2. 1
Table of Contents
I. Introduction .............................................................................................................................1
II. Design Overview....................................................................................................................1
III. Design Analysis ....................................................................................................................6
IV. Fabrication and Assembly .....................................................................................................6
V. Conclusion .............................................................................................................................6
References ..................................................................................................................................6
Appendix A-1 – Calculations ......................................................................................................6
Appendix A-2 – Part Schematics.................................................................................................6
Appendix A-3 – Attachments......................................................................................................6
I. Introduction
This report will cover the design and fabrication of a device called hydraulic pressure
energy harvester, specifically HPEH 5-3. This version of the device was designed to be
functional at higher static pressure, present in industrial hydraulic systems, while reusing
previous generation HPEH 5-2’s Parker piezoelectric stack for converting acoustic power into
electrical power. By incorporating a force-shunting mechanism achieved by the use of a
Belleville disc spring into the design, the peak stress in the piezoelectric stack can be
significantly reduced. The design process of 5-3 was assisted by earlier generations’ analyses of
HPEH devices, including but not limited to stress analysis and material selection. A final design
will be introduced including its justifications and analyses.
II. Design Overview
Force Shunting Concept. The main goal of HPEH 5-3 device is to reduce the bearing load
experienced by the previously used 5x5x20 mm3
Parker Piezoelectric stack. In previous HPEH
3. 2
designs, the maximum operable static pressure was limited by the maximum allowable stress of
the piezoelectric stack. The device specifications were made such that HPEH 5-3 device will be
functional for hydraulic fluid’s static pressures of up to 5000 psi (34.5 MPa) with dynamic
pressure assumed to be 10 percent of the static. In order to achieve this, a force-shunting
mechanism was introduced using a Belleville disc spring. A Belleville disc spring is a conical
washer that has spring-like characteristics; this will be the “shunt” of the HPEH device. The
main concept behind the design is that the disc spring would bear the load from static pressure
while the piezoelectric stack would capture the dynamic load and convert it to electrical power.
The Belleville disc spring and the Parker piezoelectric stack act as springs in parallel such that
their combined, or equivalent, stiffness is shown in Equation 1,
𝑘 𝑒𝑞 = 𝑘 𝐵𝑉 + 𝑘 𝑠𝑡𝑎𝑐𝑘 (1)
where
𝑘 𝐵𝑉 =
1
10
𝑘 𝑠𝑡𝑎𝑐𝑘 (2)
then
𝑘 𝑒𝑞 =
11
10
𝑘 𝑠𝑡𝑎𝑐𝑘
where keq is the equivalent stiffness of the parallel springs, kBV is the stiffness of the shunting
spring i.e. a Belleville disc spring, and kstack is the stiffness of the Parker piezoelectric stack.
After static pressure is reached, the altering force, from the dynamic pressure, is experienced by
the equivalent spring system. Using Hook’s spring law on the parallel spring system gives,
𝐹𝑑𝑦𝑛𝑎𝑚𝑖𝑐 = 𝛥𝑥 × 𝑘 𝑒𝑞 = 𝛥𝑥 ×
11
10
𝑘 𝑠𝑡𝑎𝑐𝑘 (3)
where Fdynamic is the total force due to the dynamic pressure (pressure ripple) in hydraulic fluid,
and Δx is the displacement of the parallel spring system. The portion of this force that is loaded
onto the Parker stack can be found by Equation 4,
𝐹𝑠𝑡𝑎𝑐𝑘 = 𝛥𝑥 × 𝑘 𝑠𝑡𝑎𝑐𝑘 (4)
4. 3
where Fstack is the force load due to dynamic pressure that is experienced by the Parker stack, Δx
is the displacement of the parallel spring system, and kstack is the stiffness of the Parker stack.
And the ratio of the force on the stack to the total dynamic load is computed by Equation 4,
𝐹 𝑠𝑡𝑎𝑐𝑘
𝐹 𝑑𝑦𝑛𝑎𝑚𝑖𝑐
=
𝛥𝑥×𝑘 𝑠𝑡𝑎𝑐𝑘
𝛥𝑥×
11
10
𝑘 𝑠𝑡𝑎𝑐𝑘
=
10
11
≅ 91% (5)
This value of 91 percent is exactly the amount of power from dynamic pressure that is
transmitted to the stack. This value will be used in determination of the shunt’s stiffness, in this
case that of the Belleville disc spring.
In order to achieve an effective sealing from highly pressurized hydraulic fluid, a very
thin steel diaphragm is employed. However, extensive deflection on the diaphragm can yield and
rip this component thus a preload is introduced such that the diaphragm will stay stationary (no
deflection) until hydraulic fluid reaches the designed. The assembled HPEH 5-3 device is shown
in Figure 1. The design is also able to be easily modified to operate at lower static pressure and
corresponding dynamic pressure. The working mechanisms will be discussed in Design Analysis
section.
Figure 1. Assembled HPEH 5-3 Device
5. 4
Material Selection. For this generation HPEH 5-3 device, stainless steel 17-4 PH was
chosen to fabricate most of the parts. This steel was purchased in 2.5 inch and 2 inch diameter
rods and came in solution annealed condition (Condition A) to meet specifications ASTM-A564.
In contrast to HPEH 5-1 and HPEH 5-2 devices, heat treatment of fabricated parts was omitted.
This decision was made because the solution annealed condition A, in which the steel rods come
in as, provides higher ultimate tensile strength (UTS) and 0.2% yield strength [1] than previously
used heat treatment, i.e. H-1050M, see Table 1. In addition, the HPEH 5-3 device was designed
to operate in normal environment temperature range thus not requiring this specific heat
treatment [2]. In future HPEH designs, other heat treatments should be considered to strengthen
the material; it may lead to a lighter and more compact device. After fabrication, the parts were
lubricated with an anti-seize food grade lubricant to prevent galling, common with stainless steel
parts.
Table 1. Mechanical Properties of 17-4 PH Stainless Steel
Property Condition A ksi (MPa) H-1050M ksi (MPa)
UTS 160 (1103) 150 (1034)
0.2% YS 145 (1000) 130 (896)
Figure 2 shows the technical drawing of the Parker piezoelectric stack used and its
overall dimensions are listed in Table 2. Table 3 includes the mechanical and electrical
properties of the stack.
6. 5
Figure 2. Technical Drawing of Parker 5x5x20 mm3
Stack
Table 1. 5x5x20 mm3
Parker Stack Dimensions
Dimension Measured Value inches (mm)
Height (contact sides) 0.213 (5.41)
Width 0.205 (5.21)
Length 0.788 (20.02)
Table 2. Mechanical and Electrical Properties of Parker 5x5x20mm3
Stack
(Abstracted from Appendix A-2)
Mechanical Performance
Min. Free Stack Displacement 0-150 V 19.0 µm
Max. displacement hysteresis 0-150 V 15%
Min. Stack Blocking Force at 150 V 800 N
Stiffness – Min. in short circuit condition 40 N/ µm
7. 6
Modulus of Elasticity 69 GPa [1]
Electrical Performance
Incoming Stack Capacitance 2.60 µF, +0 – 20%
Max. Capacitance change over temp. range -20°C to +80°C 50%
Max. Capacitance change as a function of force 0.85% per MPa
Max Capacitance change as a function of applied voltage to 150 V 30%
[1]
Property assumed similar to Aluminum
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