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Office of Energy Efficiency & Renewable Energy

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This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Additive Manufacturing: A New 

Paradigm for the Next 

Generation of High-PowerDensity Direct-Drive Electric 

Generators 

Preprint

Austin C. Hayes

Rochester Institute of Technology 

Latha Sethuraman, Lee Jay Fingersh, 

and Katherine Dykes 

National Renewable Energy Laboratory 

Presented at ASME 2018 Power & Energy Conference & Exhibition 

Lake Buena Vista, Florida 

June 24‒27, 2018 

Suggested Citation 

Hayes, A. C., L. Sethuraman, L. J. Fingersh, and K. Dykes. 2018. “Additive 

Manufacturing: A New Paradigm for the Next Generation of High-Power-Density 

Direct-Drive Electric Generators: Preprint.” Golden, CO: National Renewable 

Energy Laboratory. NREL/CP-5000-70946. 

https://www.nrel.gov/docs/fy18osti/70946.pdf

Conference Paper

NREL/CP-5000-70946

July 2018
NOTICE

This work was authored by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable 

Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding was 

provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy 

Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the 

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acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish 

or reproduce the published form of this work, or allow others to do so, for U.S. government purposes.

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Energy Laboratory (NREL) at www.nrel.gov/publications. 

U.S. Department of Energy (DOE) reports produced after 1991 

and a growing number of pre-1991 documents are available 

free via www.OSTI.gov. 

Cover Photos by Dennis Schroeder: (left to right) NREL 26173, NREL 18302, NREL 19758, NREL 29642, NREL 19795.

NREL prints on paper that contains recycled content. 
PowerEnergy2018-7140

ADDITIVE MANUFACTURING: A NEW PARADIGM FOR THE NEXT GENERATION

OF HIGH-POWER-DENSITY DIRECT-DRIVE ELECTRIC GENERATORS

Austin C. Hayes∗

Mechanical Engineering Department

Rochester Institute of Technology

Rochester, NY, 14623

Email: ach6895@rit.edu

Latha Sethuraman

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO, 80401

Email: Latha.Sethuraman@nrel.gov

Lee Jay Fingersh

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO, 80401

Email: Lee.Fingersh@nrel.gov

Katherine Dykes

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO, 80401

Email: Katherine.Dykes@nrel.gov

ABSTRACT

In recent years, there has been a growing demand for highpower-density direct-drive generators in the wind industry owing to their high reliability, torque per unit volume, and conversion efficiencies. However, direct-drive wind turbine generators are very large, low-speed electric machines, which pose remarkable design and manufacturing issues that challenge their

upscaling potential and cost of implementation. With air-gap

tolerance as the main design driver, the need for high stiffness

shifts the focus toward support-structure design that forms a significant portion of the generator’s total mass. Existing manufacturing processes allow the use of segmented-steel-weldment

disk or spoke-arm assemblies that yield stiffer structures per unit

mass but tend to be heavier and more expensive to build. As

a result, there is a need for a transformative approach to realize lightweight designs that can also facilitate series production at competitive costs. Inspired by recent developments in

metal additive manufacturing (AM), we explore a new freedom

in the structural design space with a high potential for weight

savings in direct-drive generators. This includes the feasibility

∗Address all correspondence to this author.

of using nonconventional complex geometries, such as latticebased structures as structurally efficient options. Powder-binder

jetting of a sand-cast mold was identified as the most feasible

AM technology to produce large-scale generator rotor structures

with complex geometry. A parametric optimization study was

performed and optimized results within deformation and mass

constraints were found for each design. The response to the maximum Maxwell stress due to unbalanced magnetic pull was also

explored for each design. Further, a topology optimization was

applied for each parameter-optimized design to validate results

and provide insights into further mass reduction. These novel designs catered for AM are compared in both deflection and mass

to conventional rotor designs using NREL’s systems engineering

design tool, GeneratorSE. The optimized lattice design with a Ubeam truss resulted in a 24% reduction in structural mass of the

rotor and 60% reduction in radial deflection. It is demonstrated

that additive manufacturing shifts the focus from manufacturability constraints toward lower mass.

1

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NOMENCLATURE

rs Air-gap radius

Bˆ

g Peak air-gap flux density

Br Remnant flux density

— For additional symbols refer to relevant tables

INTRODUCTION

In recent years, wind power has become one of the more

popular forms of renewable energy. Various technological innovations have led to building larger and taller wind turbines to

drive down the cost of energy while presenting remarkable challenges in design, installation, transportation, and operation. Because wind turbine components are subject to complex dynamic

loading, vibration, system fatigue, and joint stresses, numerous

manufacturing issues remain to be addressed.

