Hilty Devin Study of Splah Lubrication
-
Upload
saipriya-balakumar -
Category
Documents
-
view
249 -
download
0
Transcript of Hilty Devin Study of Splah Lubrication
AN EXPERIMENTAL INVESTIGATION OF SPIN POWER LOSSES OF
PLANETARY GEAR SETS
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By
Devin R. Hilty, B.S.
Graduate Program in Mechanical Engineering
The Ohio State University
2010
Master's Examination Committee:
Dr. Ahmet Kahraman, Advisor
Dr. Gary Kinzel
Graduate Program in Mechanical Engineering
Copyright by
The Ohio State University
2010
ii
ABSTRACT
Planetary gears are used commonly in many power transmission systems in
automotive, rotorcraft, industrial, and energy applications. Powertrain efficiency concerns
in these industries create the need to understand the mechanisms of power losses within
planetary gear systems. Most of the published work in this field, however, has been
limited to fixed-center spur and helical gear pairs. An extensive set of experiments is
conducted in this research study to investigate the mechanisms of spin power loss caused
by planetary gear sets, in an attempt to help fill the void in the literature.
A test set-up was designed and developed to spin a single-stage, unloaded
planetary gear set in various hardware configurations within a wide range of carrier
speeds. The measurement system included a high-resolution torque sensor to measure
torque loss of the gear set used to determine the corresponding spin power loss.
Repeatability of the test set-up as well as the test procedure was demonstrated within
wide ranges of speed and oil temperature.
A test matrix was defined and executed specifically to measure total spin loss as
well as the contributions of its main components, namely drag loss of the sun gear, drag
loss of the carrier assembly, pocketing losses at the sun-planet meshes, pocketing losses
iii
at the ring-planet meshes, viscous planet bearing losses, and planet bearing losses due to
centrifugal forces. Multiple novel schemes to estimate the contributions of these
components of power losses were developed by using the data from tests defined by the
test matrix. Fidelity of these schemes was tested by comparing them to each other.
Based on these calculations, major components of power losses were identified and rank
ordered. Impact of the rotational speed and oil temperature on each component was also
quantified.
iv
ACKNOWLEDGMENTS
I would like to express my appreciation to Dr. Ahmet Kahraman for inviting me
to work on this project and for supporting me throughout the course of its completion. I
have learned a lot from him, and it is through his patient leadership and guidance that I
have been able to complete this project and earn my Master’s degree in Mechanical
Engineering. I would also like to thank the project sponsor GM Powertrain and Avinash
Sing, in particular, for their support and assistance with this project. Furthermore, I would
like to thank Jonny Harianto, Sam Shon, and the members of the Gleason Gear and
Power Transmission Laboratories for their help and support throughout the course of this
project, and I would like to thank Dr. Gary Kinzel for his careful review of my thesis.
To my parents, Roger and Linda Hilty, thank you for your never ending support
and encouragement and for helping me develop the skills and work ethic to get where I
am today. Thanks to Kimberly Samberg for your love and support, and thanks to the rest
of my family and friends without which this would not have been possible.
v
VITA
April 25, 1985 ................................................Born-- Steubenville, OH March-Sept. 2005 ...........................................Engineering Intern Ethicon Endo-Surgery Blue Ash, OH Jan. 2006-Sept. 2007 ......................................Engineering Intern, Honda Research of America Raymond, OH Jan. 2007-June 2007 ......................................Undergraduate Research Assistant Department of Mechanical Engineering The Ohio State University Columbus, OH June 2008 ......................................................B.S. Mechanical Engineering The Ohio State University Columbus, OH June 2008-June 2010 .....................................Graduate Research Associate Department of Mechanical Engineering The Ohio State University Columbus, OH
FIELD OF STUDY
Major Field: Mechanical Engineering
vi
TABLE OF CONTENTS
Page
ABSTRACT ........................................................................................................................ ii
ACKNOWLEDGMENTS ................................................................................................. iv
VITA ................................................................................................................................... v
LIST OF TABLES ............................................................................................................. ix
LIST OF FIGURES ............................................................................................................ x
NOMENCLATURE ........................................................................................................ xiii
Chapters:
1. INTRODUCTION ............................................................................................... 1
1.1 Background and Motivation ......................................................................... 1
1.2 Sources of Spin Power Loss ......................................................................... 4
1.3 Literature Review ......................................................................................... 6
vii
1.4 Scope and Objective .................................................................................... 10
1.5 Thesis Outline .............................................................................................. 11
2. EXPERIMENTAL TEST METHODOLOGY .................................................. 12
2.1 Test Machine ............................................................................................... 12
2.2 Planetary Gearbox........................................................................................ 15
2.3 Lubrication System ...................................................................................... 25
2.4 Various Test Hardware Options................................................................... 31
2.5 Test Procedure ............................................................................................ 37
2.5.1 Torque-meter Set-up and Gearbox Engagement .............................. 39
2.5.2 Gear Run-in Procedure .................................................................... 40
2.5.3 Data Acquisition ............................................................................... 40
2.6 Test Matrix .................................................................................................. 43
2.7 Test Repeatability ....................................................................................... 47
3. PLANETARY GEAR SET SPIN POWER LOSS TEST RESULTS ............... 49
3.1 Introduction ................................................................................................. 49
3.2 Measured Total Planetary Spin Power Losses ............................................ 50
3.2.1 Influence of Speed ............................................................................ 50
3.2.2. Influence of Lubricant Temperature ................................................ 57
3.3 Components of Spin Power Loss ................................................................ 60
3.3.1 Determination of Spin Power Loss Components .............................. 60
viii
3.3.2 Rank Order of Spin Power Loss Components .................................. 72
3.3.3 Validation of Spin Power Loss Component Isolation Methods ........ 78
4. SUMMARY AND CONCLUSIONS ................................................................ 80
4.1 Thesis Summary ......................................................................................... 80
4.2 Main Conclusions ....................................................................................... 81
4.3 Recommendations for Future Work ........................................................... 83
REFERENCES ................................................................................................................. 87
ix
LIST OF TABLES
Table: Page
2.1 Basic design parameters of the test planetary gear set used in this
study .....................................................................................................................16
2.2 Spin power loss planetary gearing configuration test matrix ...............................44
2.3 Masses of planet gears and planet gear and bearing sets .....................................46
x
LIST OF FIGURES
Figure: Page
2.1 (a) View of efficiency test machine with planetary gearbox and (b) schematic layout of test machine specifying main components 13
2.2 View of the test gearbox designed to hold and operate planetary gear set. Lubricant cover has been removed for clarity purposes 18
2.3 Cross-sectional view of test gearbox with its lubricant housing, support flange, base plate, and slide plate 19
2.4 Three dimensional cross-sectional view of the planetary gearbox with its key components identified 20
2.5 View of components of planet-bearing assembly including planet gear, planet pin, double-row caged planet bearings and thrust washers 22
2.6 View of six-planet carrier assembly 23
2.7 View of the gears of the test gear set 24
2.8 Diagram of the two main lubricant paths implemented in this study 27
2.9 View of lubricant lines added for oil flow to lubricant catcher 28
2.10 View of dummy disc intended to occupy the space of the sun gear during tests with no sun gear 33
2.11 Three dimensional assembly cross-section of the gearbox showing implementation with dummy disk in place of sun gear 34
2.12 Pictures and cross sectional diagrams of planet gear types (a) baseline, (b) reduced face width, and (c) reduced mass (plastic 36
2.13 T time trace of six planet, baseline test at 3000 RPM and 90° C 42
2.14 Test 1A repeatability with respect to input carrier speed at (a) 40°C and (b) 90°C 48
3.1 Comparison of (a) 1AP , 2AP , and 3AP P P P
P P P P P
, (b) , , and , (c)
, , and , and (d) and as functions of ω at 40°C
1B
D
2B 3B
1C 2C 3C 2B 251
3.2 Comparison of (a) 1AP , 2AP , and 3AP P P P
P P P P P
, (b) , , and , (c)
, , and , and (d) and as functions of ω at 90°C
1B
D
2B 3B
1C 2C 3C 2B 253
3.3 Comparison of (a) 1AP P P Pω
, (b) , (c) , and (d) as functions of at 40 and 90°C
1B 1C 2D58
3.4 Comparison of P calculated using Eqs. (3.1), (3.2), and (3.3) at (a) 40°C and (b) 90°C
dc64
3.5 Comparison of P calculated using Eqs. (3.4) and (3.5) at (a) 40°C and (b) 90°C
ds65
3.6 Comparison of psP calculated using Eqs. (3.6), (3.7) and (3.8) at
(a) 40°C and (b) 90°C 66
3.7 Comparison of calculated using Eqs. (3.9) and (3.10) at (a)
40°C and (b) 90°C prP
67
3.8 Comparison of P calculated using Eqs. (3.11) and (3.12) at (a) 40°C and (b) 90°C
bv68
3.9 Comparison of calculated using Eqs. (3.13) and (3.14) at (a)
40°C and (b) 90°C bgC
69
xi
xii
3.10 Contributions of components of power loss in kW to the total power loss for test 1A at (a) 40°C and (b) 90°C 73
3.11 Contributions of components of power loss in percentage to the total power loss for test 1A at (a) 40°C and (b) 90°C 75
3.12 Comparison of the total power loss calculated from its components using Eq. (2.1) to the actual measurements from test 1A at (a) 40°C and (b) 90°C 79
NOMENCLATURE
Symbol Definition
bgC planet bearing mechanical power loss constant (W/kg)
md bearing pitch diameter (m)
1f bearing load torque application constant (unitless)
m mass of planet gear and bearings (kg)
N number of planet gears in gear set (unitless)
P spin power loss (W)
r radius of circle defined by planet gear centers (m)
T spin torque loss (N-m)
η efficiency (unitless)
ω planet carrier speed (rad/sec)
Subscript Definition
1 complete gear set
2 gear set without sun gear
3 gear set without sun or ring gear
A 6 baseline planets xiii
xiv
B 3 baseline planets
Subscript Definition
b planet bearing
C 6 reduced face width planets
c planet carrier
D 6 reduced mass planets
d viscous drag
g mechanical (centrifugal load dependant) friction
p gear mesh pumping
r ring gear or planet-ring gear mesh
s sun gear or planet-sun gear mesh
v viscous friction
1
CHAPTER 1
INTRODUCTION
1.1 Background and Motivation
Powertrain efficiency has become a major area of focus in recent years within the
transportation, aerospace, and energy industries due to continuously increasing fuel prices
and overwhelming concern over sustainability and the environmental impact of burning
fossil fuels. While they might not be as significant as those taking place in other power
train components such as the internal combustion engine and the rear axle, power losses
from transmissions have become one of the major concerns of drive train engineers.
There are two traditional types of transmissions used in automotive applications,
manual and automatic. Manual transmissions, which represent only a small portion of
the domestic market, consist of multiple fixed-center parallel shafts that hold helical
gears of different sizes. Certain gear pairs are activated manually to change the gear
ratios to better match the engine and the vehicle driving conditions. Meanwhile,
automatic transmissions rely on a controller to shift gears without any input from the
2
driver. While there are parallel-axis automatic transmissions employing similar layouts
as the manual transmissions, a great majority of automatic transmissions employ co-axial
designs where multiple stages of planetary gear sets and wet clutches are used to obtain
different gear ratios.
Vehicles with manual transmissions have long been perceived to be more efficient
than those with automatic transmissions. This was partly because they provided more
speed ratios (typically 6) than automatic transmission. More recent automatic
transmissions in the market, however, use six or more forward gear ratios, in an attempt
to close the gap in terms of efficiency while providing other benefits associated with the
shift quality.
Design of planetary automatic transmissions with increased number of speed
ratios presents major challenges to transmission engineers. While the space allowed
within the vehicle remains the same, the transmission must contain more content to be
able to provide more speed ratios. Therefore, a main challenge faced is specifying the
kinematic configurations that deliver the desired number of speed ratios within the
required ranges by using a minimum number of planetary gear sets and clutches.
