1. Study of Stirling Engine ME270 Zhiyu Gao

2. Introduction The Stirling engine uses the temperature difference between its hot end and cold end to establish a cycle of a fixed mass of gas expanding and contracting within the engine, thus converting thermal energy into mechanical power.

3. How it works Source: http://www.wikipedia.org

4. Schematic Schematic of Stirling Engine

5. Bond Graph

6. Differential Equations e1 = SE1 e2 = e5 e3=e5 e4=SE4 e5=Q5/C5+Q6/C5x6+Q8/C5x8+Q10/C5x10 e6=Q5/C6x5+Q6/C6+Q8/C6x8+Q10/C6x10 e7=SE7 e8=Q5/C8x5+Q6/C8x6+Q8/C8+Q10/C8x10 e9=e8 e10=Q5/C10x5+Q6/C10x6+Q8/C10x8+Q10/C10 e11=e10 e12=e11/T11x12 e13=e12 e14=e13/T13x14 e15=e14-e16 e16=f16*R16

7. Differential Equations f1=e1/R1+e2/R1x2 f2=e1/R2x1+e2/R2 f3=e3/R3+e4/R3x4 f4=e3/R4x3+e4/R4 f5=f2-f3 f6=e6/R6+e7/R6x7+e9/R6x9 f7=e6/R7x6+e7/R7+e9/R7x9 f8=f9 f9=e6/R9x6+e7/R9x7+e9/R9 f10=f11 f11=f12/T11x12 f12=f13 f13=f14/T13x14 f14=f15 f15=P15/I15 f16=f15

8. State Space Equations dQ5=SE1/R2x1+Q5/C5/R2+Q6/C5x6/R2+Q8/C5x8/R2+Q10/C5x 10/R2-Q5/C5/R3-Q6/C5x6/R3-Q8/C5x8/R3-Q10/C5x10/R3- SE4/R3x4 dQ6=Q5/C6x5/R6+Q6/C6/R6+Q8/C6x8/R6+Q10/C6x10/R6+SE7 /R6x7+Q5/C8x5/R6x9+Q6/C8x6/R6x9+Q8/C8/R6x9+Q10/C8x10/ R6x9 dQ8=Q5/C6x5/R9x6+Q6/C6/R9x6+Q8/C6x8/R9x6+Q10/C6x10/R 9x6+SE7/R9x7+Q5/C8x5/R9+Q6/C8x6/R9+Q8/C8/R9+Q10/C8x 10/R9 dQ10=P15/I15/T13x14/T11x12 dP15=Q5/C10x5/T11x12/T13x14+Q6/C10x6/T11x12/T13x14+Q8 /C10x8/T11x12/T13x14+Q10/C10/T11x12/T13x14-P15/I15*R16

9. Block Diagram Q5

10. Block Diagram Q6

11. Block Diagram Q8

12. Block Diagram Q10

13. Block Diagram P15

14. Simplified Bond Graph

15. Transfer Function Piston to Flywheel 8000000 1 ------- * ------------------------- 19 (100 s + 1) cos(P6) P6 is the rotated angle of the flywheel

16. Expected Result Flywheel speed VS Time