One of the issues is the gearbox used in the powertrain,

in which the manufacturers strive for weight reduction and improved assembly of threaded joints with close tolerances to improve their service lives. The move toward offshore installations

with demand for higher reliability and efficiency is encouraging

more wind turbine manufacturers to integrate higher power generators into their designs. Direct-drive generators are one of the

many technology options touted to realize these goals. The direct coupling of the generator to the turbine leads to low-speed

high-torque machines with a high pole count and very large stator

diameters that pose remarkable design and manufacturing challenges [1]. Particularly with permanent-magnet (PM) generators,

there are high magnetic forces constantly acting between the rotor and stator; hence, accurately fixing the position of the stator

teeth and the windings in the stator is immensely challenging [2].

Moreover, the air gap between the stator and rotor must be kept

uniform and small for proper torque transfer. As a result, designers are constantly seeking measures to minimize eccentricity to prevent potentially fatal distortions. Most designs employ

substantial spoke-and-rim wheel structures to maintain the necessary structural integrity required when welding overly thick

steel elements [3]. The state of the art shows that direct-drive

generators are difficult to scale up to 10 MW and beyond [4],

with traditional designs weighing between 200 and 500 tons [5].

With greater emphasis on top-head mass reduction, lightweight

designs are needed so the final system can be assembled more

easily. This need is urging manufacturers to develop, design, and

use manufacturing technologies that will enable them to produce

machines on a large-scale basis and at a competitive cost. However, this oftentimes conflicts with the need to fulfill demanding

performance specifications such as efficiency, torque quality, and

fault tolerance [1].

Conventional direct-drive generator support structures

are made of spoked-wheel structures that support rims of

iron/magnetic core laminations. Typical geometries are disks,

structural profiled spokes/tension rods, ribs, or support arms.

Their structural stiffness and interfaces are controlled by manufacturing tolerances [3]. Because these machines operate at very

low rotational speeds, their corresponding torques and diameters

have to be made large enough to generate the required power output. The air gap separating the rotor and stator of the machine

is typically 1/1000th of its diameter. Therefore, eccentricities or

closing of the air gap are major concerns. These effects drive the

structural designs to be extremely rigid and massive. The spokes

have to be increased dimensionally and in quantity or discs have

to be made stiffer by adding more steel. The spokes can be

manufactured as either continuous cast-iron or segmented-steelweldment assemblies that yield stiffer structures per unit mass;

however, they are expensive to build.

Design for Lightweight Generators

Lightweighting for large, direct-drive wind turbine generators is not a new concept. In the past, several researchers have

considered optimization of direct-drive generator designs [6,7,8],

with a focus on structural mass reduction [9, 10]. Spooner et

al. [11] explored lightweight spoked structures to reduce the

structural mass of the stator by 70%-80%. However, they used

an ironless stator for low-power machines. This spoked design

can be implemented for high-power machines, but new geometries are needed to maintain strength with decreased total mass.

A few researchers have resorted to mathematical methods such

as topology optimization (TO) algorithms for lightweighting for

direct-drive generators. Topology optimization is a mathematical method that optimizes the material layout within a given design space, for a given set of loads, boundary conditions, and

constraints. Zavvos [10] used finite-element analysis (FEA) and

topology optimization techniques to identify lightweight structures for large transverse flux PM generators. Zavvos et al. [9]

further used shape optimization that offered an additional 26%

reduction in mass. Kirschneck et al. [12] investigated possible

weight reduction for the structure of the generator rotor with emphasis on dynamic behaviour under magnetic loading. However,

the optimized results did not perform better than the original design. Lee et al. [13] used shape optimization techniques to reduce

the structural weight of an axial flux PM generator by up to 21%.

Gangl et al. [14] utilized a shape derivative during optimization

of an interior rotor PM motor. Their approach was based on a

shape-Lagrangian method adapted for magnetostatic problems

involving nonlinear partial differential equations (PDEs). The

resulting shape reduced the cost function by 27% and improved

the electric rotor’s rotation pattern and the motor’s overall performance. Numerous algorithms for Topology Optimization exist, including an open-source model by Zuo and Xie [15], which

generates an FEA mesh and topology solver using the bidirectional evolutionary structural optimization method. Advantages

of this code includes its compactness (100 lines of code), ability

to extend to other applications (open source), and utility for me2

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chanical applications (three-dimensional geometries). Figure 1

depicts the input and output of the optimization software. Commercial FEA software [16] facilitates shape optimization according to discretized load functions. However, the major limitation

of the software is that the resulting complex geometries are often

difficult to manufacture.

