝑟𝑜𝑛𝑡𝑏𝑖𝑎𝑠
) (
𝐴MC1𝐴MC2
)
2.1.4.6 CFD analysis of the SC17 front brake rotor
2.1.4.7 Material selection and design exploration
Boundary conditions
0 20 40 60 80 100
0 2000 4000 6000 8000 10000 12000 14000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Heat transfer coefficient [W/m2K]
Heat Flow [W]
Time [s]
Heat Flow [W] Heat transfer coefficient [W/m2K]
Mesh used for the design exploration study
Response surface
2.1.4.8 Detailed design of the rotors
µ𝑝𝑣 𝑝 𝑣
𝜔𝑟
Constraints
Applied loads
Meshing
-20 0 20 40 60 80 100 120
0 5000 10000 15000 20000 25000
41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79
Heat Transfer Coefficient [W/m2K]
Heat Flux [W]
Time [s]
Heat Flux
Heat transfer coefficient - Calculated Heat transfer coefficient - Reference
2.1.4.9 Simulations results
2.1.4.10 Summary of the brake rotors design
0 0.2 0.4 0.6 0.8
1Mass
Iyy
Max.
Endurance Temp.
Max Auto X Temp.
Safety Factor at Max.
Braking cond.
Min. Life (Autocross Lap Loading Cycle)
Front Brake Rotors
SC17F SC18F V6
0 0.2 0.4 0.6 0.8
1Mass
Iyy
Max. Auto X Temp.
Safety Factor at Max.
Braking cond.
Min. Life (Autocross Lap Loading Cycle)
Rear Brake Rotors
SC17R SC18R V5
Considerations for the brake carriers
■ Wheel Spacer
■ Center pins
■ Wheel hub/Transmission planetary carrier
■ Wheel center nut
■ Brake rotor (friction ring)
■ Mounting bell
■ Wheel rim
Rear carrier
Front carrier
Floating buttons
𝐹𝑏𝑢𝑡𝑡𝑜𝑛=𝑇𝑏𝑟𝑎𝑘𝑒𝑟𝑒𝑎𝑟
3 𝑟𝑏𝑢𝑡𝑡𝑜𝑛
2.1.5 Manufacturing specification
■
■
■
2.2 Unsprung components of the suspension system
Wheels
2.2.1 Uprights
2.2.1.1 Constraints
2.2.1.2 Material and process selection
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Yield strength [MPa] Tensile strength [MPa] Young Modulus [GPa]
7075-T651 516 573
71.7
7075-T6 488 567
2.2.1.3 Geometry definition
Upright
Wheel hub/Planet gears carrier Shaft seal
Wheel bearings Ring gear
Planet gear assembly Bearing preload ring Sun gear
Motor flange
Camber adjustment plates Magnetic oil cap
Flange O-ring
σ
2.2.2 Structural analyses
2.2.2.1 Single-component analysis: compliant boundary conditions based on bearing stiffness data
2.2.2.2 Suspension assembly analysis
0 0.2 0.4 0.6 0.8 1 1.2
Mass Material Efficiency
Max. Von Mises Stress at max Load
Max. Bearing seat deformation Front Upright SC18 vs SC17 -
Normalized Parameters
SC17 SC18 0
0.2 0.4 0.6 0.8 1 1.2
Mass Material Efficiency
Max. Von Mises Stress at max Load
Max. Bearing seat deformation Rear Upright SC18 vs SC17 -
Normalized Parameters
SC17 SC18
2.2.2.3 Manufacturing specification
CHAPTER 3. MANUFACTURING AND ASSEMBLY
3.1 Brake discs and mounting bells
3.2 Suspension arms and tie rods
3.3 Uprights
3.4 Integration on SC18
CHAPTER 4. TESTING AND VALIDATION
4.1 Track tests on the SC17 car
4.1.1 Tested components and instruments used
4.1.2 Location of the tests
4.1.3 Data collection procedure and tests performed
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4.1.4 Analysis of collected data
4.1.4.1 Brake load balance4.1.4.2 Deceleration capability
4.1.4.3 Brake discs temperatures
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4.2 FSAE Italy – 11
thto 16
thJuly 2018
4.3 Front brake calipers failure
4.4 Front brake discs failure
4.5 Test session of August 16
th, 2018
4.5.1 Instruments used
4.5.2 Location of the tests
4.5.3 Tests performed and data collection procedure
- - - -
- - - -
- - - -
4.5.4 Analysis of collected data
4.6 Brake rotors failure during Formula Student Spain 2018
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