A static equilibrium condition for the steady-state analysis of variable-stroke swash plate mechanism

Abstract

Variable-stoke swash plate mechanisms are widely used for compressors in automotive air-conditioning systems, but the dynamics of the system has not been investigated sufficiently. In the present study, we derived a dynamic equation based on the Lagrangian mechanics for the mechanism and solved it numerically. The solutions were compared with the ones obtained from the commercial multibody dynamics software, DAFUL. We proposed a static function that can be conveniently used to predict the steady-state behavior of the system without conducting a full dynamic analysis of the variable-stoke swash mechanism. Using the static function, for example, we showed why the stroke of the variable-stoke swash tends to increase with the driving speed and showed a simple way to reverse the tendency. Especially, we observed that the system can have multiple steady-state solutions depending on initial conditions. Based on this observation, we theoretically showed that a hysteresis phenomenon can occur in the variable-stoke swash mechanism so that the behavior of the system can depend on the operation history of the system.

Keywords

Variable-stroke swash plate static function automotive compressor Lagrangian hysteresis

Get full access to this article

View all access options for this article.

References

Vaghela

Kapadia

. A brief literature survey on an automobile air - conditioning system. IJEDR 2014; 20: 558–570.

Bedotti

Pastori

Scolari

, et al. Dynamic modeling of the swash plate of a hydraulic axial piston pump for condition monitoring applications. Energy Procedia 2018; 148: 266–273.

Tian

Dou

Yang

, et al. Instability of automotive air conditioning system with a variable displacement compressor. Part 2. Numerical simulation. Int J Refrig 2005; 28: 1111–1123.

Tian

Liao

. A mathematical model of variable displacement swash plate compressor for automotive air conditioning system. Int J Refrig 2006; 29: 270–280.

Tian

Dou

. Experimental investigation and numerical simulation on the hysteresis zone of a variable displacement wobble plate compressor. Int J Refrig 2005; 28: 988–996.

Lee G and Lee T. A study on the variable displacement mechanism of swash plate type compressor for automotive air conditioning system. In: International compressor engineering conference, Purdue, 12–15 July 2004.

Yoshida

Kasahara

Watanabe

. Dynamic behavior of variable stroke swash plate mechanism. J Syst Des Dyn 2008; 2: 561–571.

Choi J, Lim J, et al. Performance analysis on a variable capacity swash plate compressor. In: 24th International Compressor Engineering Conference, Purdue, 9–12 July 2018.

Gao

Cheng

Huang

, et al. Simulation analysis and experiment of variable-displacement asymmetric axial piston pump. Appl Sci 2017; 7: 328–343.

10.

Tian

Dou

Yang

, et al. Instability of automotive air conditioning system with a variable displacement compressor. Part 1. Experimental investigation. Int J Refrig 2005; 28: 1102–1110.

11.

Tian

Zhang

, et al. Experimental investigation on the characteristics of variable displacement swash plate compressor. Appl Therm Eng 2009; 29: 2824–2831.

12.

Goldstein

. Classical mechanics, 2nd ed. San Francisco, CA: Addison Wesley, 1980.

13.

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods .

14.

DAFUL, 4.1 user's manual. Seoul: Virtual motion Inc., 2012.

15.

Achten

. Dynamic high-frequency behavior of the swash plate in a variable displacement axial piston pump. Proc IMechE, Part I: J Systems and Control Engineering 2013; 227: 529–540.

16.

Choi

. Development of hysteresis friction model for a precise tracking control system. Proc IMechE, Part C: J Mechanical Engineering Science 2011; 226: 1338–1344.

17.

Jang

Kim

Bae

, et al. Rigid multibody model of the dynamic hysteresis and the contact force of automotive clutch damper springs. Proc IMechE, Part D: J Automobile Engineering 2013; 228: 190–198.

18.

Meng

Zhou

Jin

, et al. Modelling and experimental verification of a squeeze mode magnetorheological damper using a novel hysteresis model. Proc IMechE, Part C: J Mechanical Engineering Science 2019.

19.

Royston

. Leveraging the equivalence of hysteresis models from different fields for analysis and numerical simulation of jointed structures. ASME J Comput Nonlin Dyn 2008; 3: 031006.

20.

Xiao

Naganathan

, et al. Dynamic Preisach modelling of hysteresis for the piezoceramic actuator system. Mech Mach Theory 2002; 37: 75–89.

21.

Tan

Baras

. Adaptive identification and control of hysteresis in smart materials. IEEE Trans Autom Control 2005; 50: 827–839.