Analysis of most of the potential designs meeting the space and ratio requirements often
reveals that certain gear sets must operate at excessive speeds in some of the kinematic
configurations. In those cases, one must determine (i) whether the gears and bearings of
this particular gear set can be designed to endure such speeds, and if so (ii) what adverse
impact such high-speed operation would have on the efficiency of the gear train.
3
Power losses of any gear system can be classified in two major groups. One
group of losses, often referred to as mechanical (load dependant) power losses, are
induced by friction at the lubricated gear and bearing contacts and increases with the
torque transmitted by the gear system. The second group of losses are so-called spin
power losses. The term spin loss has been used rather loosely to define losses taking
place due to rotation of the system without carrying any load. In gearboxes that operate
in dip lubrication, spin losses represent losses associated with the churning (drag and
pocketing) of the oil surrounding the gears and bearings. In planetary systems of
automatic transmissions where oil is provided to contact interfaces through specifically
designed lubrication paths, exact lubrication conditions around the gear sets are not well-
defined. There is more windage of an air/oil mixture rather than churning of oil. Spin
losses increase exponentially with speed making them more of a concern at higher speed
ratios, especially at those kinematic configurations resulting in higher component speeds.
A review of the literature on gearbox efficiency, done in a later section, reveals
little on spin power losses of planetary gear sets. While there are some recent studies on
windage and churning of single (spur, helical, or hypoid) gear pairs, there is limited
knowledge on how many different mechanisms lead to spin losses in a planetary gear set
and how they contribute to the total spin losses. The main motivation of this
experimental study is to investigate planetary gear set spin losses in an attempt to answer
some of these questions.
1.2 Sources of Spin Power Loss
As stated earlier, there are two types of power losses associated with gears. The
major sources of mechanical power losses within a planetary gear set comprise of rolling
and sliding friction generated on gear and bearing surfaces due to torque transmitted
through the system. These will not be considered in this study. The major sources of spin
loss within a planetary gear set comprise of (i) viscous drag loss associated spinning
hardware elements, (ii) pumping of lubricant and air from the spaces between meshing
gear teeth, and (iii) friction losses existing within the bearings of the planet gears while
free spinning.
The drag power losses ( ) are those associated with the interactions of each
individual gear and the carrier assembly with the surrounding medium, where windage
refers to drag on a component spinning in air, and churning refers to drag associated with
lubricant interaction for a component partially immersed in oil. There are three main
sources of drag power losses of a planetary system: sun gear drag ( ), planet carrier
assembly drag ( ), and ring gear drag ( ). Each drag power loss term represents the
sum of (i) power loss due to oil/air drag on the periphery (circumference) of the gear or
carrier, and (ii) power loss due to oil/air drag on the faces (sides) of the gear or carrier
[1]. The total drag power loss of the planetary gear set is given as the sum of each source
as follows:
dP
dsP
dcP drP
4
rd ds dc dP P P P= + + . (1.1)
The pumping power losses ( pP ) are caused by gears squeezing (or pumping) oil
(or oil-air mixture) out of the space between the teeth contracts as they roll into mesh [1].
These losses happen at each mesh of the sun gear with planets ( psP ) as well as each mesh
of the ring gear with planets ( prP ) such that
( )p ps prP N P P= + . (1.2)
where N is the number of planet gears in the gear set.
The planet bearing spin losses ( ) can be described in terms of (i) load
dependent (mechanical) losses and (ii) viscous (load independent) power losses [2, 3].
Each planet bearing and washer is subject to viscous power loss . If the carrier
rotates at relatively high speeds, centrifugal forces
bP
bvP
2bF mr= ω
bg
are generated to act on the
planet bearings as radial forces. Here m is the mass of a planet with its bearing, r is the
radius of the circle defined by planet centers, and ω is the carrier rotational speed. They
induce load (and speed) dependent friction drag at each planet bearing. These radial
forces result in certain power losses denoted here as P . Harris [2] refined equations
developed by Palmgren [3] governing power losses in cylindrical roller bearings. These
equations are adapted here to define as bgP
m (1.3) bg gbP C=
5
6
ωwhere is a constant with being the bearing pitch diameter and 31bg mC f d r= md 1f
being an application constant determined through testing. As it will be described in
Chapter 2, planet mass m will be adapted as a parameter in this study to allow
measurement of gbC indirectly. With this, total power loss associated with all of the
bearings of the planetary gear set is given as
(1.4) ( )b bv bgP N P C m= +
Summing these three main sources of power losses, the overall spin power loss of
an N planetary gear set can be written as
. (1.5) d pP P P P= + + b
1.3 Literature Review
As stated earlier, the majority of literature concerning power losses in gears
pertains to mechanical efficiency of fixed-center, parallel-axis gearing applications.
Mechanical efficiency models based on elastohydrodynamic lubrication formulation have
been proposed in recent years to investigate the impact of lubricant parameters, surface
conditions (magnitude and lay of the surface roughness), gear geometry, and operating
conditions on contact friction and mechanical power losses [4, 5, 6, 7]. Likewise, several
detailed experimental investigations of spur and helical gear mechanical power losses
have also been done to provide experimental databases [8, 9, 10, 11]. Some of these
7
models were compared to these experimental databases to establish their accuracy. These
studies, while significant to describe load dependent power losses of gears, are of limited
relevance to this study, which focuses on spin power losses.
Some studies have been conducted to understand spin power losses of fixed-
center spur and helical gears. These studies exclude bearing losses, as fixed-center gear
systems can be studied separately from bearing losses. Studies by Dawson [12, 13], Diab
et al [14], Wild et al [15], and Al-Shibl et al [16] presented empirical and computational
fluid mechanics based models of windage power losses for single gears in air. Daily et al
[17], Mann et al [18], and Bones [19] empirically studied churning effects of single discs
and gears running partially and fully submerged in oil, thus capturing drag effects caused
by dip lubrication. Meanwhile, Akin et al [20, 21] proposed models dealing with single
gear drag in jet lubrication applications to study lubricant cooling. None of these studies
took into account interactions between gears in mesh.
Studies by Tereckov [22], Luke and Olver [23], Höhn et al [24], Chase [8],
Moorhead [9], Petry-Johnson [10], and Vaidyanathan [11] were aimed at determining
spin losses of fixed-center spur or helical gear pairs in mesh with viscous drag and
pocketing losses lumped together. Further studies by Perchesky and Whidtbrott [25] and
Diab et al [26] presented models describing pocketing behavior, and Ariura et al [27],
Seetherman and Kahraman [1, 28, 29], and Changenet and Velex [30] presented models
capable of separately characterizing pocketing and drag losses for fixed-center gear pairs
in mesh.
8
These single gear or gear pair spin loss studies form a solid foundation for
characterizing spin power losses present in fixed-center gearing applications. Their
applicability to planetary gear systems, however, is limited due to unique kinematic and
mechanical features of planetary gears including planet bearings, a planet carrier that
rotates meshing gears with it, more complex lubrication schemes, and multi-mesh gearing
interactions. Power losses from all of these components interact in much more complex
ways, and so models presented dealing with spin losses of fixed-center gears cannot be
used to accurately model spin power losses in planetary gear systems.
Most planetary gear set-ups require cylindrical roller bearings to support the
planet gears. These bearings move at high speeds and can generate large power losses
due to viscous effects and contact friction. As these bearings are an integral part of the
planetary system, their power losses also need to be studied. The large majority of
literature on roller bearings has been confined to studies of dynamics, load distribution,
and fatigue life of roller bearing elements. Studies by Jones et. al. [31], Harris et. al. [32],
and Liu et. al. [33] are examples of such load distribution and fatigue life studies
conducted on standard planet cylindrical roller bearing set-ups with planet gear bores as
outer raceways. Palmgren [2] empirically evaluated bearing resistance torque and
separated components of viscous and contact friction. Chiu and Myers [34] also
developed an empirical model for overall friction torque in needle bearings as did
Townshend et al [35] for ball bearings. Palmgren’s equations [2] were referenced by
Harris [3] and are still used widely by bearing manufacturers [36]. These equations are
used in this study to separate load and viscous friction power losses in planet bearings.
The study of power loss in planetary gear systems has mostly been done from a
gear train kinematics point of view and has little relevance to this study. References [37-
41] represent only a portion of such studies. These studies aimed at determining the
overall efficiencies of planetary drive trains using speed and torque equations to study
overall power flow circuits. They are effective in comparing different transmission
designs in terms of their approximate efficiency outcome for designing systems with
minimal power recirculation, but they all assumed a constant mechanical efficiency value
for each gear pair in contact with no account of mechanical losses of planet bearings or
spin power losses. Muller [37], for example, assumed
η
η values of 0.97-1 for a gear mesh
in contact, while Pennastri and Freudenstein [39] assumed 0.993η = . These assumed
efficiency values have no physical backing, and fail to include the speed, load, and
lubrication effects on efficiency. More importantly, they do not take into account spin
losses.
A study was conducted by Anderson et al [42] that attempted to model power
losses in planetary gears using empirical equations derived for fixed-center spur gears [2,
43]. This study took into account power losses from gear rolling and sliding friction
(modified for internal spur gear teeth) from ref. [43], windage acting on gears from ref.
[43], and viscous and mechanical friction in bearings calculated from ref. [2]. Gear mesh
pumping and churning losses were not taken into account. Also, the experiments
conducted did not isolate any source of power loss, and so it could not be determined
whether each source of power loss was accurately modeled.
9
10
1.4 Scope and Objective
The existing body of research highlighted in Section 1.3 falls short of bringing an
understanding of power losses taking place in planetary gear sets. Neither detailed
planetary efficiency models nor extensive, tightly controlled experimental studies are
available in the literature. A companion study by Talbot [44] focuses on development of
a comprehensive model of mechanical and spin power losses of planetary gear sets in an
attempt to fill the void in terms of the modeling aspects of the problem. This study
complements Talbot’s work by investigating the high-speed spin power losses of
planetary gear sets.
The purpose of this study is to experimentally investigate spin power losses in
planetary gear systems. A set of experiments is carried out on a single set of unloaded,
helical planetary gears using different hardware and gearing configurations. The data
from these experiments is then used to isolate and characterize the sources of spin power
loss displayed in Section 1.2 and their contributions to the overall spin power loss of the
planetary gear set operating throughout the ranges of speed and temperature seen in
typical automotive transmissions. The specific objectives of this study are as follows:
• Develop a test set-up capable of spinning a single set of planetary gears at high
carrier speeds under no load with controlled lubrication condition and accurately
measure power loss.
• Develop and implement a repeatable and realistic test methodology that utilizes
various hardware and gearing configurations to eliminate, change, or isolate key
components of the spin power loss.
• Present spin power loss data and comparisons that demonstrate trends in spin
power loss with respect to speed and temperature for all hardware configurations.
• Use comparisons made in test data to isolate and rank order the main components
of the spin power loss and demonstrate the magnitudes and contributions of these
components to the overall spin power loss throughout ranges of the carrier speed
and lubricant temperature.
1.5 Thesis Outline
The rest of this thesis is organized as follows. Chapter 2 provides an explanation
of the testing methodology developed for this study. The test machine, test procedure,
and testing plan designed and developed specifically for this study are presented in detail.
The reliability of the test machine and procedure are also demonstrated in a repeatability
study presented in this chapter. Chapter 3 presents results for planetary spin power loss
obtained through testing. Overall spin loss P is presented for each test configuration at
all speeds and operating temperatures. Isolated sources of spin power loss are then
equated using methods explained in Chapter 3, and their magnitudes and contributions to
P are presented at all speeds and operating temperatures. Chapter 4 provides a detailed
summary of this study and lists the major conclusions and recommendations for future
work.
