Rattle Industrial Consortium Project Eaton R & D Spicer Clutch iat CR Luk Volvo Trucks Saa Dynamic Interactions etween Loaded and Unloaded Gear Pairs under Rattle Conditions Tae-Chung Kim (Ph.D Student Rajendra Singh (Professor
Vehicle Engine Drive Train Eperimental Case Study Light truck (3/4 ton V6 Turo Diesel Rear wheel drive with two U-joints Transmissions 5 speed with overdrive dual-ais type (oth and B Sensors 3 magnetic pickups analog type triaial accelerometer (on ale earing nalyzer ROTEC [9] Channel : reference speed (flywheel Channel : each gear pair location on the counter shaft (driving Channel 3: each gear pair location on the output shaft (driven Vehicle and instrumentation specifications for an eperimental case study. Engine Speed Engaged Pair (3 rd R e la tive c c e le ra tio n θ p (peak-to-peak ra d/s Headset Pair Unloaded Pair st nd Overdrive Noise Perception 850 rpm 500 000 800 900 300 No Rattle 800 000 5000 Severe 950 rpm 300 400 (0 m/s (89 m/s (863 m/s Ra ttle Relative acceleration levels from the vehicle ( run-up eperiments. Numers within the parentheses are corresponding translational accelerations where availale.
Dual-es Type Transmission Synchronizer Input Shaft Main Shaft Headset Gear Overdrive Gear Counter Shaft Reverse Idler
Mathematical Simulation Model Typical non-linear simulation model for gear rattle analysis
Linear Simulation Viration Mode 3 4 5 Natural requency (Hz 5 959 384 58 7564 Normalized Modal Dis pla cements lywheel ( θ -0.007 0.000 0.000 0.000 0.000 Clutch Hu ( θ H 0.999.000-0.00-0.00 0.000 Headset Driver and Input Shaft ( θ IN.000-0.850.000 0.06 0.00 Headset Driven Counter Shaft + Other Gears ( θ CT.000-0.973-0.4-0.65 0.03 Engaged (Loaded Gear + Output Shaft ( θ EO.000-0.987-0.5.458 0.004 Unengaged (Unloaded Gear ( θ UO.000-0.975-0.58-0.97.4 Natural frequencies and mode shapes of the 6 degree of freedom linear model of igure in the third gear engaged condition.
Non-linear Model Clutch Torque T c ( H Multi-Staged Clutch Torque T ( ( ( c = Tc + Tc Multi-staged Stiffness φ k C φ k C H = θ θ Relative ngular Displacement H T c kc φ + kc( φ ( = kc kc φ + kc( + φ Multi-staged Hysteresis φ > φ φ < φ Multi-staged clutch non-linearity T c H H H + sgn( φ ( = H H H + sgn( + φ > 0 < 0
Non-linear Model Gear Mesh orce Backlash = ( f Gear acklash non-linearity Relative Displacement < + > = f 0.0 ( arctan( ( sgn( σ π σ ξ = ( ( ( ( ( σ ξ σ ξ f + + + = Gear orce from a acklash Smoothening unction Clearance Nonlinearity
Non-linear Model Output Shaft θ meo θ meo θ meo θ muo θ muo θ muo Oil seal earings Unloaded gear Push > meo θ muo Drag θ meo θ muo θ < Equal θ = θ meo muo Relative motions etween unloaded gear and output shaft
Results (Relative cceleration and Displacement Unloaded gear pair (O/D Engaged gear pair (3rd
Results (Clutch Torque and Gear orce Rela tive ccele ra tion θ (peak-to-peak m/s p Engaged (3 rd Headset O/D Simulation 45 45 90 Eperiment 0 89 863
Results (Clutch Torque and Gear Mesh orce Unloaded Ine rtia I UO Gear Mesh orce f ( Re la tive Dis pla ce me nt Impa ct Gear (kg/m (N ( Condition (mm Me a n Ma. Min. Minimum Ma imum st 4.000e-4 0 0 0-0.050-0.0500 None nd 3.500e-4 50 90 0-0.050-0.0436 S ingle -S ide d Overdrive.000e-4 7 436 0-0.050-0.043 S ingle -S ide d Gear mesh forces and relative displacements of unloaded gears in the third gear engaged condition.
Non-linear Model (Dual Mass lywheel k H I I θ θ k H ( ( ( T T T + = Single-staged Stiffness Single-staged Hysteresis Torque from Dual Mass lywheel k T ( = ( T < > = 0 0 ( H H T θ θ =
Effect of Dual Mass lywheel
Effect of Drag Torque Distriution Clutch torque and gear mesh forces Higher drag on Input Shaft Lower drag on Counter Shaft Impact Severe Doule-Sided Impact
Effect of Drag Torque on Gears Drag Torque ( D4 T 00 % (Baseline Mean m (degree Clutch Motion Dyna mic Range p (degree 3.97 0.59-7.35 50 % 4.08 0.7-7.45 00 % 4.7 0.90 7.65 0 % 4.3 0.96 7.68 000 % 6.04.9 0.7 (transition Impact Conditions and Relative ccelerations (m/s Unloaded P a ir Engaged P a ir He a dse t P a ir 90 535 55 None 0.6 475 45 305 None 55 None. 55 45 45 5 None 4.0 95 Summary of the effects of drag torque T D 4
Effect of Drag Torque on Gears Clutch Stiffness Transition
Conclusion The reduced 6 degree of freedom non-linear model effectively shows dynamic interactions etween engaged and unloaded gear pairs Results from the simulation demonstrate phenomena that are similar to those oserved in vehicle eperiments Significant single-sided impacts within the unloaded gear pair regime can trigger impacts within headset and engaged pairs Inertial and drag torque distriutions appear to e critical to the rattle prolem The drag torque control could e an inepensive solution ut changes associated with operating temperatures and clutch stiffness transitions should e considered