## Investigation of Acceleration Dependent Nonlinear Lubricated Friction in Hydraulic Actuation Systems

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##### Date

2016-02-05##### Author

Li, Scott

##### Type

Thesis##### Degree Level

Doctoral##### Abstract

Lubricated friction issues are central to all hydraulic actuation systems undergoing motion and any in-depth understanding of the nature of lubricated friction will advance future component design. The classic friction models of hydraulic actuation systems under steady state conditions and their dependency on velocity and temperature have been studied extensively over the past years. A model which is commonly employed to represent the characteristics of friction is that of Stribeck in which the dependency of the friction force is based on velocity alone. However, experimentally, it has been found that lubricated friction is dependent on acceleration. Thus, the Stribeck model can be considered as a subset of a dynamic friction model in which acceleration is zero. Thus, it can be concluded that the Stribeck model is best applied to cases when the change rate of the velocities is very small.
This thesis considers the dependency of lubricated friction on acceleration when pressure and temperature changes are relatively constant. As such, the basic hypothesis for this study was proposed as follows: “Lubricated friction in hydraulic actuation systems is not only a function of velocity, but is also a function of both velocity and acceleration”.
In this thesis several terms are defined which facilitate the description under which friction models are developed. For example, the term non-steady state friction is used to account for the effect of acceleration on lubricated friction force while in motion. Further, the lubricated friction models are divided into two groups: steady state friction models and non-steady state friction models.
Nonlinear friction modeling and measuring methods are reviewed in this dissertation. This review also includes nonlinear lubricated friction modeling in hydraulic actuation systems. A conclusion from this review was that limited research has been done in documenting and explicitly demonstrating the role of acceleration on lubricated friction.
The research first introduced a methodology to experimentally measure friction as a function of acceleration and to demonstrate this dependency in the form of a three dimensional graph. A novel technique to experimentally obtain data for the lubricated friction model was introduced. This allowed the lubricated friction forces to be measured as a function of velocity in a continuous manner, but with acceleration being held constant as a family parameter. Two different valve controlled hydraulic actuation systems (VCHAS) were studied under a wide variety of accelerations at constant temperature and pressure. To enable repeatable data collection for the different friction conditions and to accommodate for the effect of hysteresis, a periodic parabolic displacement waveform was chosen which enabled the acceleration to be a family parameter.
The second phase of the research introduced a method of representing the data (lubricated friction model) in a lookup table form. The relationship of lubricated friction (in this work, pressure differential, ΔP across the actuator) as a function of velocity and acceleration was presented in a unique semi-empirical 2D lookup table (2D LUT). Limitations of this experimental approach were identified, but the dependency on acceleration was clearly established.
The last phase of the study implemented this 2D LUT model into a practical software model of an actuator and demonstrated its accuracy when compared to its experimental counterpart. The semi-empirical model (2D LUT) was experimentally verified by implementing the semi-empirical and Stribeck models into a real time simulation of an actuator and by comparing the experimental outputs against simulated outputs for a common sinusoidal input. A sinusoidal actuator displacement input was chosen to test the simulations as it was not used in the collection of the original data. The output of the simulation was compared to the experimental results and it was evident that for the range in which data could be collected in developing the model, the proposed 2D LUT model predicted an output that was superior to a model which used a standard Stribeck model. It was concluded that the semi-empirical model could be integrated into a simulation environment and predict outputs in a superior fashion when compared to the Stribeck friction model.
Thus it was concluded that the stated hypothesis is consistent with the experimental evidence shown by all hydraulic actuators considered. Further, it was also observed that the traditional Stribeck form (steady state dynamic friction) does change with increasing acceleration to the point that the standard breakaway friction almost disappears.
It is evident that the 2D LUT is a viable tool for modeling the non-steady state friction of hydraulic actuation systems. The semi-empirical 2D LUT model so developed is a more global representation of hydraulic actuator lubricated friction. In this research, only linear hydraulic actuators were considered; however, the novel nonlinear semi-empirical 2D LUT lubricated friction model can be applied to any actuator (linear and rotary) and provides a new way in which the dynamic friction can be viewed and modeled.

##### Degree

Doctor of Philosophy (Ph.D.)##### Department

Mechanical Engineering##### Program

Mechanical Engineering##### Supervisor

Burton, Richard; Habibi, Saeid##### Committee

Fotouhi, Reza; Zhang, Chris; Chen, Daniel; Gokaraju, Ramakrishna; Fales, Roger##### Copyright Date

January 2016##### Subject

Nonlinear Lubricated Friction

Stribeck

Acceleration Dependent

Hydraulic Actuation Systems

EHA

VCHAS

Parabolic

Differential Pressure

Steady State Friction

Non-Steady State Friction

Hysteresis

Modeling and Simulation

Semi-empirical Model

2D LUT

Model Verification, Validation and Implementation