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THERMAL ANALYSIS OF THE HYDRAULIC SYSTEM
FOR A
GARBAGE TRUCK
Peter J. Weller, PE
Introduction
A sometimes overlooked characteristic of hydraulic systems used on industrial trucks
such as garbage trucks is the tendency of operating the system to cause increases in hydraulic
fluid temperature. High fluid temperatures can result in destruction of seals in the hydraulic
system, degradation of performance, and possible safety hazards to operating personnel. A
finite-difference model for a typical garbage truck hydraulic system was derived by the author to
predict these temperatures. Actual weather data for a sea-level southwestern American city in
the middle of summer were used as input parameters for the model, to represent an actual worst
case condition. This model included consideration of the pressure losses in the hydraulic system
due to viscous effects and friction during operation. These losses result in increases in internal
energy of the fluid, which are manifest as increases in fluid temperature. Calculation of heat
transfer to and from the hydraulic system was also incorporated in the model. The system
receives solar radiation and expels heat by convection to the ambient air.
Summary of Results
The model predicts fluid temperatures of up to 300 degrees F during normal operation of
each truck on a day when the ambient air temperature reaches 115 degrees F. The 300 degree
F temperature produced by a garbage truck under such conditions significantly exceeds the
recommended 180 F limit on hydraulic fluid temperature.
The model is conservative in that it was based on estimates for pressure loss and
thermal parameters that tend to underestimate the predicted fluid temperatures. Actual fluid
temperatures for the given meteorological parameters will be higher than those in the model
output.
Approach
The algorithm in the model was based on the First Law of Thermodynamics, which states
that the heat transferred to a system is equal to the sum of the increase in internal energy of the
system and the work done by the system. The increase in the internal energy of an
incompressible fluid is equal to the product of the specific heat of the fluid and the increase in
temperature of the fluid. Hydraulic fluid can be considered incompressible, and the specific heat
is a well documented property. The fluid temperature can therefore be calculated if the initial
fluid temperature is known and the temperature change is calculated by evaluating the heat
transferred to or from the system and the work done by or on the system.
Heat transfer evaluated by the model includes solar radiation into the hydraulic system
and convection of heat from the system to the ambient air. Solar radiation data were obtained
from a state Meteorological Data Base (Ref. 16.) for a day when the ambient temperature
reached almost 115 degrees F. These data give the amount of solar energy incident on a
horizontal surface by hour of the day. It was estimated that the hydraulic system absorbs 80
percent of incident radiation, based on documented emissivities of similar materials.
Both free convection and forced convection were evaluated as mechanisms for
transferring heat from the hydraulic system to the air. Free convection is a process in which
molecules of a fluid (ambient air in this analysis) in contact with a warmer body absorb heat,
become buoyant, and are displaced by molecules with less internal energy. It was assumed, for
the sake of simplicity, that there is no temperature gradient between the hydraulic fluid and the
ambient air, and that the wall temperature is the same as the hydraulic fluid temperature. In
reality, the walls of the hydraulic hoses, pipes, valves, and fittings tend to absorb heat and
insulate the fluid and will be lower in temperature. The heat transfer rate varies directly with the
difference between the wall temperature and the temperature of the air, so the actual heat
transfer rate from the fluid to the ambient air by free convection will be less than that estimated
by the model, and the model is conservative. Mathematical relationships expressing the free
convection heat transfer rate as a function of temperature difference and properties of the
absorbing fluid have been developed and are reported in the literature (10.)
Forced convection occurs when a fluid (ambient air) is directed at some nonzero velocity
against a warm surface. Heat is transferred by a combination of buoyant effects and momentum
as energy is transferred from the warm surface by conduction to molecules of air, and the
molecules are replaced by other molecules lower in internal energy. Wind promotes forced
convection. Meteorological data for a sea-level southwestern US city (13.) were inspected, and it
was found that the maximum wind speed for many days remains below eight miles per hour
during the hours of operation for the packer trucks. For significant portions of many days, the
historical data indicate no measurable wind speed. It was assumed, for this analysis, that the
wind flows directly across the hydraulic system and hydraulic oil reservoir in the direction most
beneficial for the promotion of cooling for the system. In addition, the outer wall of the reservoir
is partially exposed to the air as the truck is driven. An average effective wind speed, relative to
the reservoir, of 12.5 miles per hour was calculated, based on the estimated truck speed and
portion of the day during which the truck is moving. Forced convection of heat from this surface
was calculated based on the higher effective wind speed. Because the rate of heat transfer
varies directly with the wind speed, these choices for wind speed values are conservative. As in
the free convection analysis, wall temperatures were equated with hydraulic fluid temperatures,
and this is also conservative.