11
12
CHAPTER 2
EXPERIMENTAL TEST METHODOLOGY
2.1 Test Machine
A planetary gearbox was designed and procured to be used with an existing high-
speed efficiency test machine for completion of this study. The gearbox was intended to
support a planetary gear set for operation under unloaded conditions. Figure 2.1(a) shows
the test machine with the planetary gear test fixture. As shown schematically in Figure
2.1(b), the test machine comprises of a high-speed AC motor drive and a belt drive
connecting the AC motor to a high speed spindle. At the end of the spindle, a precision
torque sensor and a flexible coupling are placed to measure the torque provided to any
gearbox mounted on the test bed. This test machine was used earlier with various other
fixtures to measure loaded spur gear efficiency [5, 8, 10, 45], spur gear oil churning
power losses [1, 10], and helical gear efficiency [9, 11]. In all of these cases the loaded
conditions were created through a four-square power circulation scheme.
Figure 2.1: (a) View of efficiency test machine with planetary gearbox and (b) schematic
layout of test machine specifying main components.
AC drive motor
Planetary gearbox Spindle
Belt speed increaser
Flexible coupling
Torque sensor
(a)
(b)
13
The test machine was designed to rotate any test gearbox at speeds up to 10,000
rpm. An external lubrication system provides lubricant to the test gearbox at a desired
flow rate and temperature within the range of 30 to120 . Details of the test machine
can be found in earlier studies, specifically in Chase [8] and Petry-Johnson [10].
C
The drive system consists of a 40 HP AC motor that is digitally speed controlled
to within 2 rpm [8]. The motor speed can be set by the computer interface that controls
the test. The motor rotates a belt speed increaser that drives a precision Setco spindle
followed by a Lebow 900 series optical telemetry digital torque meter [8], as shown in
Figure 2.1(b). The torque meter has a maximum speed range of 25,000 rpm and a
maximum torque range of 50 Nm with a resolution of 0.01% and an accuracy of 0.05% of
full scale. The torque meter’s digital signal was recorded and time averaged to determine
the torque loss of the gearbox. Calibration of the torque meter was carried out prior to
testing using the procedure developed by Chase [8].
The speed was measured by a BEI Model H25 incremental encoder attached to
the AC drive motor that produces 16 pulses per revolution. The speed was logged
digitally throughout the duration of each test. More information about the encoder as well
as its calibration can be found in Chase [8].
14
15
2.2 Planetary Gearbox
As stated in Chapter 1, one of the main objectives of this study was the design and
development of a gearbox to allow high-speed unloaded operation of a planetary gear set.
Given the test capability afforded by the test machine of Figure 2.1, it was required that a
planetary gearbox be designed such that it could be used with the test machine.
Therefore, a base that fits precisely on the sliding table of the test bed and a vertical
flange that holds the planetary gear box at the desired elevation and position were
designed.
The example planetary gear set identified for this study was used earlier by Ligata
[46, 47, 48] for planet load sharing studies and by Inalpolat [49, 50, 51] for planetary
sideband modulation studies. In all earlier investigations, the gear set was operated in a
back-to-back power circulation scheme to allow testing under loaded gearing
configurations. In those studies, torque was input through the sun gear, while the planet
carrier was the output member. The ring gear was held stationary though external
splines. In this kinematic configuration, with the design parameters of the test gear set
defined in Table 2.1, a carrier to sun gear speed ratio of 1:2.712 was achieved. With the
sun gear as the input, the maximum speed of 10,000 rpm allowed by the test machine
would correspond to a carrier speed of 3687 rpm. This speed was lower than that require
for this study. For this reason, a kinematic configuration was chosen with the planet
carrier as the input member and the ring gear as the fixed member. In this kinematic
configuration, a carrier speed of 4000 rpm could be achieved conveniently to correspond
16
Table 2.1: Basic design parameters of the test planetary gear set used in this study.
Parameter Sun
Planet
Ring
Number of teeth 73 26 125
Normal module 1.81 1.81 1.81
Pressure angle [°] 23 23
Helix angle [°] 13.1 13.1
Center distance [mm] 92.1
Active face-width [mm] 25 25
17
to a sun gear speed of about 10,800 rpm and a planet bearing speed (relative to its carrier)
of about 19,200 rpm. These maximum speed values were deemed sufficient to study spin
losses of planetary gear sets used for automotive applications.
Figure 2.2 shows a view of the planetary gearbox designed and developed for this
study with the lubrication covers removed for clarity purposes. A cross-sectional view of
the gearbox is provided in Figure 2.3 to specify its support flange and base plate, which
were designed for the gearbox to be compatible with the existing test machine. Also
illustrated in this figure is the lubricant reservoir housing around the gearbox. The design
and operation of this reservoir are explained in section 2.2.
Focusing on critical details of the gearbox design, Figure 2.4 shows a three-
dimensional cross-sectional view with all key components labeled. The input shaft
shown in this figure was supported by two rolling element bearings (SKF 6207 deep
groove ball bearing with maximum speed of 13000 rpm). A flange in the middle of the
shaft was press-fit into the planet carrier and fastened with a set of bolts such that (i) the
carrier is the input member and (ii) it was supported rigidly in both radial and axial
directions. Both rolling element bearings were supported on their outer races by a two-
piece housing. The front side of the housing was mounted on the vertical support flange
to achieve a position such that when the sliding test bed was moved to forward position,
the splined end of the input shaft engaged the flexible coupling on the machine.
Figure 2.2: View of the test gearbox designed to hold and operate planetary gear set.
Lubricant cover has been removed for clarity purposes.
18
Figure 2.3: Cross-sectional view of test gearbox with its lubricant housing, support
flange, base plate, and slide plate.
Lubricant housing
Gearbox
Base plate Support
flange
19
Figure 2.4: Three dimensional cross-sectional view of the planetary gearbox with its key
components identified.
Housing – front
Retaining ring - front
Housing - back
Retaining ring – back
(lube catcher)
Thrust bearings
Shaft support bearing - back
Sun gear
Ring gear Ring gear adaptor
Oil seal
Input shaft
Shaft support bearing - front
Planet gear
Planet carrier
Planet bearing
Planet pin
Planet washers Lubricant drain
holes
20
21
The two sides of the housing were piloted radially by the ring gear adaptor, which was
sandwiched between the front and back housing details via a set of bolts. The inner
surface of the ring adaptor had internal splines designed to hold the ring gear stationary.
The ring gear was constrained axially by the pieces of the housing. This can all be seen
in Figure 2.4.
Each planet gear was mounted to the carrier through a pin, two rows of needle
bearings and two thrust washers as labeled in Figure 2.4 and shown in Figure 2.5. Figure
2.6 shows an assembled carrier with six planets. Since the carrier was designed to be
taken apart to replace planet components, two retaining rings were devised, one on each
side of the carrier, to prevent axial movement of planet pins. In addition, the front pin
retaining ring prevented any rotations of the pins with respect to the carrier while the
back retaining ring acted as a lubricant catcher to increase the oil flow to the planet
bearings.
The sun gear was held in position axially between the carrier and the back
housing detail by a pair of thrust bearings (SKF AXK 90120). As the gears are of helical
type the axial thrust force acting on the sun gear was taken by these thrust bearings
shown in Figure 2.4. No radial constraints were applied to the sun gear. Therefore, an
ideal “floating” condition could be achieved to prevent undesirable load sharing issues
[46]. Figure 2.7 shows a view of the ring, sun, and planet gears.
Figure 2.5: View of components of planet-bearing assembly including planet gear, planet
pin, double-row caged planet bearings and thrust washers.
22
Figure 2.6: View of six-planet carrier assembly.
23
Figure 2.7: View of the gears of the test gear set.
24
25
2.3 Lubrication System
Lubrication of the contacts of a planetary gear set is more complex than that of
fixed-center gearing. In fixed-center applications, the dip lubrication method is common
when gear speeds are relatively low. In such cases as manual and dual clutch
transmissions, transfer cases, and axles; gears are partially immersed in oil. Churning of
the oil, as gears rotate, causes sufficient interactions between the medium (air-oil mixture
or mostly oil) and the gear bodies to provide proper conditions for heat removal as well
as supplying sufficient oil supply to the gear mesh contacts. In cases where the gear
speeds are high, dip lubrication is less effective due to excessive oil churning power
losses [29] and adverse effects such as foaming. In such high speed applications,
exemplified by most rotorcraft and aerospace gearbox applications, jet lubrication is
preferred. This lubrication method involves high-pressure oil jets delivering lubrication to
the gear meshes through calibrated nozzles.
Neither the dip lubrication method nor the jet lubrication method is optimal for
planetary gears. Since the planets rotate in most cases, application of dip lubrication at a
certain oil level is risky since planet meshes are forced to operate above the oil level for
certain portions of carrier rotation. Likewise, it is not practical to design oil manifolds
that rotate with the carrier such that the nozzles of jet lubrication follow the meshes of the
rotating planets. The most common planetary lubrication system used in various systems
such as automatic transmissions has been the application of the oil from the rotational
center of the planetary gear set. This way, the centrifugal forces push the oil radially
26
outward, directing it to gear mesh and bearing locations through carefully designed paths.
This lubrication method was applied to the planetary gearbox designed for this study.
Labeled as Path A in Figure 2.8, pressurized oil was provided to the space between the
front ball bearing and a bronze oil dam pressed into the housing, which was forced to the
center of the hollow input shaft through eight radial holes, each at 7 mm diameter. The
bronze dam and the oil seal on the other side of the bearing restricted the movement of
the oil in any other directions. Oil at the center of the input shaft was then pushed out
through holes lined up with the bearing washer locations in an attempt to lubricate sun-
planet gear meshes, ring-planet gear meshes, planet bearings, and planet washers. The
plug placed at the open end of the input shaft ensured that all of the oil pumped in
through Path A flowed to the needed locations.
This was the only path designed and implemented initially, and it worked well for
carrier speeds up to 2500 rpm (planet bearing speeds up to 12,019 rpm). Beyond such
speeds, severe temperature-induced planet bearing failures were observed in initial tests,
indicating that amount of oil delivered to the planet bearings was not sufficient. To
alleviate this situation a second forced lubrication path (Path B in Figure 2.8) was
designed and implemented. This path required several component additions and
modifications:
• A set of oil lines were devised to bring sufficient amounts of oil to the back
ends of the planet bearings as shown in Figure 2.9.
Figure 2.8: Diagram of the two main lubricant paths implemented in this study.
BA
27
Figure 2.9: View of lubricant lines added for oil flow to lubricant catcher.
28
29
• One of the pin retainers was modified so that it acts as a lube catcher,
capturing the oil discharged by these lines as well as some of the oil spreading
out from the center of the gear set. This lube catcher formed a dam for oil to
accumulate.
• A new lube path was created through modifications to the carrier and drilled
holes to the planet pins such that the oil has a direct path to the space between
the two rows of caged needle bearings.
These two lubricant paths A and B were found to be sufficient for unloaded operation of
the planetary gear set at carrier speeds up to 4000 rpm (bearing speeds up to 19,231 rpm).
The gearbox was lubricated using a typical automatic transmission fluid (ATF).
The lubricant was supplied and extracted from the gearbox by a temperature controlled
external lube system with a large reserve. This system is capable of holding the
temperature of the fluid within 5 degrees of desired set temperature. Temperature of the
oil was measured within the reservoir and at the inlet to the gearbox.
The lubricant flow rate was held constant at 18 lpm throughout all tests. Of this,
12 lpm was applied through Path A and the remaining 6 lpm was applied through path B.
This flow rate was established through run-off tests to ensure that just enough lubricant
was provided to the planet bearings to allow them to function properly at high speeds.
Such a flow rate is obviously much more than those used in automotive applications that
used this gear set. Yet, the speeds at which the gear set operated in this study were
significantly higher than those in its production application.
30
The flow rate of the lubricant system was set by restriction ball valves down-
stream of the inlet pump. The fluid branched off to two separate lines at the test machine.
One line provided lubricant to path A while the other line provided lubrication to the
extra lube jets of path B. Both of these lines had restriction valves. Downstream of the
restriction valve on each line, a mechanical flow meter with resolution to 1 lpm flow rate
was placed as well as a liquid pressure gauge with resolution to 1 psi gauge pressure.
