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TECHNICAL PAPERS

Modeling and Analysis of Automatic Transmission Engagement Dynamics-Linear Case

[+] Author and Article Information
Joško Deur

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, I. Lučića 5, HR-10000, Zagreb, Croatiajosko.deur@fsb.hr

Jahan Asgari

 Ford Research and Advanced Engineering, MD 2036, P.O. Box 2053, Dearborn, MI 48121jasgari@ford.com

Davor Hrovat

 Ford Research and Advanced Engineering, MD 2036, P.O. Box 2053, Dearborn, MI 48121dhrovat@ford.com

Petar Kovač

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, I. Lučića 5, HR-10000, Zagreb, Croatia

In the (realistic) case of unequal stiffness coefficients khs,l and khs,r of the left and right half shafts, the equivalent stiffness coefficient ka (and correspondingly the equivalent damping coefficient ba) is calculated as (1-2): ka=4(1khs,l+1khs,r)1.

For the plate clutch kc=NfApμCre is valid, where Nf is the number of active friction surfaces, Ap is the piston area, μC is the Coulomb friction coefficient, and re=2(rout3rin3)[3(rout2rin2)] is the equivalent clutch radius (with rout and rin denoting outer and inner radii, respectively).

J. Dyn. Sys., Meas., Control 128(2), 263-277 (May 31, 2005) (15 pages) doi:10.1115/1.2192827 History: Received March 30, 2004; Revised May 31, 2005

A control-oriented model of a typical four-speed automatic transmission is developed by using the bond graph modeling method. The planetary gear set model utilizes the Karnopp friction model for hydraulic and one-way clutches, in order to provide a favorable computing efficiency. The full gear set model is reduced for various phases of the park/reverse and park/drive engagements. The reduced gear set models and linearized torque converter model are used as a basis for an algebraic analysis of the engagement dynamics. The analysis is originally conducted for the basic case of fully applied brake, and it is then extended by an analysis of the influence of wheel dynamics in the brake-off case. The analysis results are verified by computer simulations and experiments.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Power train model for brake-on case: schematic (a), bond graph (b), and block diagram (c).

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Figure 2

Schematic of gear set. FC—forward clutch, RC—reverse clutch, DC—direct clutch, BC—band clutch, LRC—low/reverse clutch, OWC1—one-way clutch 1, OWC2—one-way clutch 2, R1-C1-S1—first planetary gear, R2-C2—S2-second planetary gear.

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Figure 3

Bond graph model of gear set

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Figure 4

Bond graph model of gear set for park/reverse engagement

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Figure 5

Static friction model (a), and its modifications: classical model (b) and Karnopp model (c)

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Figure 6

Block diagram of Karnopp model for hydraulic clutch, and its modification (dashed lines in N1 and N2) for series connection of hydraulic and one-way clutches

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Figure 7

Static friction models for parallel (a) and series (b) connections of hydraulic clutch and one-way clutch.

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Figure 8

Block diagram of Karnopp model for parallel connection of hydraulic and one-way clutches

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Figure 9

Principal block diagram of overall gear set model based on Karnopp clutch friction model

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Figure 10

Torque converter static curves

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Figure 11

Nonlinear static model of torque converter (a) and its linearized form (b)

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Figure 12

Linearized power train model for low/reverse clutch engagement phase

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Figure 13

Linearized power train model for final park/reverse engagement phase

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Figure 14

Principal scheme and bond graph of halfshaft/wheel/vehicle mass subsystem for brake-off case (a),(b), and corresponding scheme and bond graph when wheel inertia and vehicle mass influences are neglected (c),(d)

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Figure 15

Bond graph model of gear set for park/drive engagement

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Figure 16

Linearized power train model for forward clutch engagement phase

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Figure 17

Comparative simulation and experimental responses of park/reverse engagement

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Figure 18

Comparative simulation and experimental responses of park/drive engagement

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Figure 19

Transformation of bond graph in Fig. 3 to bond graph (b) using rules (a)

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