FIGURE 1. topology optimization of disk geometry [15]

Design for Manufacturability

More recently, attempts have been made to investigate designs that can potentially reduce manufacturing costs of generators. Tessarolo et al. [1] proposed a highly modular design to segment the generator into independent units that can be connected

in parallel and used to feed separate power converters. The generator design had intrinsic fault tolerance through simple part replacement and repairs in case of a fault. Skemkken [17] proposed slanted spoke structural wheel architectures, which were

constructed using layered sheet-steel elements to form the spokes

and rim of the wheel faces. In a wind turbine, direct-drive electric

generators can be subjected to continual flexing and extreme temperatures that can be potentially catastrophic. Eliminating deep

structural welds can significantly reduce manufacturing cost and

avoid problems associated with fatigue cracking and failure of

welded connections [17]. Data from a global wind report [18]

suggest that the cost per mass (inactive structural cost and labor

cost) of a 5-MW PM direct-drive (PMDD) generator is $6.04/kg.

However, the validity of material cost, labor, and allocation assumptions, and costs of stator casing, active components, burden,

or engineering costs are not available for reference. At the same

time, as new manufacturing techniques evolve, it is important to

gain greater understanding of their associated costs.

Additive Manufacturing for Direct-Drive Generators

In recent years, metal additive manufacturing has gained

momentum and is emerging across a broad range of sectors,

including automotive, medical, and aerospace. A vast range

of metallic materials, including several types of steel, titanium,

cobalt, and aluminum alloys, are printable. Newer materials for

soft-magnetic cores are being introduced and show promising results for manufacturing laminations in electric machines [19,20].

AM technologies such as selective laser melting and direct

metal laser sintering provide great potential for weight savings

[21,22], thereby allowing the manufacturing of complex geometries arising from topology optimization. Binder-jetting for sand

casting is also being considered as an attractive process for making metal parts [23]. With binder-jetting, there are no induced

thermal stresses. Further, it is capable of producing very largescale molds that can be used for casting direct-drive generators.

The use of 3-D sand-cast printing allows for complex geometries and undercuts without the need for conventional mold cores.

Because sand-cast printing is more complex and therefore more

expensive, the ability to decrease related costs helps reduce the

manufacturing difficulty, thereby making this method more economically feasible [24]. AM has the potential to realize designs

that are structurally efficient, yet complex structures that enable

high stiffness and reduced weight. However, there is relatively

little information available in the literature about designing largescale components, particularly concerning design tools, structural analysis, and postprocessing for functional metallic components [25].

Inspired by these recent developments and challenges, this

study attempts to identify manufacturing solutions by designing

an innovative, lightweight direct-drive PM generator for a wind

turbine. The resulting design aims to provide better power scalability and weight reduction, as well as reduce series manufacturing costs while preserving its structural integrity. Specifically,

powder-binder jetting of a sand-cast mold is selected as a potential process to manufacture complex rotor geometries. The geometries in this study include a hollow truss lattice and U-beam

lattice truss design for a 5-MW direct-drive generator. These geometries were analyzed using FEA in an ANSYS environment

and an optimization study was performed to determine optimal

geometric parameters. The results were compared against reference geometries created using the National Renewable Energy

Laboratory’s (NREL’s) GeneratorSE [26] to identify potential

improvements.

3

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Permanent-Magnet Direct-Drive Generator Rotor Design − An Overview

For this study, a 5-MW radial flux permanent-magnet synchronous generator with interior rotor arrangement was chosen

as the baseline design. This design endures torque to the order of 4.14 MNm. High-strength permanent magnets are fixed

circumferentially around the rotor in a wheel-type arrangement

that is mounted onto a shaft coupled to the turbine hub. Common

structures for the rotor geometry employ spoked-arm or disk construction that ensure adequate structural stiffness against forces

that act to close the air gap. Figure 2 and Table 1 provide a

visualization of the structural design variables. NREL’s rigorous structural analyses for these designs [26] provided the optimized design parameters for the baseline design with estimates

for structural mass (Table 2). Note that both designs have significantly different magnitudes of deflections,however they are both

considered negligible.Also, the lower deflections for the disk design is accomplished by the considerable increase in structural

stiffness (solid disk weighs more than the spoked arms).