These measurement devices were used to set the flow rate for the tests and to ensure that
it was consistent for all tests. Before each test, the flow meters and pressure gauge
readings were checked and recorded to ensure repeatability of all tests.
Large openings machined in front and back sides of the housing, as shown in
Figure 2.4, ensured that the oil pumped through the gear set drained out of the gearbox
instead of causing any dip-lubrication conditions. The lubricant drained from the
gearbox was accumulated in a large reservoir that contained the gearbox, as shown in
Figure 2.3. The Lower half of the reservoir was firmly attached to the base of the
gearbox flange while the upper half was designed to slide tightly inside of the lower
housing to collect any oil splashed upward. Oil collected in the bottom of the reservoir
was pumped by a sump pump back to the external lubrication system.
2.4 Various Test Hardware Options
31
P P
The load-independent (spin) power loss of a planetary gear set can be considered
as the sum of power losses caused by various friction, viscous drag and pumping effects
defined in Chapter 1. Per the scope of this study, the power losses caused by viscous
air/oil drag on the sun gear and planet carrier, and , air/oil pumping at each sun-
planet and ring-planet meshes,
ds dc
psP and pr
bgP
P
)
, and the viscous and load dependant friction
within the planet bearings, and , were considered in this study. Drag losses
attributed to the ring gear were neglected in this case since it was stationary. With that,
the total spin power loss of an N-planet planetary gear set can be written as
bvP
. (2.1) ( ) (ds dc ps pr bv bgP P P N P P N P P= + + + + +
As stated Chapter 1, one objective of this study was to determine and rank-order
contributions of each power loss component. For this purpose, variations to the baseline
gear set configuration were designed and implemented. These variations included
running tests with missing hardware or modified hardware. The intent of testing with
these variations was to collect data under conditions when some of the components of the
power loss specified in Eq. (2.1) were changed or absent. These conditions and associated
hardware variations are described below.
32
P
(i) Case of no sun related power losses. This variation required operation without
a sun gear, therefore removing sun drag ( ) and sun-planet pumping losses (ds
psP ) from Eq. (2.1). While the planetary gear set can be rotated with no sun
gear, the additional space created in the absence of the sun gear impacts the
lubricant flow paths, potentially influencing the other components of power
loss. To avoid changes in the lubricant flow, a dummy disk made out of a
polymer material was designed to occupy the space of the sun gear. Figure 2.10
shows a picture of this dummy disk. This disk has the same dimensions as the
sun gear blank, except its outside diameter is low enough to avoid contact with
the planets. It was fabricated from unreinforced 1700 grade polysulfone plastic
resin. This material was selected because it was easy to machine and had a
thermal expansion coefficient of 31 ppm/°F, and a density of 1240 kg/m3 [52].
These thermal properties allow the material to withstand temperatures above
90°C with minimal thermal expansion. The low density of the material also
mitigates any inertial effects of the disc. The disk was press fit on the input shaft
such that it rotated with the carrier at a speed about 37% of the actual sun speed
to minimize sun drag effects. Figure 2.11 shows the planetary gear box in the
configuration with no sun gear.
Figure 2.10: View of dummy disc intended to occupy the space of the sun gear during
tests with no sun gear.
33
Figure 2.11: Three dimensional assembly cross-section of the gearbox showing
implementation with dummy disk in place of sun gear.
Dummy sun disc
34
(ii) Case of no pumping losses. It was shown earlier by [29] that losses associated
with the pumping of medium from the gear mesh cavities were strongly related to
the affective face widths of the gears. In order to create a condition when all the
power loss components in Eq. (2.1) were present except the pumping losses psP
and prP , a set of planetary gears with significantly reduced face widths were
designed and fabricated. Figure 2.12(a) shows a baseline full face width planet
gear with a 25 mm face width while Figure 2.12(b) shows a reduced face width
version with only 3.175 mm face width.
(iii) Case of reduced centrifugal effects. As stated earlier, the term in Eq. (2.1)
was intended to represent bearing losses caused by the centrifugal forces of
planets rotating with the carrier. In order to create an operating condition where
these forces were significantly less, another variation of planet gears with reduced
mass was designed and procured. As shown in Figure 2.12(c), these had the same
geometrical features as the baseline planets but had a much lower mass. These
gears were made of KTN-820 unreinforced polyetheretherketone (PEEK) plastic
resin. The PEEK material had a glass transition temperature of 150° C and a
specific gravity of only 1300 kg/m3, compared to 7800 kg/m3 of steel [53, 54].
Therefore, the material maintained the shape mimicking steel gears throughout
the testing temperature range while only contributing a fraction of the weight of
steel gears. Since the bores of planets serve as the outer raceways for the planet
bgP
35
36
(a)
(b)
(c)
Figure 2.12: Pictures and cross sectional diagrams of planet gear types (a) baseline,
(b) reduced face width, and (c) reduced mass (plastic).
Steel inserts
Plastic
bearings, a thin (3.2 mm) steel insert was pressed into each plastic planet. This
ensured that the interactions between the bearings and washers with the planet
remained the same as the baseline conditions. The mass of a plastic gear, shown
in Figure 2.12(c), was only 0.06 kg, slightly over one third of the 0.17 kg baseline
planet gears.
In addition to above variations requiring different hardware, the existing hardware could
also be used in different configurations to represent different power loss combinations.
One such configuration was obtained by using the current carrier with only three planets.
In this case, while the drag components of losses were retained the planet related losses
were reduced to half. Another configuration involved the gear set operated without the
sun and ring gears. In this case, no meshing action took place, so the velocity of the
planets relative to the carrier was zero. Therefore, the only active power loss component
was expected to be , which also included the losses associated with the rolling
element bearings holding the carrier shaft and the oil seal.
dcP
2.5 Test Procedure
The gearbox was torn apart and inspected between each group of tests. One test
group consisted of tests of a single gearbox configuration at all test speeds and a given
temperature setting. As the speeds sought were far beyond the speeds the gear set was
originally designed for, the gearbox hardware had to be inspected for any signs of
damage or noticeable wear throughout each test.
37
38
Special care was taken to ensure that the same hardware and gearing alignments
were used for every test. This was done to ensure that any small amount of power loss
caused by hardware manufacturing errors was consistent throughout all tests where
possible. The same sun and ring gears were used for every test in which a sun or ring gear
was present. Planet gears, washers, and bearings were replaced on a few occasions
between testing, but an extensive gear run-in procedure was followed after each hardware
change to ensure that the friction properties within the gearbox did not drastically change
during testing due to gears running in. Planet gears were labeled with numbers one
through six. These numbers represented which pin locations on the carrier they would
occupy. One tooth on each planet was marked as a reference tooth, and planets were
assembled in the gearbox such that these reference teeth were positioned radially
outwards. Likewise marked reference teeth on the sun and ring gears were aligned
initially with the first planet. This way, any run-out or eccentricity related effects would
be repeated in each test in an attempt to reduce variability [46].
For the tests with three planets, the planets, washers, and bearings housed in the
first, third, and fifth planet locations in the carrier were removed. The planet gear pins
associated with the removed planets remained installed in the test machine to ensure
consistent lubrication system behavior between tests run with six and three planet
configurations.
39
Before initiating each test group, the lubricant system was started up and allowed
to run for 40 minutes. This allowed the components of the gearbox to heat up to
temperatures close to the oil inlet temperature before the test was started.
During some of the higher speed tests conducted, some of the fluid within the
sealed gearbox reservoir mixed with the air to form a mist surrounding the gears.
Research has indicated that this mist may affect the power loss caused by drag within the
gearbox to a certain extent [29]. Since such misting conditions could not be eliminated,
steps were taken to ensure that these conditions were consistent for each test. After each
test, the top housing of the reservoir was opened to exhaust any built up mist within the
reservoir. This exhaustion ensured that each test started with the same drag conditions.
2.5.1 Torque-meter Set-up and Gearbox Engagement
The strength of the reception of the torque reading within the optical telemetry
torque-meter is critical. If the signal strength is not sufficiently high, the torque meter
may take inaccurate torque measurements [8]. Therefore, the quality of the torque meter
signal strength was checked before conducting each test group by using the procedure
defined by Chase [8]. Adjustments were made if this quality measurement was not
sufficiently high.
Due to the high accuracy required in tests and the nature of the torque-meter to
drift slightly during testing, the testing procedure required that the torque meter be set to
zero before each test and that the drift of the torque meter from zero be recorded after the
test. For this, the gearbox was disengaged from the drive system before each test and the
torque-meter was zeroed within the torque-meter software.
2.5.2 Gear Run-in Procedure
As stated earlier, the gear system was put through a run-in cycle before testing if
any new hardware was added to the system. This run-in cycle was intended to ensure no
large changes in surface roughness on gear and bearing surfaces occurred during testing
as a result of gears breaking in. The run-in cycle consisted of at least three, one-hour
segments of tests at 1000 rpm and 90°C. The average torque measurements for each run-
in segment were recorded and such segments were repeated until measured torque values
converged.
2.5.3 Data Acquisition
Each test was conducted by starting up the test machine at the desired test speed
and recording (i) input torque to the gearbox, (ii) planet carrier speed, and (iii) the
temperatures at the fluid system reservoir and the inlet to the shaft lubrication system. All
data was then averaged over the test period to arrive at a set of representative values of
spin torque loss T , input (or carrier) speed ω , and reservoir and shaft inlet temperatures
for each test. Each test was run for a period of ten minutes. The ten minute testing period
was decided on after running a series of practice tests in which data was taken for
extended periods of time. The time traces of data were studied, and it was determined that
40
about eight minutes of data was required to ensure that all transient, cyclic behavior of
the torque trace would not influence the final torque measurement. It was also determined
that the first two minutes of data should not be included in the recorded torque
measurement because it was affected by the transient nature of the gearbox establishing
test speed as well as a 100 point running average applied to the torque measurement trace
to further decrease transient behavior of T [8]. Figure 2.13 shows an example 10-minute
segment of measured T of which the last eight-minute segment was used to determine
the T value of the test. The total spin power loss of the gearbox was the computed using
P T= ω.
41
Figure 2.13: T time trace of six planet, baseline test at 3000 RPM and 90° C.
0
2
4
6
8
10
12
0 2 4 6 8 10
Data range considered
T
[Nm]
Time [minutes]
42
2.6 Test Matrix
A test matrix shown in Table 2.2 was defined to generate data for four different
variations. Tests A used a 6-planet carrier with baseline, full face width planets. Tests B
again used baseline planets, but in a 3-planet carrier arrangement. Tests C were done
using a 6-planet arrangement with reduced face width steel planets while Tests D were
performed by using the 3-planet arrangement with the reduced mass plastic gears. For
tests A to C, three variations were considered: (1) complete gear set with both sun and
ring gear active, (2) gear set without the sun gear (with the dummy disk in place of the
sun gear) and (3) gear set without both sun and ring gears. With this notation, Test 3C,
for instance, represents tests with no sun or ring gear and with a 6-planet carrier housing
reduced face width planet gears. Meanwhile, Tests D were only conducted using
variation (2) with no sun gear. Accordingly, measured spin power loss values for each
test configuration represented the following variations of Eq. (2.1):
1 6( ) 6( )A ds dc ps pr bv bg ABP P P P P P C m= + + + + + , (2.2a)
2 6 6( )A dc pr bv bg ABP P P P C m= + + + , (2.2b)
3A dcP P= , (2.2c)
, (2.2d) 1 3( ) 3( )B ds dc ps pr bv bg ABP P P P P P C m= + + + + +
, (2.2e) 2 3 3(B dc pr bv bg ABP P P P C m= + + + )
c , (2.2f) 3B dP P=
43
Table 2.2: Spin power loss planetary gearing configuration test matrix.
