Abstract
A novel arc-cylinder type dielectric elastomer generator (AVI-DEG) is proposed in this paper to scavenge energy from rotational environment. The proposed AVI-DEG consists of a hollow arc cylinder, an inner rigid ball, two pairs of identical cylindrical frames and two pre-stretched dielectric elastomer membranes (DEMs). When the system is subjected to rotations, the rotational energy can be harvested through the impacts between the ball and the membranes. To simplify the complex rotations resulting from torsional vibrations and pendulum, etc., a harmonic rotational excitation is considered to act on the proposed AVI DEG. The dynamical behaviors of the proposed AVI-DEG are first analyzed theoretically, based on which the system’s energy harvesting (EH) process is further derived. The experiments measuring the output voltages of a DEM under the impacts of a ball using a single-sided impact (SSI) model, which has been conducted previously, are introduced to verify the EH process of the AVI-DEG at each impact. Furthermore, the numerical simulations are conducted to present the dynamical and electrical responses of the system under different rotational excitations, and the parametric influences of the rotational excitation (frequency and amplitude) and system’s dimensions on the system’s EH performance are discussed in detail. Research results show that appropriately setting these parameters can significantly improve the system’s EH performance. This work is also beneficial to investigating the EH performance of the system with given dimensions, or optimizing the system’s dimensions under a given rotational excitation.
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Abbreviations
- \(d_{0}\) :
-
Inner diameter of the hollow arc cylinder
- \(f_{0} \) :
-
Frequency of the angular velocity
- \(g \) :
-
Gravitational acceleration
- \( h_{0} \) :
-
Initial thickness of the pre-stretched DEM
- \( h_{1} \) :
-
Smallest thickness of the pre-stretched DEM reaching its largest deformation
- \( h_{c} \) :
-
Thickness of the hollow arc cylinder
- \( i \) :
-
\(i{{\rm th}} \) impact
- \(\Delta k_{i} \) :
-
Kinetic energy loss of the ball at the \(i{{\rm th}} \) impact
- \(m \) :
-
Mass of the ball
- \(r \) :
-
Restitution coefficient of the pre-stretched membrane
- \(r_{b} \) :
-
Radius of the ball
- \(t_{1}, \) \( t_{2} \) :
-
Start time and end time of the AVI-DEG operation
- \(v_{{m - }}, \) \(v_{{m + }} \) :
-
Tangential velocities of the ball just before and after each impact
- \( v_{M} \) :
-
Tangential velocity of the cylinder
- \( v_{{M - }},\) \(v_{{M + }} \) :
-
Tangential velocities of the cylinder just before and after each impact
- \(\Delta v \) :
-
Relative velocity between the ball and the pre-stretched DEM before each impact
- \( v_{{m - }}^{i} \) :
-
Tangential velocity of the ball before the \( i{{\rm th}}\) impact
- \( v_{{M - }}^{i} \) :
-
Tangential velocity of the cylinder before the \( i{{\rm th}}\) impact
- \(A \) :
-
Amplitude of the angular velocity
- \(A_{0} \) :
-
Initial surface area of the pre-stretched DEM
- \(A_{1} \) :
-
Largest surface area of the pre-stretched DEM reaching its largest deformation
- \(A_{{End}}, \) \(B_{{End}} \) :
-
\( A_{{End}}\) pre-stretched DEM and \( B_{{End}}\) pre-stretched DEM
- \(C_{{\max }}, \) \( C_{{\min }} \) :
-
Maximum and minimum capacitances of the pre-stretched DEMs at each impact
- \(N_{T} \) :
-
Total number of impacts during the time interval of the AVI-DEG operation
- \(R_{0} \) :
-
Effective radius of the pre-stretched DEM
- \(R_{1}, \) \(R_{2} \) :
-
Inner curved radius and outer curved radius of the hollow arc cylinder
- T:
-
Environment temperature
- \(Vol \) :
-
Volume of the pre-stretched DEM
- \( W \) :
-
Electric energy gain
- \(W_{i} \) :
-
Electric energy gain at the \(i{{\rm th}} \) impact
- \( W_{{total}} \) :
-
Total electric energy gain
- \( \delta _{{\max }} \) :
-
Largest central deflection of the pre-stretched DEM
- \(\varepsilon _{0} \) :
-
Vacuum permittivity
- \( \varepsilon \) :
-
Relative permittivity of the DE materials
- \(\eta \) :
-
Energy conversion efficiency of the AVI-DEG
- \(\theta _{b}, \) \(\theta _{c} \) :
-
Angular displacements of the ball and the hollow arc cylinder
- \(\theta _{c} (0) \) :
-
Initial angular displacement of the hollow arc cylinder
- \( \theta _{s} \) :
-
Angle between the \(A_{{End}} \)pre-stretched DEM and the \(B_{{End}} \) pre-stretched DEM
- \(\Delta \theta \) :
-
Relative angular displacement between the ball and the hollow arc cylinder
- \(\Delta \theta _{{\max }} \) :
-
Maximum angle that the ball can move inside the hollow arc cylinder
- \( \theta ^{\prime}_{b},\) \( \theta ^{\prime\prime}_{b} \) :
-
Angular velocity and acceleration of the ball
- \(\lambda _{{pre}} \) :
-
Pre-stretched ratio of the pre-stretched DEM
- \(\phi _{{in}}, \) \( \phi _{{out}}\) :
-
Input voltage and output voltage of the AVI-DEG
- \(\omega _{b}, \) \( \omega _{c} \) :
-
Angular velocities of the ball and the hollow arc cylinder
- \(\Delta \omega \) :
-
Relative angular velocity between the ball and the hollow arc cylinder (before each impact)
- \( \omega _{{b - }}, \) \(\omega _{{b + }} \) :
-
Angular velocities of the ball just before and after each impact
- \(\omega _{{b - }}^{i} \) :
-
Angular velocity of the ball before the \(i{{\rm th}} \) impact
- \( \omega _{c}^{i} \) :
-
Angular velocity of the hollow arc cylinder at the \(i{{\rm th}} \) impact
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Zhang, J.W. Rotational energy harvesting from a novel arc-cylinder type vibro-impact dielectric elastomer generator. Int J Mech Mater Des 18, 587–609 (2022). https://doi.org/10.1007/s10999-022-09594-w
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DOI: https://doi.org/10.1007/s10999-022-09594-w