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1 Copyright © 2010 by ASME
Proceedings of the International Mechanical Enginee ring Congress and Exposition IMECE 2010
November 12-18, 2010, Vancouver, British Columbia, Canada
IMECE2010-37514
A VIBRATION STUDY OF A HYDRAULICALLY-ACTUATED LEGGE D MACHINE
Emanuele Guglielmino, Ferdinando Cannella , Claudio Semini, Darwin G. Caldwell
Nestor Eduardo Nava Rodríguez, Guillermo Vidal
Department of Advanced Robotics
Italian Institute of Technology Via Morego 30, 16163 Genoa, Italy
Email: [email protected]; [email protected];
[email protected]; [email protected]
Robotics Lab Carlos III University
Calle Universidad 30, 28911 Leganes (Madrid), Spain
Email: [email protected]; [email protected]
ABSTRACT This paper presents a study on the impact of the
vibration on a hydraulically-actuated legged robot designed for
outdoor operations. The choice of using hydraulic actuation in
lieu of electric actuation as is common in robotics has been
driven by the need to cope with heavy loads and respond
swiftly to external inputs and disturbances. However in such
machines hydraulically-induced vibration (fluid borne noise
and structure borne noise) is a major issue. Volumetric pump-
motor assembly is a primary cause of vibration. These are
transmitted to the robotic structure, which has been designed as
light as possible to minimise the robot’s total weight and power
consumption and make it more agile. Initially a multi-body
analysis of the robot was carried out to select an appropriate
vibration isolation system. Subsequently a numerical and
experimental modal analysis was carried out on the structure.
This has allowed identifying the main modes of vibration of the
structure. The pros and cons of this approach are described and
areas of improvements identified.
1. INTRODUCTION To achieve the high performance required by autonomous
legged robotic locomotion there is a need for actuation systems
with high power-to-weight ratios, swift dynamic response and
the ability to work reliably and robustly in an outdoor
unstructured environment. Furthermore some compliance is
beneficial to achieve an efficient gait in legged machines.
Hydraulic actuators can meet these requirements and indeed in
the early development (1960-70s) of the robotic technology
hydraulic power was commonly used [1, 2]. Albeit today’s
robots are typically electrically-actuated, there has recently
been a renewed interest in hydraulic power and advanced
bipedal [3, 4] and quadupedal platforms [5] have been
developed. This despite hydraulics has been negatively
perceived in the robotic community for many years as it was
considered dirty (leaks), potentially dangerous (oil is
flammable), noisy and considered difficult to control in high
dynamic applications due to its non-linear behaviour.
An aspect which is crucial in a hydraulically-powered
machine is noise and vibration. This is an important attribute in
mobile robots and like other specifications of performance,
dynamics, energy efficiency and safety, it has to be considered
closely in the design process. Vibration reduction has become
an important consideration in robotics and in mobile machines
where on one side the need to reduce weight and cost has
brought to lightweight designs (that are more prone to
vibration) [6] but on the other side it is necessary to meet ever
more stringent noise legislation.
The need for quieter operation was also remarked on the
advanced hydraulically-actuated quadruped robot BigDog [5].
Fluid-structure interactions are hence a crucial consideration in
the design of hydraulically-powered robots.
Even if the power losses due to noise and vibration are
negligible, noise may impair performance in other ways, by
causing leakage and valve oscillations. This often deteriorates
the performance of nominally sophisticated control algorithms
[7].
Fluid-structure interaction problems are multi-domain
problems often too complex to treat mathematically and so they
have to be analysed by means of experimental work along with
appropriate numerical simulations [8].
The results reported in this paper are within the scope of a
larger project targeting to develop a hydraulically-actuated
autonomous quadruped robot named HyQ whose size is similar
to that of a small horse. The main aim of the project is to
develop a robot able to perform dynamic tasks such as walking,
trotting running and jumping, and operate outdoors with an
acceptable degree of autonomy. The paper is structured as
2 Copyright © 2010 by ASME
follows. Section 2 describes the HyQ robot and its features
more related to this issue. Section 3 introduces some fluid
borne issues and the way to reduce them at design level.
Section 4 presents a multi-body simulation of the robot aimed
at selecting appropriate vibration isolation devices and section
5 presents a numerical and experimental assessment of the
vibration in the upper part of the robot. Finally section 6 draws
conclusions.
2. THE HyQ ROBOT HyQ is a hydraulically-actuated quadruped robot
composed by a torso and four legs [9]. A drawing of the robot is
depicted in Fig. 1. Each leg is actuated by a hydraulic system
consisting of two compact 4-way electrohydraulic proportional
valves. The valves provide flow to unequal area hydraulic
cylinders controlling the motion of each leg (hip and knee
rotations). A centralised volumetric pump and a hydraulic
accumulator supplies oil to all four legs. A third electrically-
actuated degree of freedom is present in each leg to account for
roll, but is not considered in this analysis. Fig. 2 shows a
schematic of the hydraulic system.
