1. Dynamic Performance Analysis of a Full Toroidal IVT - a theoretical approach - 2004 International CVT and Hybrid Transmission Congress CVT2004 R. Fuchs, Y. Hasuda Koyo Seiko Co. Ltd. I. James Torotrak Development Ltd. 1/21

2. Performance Analysis of a Full Toroidal IVT - a theoretical approach - Content Motivations Approach Dynamics of the full toroidal variator Interaction variator-hydraulic Variator system damping Conclusion 2/21

3. Motivations IVT dynamic in the frequency domain Prediction of system behavior System design Transmission and driveline control Performance Analysis of a Full Toroidal IVT - a theoretical approach - 3/21

4. Approach Interaction Variator-hydraulic Interaction Variator-driveline (engine side) Interaction Variator-driveline (vehicle side) Performance Analysis of a Full Toroidal IVT - a theoretical approach - 4/21

5. The Full Toroidal Variator Dynamic model (4 inputs, 4 outputs) Variator (roller) ii oo PePe PpPp TiTi ToTo xpxp dx p /dt Performance Analysis of a Full Toroidal IVT - a theoretical approach - 5/21

6. Variator Dynamic: 2 Main Mechanisms 2 mains mechanisms dictates variator stability Performance Analysis of a Full Toroidal IVT - a theoretical approach - ② Castor angle  roller self-alignment.  castor angle and disc rotational direction linked. ① Traction drive  power transmission.  basic control law for piston and endload forces. 6/21

7. Variator Dynamic: Static Response Soft nonlinearities only due to toroidal geometry  Linearization possible Torque controlPiston position Performance Analysis of a Full Toroidal IVT - a theoretical approach - 7/21

8. Variator Stability: Frequency Response The full toroidal variator is a nonlinear MIMO system. Performance Analysis of a Full Toroidal IVT - a theoretical approach - 8/21

9. Variator Dynamic: Parametric Study Dominant parameters Roller speed, dx p /dt /F p 100Hz Performance Analysis of a Full Toroidal IVT - a theoretical approach - Castor angle, dx p /dt/F p Castor angle  Damping Endload force  Gain Roller speed  Stiffness 9/21

10. Hydraulic Interaction: Closed-Loop Mechanism of interaction Variator ratio change produces pressure perturbation. Performance Analysis of a Full Toroidal IVT - a theoretical approach - 10/21

11. Performance Analysis of a Full Toroidal IVT - a theoretical approach - Block diagram Hydraulic Interaction: Closed-Loop 11/21

12. Hydraulic Interaction: 2 Circuit Concepts Pressure control circuits based on flow control valve and pressure reducing valve Flow control valve (FCV) Valve spool not sensitive to pressure perturbation. FCV Pressure-reducing valve (PRV) Valve spool sensitive to pressure perturbation. PRV Performance Analysis of a Full Toroidal IVT - a theoretical approach - 12/21

13. Hydraulic Interaction: Frequency Response Comparison of frequency response of hydraulic circuit: F p /dx p /dt  bandwidth damping Pressure reducing valve Low pass. Resonance peak. Load compliance dependent Performance Analysis of a Full Toroidal IVT - a theoretical approach - 13/21 Low pass. Load pressure dependent.  gain  bandwidth Flow control valve

14. Hydraulic Interaction: Variator-FCV Circuit Stable interaction Hydraulic damping when variator resonance frequency is higher than hydraulic cut-off frequency Stability Performance Analysis of a Full Toroidal IVT - a theoretical approach - 14/21 Closed-loop: Hydraulic damping

15. Hydraulic Interaction: Variator-PRV Circuit Valve stability can be guaranteed using conventional hydraulic design techniques Stable example Performance Analysis of a Full Toroidal IVT - a theoretical approach - Closed-loop: Hydraulic damping 15/21

16. Hydraulic Interaction: Summary 2 basic circuits Performance Analysis of a Full Toroidal IVT - a theoretical approach - Flow control valve circuit Interaction stable. Hydraulic damping. Technically not optimum for control. Pressure reducing valve Interaction stable for high load compliance. Hydraulic damping. Technically good for control. 16/21 Importance of sub-system design for system stability.

17. System Damping: 2 Methods Performance Analysis of a Full Toroidal IVT - a theoretical approach - Flow control valve (FCV) Pressure-reducing valve (PRV) Differential hydraulic (major effect for FCV circuits) Damping orifices (major effect for PRV circuits) 17/21

18. System Damping: FCV Differential Circuit Performance Analysis of a Full Toroidal IVT - a theoretical approach - Frequency responses F p /dx p /dt for null differential pressures FCV hydraulic As pressures increases: Hydraulic gain increases & bandwidth decreases System damping 18/21 Variator + FCV hydraulic

19. System Damping: PRV Circuit with Restriction Performance Analysis of a Full Toroidal IVT - a theoretical approach - Frequency responses F p /dx p /dt for different restriction areas PRV hydraulic Variator + PRV hydraulic As the area decreases: Hydraulic gain & damping increase System damping 19/21

20. Conclusion The variator-hydraulic system is stable For a given variator design, the system performance is determined by the hydraulic circuit. Additional response tuning possible with control. Performance Analysis of a Full Toroidal IVT - a theoretical approach - System design This analysis is a key step in a theoretical approach of system design. It should be applied at the design stage to provide a system optimised for fast but well damped response. 20/21

21. Outlook Extension to the complete IVT driveline Complete theoretical investigation including dynamic response of the driveline. Experimental validation and implication on driveability Using test rigs and prototype vehicles. >> Future publications Performance Analysis of a Full Toroidal IVT - a theoretical approach - 21/21