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

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