Test Number of Planets, n Sun gear Ring gear Planet gears
1A
6
Yes Yes Baseline
2A No Yes Baseline
3A No No Baseline
1B
3
Yes Yes Baseline
2B No Yes Baseline
3B No No Baseline
1C
6
Yes Yes Reduced face-width
2C No Yes Reduced face-width
3C No No Reduced face-width
2D 3 No Yes Reduced mass
44
, (2.2d)
1 6( )C ds dc bv bg CP P P P C m≅ + + +
45
6( )P P P C m≅ + +
c
)
m
, (2.2h) 2C dc bv bg C
, (2.2i) 3C dP P=
. (2.2j) 2 3 3(D dc pr bv bg DP P P P C m= + + +
Here, the load-dependent bearing power loss is described by the relation as
explained in Chapter 1, where
bg bgP C=
ABm
m
is the mass of a full face width steel planet gear as
shown in Figure 2.12(a), is the mass of a reduced face width steel planet gear as
shown in Figure 2.12(b) and
C
Dm is the mass of a reduced-mass plastic planet gear as
shown in Figure 2.12(c). Table 2.3 specifies the numerical values of masses of the
variations of planet gears. As it will be discussed in the next chapter, these 10 variations
of spin loss measurements were then used to estimate the contributions of different power
loss components defined in Eq. (2.1).
Each test configuration was run at two different oil temperatures of 40°C and
90°C. These temperatures were chosen because they span the temperature range at which
most automotive transmissions typically operate. Testing at the upper and lower ends of
the temperature range was deemed necessary since ATF experiences sizable changes in
viscosity with respect to temperature [55, 7]. Each test variation at each temperature level
was run at 8 discrete input (carrier) speeds ranging from 500 to 4000 rpm (in increments
of 500 rpm). With 10 hardware variations (1A to 2D in Table 2.2), two temperature
Table 2.3: Masses of planet gears and planet gear and bearing sets.
Gear type Gear mass (kg)
Gear and bearing set
mass, m (kg) Nomenclature
Baseline 0.17 0.21 ABm
Reduced face-width 0.11 0.15 Cm
Reduced mass (plastic) 0.06 0.10 Dm
46
levels and 8 speed values at each temperature value, a total of 160 pieces of data were
defined in this test matrix excluding repeatability validation tests.
2.7 Test Repeatability
47
P
Given the large time requirements to set-up and run each test and the many
hardware changes taking place between tests, it was not possible to duplicate or
randomize tests in a manner that would demonstrate full statistical confidence in the test
data and conclusions. Therefore, in order to demonstrate the repeatability of the
measurements, test group 1A in Table 2.2 was chosen as the repeatability test condition,
and several 1A tests were performed at various stages of the test program. These tests
were staggered throughout the entire test program to ensure that no tangible changes took
place to the test conditions, the measurement system, or the test articles that would have
an effect on measurements.
Figure 2.14 compares the values measured through five different 1A tests at
various input speed values and temperatures (a) 40°C and (b) 90°C. The repeatability of
the results at 90°C is very good, as shown in Figure 2.14(a), with less than a 5% spread in
test data about the mean value for all speeds tested. The repeatability at 40°C is also
acceptable overall. The repeatability at 3000 and 3500 rpm are the poorest with 11% and
16% spread over the mean value. The slope of the viscosity-temperature curve of ATF
used here is very steep at 40°C [55, 7], making the measured losses more susceptible to
oil inlet temperature as well as the instantaneous temperature state of the gearbox.
P
Figure 2.14: Test 1A, P repeatability with respect to input carrier speed at
(a) 40°C and (b) 90°C.
0
1
2
3
4
5
1000 2000 3000 4000
Test 1Test 2Test 3Test 4Test 5
0
1
2
3
4
5
1000 2000 3000 4000
Test 1Test 2Test 3Test 4Test 5
(b)
P
[kW]
P
[kW]
ω[rpm]
48
CHAPTER 3
PLANETARY GEAR SET SPIN POWER LOSS TEST RESULTS
3.1 Introduction
This chapter presents the measured spin power loss results from the tests listed in
Table 2.2, performed by using the test procedure defined in Chapter 2. The power loss
values 1AP through 2DP measured from tests 1A through 2D will be presented first
within each sub-set A to D to compare them directly as functions of carrier speed ω at
different lubricant temperature values.
The spin power loss values 1AP through 2DP
bvP
were shown in Eq. (2.2) to represent
a certain sub-set or variations of the total planet gear set spin power loss expression given
in Eq. (2.1). A direct measurement of each component of the spin power loss without
others present is not possible as these components cannot be separated physically. For
instance, one cannot measure bearing viscous loss without having the centrifugal loss
. Likewise, pocketing losses bgP psP and prP cannot be isolated from the drag losses dsP
49
50
Pand . However, each component of power loss in Eq. (2.1) can be estimated indirectly
by comparing the results from each test variation
dc
1AP to 2DP
ω
. Here, the term
“estimation” is used in place of “measurement” to indicate that the results are a
composite of two or more separate experiments. While special attention was given to
controlling the test conditions and reducing the measurement errors as much as possible,
any variations within the repeatability of the test set up as a gauge should be expected to
influence these results especially when the values of the spin loss components are small.
3.2 Measured Total Planetary Spin Power Losses
3.2.1 Influence of Speed
Figures 3.1 and 3.2 display the power loss values measured as functions of the
carrier speed at 40 and 90°C, respectively. In these figures, individual graphs are
provided to compare ( 1AP , 2AP , 3AP ), ( , , ) and ( , , and ) as
well as a separate plot for
1BP 2BP 3BP 1CP 2CP 3CP
2DP . In Figure 3.2, it can be seen that the 90° tests all display
very smooth trends, where P increases with speed at a polynomial rate. At 40°C (seen in
Figure 3.1), this same trend is demonstrated for 2,500ω< rpm. Above this range, this
trend diminishes for 1AP , 2AP , , and . This might likely be caused by a decrease
in lubricant viscosity caused by an increase of the oil temperature at bearing locations
during these tests. Lubricant temperature has shown to have a large effect on power
losses as will be explained later.
1PB CP
51
Continue
d
Figure 3.1: Comparison of (a) 1AP , 2AP , and 3AP , (b) 1BP , 2BP , and 3BP , (c) 1CP , 2CP ,
and 3CP , and (d) 2BP and 2DP as functions of ω at 40°C.
0
1
2
3
4
5
0 1000 2000 3000 4000
1A2A3A
0
1
2
3
4
5
0 1000 2000 3000 4000
1B2B3B
P
[kW]
P
[kW]
ω [rpm]
1
2
3
A
A
A
PPP
1
2
3
B
B
B
PPP
(b)
(a)
Figure 3.1 continued
0
1
2
3
4
5
0 1000 2000 3000 4000
1C2C3C
0
1
2
3
4
5
0 1000 2000 3000 4000
2B2D
ω [rpm]
P
[kW]
P
[kW]
1
2
3
C
C
C
PPP
2
2
B
D
PP
(c)
(d)
52
53
Continue
d
Figure 3.2: Comparison of (a) 1AP , 2AP , and 3AP , (b) 1BP , 2BP , and 3BP , (c) 1CP , 2CP ,
and 3CP , and (d) 2BP and 2DP as functions of ω at 90°C.
0
1
2
3
4
5
0 1000 2000 3000 4000
1A2A3A
0
1
2
3
4
5
0 1000 2000 3000 4000
1B2B3B
ω [rpm]
P
[kW]
P
[kW]
1
2
3
A
A
A
PPP
1
2
3
B
B
B
PPP
(b)
(a)
Figure 3.2 continued
0
1
2
3
4
5
0 1000 2000 3000 4000
1C2C3C
0
1
2
3
4
5
0 1000 2000 3000 4000
2B
2D
(c)
(d)
ω [rpm]
P
[kW]
P
[kW]
1
2
3
C
C
C
PPP
2
2
B
D
PP
54
In Figures 3.1(a) and 3.2(a), the contributions from psP and can be seen as
the difference between
dsP
1AP from the example gear set under baseline condition 1A (with
six full-face width steel planets and sun and ring gear), and 2AP
1
from test 2A with no sun
gear (no sun drag and pocketing losses). In these figures, AP is about 3.85 kW at 3000
rpm and 40°C while the 2AP reaches only about 2.92 kW at the same speed and
temperature value. A similar difference is also observed at 90°C in Figure 3.2(a), where
1AP and 2AP are 2.98 and 2.51 kW at 3000 rpm respectively. The contributions of prP ,
, and with the mass of the baseline planet gear bvP bgP ABm can be viewed as the
difference between tests 2AP and 3AP . 3AP represents the test condition 3A, where the
sun and ring gears are removed (only the contribution of is present). At 3,000 rpm, dcP
3AP is measured to be only 0.35 kW at 40°C and 0.26 kW at 90°C.
The corresponding tests 1B, 2B and 3B with the 3-planet carrier yield results
(Figures 3.1(b) and 3.2(b)) considerably less than those for the 6-planet carrier. It can be
seen in Figures 3.1(a) and 3.1(b) that is about 1.48 kW lower than 1BP 1AP at 40C and
1.18kW lower than 1AP at 90C. This decrease represents the losses associated with the
three missing planets. Values of and are again smaller compared to , as
expected.
2BP P P3B 1B
The tests with reduced face width planets (1C, 2C) In Figures 3.1(c) and 3.2(c)
reveal lower loss values than those from full face width planet tests (1A and 2A) in
55
56
PFigures 3.1(a) and 3.2(a). For instance, at 3,000 rpm, is about 0.88 kW lower than 1C
1AP
6( )
at 40°C and 0.61 kW lower at 90°C. This reduction in power loss can be attributable
to the pocketing loss term ps prP P+ in Eq. (2.1).
Finally, in Figures 3.1(d) and 3.2(d), measured 2DP
2BP
(representing test 2D with
reduced mass gears and no sun gear) values are presented for conditions at 40 and 90°C,
respectively. They are compared to the corresponding values in these figures to
illustrate the influence of losses associated with the centrifugal loads due to the planet
mass. At 90°C, is about 0.17 kW higher than 2BP 2DP at 3000 rpm. This difference
drops to about 0.05 kW at 40°C. 2DP is believed to be overestimated at 40°C due to
experimental error, as will be discussed in the next section.
One can represent the variations in P observed in Figures 3.1 and 3.2 with ω as
, where each term represents a single source of power loss and can be
described by the relation . In Section 3.3, these components of power loss will
be quantified and their dependence on speed will be estimated individually to establish
such trends.
iP =∑P P
b
i
ii iP a= ω
3.2.2. Influence of Lubricant Temperature
In order to illustrate the influence of the lubricant temperature on the spin power
losses of the planetary gear sets, direct comparisons between the measurements at 40 and
90°C are made in Figure 3.3. The viscosity of the ATF lubricant is a key parameter for
all of the components of power loss. A decrease in oil viscosity was shown to decrease
both pumping and drag power losses of spur gears [1, 9, 8, 10, 27] operating under jet or
dip lubrication conditions as well as helical gears [11] and hypoid gear [56].
The ATF used in this study has a kinematic viscosity of 29.5 centistokes at 40°C
and only 7.15 centistokes at 90°C [7, 55]. As seen in Figure 3.3, this directly impacts the
resultant spin loss values shown in Figure 3.3. In Figure 3.3(a), the 1AP
1P
values at 40°C
are considerably higher than those at 90°C. For instance, at 3,000 rpm, kW at
40°C and only 2.98 kW at 90°C. This 0.87 kW (25%) difference seen in
3.85A
1
=
AP is directly
attributable to the oil temperature. Similar trends are observed in Figures 3.3(b) to 3.3(d)
for , and 1BP 1CP 2DP , respectively, further demonstrating the influence of oil
temperature and resultant changes in oil viscosity.
57
58
Continued
Figure 3.3: Comparison of (a) 1AP , (b) 1BP , (c) 1CP , (d) 2DP as functions of ω at
40 and 90°C.
