The role of the tyre in traction-induced driveline vibrations By Matthew Bartram and George Mavros Department of Aeronautical and Automotive Engineering Loughborough University United Kingdom Vehicle Dynamics and Control 211 5 April 211 Cambridge, UK
Overview of presentation q Low speed traction and associated problems q Scope of research method of attack q Modelling and simulation q Experimental investigation q Concluding remarks
Low speed traction and associated problems Wheel speed variation of a 4WD vehicle during traction manoeuvre on split-µ surface Observations: a) Nominal shuffle freq. on high friction road: 2.1-2.2 Hz b) Low/split-µ surfaces lead to frequency migration (5.5 Hz) c) Phenomenon initially attributed to changing levels of damping in the driveline Pawar, J., Biggs, S. and Jones, R.P., 27. Sensitivity of System Boundary Conditions on the Migration of Low Frequency Modes Controlling Longitudinal Vehicle Response. 21 st Biennial ASME Conference on Mechanical Vibration and Noise.
Scope of research a) To understand the effect of the tyre-road contact on the severity and frequency content of low frequency driveline oscillations during traction manoeuvres b) To understand the contribution of low frequency tyre structural dynamics in driveline oscillations c) To investigate the influence of secondary components such as the suspension d) To create predictive tools that will allow driveline refinement at an early stage of design
Method of attack a) Create driveline/vehicle models of 2WD and 4WD vehicles b) Combine driveline/vehicle models with tyre models of increasing complexity c) Obtain results in the time and frequency domains d) Linearise models and study the relevant vibration modes of the driveline e) Supplement with experimental measurements
Modelling and simulation Driveline/vehicle modelling Driveline schematic Lumped parameter model Models implemented: a. Manual RWD driveline with open differential b. RWD driveline with auto transmission/torque converter c. 4WD driveline with manual transmission coupled with 6 DOF vehicle model + suspension kinematic model
Models implemented: Modelling and simulation Tyre modelling a. Tyre as a torsional spring with its belt geared to the ground (kinematic relationship) b. Steady-state (Magic Formula) c. Non-linear relaxation length + Magic Formula model d. Rigid ring model with torsional and translational belt modes (in-plane) + Magic Formula a. b. c. d.
Modelling and simulation Forward speed:.5 m/s Forward speed: 5 m/s Mode Baseline results for RWD driveline with open differential on high-µ road Model Torsional spring Magic Formula Relaxation length Damping Damped Damping Damped Damping Damped freq ratio freq (Hz) ratio freq (Hz) ratio (Hz) Mode 6.172 443.5.173 443.5.172 443.5 5.71 226.8.76 225.1.71 226.8 4.764 73.7.85 72.6.764 73.7 3.71 3.8 > 1.81 3.8 2. 2.6 > 1.32 2.6 1.3 2.4.24 3.6.159 2.4. (RB). (RB). (RB) Model Torsional spring Magic Formula Relaxation length Damping Damped Damping Damped Damping Damped freq ratio freq (Hz) ratio freq (Hz) ratio (Hz) 6.172 443.5.173 443.5.172 443.5 5.71 226.8.16 225.6.71 226.8 4.764 73.7.829 72.6.764 73.7 3.71 3.8 > 1.165 3.8 2. 2.6 > 1.321 2.6 1.3 2.4.237 3.5.1559 2.4. (RB). (RB). (RB) Shuffle mode
Modelling and simulation Example results for RWD driveline with open differential on low/low split-µ and high/low split-µ (non-linear relaxation length tyre model) 4 Half shaft torque 18 Half shaft torque 35 16 3 14 Halfshaft torque (Nm) 25 2 15 Halfshaft torque (Nm) 12 1 8 6 1 4 5 2.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Time (s).2.4.6.8 1 1.2 1.4 1.6 1.8 2 Time (s) High/low split-µ Low/low split-µ
Modelling and simulation Frequency domain results for RWD driveline with open differential on uniform low-µ, low/low split-µ and high/low split-µ (non-linear relaxation length tyre model) Original results by linearisation of non-linear model Model Relaxation length Mode Damping ratio Damped freq (Hz) 6.172 443.5 2 18 16 14 12 Half shaft torque (Nm) Uniform low-mu High/low split-mu Low/low split-mu 5.71 226.8 4.764 73.7 3.81 3.8 2.32 2.6 1.159 2.4. (RB) Y(f) 1 8 6 4 2 12 Hz 23 Hz 29 Hz 5 1 15 2 25 3 35 4 45 5