Pure conduction of heat from the hydraulic system and reservoir to another solid body
was not considered a significant mechanism for cooling because the contact areas are small and
because other nearby bodies are also heat sources (the truck engine and exhaust). Conduction
between solid bodies is proportional to the contact area and the temperature difference.
Radiation and convection of heat from the road surface to the hydraulic system and
reservoir were not considered in this analysis because of the difficulty in describing these
mechanisms mathematically and because assuming them to be negligible is conservative.
Mechanical work is put into the system (“shaft work”) by the Power Takeoff (PTO)
driving the hydraulic pump. Mechanical work output from the system is the work done by the
hydraulic actuators (cylinders) lifting and compacting the solid waste. The difference between
the input mechanical work and the output mechanical work becomes pressure losses in the
system as the hydraulic fluid is moved through the hoses, pipes, tubes, filters, fittings, and
valves. Empirical data relating pressure loss to fluid flow rate for different types of hose and pipe
are available in the literature. Pressure losses in hydraulic hose have been documented by
Parker (2.). Hose sizes were taken from the specifications for an actual sideload compactor truck
and pressure losses were obtained from these data. Pressure losses for pipe and standard
fittings (elbows, tees, sudden expansions, sudden contractions) are related to fluid velocity,
density, and viscosity and are proportional to empirical factors reported in the literature. The
sizes of pipe and fittings were obtained from the drawings, and losses were tabulated after
calculations were made using these relationships and data. Pressure losses through filters,
directional control valves, check valves, and proportional control valves were obtained from the
actual manufacturers’ technical catalogs for each model (4.,6.,8.,11.) Properties of a typical
hydraulic fluid recommended for use in such climates (Texaco Rando HD46) were obtained from
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literature published by Texaco for that fluid (19.). Because there were no available data
describing the operation of relief valves in the system, it was assumed that they were not
actuated during normal operation, even though there were many relief valves in the system. In
reality, relief valves are actuated every time a hydraulic cylinder is extended to its full stroke and
any time a cylinder capacity is exceeded. Because relief valves produce significant losses in
pressure, omitting them in this analysis leads to underestimated fluid temperatures. In addition,
there are typically orifices in the hydraulic system for the such trucks. These were also omitted
from the analysis because no data describing their geometry were available. They also produce
significant pressure losses, and omitting them tends to further underestimate fluid temperatures.
Perfect data cannot be obtained for any analysis. In cases in which directly applicable
data were not available for this analysis from available garbage truck specifications, drawings, or
in the literature, or calculation of input parameters or data was not straightforward, assumptions
were made that could be reasonably supported. When no reasonable assumption could be
made, data which would lead to higher predicted fluid temperatures were not used, in order that
the analysis remain conservative.
It was assumed that the packer trucks are operated on a ten hour daily shift. The actual
time that each truck is collecting (and, therefore, operating the boom circuit and pack circuit in
the hydraulic system) is approximately six hours per day. The pack circuit is continuously
operating while the truck is collecting, then is turned off when the truck is driven to and from
the dump/transfer station or to and from the city yard. The boom is operated intermittently,
while the truck is loading cans at a house, then is inactive when the truck is driven between
houses. Based on discussion with waste management personnel, it was assumed that each
truck collects the solid waste from 1200 to 1300 houses a day. Using these parameters, duty
cycles were evaluated for the boom circuit and for the pack circuit and were applied by the model
to the calculation of pressure losses, since no pressure losses are generated when the hydraulic
system is not actuated. Heat transfer occurs continuously. For much of the time, the pack
circuit is actuated, but the boom circuit is not. During these times, the model calculates no
losses for the boom circuit. However, hydraulic fluid is still flowing through the control valve for
the boom circuit and back to the reservoir, even though no work port on the control valve sees
flow. In reality there is, therefore, still some pressure loss from this flow when only the pack
circuit is actuated. Omitting this loss tends to underestimate fluid temperatures and is
conservative.
Discussion of Results
The results of the analysis are shown in Table 1. for an 8 second cycle time, in Table 2.
for a 10 second cycle time, and in Table 3. for a 14 second cycle time. Actual cycle times are
usually in the 10 to 14 second range. Resulting hydraulic fluid temperatures in the tables are
similar for corresponding times of the day. The tables show operation of one truck for the ten
hour shift beginning at 6 am and ending at 4 pm.