0
1
2
3
4
5
0 1000 2000 3000 4000
40°C90°C
0
1
2
3
4
5
0 1000 2000 3000 4000
40°C90°C
ω [rpm]
P
[kW]
P
[kW]
(b)
(a)
Figure 3.3 continued
0
1
2
3
4
5
0 1000 2000 3000 4000
40°C90°C
0
1
2
3
4
5
0 1000 2000 3000 4000
40°C90°C
ω [rpm]
P
[kW]
P
[kW]
(c)
(d)
59
3.3 Components of Spin Power Loss
3.3.1 Determination of Spin Power Loss Components
Using the test data presented in Figures 3.1 and 3.2 in view of the set of equations
(2.2), individual components of spin power loss defined in Eq. (2.1) can be estimated. As
stated earlier, these estimations are done by using results from two or more separate
experiments. Therefore, their fidelity is impacted by the uncertainty and variability
associated with each test result employed.
The rest of this section presents schemes to estimate (i) the viscous drag losses
and from the planet carrier and the sun gear , (ii) gear mesh pumping losses dcP dsP psP
and prP
P P
P
from the planet-sun and the planet-ring gear meshes, and (iii) planet bearing
viscous and mechanical friction losses ( and ). bv bg
According to Eq. (2.2), the carrier viscous drag loss should dictate the bulk
of the losses in tests 3A, 3B and 3C, The losses associated with the input shaft bearings
and the seal also lumped with these measurements. Accordingly, the values from
these tests are given as follows:
dcP
dc
, (3.1) 3dc AP P=
, (3.2) 3dc BP P=
. (3.3) 3dc CP P=
60
While any of these tests could be used to determine values, these three separate tests
provide further confidence in accuracy of this measurement.
dcP
The sun gear viscous drag loss can be estimated by processing the losses
from tests 1A, 2A, 1B and 2B. Alternatively, results of tests 1C and 2C can be used more
directly to estimate the same. The following equations are used for this purpose:
dsP
, (3.4) 2 1 1 22 2ds A A B BP P P P P= − + −
. (3.5) 1 2ds C CP P P= −
Next, the pumping power loss of a single planet-sun gear mesh ( psP ) is estimated as
[ 1 2 1 213ps A A B B ]P P P P P= − − + , (3.6)
[ ]11 2 1 26ps A A C CP P P P P= − − + , (3.7)
[ 1 2 1 213ps B B C CP P P P P= − − + ] . (3.8)
Likewise, the equations to calculate the pumping power loss of a single planet-ring gear
mesh ( prP ) are given as
[ ] [ ]1 1
2 3 2 3 2 3 26 6( )( ) 2( )
C ABpr A A C C A A D
AB D
m mP P P P P P P Pm m
−= − − − + + −
−, (3.9)
61
[ ] [ ]1 1
2 3 2 3 2 26 3( )2 2( )
C ABpr B B C C B D
AB D
m mP P P P P P Pm m
−= − − + + −
−. (3.10)
In each of these equations, the first term would be sufficient to estimate prP with the
assumption that the differences in masses of the full face width and reduced face width
planets ( ABm and ) are small enough to cause the same levels of bearing power
losses. The second term in each equation is present to correct for any differences in
bearing power losses caused by change in the mass of the planet gears.
Cm
Meanwhile, the viscous (load-independent) power loss of a single bearing can
be estimated in two ways:
bvP
[ ] [ ]1 12 3 2 3 26 6 2
( )C
bv C C A A DAB D
mP P P P P Pm m
= − − + −−
, (3.11)
[ ] [1 1
2 3 2 26 3 ( )C
bv C C B DAB D
mP P P P Pm m
= − − −−
]
m
. (3.12)
Again, the second terms in the above equations are to account for the differences in
planet masses. Finally, the planet bearing mechanical power loss parameter (
) can be found by using either one of the following two equations:
bgC
bg bgP C=
[ ]1C P P P= + −2 3 22
6( )bg A A DAB Dm m−
, (3.13)
[ ]2 2
13( )bg B D
AB DC P
m m= −
−P . (3.14)
62
Using Eqs. (3.1) through (3.14), each of the six power loss sources were isolated
and the magnitudes of their contributions to overall were quantified. In Figures 3.4 to
3.9, these six power loss components are given as functions of
P
ω at both (a) 40°C and (b)
90°C. Due to limitations in their designs, the reduced face width planets could only be
tested up to 3,500 rpm, and the reduced mass planets could only be tested up to 3,000
rpm. Equations (3.5), (3.7), and (3.8) incorporate data from tests using reduced face
width planets, and Eqs. (3.9) through (3.14) incorporate data from tests using reduced
mass planets. As a result, Eqs. (3.5), (3.7), and (3.8) were only used through 3,500 rpm,
and Eqs. (3.9) through (3.14) were only used through 3,000 rpm. Therefore, and dsP psP
were determined through 3,500 rpm while the range for prP , , and bvP gbP was limited to
3,000 rpm.
The values of the carrier drag power loss calculated by using Eqs. (3.1) to
(3.3) are compared in Figure 3.4. It is observed that each equation yielded very similar
values of for at both 40 and 90°C. At speeds below 3,000 rpm at 40°C and below
2,500 rpm at 90°C, exhibits a trend with about a
dcP
dcP
dcP
dcP 2∝ ω relationship to speed. This
is similar to models proposed by Seetharaman and Kahraman [1, 27]. Their models
predicted on the periphery and 2.∝ ω 5dcP 2
dcP ∝ ω on the sides of a cylinder, with the
latter component being more significant. While certain minor differences are observed
above 3,000 rpm, all three equations (representing data for tests 3A, 3B or 3C) appear to
be reasonably close at evaluating the drag power losses of the carrier assembly.
63
64
Figure 3.4: Comparison of dcP calculated using Eqs. (3.1), (3.2), and (3.3) at (a) 40°C
and (b) 90°C.
0
100
200
300
400
500
600
0 1000 2000 3000 4000
Eq. (3.1)Eq. (3.2)Eq. (3.3)Average
0
100
200
300
400
500
600
0 1000 2000 3000 4000
Eq. (3.1)Eq. (3.2)Eq. (3.3)Average
ω [rpm]
dcP
[W]
dcP
[W]
(b)
(a)
65
Figure 3.5: Comparison of dsP calculated using Eqs. (3.4) and (3.5) at (a) 40°C and
(b) 90°C.
-400
-200
0
200
400
600
0 1000 2000 3000 4000
Eq. (3.4)Eq. (3.5)Average
-400
-200
0
200
400
600
0 1000 2000 3000 4000
Eq. (3.4)Eq. (3.5)Average
ω [rpm]
dsP
[W]
dsP
[W]
(b)
(a)
66
Figure 3.6: Comparison of psP calculated using Eqs. (3.6), (3.7) and (3.8) at
(a) 40°C and (b) 90°C.
-100
0
100
200
0 1000 2000 3000 4000
Eq. (3.6)Eq. (3.7)Eq. (3.8)Average
-100
0
100
200
0 1000 2000 3000 4000
Eq. (3.6)Eq. (3.7)Eq. (3.8)Average
ω [rpm]
psP
[W]
psP
[W]
(b)
(a)
67
Figure 3.7: Comparison of prP calculated using Eqs. (3.9) and (3.10) at (a) 40°C and
(b) 90°C.
0
50
100
150
200
0 1000 2000 3000 4000
Eq. (3.9)Eq. (3.10)Average
0
50
100
150
200
0 1000 2000 3000 4000
Eq. (3.9)Eq. (3.10)Average
ω [rpm]
prP
[W]
prP
[W]
(b)
(a)
68
Figure 3.8: Comparison of bvP calculated using Eqs. (3.11) and (3.12) at (a) 40°C and
(b) 90°C.
0
100
200
300
400
500
600
0 1000 2000 3000 4000
Eq. (3.11)Eq. (3.12)Average
0
100
200
300
400
500
600
0 1000 2000 3000 4000
Eq. (3.11)Eq. (3.12)Average
ω [rpm]
bvP
[W]
bvP
[W]
(b)
(a)
69
Figure 3.9: Comparison of bgC calculated using Eqs. (3.13) and (3.14) at (a) 40°C and
(b) 90°C.
-1100
-700
-300
100
500
900
0 1000 2000 3000 4000
Eq. (3.13)Eq. (3.14)Average
-1100
-700
-300
100
500
900
0 1000 2000 3000 4000
Eq. (3.13)Eq. (3.14)Average
ω [rpm]
bgC
[W/kg]
bgC
[W/kg]
(b)
(a)
70
dsP
dsP
dsP
dsP
dsP
dsP
dsP
dcP
Figure 3.5 displays the values of determined by Eqs. (3.4) and (3.5) as
function of ω at both oil temperature values. Here it is clear that the values
calculated by using these two equations are not in good agreement. The spread in values
between the two different calculation methods of may be caused by the power losses
within thrust bearings that are lumped in with . With the reduced face width planets,
any axial trust created on the sun gear and hence on the thrust bearing is minimized,
potentially influencing the values obtained from Eq. (3.5). This argument, if true,
further suggests that Eq. (3.4) is a better representation of the true power losses
within the planetary gear system. Given this poor correlation in the data, no good
trend could be established with respect to speed. However, it is believed that a similar
trend should be expected as was seen for with much lower values since the radius of
the carrier is much larger than the radius of the sun gear.
Figure 3.6 displays the values of psP calculated from Eqs. (3.6) through (3.8) at
40 and 90°C. The psP trends from these equations agree reasonably well. At both
temperatures, the power loss due to psP is very small at low speeds. It is only at about
2,000 rpm that psP begins to climb significantly, reaching values of about 100 W on
average at 3,000 rpm for both test temperatures. The relationship between psP and ω is
somewhere between linear and second order for both test temperatures. A spread in data
exists between Eqs. (3.6) through (3.8) at higher speeds. This spread is as high as 190 W
at 40°C and 170 W at 90°C. This is most likely the result of the small scale at which psP
is being computed for this test. However, this spread is very consistent and smooth, and
the average of all of the results fits very close to the center of the data spread. Therefore,
the average is believed to be a good representation of psP with respect to speed for both
40 and 90°C results.
Figure 3.7 displays the values of prP calculated by Eqs. (3.9) and (3.10). As seen
in this figure, Eqs. (3.9) and (3.10) are in reasonable agreement. Any spread in data can
be attributed to small measurement errors in the large amounts of tests used to calculate
prP . The increase of prP is quite linear with speed to about 140 W at 40°C and 30 W at
90°C. The calculation made in Eq. (3.25) is closely related to the equation for
mechanical bearing loss. Due to issues in the mechanical bearing loss calculation
discussed later, it is believed that the 40°C results for are slightly overestimated. prP
2
Figure 3.8 displays the values of according to Eqs. (3.11) and (3.12). At both
temperatures, increases at a rate of about
bvP
bvP bvP ∝ ω and achieves significant power
loss values for a single planet bearing set, hitting average values of about 300 W at 90°C
and 450 W at 40°C. This clearly indicates that the total power losses account for a
significant portion of the overall spin losses within the planetary system with multiple
planet gears. The viscosity effects are also visible in Figure 3.8, where a higher
temperature resulted in lower viscous bearing losses.
bvP
71
Figure 3.9 displays the values of calculated using Eqs. (3.13) and (3.14). bgC gbP
can be found using the relation explained earlier. At speeds up to 2500 rpm,
values of attained though testing at 90°C roughly display a trend, similar
to what is expected using manipulation of equations by [2, 3]. These values attain a
significant power loss of up to about 180 W at 2,500 rpm. The behavior, however, is
erroneous beyond this point. The potential reason for such behavior lies in the
difficulties faced with reducing the masses of the planets without altering the bearing
conditions. These three-piece steel-plastic planet gears experienced various durability
problems beyond 2,000 rpm as the separation of the steel inserts from the plastic gear
blanks was a major issue. For this reason the data points beyond 2,000 rpm in Figure 3.9
are deemed unreliable.
bg bgP C m=
3bgC bgC ∝ω
3.3.2 Rank Order of Spin Power Loss Components
The major power loss components of the planetary gear set computed in Section
3.3 are compared to one another in Figures 3.10 and 3.11 at both 40 and 90°C. In Figure
3.10, contributions of components , , dsP dcP 6 prP , 6 psP , and 6 to the total
power loss are shown. Here, P is calculated for test 1A as the sum of these components
rather than using the actual
6 bvP bgP
1AP measurements from test 1A. The same data is presented
in Figure 3.11 in a different form to show the percent contributions of each component to
the total power loss. Several observations are made from Figure 3.10 and 3.11:
72
73
Continued
Figure 3.10: Contributions of components of power loss in kW to the total power loss for
test 1A at (a) 40°C and (b) 90°C.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
500 1000 1500 2000 2500 3000
6 vbP
dsP
6 gbP dcP
6 psP
6 prP
ω [rpm]
P
[kW]
(a)
74
Figure 3.10 continued
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
500 1000 1500 2000 2500 3000
(b)
ω [rpm]
P
[kW]
6 vbP
dsP
6 gbP
dcP
6 psP
6 prP
75
Continued
Figure 3.11: Contributions of components of power loss in percentage to the total power
loss for test 1A at (a) 40°C and (b) 90°C.