Due to the tight space constraints and the need to design a
lightweight structure, the hydraulic drive was not sized using
classical design procedures for mobile hydraulics as this would
have resulted in a heavier and bulkier system. The torso and
most of the components (manifolds etc) were made as compact
and as lightweight as structurally feasible in an aluminium
alloy. The tank was made as small as possible and a compact
cooler chosen after an accurate thermal analysis Fig. 3 shows
the hydraulic drive layout mounted in the robot torso.
FIG. 1. CAD DRAWING OF THE HYQ ROBOT
FIG. 2. HYDRAULIC ACTUATION SYSTEM
FIG. 3. LAYOUT OF THE HYDRAULIC ACTUATION
3. FLUID BORNE NOISE ABATEMENT In a hydraulic system, the pressurised fluid in motion in the
hydraulic circuit generates fluid borne noise. This in turn causes
structure borne noise by exciting vibration in any component
with which it is mechanically connected. The transfer of fluid-
and structure-induced vibration to the air results in air borne
noise (whose analysis is out of the scope of this paper).
The pump is the dominant source of noise. The flow
produced by volumetric pump is not constant over time, but has
a flow ripple due to the meshing of gears. Due to the circuit
downstream flow ripple converts into a pressure ripple which is
strongly dependent on the system characteristics. These
pulsations create fluid borne noise, which causes all
downstream components to vibrate.
A second potential cause of noise is local cavitation [10]
that causes noise and vibration when air bubble suddenly
collapses.
Fluid borne noise can be reduced but cannot be completely
eliminated. Appropriate countermeasures do not only involve
the selection of low noise components but an appropriate
design of the circuit, as subsequently described.
Firstly in order to reduce pressure pulsations a hydraulic
accumulator was used as a dampener (behind supplying
additional flow for peak flow demand).
3 Copyright © 2010 by ASME
Preventing cavitation can be achieved by minisiming the air
entrapped in the circuit by setting an appropriate pressure level.
An increase in pressure any free air present is more likely to
dissolve into the liquid [11], hence the pressure was kept as
high as possible (160 bar) relative to other constraints. High
pressure results also in smaller flow for a given power. This is
also beneficial for connecting hosing selection.
The selection of appropriate flexible hoses, fittings and
clamp mountings [12] is crucial as fluid velocity, pressure, and
line size all contribute to the vibration. Since hoses are
connected to assemblies which themselves vibrate, it was
decided to use hoses rather than rigid metallic tubes avoiding
too long, unsupported conductor runs. Finally in this mobile
application, the physical movement of the reservoir itself has
suggested the use of a higher sided design to reduce fluid
sloshing.
4. VIBRATION ISOLATION SYSTEM Structural vibration is dictated by the resonant modes of
the structure. For good isolation the supporting structure should
ideally have high mechanical impedance, but this can be
achieved only if this is heavy, not lightweight. The propagation
of vibration structure borne noise can be minimised through the
elimination of sound bridges between the power unit and the
mounting base. Hence it is important to introduce sufficient
damping between the noise source and the structure.
Furthermore appropriate isolating rubber mountings should be
selected.
Hence a multi-body dynamic simulation was carried out
in MSC.ADAMS in order to choose an appropriate isolation
system. The criterion for isolator selection was the acceleration
levels of the pump and of the supporting structure. The model
was developed based on robot design parameters and
component datasheets. Simulations of the walking, running and
jumping on a flat terrain were performed. The vibration levels
were assessed with and without an isolation system with a 3-
stage simulation process:
-Stage 1: a simulation of the full robot was carried out not
considering the pump vibration.
-Stage 2: a model of the vibration transmitted by the pump was
included without any isolation system and based on that the
isolator selected.
FIG. 4. MSC.ADAMS MODEL OF THE ROBOT
(a)
(b)
FIG. 5. (A) PUMP MODEL; (B) TRANSMITTED FORCE TREND
-Stage 3: the effectiveness of the isolator system was assessed.
Fig 4 shows the model. The pump was considered the source of
vibration (Fig. 5).
It was assumed that the pump was generating a radial
force. From the analysis the worst condition for selecting the
isolation system were defined. This has allowed to size the
rubber isolator (stiffness and damping) based on the identified
natural frequency [11].
where m is the pump mass, ζ is the damping coefficient and Ccr
is the critical damping coefficient. Fig. 6 shows a simulation
results during jumping operation. In particular, the
displacement and acceleration of robot torso along vertical axis
(stage 1 in solid line, stage 2 in dashed line and stage 3 in
dotted-dashed line).