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The activities during allotted time periods are shown. This scenario of activities is
proposed as typical based on the author’s experience for daily collection operations. It
undoubtedly varies from day to day and from truck to truck. It is not expected that these
variations would alter the conclusions for this analysis.
Solar radiation as energy incident on a horizontal surface per unit time was obtained for
a southwestern US city for the subject day (2 July 2001) and is shown on the table.
The time increments shown generally conform to the operational activities for the truck,
except in the early hours, where time increments were reduced to promote accuracy in exercising
the model. During this early period, the thermal dynamics of the system are changing rapidly
because the hydraulic system is starting to transfer energy to the fluid, and more data points are
needed.
The duty cycles for the pack circuit and the boom circuit are shown. The pack cylinders
are operated continuously while the truck is collecting waste in a neighborhood, while the boom
circuit is operated only when the truck is handling a container.
The columns labeled Pack Loss and Boom Loss represent the energy in Btu per hour put
into the fluid by the pressure drops in the pack-eject and boom circuits, respectively. The
columns labeled Q-HS and Q-Res are the total rates of heat transfer from the Hydraulic System
(excluding the reservoir) and the Reservoir, respectively, for all heat transfer mechanisms - solar
radiation, free convection, and forced convection - in Btu per hour.
The last two columns show the change in fluid temperature from the last time period and
the fluid temperature for the indicated time period, respectively. The model calculates the
change in temperature due to the energy input to the fluid, less the heat energy transferred from
the fluid, during the prior time period and adds the temperature difference to the fluid
temperature for the last time period to obtain the value shown.
The tables indicate that the temperature of the modeled fluid exceeds 180F early in the
day. Operator breaks and down time at the dump/transfer station promotes cooling, as
convection removes heat from the hydraulic system and no pressure losses are produced.
However, internal energy is generated at such a high rate due to the pressure losses in the
system during operation that the fluid remains at excessive temperatures for almost the entire
day because the heat transfer rate from the fluid is insufficient for cooling it. These results are
conservative in that, if input parameters for quantifying the model could not be evaluated with
certainty, they were chosen from a range of likely values in such a way that fluid temperatures
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were underestimated, rather than overestimated. When there was insufficient information for
reasonable estimates for a pressure loss or heat flow mechanism, these mechanisms were
ignored if the effect of the mechanism would be to increase fluid temperatures.
Standard seal materials for normal industrial applications have maximum recommended
temperature ranges that go up to 250F or 300F, depending on the actual compound (20.). For
most of these, temperatures from 250F to 300F are allowable for only brief periods of time. For
Buna-S, the temperature range goes to 225F. (Viton seals can sometimes be specified at extra
cost for hydraulic components, but the temperature range for Viton goes to only 250F.) This
analysis indicates that fluid temperatures higher than 300F can be expected on hot days in such
climates. This means that the seals in the hydraulic components would be expected to soften
during operation of the packer trucks. As the seals soften, they would tend to extrude into the
space between the parts they are sealing and eventually break. Hydraulic fluid would begin
leaking when the seal extrudes and possibly catastrophic leaks would occur when a seal breaks.
The hydraulic fluid suffers damaging effects from high temperature operation, also. Data
for Texaco Rando HD 46 were used to describe a typical fluid for use in such hydraulic systems.
The number 46 indicates a standard rating for hydraulic fluid which relates to the viscosity of the
fluid. Literature on this fluid from Texaco (19.) shows properties of the fluid up to a maximum of
180F. Literature for competitive but similar fluids of the same grade (21.) indicate operating
ranges for No. 46 grade fluid of 32F to 160F. Parker Fluid Power recommends a maximum
reservoir fluid temperature of 145F (2.). There are deleterious effects from temperature other
than seal failure. Hydraulic fluid at high temperatures produces an oxidation product called
varnish which clogs orifices, corrodes metal parts, forms sludge, and causes rapid wear of metal
parts. Hydraulic fluids come in several grades, typically from No. 32 to No. 150. (The higher the
grade, the more viscous – heavier – the fluid is at a given temperature.) However, specifying a
higher weight fluid is not the solution to the thermal problem in this analysis. Even the heaviest
fluid is not recommended for operating over 230F, and, while the maximum operating
temperature is greater for the higher viscosity fluids, the minimum operating temperature is
greater, also, and this higher viscosity at starting temperatures consumes more energy for
overcoming viscous effects and friction when the fluid is cold. For these reasons, the use of the
heaviest fluids is impractical.
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