0
10
20
30
40
50
60
70
80
90
100
500 1000 1500 2000 2500 3000
6 vbP
dsP
6 gbP
dcP
6 psP
6 prP
ω [rpm]
P
[%]
(a)
76
Figure 3.11 continued
0
10
20
30
40
50
60
70
80
90
100
500 1000 1500 2000 2500 3000
(b)
ω [rpm]
P
[%]
6 vbP
dsP
6 gbP
dcP
6 psP
6 prP
77
6P
6P
P
6
• The power losses caused by viscous effects at the planet bearings appear to be the
most dominant components of the planetary spin loss. This is true at different
temperatures as well as throughout the entire carrier speed range. The
values constitute as much as 56% of the total power loss at 40°C and 62% of the
power loss at 90°C. These percentages are rather consistent with speed.
bv
• Load dependent bearing losses caused by centrifugal forces represented by
in Figures 3.10 and 3.11 are almost nonexistent at lower speeds. At 90°C,
however, the contribution of increases sharply, achieving as much as 39% of
the total power loss.
bg
bg
• The gear mesh pumping losses are also a major contributor to the overall power
loss. Here prP constitutes as much as 28% of the total power loss at lower
speeds for both temperatures, but its contributions decrease at higher speeds. This
may indicate that it does not rise as sharply with speed as some of the other forms
of power loss. psP , on the other hand, is negligible at lower speeds, but increases
sharply, attaining as much as about 14% of the total power loss at high speeds for
both temperatures.
• The power losses caused by viscous drag, and , do not appear to be major
contributors to P at 40°C or 90°C. In fact, is almost negligible at high speeds
for both test temperatures, constituting only about 10% of the total power loss at
its highest and dwindling to less than 2% at 3,000 rpm. maintains about 7%
of the total power loss at 40°C and about 9% at 90°C throughout the range of
dsP
dsP
dcP
dcP
ω .
78
3.3.3 Validation of Spin Power Loss Component Isolation Methods
In order to show that the methods used to separate sources of power loss are
reasonable, power loss values predicted using Eq. (2.1) for a six planet system, displayed
in Figure 3.10, were compared to actual 1A test data obtained through experiments. This
comparison is presented in Figure 3.12 for (a) 40°C and (b) 90°C. For both
temperatures, spin loss P, calculated as sum of its components, matches the direct
measurements from test 1A (baseline 6-planet gear set) quite well. A difference below
10% is observed between the values calculated by using Eq. (2.1) and actual
measurements for the entire speed and temperature ranges. This difference can be
viewed to be reasonably small, considering that many components of power loss were
calculated using data from different tests.
Figure 3.12: Comparison of the total power loss calculated from its components using
Eq. (2.1) to the actual measurements from test 1A at (a) 40°C and (b) 90°C.
0.0
1.0
2.0
3.0
4.0
5.0
0 1000 2000 3000 4000
Eq. (2.1)Measured
0.0
1.0
2.0
3.0
4.0
5.0
0 1000 2000 3000 4000
Eq. (2.1)Measured
(b)
ω [rpm]
P
[kW]
P
[kW]
(a)
79
80
CHAPTER 4
SUMMARY AND CONCLUSIONS
4.1 Thesis Summary
An extensive experimental study was conducted to investigate the mechanisms of
spin power loss caused by planetary gear sets. A test set-up was developed for this
purpose with the capability of spinning a single, unloaded planetary gear set in various
hardware configurations at desired test speeds while measuring torque provided to the
gear set. This torque value, representing the torque loss of the gear set, was used to
determine the spin power loss at a given speed value. It has been shown that this test
machine as well as the test procedure implemented is capable of producing repeatable
power loss measurements within a range of input (carrier) speeds up to 4,000 rpm at both
lubricant temperature values.
A test matrix was defined specifically not only measure total spin loss but also
provide test variations that can be used to determine the contributions of the following
main components of the power loss: (i) drag loss of the sun gear, (ii) drag loss of the
81
carrier assembly, (iii) pocketing losses at the sun-planet meshes, (iv) pocketing losses at
the ring-planet meshes, (v) viscous planet bearing losses, and (vi) planet bearing losses
due to centrifugal forces. For this purpose, planetary gear-set configurations were
developed with different sets of hardware. These included reduced face-width planets to
eliminate the pocketing losses at the gear meshes and reduced mass planets to alter the
bearing losses caused by centrifugal effects. In addition, the test fixtures were designed
to allow operation without the sun gear or the ring gear to isolate the losses associated
with them.
Multiple schemes to estimate the contributions of various components of power
losses were developed by using the data from tests defined in the test matrix. Fidelity of
these schemes was observed by comparing them to each other. In addition, the sums of
the power loss components were compared to the actual measurements for the baseline 6-
planet gear set to further access fidelity of isolation schemes. Based on these
calculations, major components of power losses were identified. Impact of rotational
speed and temperature were also quantified.
4.2 Main Conclusions
Based on the results presented in the previous section, the following conclusions
can be made in regards to spin power losses of planetary gear sets:
• The main premise of this study was that that spin power loss of a planetary gear
set could be represented by a set of components consisting of viscous drag power
losses on the sun gear and the planet carrier, gear mesh pumping losses in the
planet-sun meshes and planet-ring meshes, and losses in the planet bearings
attributed to viscous and mechanical (centrifugal load dependant) friction. Tests
have shown that this supposition is indeed valid, i.e. the total power loss can be
considered as the sum of these relatively independent components. This is rather
significant especially for modeling efforts, indicating that individual models to
predict these power loss components can be superimposed to obtain the total spin
power loss of a planetary gear set.
• Power losses caused by viscous friction within the planet bearings were shown to
be by far the most dominant sources of spin power loss, accounting for about one-
half of the spin power loss at all temperatures in a 6-planet gear set. These
viscous bearing power losses were shown to increase with speed according to the
relation . 2bvP ∝ ω
• Power losses caused by mechanical (centrifugal load dependant) friction were
shown to kick in only at high speeds ( 2000ω ≥ rpm). This data agreed with the
trend mentioned in the literature [2]. The assumption that increases
linearly with planet mass [2] was also shown to be valid.
3bgP ∝ ω bgP
• The gear mesh pumping losses ( and ) were also shown to be primary
contributors to the spin power losses. These power losses demonstrated lower
order relationships with speed. Tests indicated that
prP psP
prP increases rather linearly
82
with speed, while psP shares a relationship somewhere between linear and
second order with speed.
• The contributions of the power losses caused by viscous drag ( and ) were
shown to secondary. Trends of were shown to have a squared relationship
with speed similar to predictions by Seetharaman and Kahraman [1]. No clear
speed relationship could be established for .
dsP dcP
dcP
dsP
• The temperature of the lubricant was shown to dramatically influence spin power
losses. An increase in lubricant test temperature was shown to produce a sizeable
decrease in overall spin power loss. Tests also showed that , bvP prP , and
decreased with an increase in lubricant temperature, while increased with
lubricant temperature. No direct temperature correlation could be made for
and .
dcP
dsP
bgP
psP
4.3 Recommendations for Future Work
This study presents a set of data that provides a picture of spin power loss
behavior in planetary gear systems. However, it makes no effort to characterize
mechanical (load dependant) power losses in planetary gear systems. It also does not
take into account planetary gear sets of different sizes or of kinetic configurations other
than the fixed ring gear arrangement. As automatic transmission efficiency becomes a
more important topic in the automotive industry, it will be necessary to expand on this
83
84
study to include planetary gear trains representative of a range of applications. With this,
the following specific recommendations are proposed for future work:
• Expand experiments to include mechanical power losses: As stated earlier,
mechanical (load dependant) power losses are also a major contributor to the
efficiency of planetary gear systems. An effort should be made to also study
these forms of power loss so as to be able to accurately describe the overall
efficiency of a planetary gear system operating under loaded conditions.
• Include planetary gear sets of different sizes, types, and arrangements: Viscous
drag power losses are highly dependent on the geometries of spinning hardware.
Also, mesh pumping losses change drastically with helix angle and face width [1].
Since planetary gear sets of different sizes, shapes, and types are used in different
applications, the effects that gear geometry changes have on these power losses
should be studied. Furthermore, the viscous drag power losses on the ring gear
should be included in future studies, as many planetary gear applications employ
a rotating ring gear.
• Experiments to measure power losses in planet bearings separately: The viscous
power losses within the planet bearings have been shown to be the most dominant
forms of spin power loss. It is believed that minimizing these power losses will
drastically reduce overall spin power losses in planetary gear systems. Therefore,
a more direct experiment that allows the operation of single bearing at
representative conditions should be undertaken to determine what bearing and
lubricant characteristics contribute to these high power losses.
85
• Expand the study to include more lubricant types and different lubrication
methods and characteristics: It has been demonstrated in this study that the
lubricant plays an important role in all sources of spin power loss. In order to
further understand these power losses, the effects that lubricant properties and
application methods have on these losses should be quantified. Therefore, the
study should be expanded to incorporate different lubrications and application
methods.
• Develop a model to explain power losses in planetary gear systems: Many
theoretical models have been developed and employed to predict power losses in
fixed-center spur and helical gear systems. Some of the more recent models have
proven to be quite accurate, correlating well with experimental data. However,
little effort has been made to model planetary gear power losses, and planetary
systems are too complex to be modeled using existing fixed-center gear models.
Therefore, there is a definite need for a validated model that can be used to predict
power losses in planetary gear systems. This study shows clearly that
experimental investigations of planetary gear set power losses are costly and time-
consuming and that there is great incentive for modeling efforts like the one taken
by a companion study [44].
Furthermore, some changes to the existing test machine and testing methodology
can be implemented to increase the accuracy and effectiveness of the methodology
proposed in this study. Some of these recommended modifications are listed below.
86
• Develop more reliable methods to isolate planet bearing centrifugal load
dependant power losses: Major mechanical difficulties were faced in
manufacturing and operating the three-piece, reduced-mass planet gears used to
help isolate planet bearing centrifugal load dependant power losses. It was
difficult to duplicate the same geometric and surface roughness (amplitude and
direction) conditions in these reduced mass replacement planets. New designs of
reduced mass planets might be required to achieve the exact bearing conditions of
the baseline gear set while providing significant mass differential.
• Modifications to control lubricant temperature better: The lubricant temperature
was shown to play an important role in the magnitudes of many of the spin power
losses measured. As a change in this temperature could affect test repeatability
and data accuracy, efforts should be made to incorporate tighter controls on the
lubricant temperature. Possible measures for this purpose are reducing the size of
the reservoirs that are not associated with the lubricant control system and
shortening and isolating the lubricant lines.
87
REFERENCES
[1] Seetharaman, S., and Kahraman, A., 2009, “Load-Independent Power Losses of a
Spur Gear Pair: Model Formulation,” Journal of Tribology, Proceedings of the
ASME, 131, p. 022201.