Modelling and simulation Frequency domain results for RWD driveline with open differential on uniform low-µ, low/low split-µ and high/low split-µ (non-linear relaxation length tyre model) 1.8.6 Symmetric modes by linearisation 2 18 16 Half shaft torque (Nm) Uniform low-mu High/low split-mu Low/low split-mu Relative magnitude of oscillation.4.2 -.2 -.4 -.6 -.8-1 443.5 Hz 73.7 Hz 3.8 Hz 2.4 Hz Veh WheL DifL GbIn Flyw GbIn DifR WheR Veh Position Y(f) 14 12 1 8 6 4 2 12 Hz 23 Hz 29 Hz 5 1 15 2 25 3 35 4 45 5
Modelling and simulation Frequency domain results for RWD driveline with open differential on uniform low-µ, low/low split-µ and high/low split-µ (non-linear relaxation length tyre model) 1.8.6 Anti-symmetric modes by linearisation 226.8 Hz 2.6 Hz 2 18 16 Half shaft torque (Nm) Uniform low-mu High/low split-mu Low/low split-mu Relative magnitude of oscillation.4.2 -.2 -.4 -.6 -.8 Y(f) 14 12 1 8 6 4 2 12 Hz 23 Hz 29 Hz -1 Veh WheL DifL GbIn Flyw GbIn DifR WheR Veh Position 5 1 15 2 25 3 35 4 45 5
Modelling and simulation Example results for RWD driveline with open differential on uniform low-µ, low/low split-µ and high/low split-µ (non-linear relaxation length tyre model) Longitudinal tyre force (N) 4 35 3 25 2 15 1 5 A case for partial tyre-road decoupling X:.3 Y: 248 X:.42 Y: 1942 Tyre-road decoupling mu = 1 mu =.5 Y(f) 2 18 16 14 12 1 8 6 4 2 Half shaft torque (Nm) 12 Hz 23 Hz 29 Hz Uniform low-mu High/low split-mu Low/low split-mu.5.1.15.2.25 Practical slip ratio 5 1 15 2 25 3 35 4 45 5
Modelling and simulation Frequency domain results for RWD driveline with open differential on uniform low-µ, low/low split-µ and high/low split-µ (non-linear relaxation length tyre model) Linearisation using the concept of full/partial decoupling Model Wheels fully decoupled from road One wheel coupled to road Mode Damping ratio Damped freq (Hz) Damping ratio Damped freq (Hz) 6.172 443.5.172 443.5 5.71 226.8.71 226.8 4.769 73.6.766 73.6 3.81 23.2.71 28.6 2 >1..33 12. 1.... Y(f) 2 18 16 14 12 1 8 6 4 2 12 Hz Half shaft torque (Nm) 23 Hz 29 Hz Uniform low-mu High/low split-mu Low/low split-mu 5 1 15 2 25 3 35 4 45 5
Experimental investigation Traction tests carried out on split-µ surfaces
Experimental investigation Wheel speeds superimposed on a wavelet graph of measured vibration on wheel hub (left wheel on low-µ surface) Detail
25 2 Experimental investigation Acceleration traces measured at the wheel hubs 1.4 Left 1.2 Left Acceleration (m/s 2 ) 15 1 5-5 -1-15 FFT Y(f) (m/s 2 ) 1.8.6.4.2-2 26.2 26.4 26.6 26.8 27 27.2 27.4 27.6 Time (s) 6 4 Right 1 2 3 4 5 6 7 8 9 1.7 Right.6 2 Acceleration (m/s 2 ) -2-4 -6 FFT Y(f) (m/s 2 ).5.4.3.2-8 -1.1-12 26.2 26.4 26.6 26.8 27 27.2 27.4 27.6 Time (s) 1 2 3 4 5 6 7 8 9 1
Experimental investigation 1.4 1.2 Left 18 12 Accel. on low-µ side Y(f) (m/s 2 ) 1.8.6.4 Phase angle (deg) 6-6 Phase angle.2-12 Accel. on high-µ side Y(f) (m/s 2 ) 1 2 3 4 5 6 7 8 9 1.7 Right.6.5.4.3.2.1 1 2 3 4 5 6 7 8 9 1 Relative magnitude of oscillation (rads) -18 1 2 3 4 5 6 7 8 9 1 1.8.6.4.2 -.2 -.4 -.6 -.8-1 37 Hz 18 Hz 7 Hz TBLx WhLx TBL WhL DOL DOR WhR TBR WhRx TBRx Degree of freedom Eigenvectors
Experimental investigation 1.4 1.2 Left 18 12 Accel. on low-µ side Y(f) (m/s 2 ) 1.8.6.4 Phase angle (deg) 6-6 Phase angle.2-12 Accel. on high-µ side Y(f) (m/s 2 ) 1 2 3 4 5 6 7 8 9 1.7 Right.6.5.4.3.2.1 Relative magnitude of oscillation (rads) -18 1 2 3 4 5 6 7 8 9 1 1 55 Hz.8.6.4.2 -.2 -.4 -.6 -.8 Eigenvectors 1 2 3 4 5 6 7 8 9 1-1 TBL WhL WhR TBR Degree of freedom
Concluding remarks a) Steady-state tyre models cannot accurately predict the shuffle response - a flexible connection between the rim and the road is essential b) The tyre-road interface largely determines the damping of the lower frequency modes of the driveline, up to approx. 3 Hz c) The above damping is forward-speed dependent, with the dependency reducing as the frequency of the mode increases d) Frequency migration on split-µ surfaces can be predicted via the notion of tyre-road decoupling e) A structural tyre model including in-plane torsional and translational modes is essential in order to capture the full extent of important interactions f) Acceleration measurements at the wheel hubs can provide an indication of driveline response and assist with model validation
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