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Research Papers: Internal Combustion Engines

# Dynamics Analysis of the Triangular Rotary Engine Structures

[+] Author and Article Information
Chiu-Fan Hsieh

Department of Mechanical and
Computer-Aided Engineering,
National Formosa University,
Huwei 63201, Yunlin, Taiwan
e-mail: cfhsieh@nfu.edu.tw

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 9, 2017; final manuscript received March 7, 2018; published online July 9, 2018. Assoc. Editor: Alexandrina Untaroiu.

J. Eng. Gas Turbines Power 140(11), 112804 (Jul 09, 2018) (12 pages) Paper No: GTP-17-1052; doi: 10.1115/1.4039810 History: Received February 09, 2017; Revised March 07, 2018

## Abstract

A triangular rotary engine includes several main components such as an eccentric shaft, a sun gear, a triangular rotor, a chamber, and apex seals. This study constructs the mathematical models for the chamber and triangular rotor profiles in a rotary engine, as well as for the kinematics and contact force of its apex seals by using the epitrochoid and envelope principles. The chamber profile is represented by design parameter, trochoid ratio, whose limitations are investigated together with the volume ratio. To simplify the calculation, the dynamics analysis model ignores the effects of combustion and thermal conditions in rotary engines. Gas force effect is taken into account by first constructing a fluid analysis model that measures the gas fluid moment on the triangular rotor. Then, based on the mathematical models of chamber and rotor, a systematic dynamics analysis model for a rotary engine is built. It allows analyzing the kinematics and the stress variations in all components of the engine. The dynamics model considers both output shaft torsion and fluid moment. The dynamics analysis then uses three cases of trochoid ratio to illustrate the effects of chamber profile design on the system dynamics properties of rotary engines. The results not only show the dynamic properties and differences in various mechanism designs but also indicate the stability and stress level in the components. In conclusion, the higher trochoid ratio with a larger variation in the chamber profile curvature reduces system stability and increases vibrations, stress fluctuations, and large stress peaks risk.

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## Figures

Fig. 1

Generation principle of profile

Fig. 2

Design results of theoretical profile

Fig. 3

Illustration of rotational position

Fig. 4

(a) Volume and (b) volume ratio variation

Fig. 5

Grid generation

Fig. 6

Pressure and stream line for λ=0.5: (a) pressure and stream line at 0.11 s, (b) pressure and stream line at 0.15 s, and (c) pressure and stream line at 0.19 s

Fig. 7

Turbulent kinetic energy within engines: (a) turbulent kinetic energy (TKE) and (b) TKEmax–TKEmin

Fig. 8

Results of fluid moment on the triangle rotors

Fig. 9

Design results of triangle rotors with same weight: (a) λ = 0.3, (b) λ = 0.4, and (c) λ = 0.5

Fig. 10

Size of a one-piece leaf spring

Fig. 11

Angular velocity analysis of the apex seal: (a) angular velocity and (b) statistical analysis

Fig. 12

Translational velocity analysis of the apex seal: (a) translational velocity and (b) statistical analysis

Fig. 13

Results of mesh and stress: (a) mesh calculation and (b) stress calculation

Fig. 14

Stress comparisons of the eccentric shaft: (a) higher stress part and (b) lower stress part

Fig. 15

Stress comparisons of the sun gear: (a) higher stress part and (b) lower stress part

Fig. 16

Statistical results and comparisons

Fig. 17

Stress comparisons of the triangle rotor: (a) higher stress part and (b) lower stress part

Fig. 18

Stress comparisons of the apex seal: (a) higher stress part and (b) lower stress part

Fig. 19

Average stress and comparisons

Fig. 20

Stress peaks positions and conditions for λ=0.5: (a) 46 deg, (b) 136 deg, (c) 226 deg, and (d) 316 deg

Fig. 21

Large stress peak positions and conditions of apex seal for λ=0.5: (a) 81 deg, (b) 125 deg, and (c) 286 deg

## Errata

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