Modeling the light-powered self-rotation of a liquid crystal elastomer fiber-based engine

Self-oscillating systems possess the ability to convert ambient energy directly into mechanical work, and new types of self-oscillating systems are worth designing for practical applications in energy harvesters, engines and actuators. Taking inspiration from the four-stroke engine. A concept for a self-rotating engine is presented on the basis of photothermally responsive materials, consisting of a liquid crystal elastomer (LCE) fiber, a hinge and a turnplate, which can self-rotate under steady illumination. Based on the photo-thermal-mechanical model, a nonlinear theoretical model of the LCE-based engine under steady illumination is proposed to investigate its self-rotating behaviors. Numerical calculations reveal that the LCE-based engine experiences a supercritical Hopf bifurcation between the static regime and the self-rotation regime. The self-rotation of the LCE-based engine originates from the photothermally driven strain of the LCE fiber in illumination, and its continuous periodic motion is sustained by the correlation between photothermal energy and damping dissipation. The Hopf bifurcation conditions are also explored in detail, as well as the vital system parameters affecting self-rotation frequency. Compared to the abundant existing self-oscillating systems, this conceptual self-rotating LCE-based engine stands out due to its simple and lightweight structure, customizable dimensions and high speed, and it is expected to offer a broader range of design concepts applicable to soft robotics, energy harvesters, medical instruments, and so on.

Figure 1

Schematics of a self-rotating engine, consisting of an LCE fiber, a hinge and a turnplate. (a) Four-stroke engine. (b) Reference state (front view). (c) Reference state (end view). (d) Initial state. (e) Non-illuminated state. (f) Illuminated state. Half of the system is steadily illuminated. The LCE-based engine can maintain a continuous periodic rotation under steady collimated illumination.

Figure 2

Time histories and phase trajectories for the two motion regimes of the LCE-based engine. (a) and (b) are the self-rotation regime with $\overline{q}=0.2$; (c) and (d) are the static regime with $\overline{q}=0.05$. The other parameters are $C_0=0.3, \overline{k}=40, \overline{\beta }=0.02, {\theta }_0=0, \overline{R}=0.05$, and ${\stackrel{\cdot }{\overline{\theta }}}_0=2$. The LCE-based engine under steady illumination can develop into two motion regimes: the static regime and the self-rotation regime, which means that the engine experiences a supercritical Hopf bifurcation as described in Sec. 4.

Figure 3

Mechanism of the self-rotation for the typical case in 3 (a) and (b). (a) Time history curve of the temperature $\overline{T}$ in the LCE fiber. (b) Time history curve of the photothermally induced fiber length change. (c) Time history curve of the tension of the LCE fiber. (d) Time history curve of the rotational moment. (e) Relationship between rotational moment and angular position. (f) Relationship between damping moment and angular position.

Figure 4

Snapshots of the self-rotation of the LCE-based engine within one cycle for the typical case in Figs. 2 and 2. Under steady illumination, the LCE-based engine will exhibit a continuous periodic rotation.

Figure 5

Influence of heat flux on the self-rotation, for $C_0=0.3, \overline{k}=40, {\stackrel{\cdot }{\overline{\theta }}}_0=2, \overline{\beta }=0.02, \overline{R}=0.05$, and ${\overline{\theta }}_0=0$. (a) Limit cycles. (b) Frequency variation with heat flux. There exists a critical heat flux of $\overline{q}\approx 0.06$ for the supercritical Hopf bifurcation between the static regime and the self-rotation regime. With the increase of heat flux $\overline{q}$, the frequency of self-rotation presents an upward trend.

Figure 6

Influence of contraction coefficient on the self-rotation, for $\overline{q}=0.2, \overline{k}=40, {\stackrel{\cdot }{\overline{\theta }}}_0=2, \overline{\beta }=0.02, \overline{R}=0.05$, and ${\overline{\theta }}_0=0$. (a) Limit cycles. (b) Frequency variation with contraction coefficient. A critical contraction coefficient of $C_0\approx 0.1$ is present for the supercritical Hopf bifurcation between the static regime and the self-rotation regime. As the contraction coefficient $C_0$ increases, the frequency of self-rotation tends to increase.

Figure 7

Influence of damping coefficient on the self-rotation, for $\overline{q}=0.2, \overline{k}=40, {\stackrel{\cdot }{\overline{\theta }}}_0=2, C_0=0.3, \overline{R}=0.05$, and ${\overline{\theta }}_0=0$. (a) Limit cycles. (b) Frequency variation with damping coefficient. A critical damping coefficient of $\overline{\beta }\approx 0.055$ exists for the supercritical Hopf bifurcation between the static regime and the self-rotation regime. The increase of damping coefficient $\overline{\beta }$ results in the decline of the self-rotation frequency.

Figure 8

Influence of spring constant on the self-rotation, for $C_0=0.3, \overline{\beta }=0.02, \overline{q}=0.2, {\overline{\theta }}_0=0, \overline{R}=0.05$, and ${\stackrel{\cdot }{\overline{\theta }}}_0=2$. (a) Limit cycles. (b) Frequency variation with spring constant. There is a critical spring constant of $\overline{k}\approx 4$ for the supercritical Hopf bifurcation between the static regime and the self-rotation regime. With the increase of spring constant $\overline{k}$, the frequency of self-rotation displays an increasing trend.

Figure 9

Influence of turnplate radius on the self-rotation, for $C_0=0.3, \overline{k}=40, \overline{q}=0.2, \overline{\beta }=0.02, {\overline{\theta }}_0=0$, and ${\stackrel{\cdot }{\overline{\theta }}}_0=2$. (a) Limit cycles. (b) Frequency variation with turnplate radius. A critical turnplate radius of $\overline{R}\approx 0.01$ is present for the supercritical Hopf bifurcation between the static regime and the self-rotation regime. As the turnplate radius $\overline{R}$ increases, the frequency of self-rotation increases.

Figure 10

Influence of initial velocity on the self-rotation, for $C_0=0.3, \overline{k}=40, \overline{q}=0.2, \overline{\beta }=0.02, \overline{R}=0.05$, and ${\overline{\theta }}_0=0$. (a) Limit cycles. (b) Frequency variation with initial velocity. A critical initial velocity of ${\stackrel{\cdot }{\overline{\theta }}}_0\approx 0.67$ exists for triggering the self-rotation, while the initial velocity ${\stackrel{\cdot }{\overline{\theta }}}_0$ has no effect on the frequency of self-rotation.