Politecnico di Milano IV Facoltà di Ingegneria Master Degree in Mechanical Engineering GRADUATION THESIS Lateral Dynamics of a Sidecar Vehicle Definition of a simplified model and parameters optimization Supervisor Author Prof. Stefano Melzi Simone Dovico Co-Supervisor Ing. Giuseppe Guerra Academic Year 2017-2018 Lateral Dynamics of a Sidecar Simone Dovico 1 Lateral Dynamics of a Sidecar Simone Dovico Summary 1. Introduction ................................................................................................................................... 10 1.1 A Short Hystory of Sidecars ...................................................................................................... 11 1.2 Modern Sidecars ....................................................................................................................... 12 1.3 Sidecar competitions ................................................................................................................ 13 2. Sidecar Modelling .......................................................................................................................... 15 2.1 Hypothesis of the simplified model.......................................................................................... 15 2.1.1 Aerodynamic Forces .......................................................................................................... 16 2.1.2 Rolling Resistance .............................................................................................................. 17 2.1.3 Pilot and Passengers modelling ......................................................................................... 19 2.2 System mass geometry ............................................................................................................. 19 2.3 Traction and Braking System .................................................................................................... 21 2.3.1 Hypothesis and model of the engine ................................................................................ 21 2.3.2 Hypothesis and model of the braking system ................................................................... 24 3. Dynamic model of a sidecar vehicle ............................................................................................. 28 3.1 Selection of the reference system ............................................................................................ 28 3.2 Kinetic analysis of a sidecar vehicle .......................................................................................... 29 3.2.1 Front wheel kinematics ..................................................................................................... 29 3.2.2 Rear wheel kinematics ....................................................................................................... 31 3.2.3 Side wheel kinematics ....................................................................................................... 32 3.3 Pneumatic tyres and contact forces ......................................................................................... 33 3.3.1 Pneumatic tyres ................................................................................................................. 33 3.3.2 Tyre and wheel contact model .......................................................................................... 34 3.3.2.1 The Magic Formula of Pacejka .................................................................................... 35 3.3.3 Combined friction model ................................................................................................... 37 3.4 Lateral sidecar dynamics .......................................................................................................... 39 3.4.1 Steering torque calculation ............................................................................................... 42 4 Experimental tests and model validation ...................................................................................... 44 4.1 Prototype build up .................................................................................................................... 44 4.2 Acquisition data system ........................................................................................................... 48 4.2.1 Sensor types used on the vehicle ...................................................................................... 49 4.2.2 Acquisition data system wiring .......................................................................................... 51 4.3 Experimental test ..................................................................................................................... 57 2 Lateral Dynamics of a Sidecar Simone Dovico 4.4 Validation process .................................................................................................................... 60 4.4.1 Rearrangement of experimental data ............................................................................... 61 4.4.2 Mathematical model validation ........................................................................................ 64 4.4.3 Coefficients adjustment .................................................................................................... 66 4.5 Additional tests ......................................................................................................................... 67 5 Sensitivity analysis and Optimization ............................................................................................ 69 5.1 Design Variables and Performances of the system .................................................................. 69 5.1.1 Sensitivity Analysis for a steering pad left ......................................................................... 71 5.1.2 Sensitivity Analysis for a steering pad right....................................................................... 73 5.2 Sidecar dynamics parameters optimization ............................................................................. 74 5.2.1 Selection of the objective functions .................................................................................. 75 5.2.2 Spearman Coefficient ........................................................................................................ 76 5.2.3 Objective Functions Approximation .................................................................................. 77 5.2.4 Optimization Algorithms ................................................................................................... 80 6 Conclusions ..................................................................................................................................... 85 6.1 Conclusions and Further Development .................................................................................... 87 Attachment A – Description of the company and Vehicle............................................................... 89 A.1 The RMG-Tech s.r.l. Company .................................................................................................. 89 A.2 The Black Dougles Motorcycles – Sterling Autocycle MK V ..................................................... 90 A.3 The Black Dougles Motorcycles – Military version and Sidecar coupling ................................ 92 Attachment B – Sidecar in the World ............................................................................................... 95 B.1 Sidecars in England ................................................................................................................... 95 B.2 Sidecars in Germany ................................................................................................................. 98 B.3 Sidecars in USA ......................................................................................................................... 99 B.4 Sidecars in Japan .................................................................................................................... 105 Attachment C – Sidecar Datasheet ................................................................................................. 108 C.1 Vehicle Draw ........................................................................................................................... 108 C.2 Datasheet of the Vehicle ........................................................................................................ 109 Attachment D – Preliminary Results ............................................................................................... 110 D.1 Steering Pad Left .................................................................................................................... 110 D.2 Steering Pad Right .................................................................................................................. 115 Attachment E - Validation Results .................................................................................................. 121 E.1 Straight Line Constant Speed ................................................................................................. 121 3 Lateral Dynamics of a Sidecar Simone Dovico E.2 Straight Line Acceleration....................................................................................................... 122 E.3 Straight Line Braking ............................................................................................................... 124 E.4 Steering Pad Left ....................................................................................................................