Dynamic Interactions between Loaded and Unloaded. Gear Pairs under Rattle Conditions
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1 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
2 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 No Rattle Severe 950 rpm (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.
3 Dual-es Type Transmission Synchronizer Input Shaft Main Shaft Headset Gear Overdrive Gear Counter Shaft Reverse Idler
4 Mathematical Simulation Model Typical non-linear simulation model for gear rattle analysis
5 Linear Simulation Viration Mode Natural requency (Hz Normalized Modal Dis pla cements lywheel ( θ Clutch Hu ( θ H Headset Driver and Input Shaft ( θ IN Headset Driven Counter Shaft + Other Gears ( θ CT Engaged (Loaded Gear + Output Shaft ( θ EO Unengaged (Unloaded Gear ( θ UO Natural frequencies and mode shapes of the 6 degree of freedom linear model of igure in the third gear engaged condition.
6 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
7 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
8 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
9 Results (Relative cceleration and Displacement Unloaded gear pair (O/D Engaged gear pair (3rd
10 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 Eperiment
11 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 None nd 3.500e S ingle -S ide d Overdrive.000e S ingle -S ide d Gear mesh forces and relative displacements of unloaded gears in the third gear engaged condition.
12 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 =
13 Effect of Dual Mass lywheel
14 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
15 Effect of Drag Torque on Gears Drag Torque ( D4 T 00 % (Baseline Mean m (degree Clutch Motion Dyna mic Range p (degree % % % % (transition Impact Conditions and Relative ccelerations (m/s Unloaded P a ir Engaged P a ir He a dse t P a ir None None 55 None None Summary of the effects of drag torque T D 4
16 Effect of Drag Torque on Gears Clutch Stiffness Transition
17 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
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