[2] Harris, T.A., and Kotzalas, M., 2007, Roller Bearing Analysis: Essential Concepts
of Bearing Technology, 3rd ed., CRC Press, Taylor & Francis Group, Boca Raton,
FL, pp. 181-193.
[3] Palmgren, A., 1959, Ball and Roller Bearing Engineering, 3rd ed., John Wiley &
Sons Inc., New York, pp.504-510.Chui & Myers.
[4] Cioc, C., Kahraman, A., Moraru, L, Cioc, C., and Keith, T., 2002, “A
Deterministic Elastohydrodynamic Lubrication Model of High-Speed Rotorcraft
Transmission Components,” Tribology Transactions, The Society of Tribologists
and Lubrication Engineers, 45(4), pp. 556-562.
[5] Xu, H., Kahraman, A., Anderson, N. E., and Maddock, D. G., 2007, “Prediction
of Mechanical Efficiency of Parallel-Axis Gear Pairs,” Journal of Mechanical
Design, Transactions of the ASME, 129, pp. 58–68.
[6] Li, S., 2009 “Lubrication and Contact Fatigue Models for Roller and Gear
Contacts,” PhD thesis, The Ohio State University, Columbus, Ohio.
88
[7] Li, S., and Kahraman, A., 2009 “A Mixed EHL Model with Asymmetric
Integrated Control Volume Discretization” Tribology International, Elseveir, 42,
No. 8.
[8] Chase, D. 2005, “The Development of an Efficiency Test Methodology for High
Speed Gearboxes,” MS thesis, The Ohio State University, Columbus, Ohio.
[9] Moorhead, M., 2007, “Experimental Investigation of Spur Gear Efficiency and
the Development of a Helical Gear Efficiency Test Machine,” MS thesis, Ohio
State University, Columbus, OH.
[10] Petry-Johnson, T. 2007, “An Experimental Investigation of Spur Gear
Efficiency,” MS thesis, The Ohio State University, Columbus, Ohio.
[11] Vaidyanathan, A. 2009, “An Experimental Investigation of Helical Gear
Efficiency,” MS thesis, The Ohio State University, Columbus, Ohio.
[12] Dawson, P. H., 1984, “Windage Loss in Larger High-Speed Gears,” Proceedings
of the Institution of Mechanical Engineers, Part A: Power and Process
Engineering, 198(1), 51–59.
[13] Dawson, P. H., 1988, “High Speed Gear Windage,” GEC Review, 4(3), pp. 51-59.
[14] Diab, Y., Ville, F., and Velex, P., 2006, “Investigations on Power Losses in High
Speed Gears,” Journal of Engineering Tribology, Transactions of the ASME, 220,
J., pp. 191–298.
89
[15] Wild, P. M., Dijlali, N., and Vickers, G. W., 1996, “Experimental and
Computational Assessment of Windage Losses in Rotating Machinery,” Journal
of Fluids Engineering, Transactions of the ASME, 118, pp. 116–122.
[16] Al-Shibl, K., Simmons, K., and Eastwick, C. N., 2007, “Modeling Gear Windage
Power Loss From an Enclosed Spur Gears,” Proc. Inst. Mech. Eng., Part A,
221(3), pp. 331–341.
[17] Daily, J. W., and Nece, R. E., 1960, “Chamber Dimensional Effects on Induced
Flow and Frictional Resistance of Enclosed Rotating Disks,” Journal of Basic
Engineering, Transactions of the ASME, 82, pp. 217–232.
[18] Mann, R. W., and Marston, C. H., 1961, “Friction Drag on Bladed Disks in
Housings as a Function of Reynolds Number, Axial and Radial Clearance and
Blade Aspect Ratio and Solidity,” Journal of Basic Engineering, Transactions of
the ASME, 83(4), pp. 719–723.
[19] Boness, R. J., 1989, “Churning Losses of Discs and Gears Running Partially
Submerged in Oil,” Proceedings of the ASME Fifth International Power
Transmission and Gearing Conference, Chicago, IL, pp. 355–359.
[20] Akin, L. S., and Mross, J. J., 1975, “Theory for the Effect of Windage of the
Lubricant Flow in the Tooth Spaces of Spur Gears,” J. Eng. Ind., Transactions of
the ASME, 97, pp. 1266–1273.
[21] Akin, L. S., Townsend, J. P., and Mross, J. J., 1975, “Study of Lubricant Jet Flow
Phenomenon in Spur Gears,” Journal of Lubrication Technology, Transactions of
the ASME, 97, pp. 288–295.
90
[22] Terekhov, A. S., 1991, “Basic Problems of Heat Calculation of Gear Reducers,”
JSME International Conference on Motion and Power Transmissions, pp. 490–
495.
[23] Luke, P., and Olver, A., 1999, “A Study of Churning Losses in Dip-Lubricated
Spur Gears,” Journal of Aerospace Engineering, 213, pp. 337–346.
[24] Höhn, B. R., Michaelis, K., and Völlmer, T., 1996, “Thermal Rating of Gear
Drives: Balance between Power Loss and Heat Dissipation,” AGMA, Fall
Technical Meeting, pp. 1–12, Paper No. 96FTM8.
[25] Pechersky, M. J., and Wittbrodt, M. J., 1989, “An Analysis of Fluid Flow
Between Meshing Spur Gear Teeth,” Proceedings of the ASME Fifth
International Power Transmission and Gearing Conference, Chicago, IL, pp. 335–
342.
[26] Diab, Y., Ville, F., Houjoh, H., Sainsot, P., and Velex, P., 2005, “Experimental
and Numerical Investigations on the Air-Pumping Phenomenon in High-Speed
Spur and Helical Gears,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 219,
pp. 785–800.
[27] Ariura, Y., Ueno, T., and Sunamoto, S., 1973, “The Lubricant Churning Loss in
Spur Gear Systems,” Bull. JSME, 16, pp. 881–890.
[28] Seetharaman, S., 2009 “An Investigation of Load-Independent Power Losses of
Geared Systems,” PhD thesis, The Ohio State University, Columbus, Ohio.
91
[29] Seetharaman, S., Kahraman, A., Moorhead, M. D., and Petry-Johnson, T. T.,
2009, “Oil Churning Power Losses of a Gear Pair: Experiments and Model
Validation,” Journal of Tribology, Proceedings of the ASME, 131, p. 022202.
[30] Changenet, C., and Velex, P., 2006, “A Model for the Prediction of Churning
Losses in Geared Transmissions—Preliminary Results,” Journal of Mechanical
Design, Proceedings of the ASME, 129(1), pp. 128–133.
[31] Jones, A.B., and Harris, T.A., June 1963, “Analysis of Rolling Element Idler Gear
Bearing Having a Deformable Outer-Race Structure,” Journal of Basic
Engineering, Transactions of the ASME, pp. 273-278.
[32] Harris, T.A., and Broschard, J.L., September 1964, “Analysis of an Improved
Planetary Gear- Transmission Bearing,” Journal of Basic Engineering,
Transactions of the ASME, pp. 457-462.
[33] Liu, J.Y.., and Chui, Y.P., January 1976, “Analysis of Planetary Bearing in a Gear
Transmission System,” Journal of Lubrication Technology, Transactions of the
ASME, pp. 40-46.
[34] Chiu, Y., and Myers, M., 1998, “A Rational Approach for Determining
Permissible Speed for Needle Roller Bearings,” SAE Tech. Paper No. 982030.
[35] Townshend, D.P., Allen, C.W., and Zaretsky, E.V., October 1974, “Study of Ball
Bearing Torque under Elastohydrodynamic Lubrication,” Journal of Lubrication
Technology, Transactions of the ASME, pp. 561-571.
[36] SKF, 1997, General Catalog 4000, US, 2nd Ed.
92
[37] Muller, H.W., and Dreher, K., 1981, “Computer Aided Design and Optimization
of Compound Planetary Gears,” International Symposium of Gearing and Power
Transmissions, Tokyo, Japan.
[38] Krstich, A.M., 1987, “Determination of the General Equation of the Gear
Efficiency of Planetary Gear Trains,” International Journal of Vehicle Design, 8
(3), pp. 365-374.
[39] Pennastri, E., and Freudenstein, F., 1993, “The Mechanical Efficiency of
Epicyclic Gear Trains,” Journal of Mechanical Design, Transactions of the
ASME, 115, pp. 645-651.
[40] Hsei, H.I., and Tsai, L.W., 1998, “The Selection of the Most Efficient Clutching
Sequence Associated with Automatic Transmission Mechanisms,” Journal of
Mechanical Design, Transactions of the ASME, 115, pp. 645-651.
[41] Del Castillo, J.M., 2001, “The Analytical Expression of Efficiency of Planetary
Gear Trains,” Mechanism and Machine Theory, Elsevier, 37, pp. 197-214.
[42] Anderson, N.E., Loewenthal, S.H., and Black, J.D., 1984, “An Analytical Method
to Predict Efficiency of Aircraft Gearboxes,” NASA Technical Memorandum,
0499-9320.
[43] Anderson, N.E., and Loewenthal, S.H., 1980, “Spur Gear Efficiency at Part and
Full Load,” NASA Technical Memorandum, 1622.
[44] Talbot D., 2010, “Development and Validation of an Efficiency Model of
Planetary Gear Sets,” The Ohio State University, Columbus, OH, (in progress).
93
[45] Petry-Johnson, T., Kahraman, A., Anderson, N.E., Chase, D.R., 2008, “An
Experimental Investigation of Spur Gear Efficiency,” Journal of Mechanical
Design, Transactions of the ASME, 130, 062601-1.
[46] Ligata, H. 2007, “Impact of Systems Level Factors on Planetary Gear Set
Behavior,” PhD Dissertation, The Ohio State University, Columbus, Ohio.
[47] Ligata, H. 2008, “An Experimental Study of the Influence of Manufacturing
Errors on the Planetary Gear Stresses and Planet Load Sharing,” Journal of
Mechanical Design, Transactions of the ASME, 130, 041701-1.
[48] Ligata, H., Kahraman, A., 2009, “A Closed-Form Planet Load Sharing
Formulation for Planetary Gear Sets Using Translational Analogy,” Journal of
Mechanical Design, Proceedings of the ASME, 131, 021007-1.
[49] Inalpolat, M. 2009, “A Theoretical and Experimental Investigation of Modulation
Sidebands of Planetary Gear Sets,” PhD Dissertation, The Ohio State University,
Columbus, Ohio.
[50] Inalpolat, M., Kahraman, A., 2008, “Dynamic Modeling of Planetary Gears of
Automatic Transmissions,” IMechE, Part K: Journal of Multi-body Dynamics,
222, 229-242.
[51] Inalpolat, M. 2009, “A Theoretical and Experimental Investigation of Modulation
Sidebands of Planetary Gear Sets,” Journal of Sound and Vibration, Transactions
of the ASME, doi:10.1016/j.jsv.2009.01.004.
[52] UDEL Polysulfone Design Guide, Solvay Advanced Polymers, v. 2.1,2002.
94
[53] Ketaspire KT-820 CF 130 Product Data Sheet, Solvay Advanced Polymers, v.
1.4, 2002.
[54] “8620 Alloy Steel Material Properties Data Sheet,” Matweb Material Property
Data, 19 May, 2010, <http://www.matweb.com/search/DataSheet.aspx?MatGUID
=ff9be3b853af434cb8ea99965f921856&ckck=1>.
[55] “Mobil Dexron VI ATF,” Exxon Mobil Corporation, 19 May, 2010, <
http://www.mobil.com/USA-English/Lubes/PDS/GLXXENPVLMOMobil
_Dexron-VI_ATF.asp#SpecsApprovalsTitle> .
[56] Hurley, J. 2009, “An Experimental Investigation of Thermal Behavior of an
Automotive Rear Axle,” MS thesis, The Ohio State University, Columbus, Ohio.