5. EXPERIMENTAL AND NUMERICAL MODAL ANALYSIS In order to investigate the dynamic behaviour of the
structure, several measurement sessions were carried out. Four
types of experiments were made: on the torso alone (removing
the pump), on the torso with and without the pump-motor
assembly and with and without rubber isolators. The legs were
not considered in what reported in this paper. This will scope of
further analysis subsequently. Table 1 lists the experiments:
4 Copyright © 2010 by ASME
FIG. 6. ROBOT DISPLACEMENT ALONG Y AXIS AND ACCELERATION ALONG Z AXIS
TABLE1: MEASUREMENT TESTS ON THE STRUCTURE
Description Name
torso
(with hammer) Test 1
torso, hydraulic system
(with hammer) Test 2
torso, hydraulic system, pump-motor
(with hammer) Test 3
torso, hydraulic system, pump-motor, rubber
(with hammer) Test 4
torso, hydraulic system, pump-motor
(pump running) Test 5
torso, hydraulic system, pump-motor, rubber
(pump running) Test 6
The measurements were carried out using six
piezo-resistive accelerometers (Dytran 3097A3) plus
appropriate condition and filtering units, mounted in the most
significant places for investigating the shape modes, as shown
in Fig. 7a and Fig. 7b and the excitation was provided by a
modal impact hammer to investigate the natural resonance
frequencies (for tuning the numerical model) then by the pump
running at 30 Hz, 40 Hz and 50 Hz. Some experimental results
are shown in Fig. 8 a-e. At the same time a finite element model
was developed in MSC.NASTRAN in order to have a virtual
prototype of the torso, as shown in Fig. 9. The model included
not only the geometrical parameters of the robots, but also the
real properties of the rubber used, measured on a stress-strain
machine. The agreement between numerical (Fig 10a, b) and
experimental data (Fig. 8c, d) is shown, as an example, in case
of tests 3 and 4. The difference among the main resonant
frequencies is about 10%. Analogous results were obtained in
the other cases. From the analysis of the data it is clear that the
amplitude of the accelerations is higher without rubber as
expected. Moreover it is evident that the masses isolated by the
rubber (pump-motor and oil tank) behave differently from a
dynamic standpoint. In test 3 they can be considered tied to the
rest of torso, in test 4 are independent and they increase their
mobility.
FIG. 7A. SET UP FOR TEST 1 AND MEASUREMENT SYSTEM
FIG. 7B. SET UP FOR TEST 4
FIG. 8A. TEST 1 – ACCELERATION EXPERIMENTAL SPECTRUM
5 Copyright © 2010 by ASME
FIG. 8B. TEST 2 – ACCELERATION EXPERIMENTAL
SPECTRUM
FIG. 8C. TEST 3 – ACCELERATION EXPERIMENTAL SPECTRUM
FIG. 8D. TEST 4 – ACCELERATION EXPERIMENTAL SPECTRUM
The tuning of the virtual prototype with the
experimental data was instrumental to have a tool to forecast
the dynamic behaviour of the robot in future investigation,
including locomotion modes (walking, trotting and running).
Finally Fig. 11a-d shows some mode shapes; at those
frequencies the masses move up and down (Fig. 11a, b, c) or
the structure bends (Fig. 11 b, d).
6. CONCLUSIONS A theoretical and experimental analysis of the vibration in a
hydraulically-actuated quadruped robot was carried out. Fluid
borne noise issues were taken into account into the design
phase.
FIG. 8E. TEST 5 – ACCELERATION EXPERIMENTAL
SPECTRUM
FIG. 9. TEST 1 AND TEST 4 FINITE ELEMENT MODEL FOR DYNAMIC ANALISIS
FIG. 10A. TEST 3 – ACCELERATION NUMERICAL SPECTRUM
6 Copyright © 2010 by ASME
FIG. 10B. TEST 4 – ACCELERATION NUMERICAL SPECTRUM
a) 1.0Hz b) 8.7Hz
c) 8.9Hz d) 11.3Hz
FIG. 11. TEST 1 – NUMERICAL MODAL SHAPES
Subsequently appropriate rubber mountings were selected
via a multi-body simulation. An experimental modal analysis
was then carried out and a finite element model developed. The
experimental tests allowed to analyse the dynamic behaviour of
the robot torso, and they also permitted to tune the numerical
model which will be a key tool for future design improvements.
Future works will also involve further numerical analysis to
study the forced resonance frequencies and relative forced
mode shapes as well as acoustic analysis to assess air borne
noise and sound level, which is another critical issue in
hydraulic robots.
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