FIGURE 2. Structural design variables of a permanent-magnet synchronous generator rotor [26]

LARGE-SCALE METAL ADDITIVE MANUFACTURING

Metal additive manufacturing poses significant challenges

compared to fused deposition modeling or stereo lithography,

namely that the feedstock is a metal powder that must be fused.

Popular powder bed fusion processes, such as direct metal laser

sintering, use a laser beam to create a high-temperature melt pool

in which powder fuses to form the part. This type of sintering is

TABLE 1. DESIGN VARIABLES

Symbol Design dimension

td rotor disc thickness

nr number of rotor arms

hyr thickness of rotor back iron

br Circumferential arm dimension

l disc length

d arm depth

tw arm thickness

TABLE 2. BASELINE DESIGN: MASS AND DEFORMATION

Parameter Unit Spoked Arm Disk

Radial Deformation mm 0.56 0.33

Axial Deformation mm 0.01 2.23 x10−7

Torsional Deformation mm 2.35 0.58

Active Mass mT 16.93 11.35

Structural Mass mT 16.45 41.22

common for small, detailed parts; however, it lacks speed and

requires thermal management and postprocessing [27]. Electron

beam melting consists of an electron beam in a vacuum chamber

that fuses the powder. This process has the advantage of higher

deposition rates and power efficiency, yet it has high structural

costs due to radiation concerns. Both electron beam melting and

direct metal laser sintering machines use a powder bed, which,

for a large part such as a direct-drive generator, results in unacceptable material costs to fill the powder bed. Also, developing process parameters for new materials in powder bed fusion processing is extremely difficult. Owing to these challenges,

few companies [28, 29] are considering indirect AM as a feasible option to produce large, complicated geometries. The technique employs powder-binder jetting of sand to create a sand-cast

mold. Printing a mold allows for unique geometries and undercuts that are achievable with AM while also allowing traditional

casting for the finished part. Typical build platforms are 2.2 x

1.2 x 0.6 m in size [28]. First, during printing, a “green” part

is created by alternating a layer of 100 μm sand with a layer of

binder from an inkjet printer head. Next, the z-axis powder stage

moves up 100 μm and a roller ensures an even coating over the

work bed. An inkjet printer head then deposits a layer of aque4

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ous binder in the correct location to build up the part. The binder

is cured under an ultra-violet light and another 100 μm layer of

powder deposited on the build platform. This process is repeated

layer by layer until the finished part is produced. Fig. 3 depicts

the powder-binder-jetting printing process.

FIGURE 3. Powder-binder printing schematic

Through powder-binder printing, the sand-cast mold can be

directly printed. In this way, the mold cavity, risers, and cope are

all directly printed in one step. Next, molten steel can be poured

to create the optimized rotor geometry such as a lattice. Figure 4

shows the top and bottom molds used to print a lattice design.

FIGURE 4. Molds for printing a lattice design: (a) bottom mold, and

(b) top mold

A unique feature about sand-cast printing is that “complexity is free.” Unlike traditional casting in which the price of

the mold dramatically increases with complexity, an AM-printed

mold’s cost is solely based on materials; therefore, increasing the

complexity while maintaining constant volume results in a constant cost, as shown in Fig. 5.

FIGURE 5. Cost versus complexity of AM and conventional mold

making

ROTOR REDESIGN AND STRUCTURAL ANALYSIS

First, the baseline models from GeneratorSE [26] were evaluated for their potential for mass reduction. To make a reasonable comparison and avoid changes to the electromagnetic design, we chose to retain the thickness of the rotor cylinder to

be the same as the baseline rotor. The rest of the existing design space (the region occupied by the disk and arms) was reevaluated for optimal material layout for a given set of loads,

boundary conditions, and constraints, with the goal of minimizing the weight. As a next step, two alternative designs involving complex lattice structures were evaluated as potential design

solutions. Lattice structures are open cellular structures with a

continuous network of truss-like members that can be arranged

in various configurations to achieve different strengths suitable

for specific applications [25]. The cross section of the trusses

can be designed to be hollow, circular, square, or any desired

shape that gives them high, compressive load-bearing capacity.

Although lattice structures have the potential to serve as structural members, the final components often have a complex topology, which is difficult to fabricate using conventional subtractive

manufacturing methods such as machining. However, powderbinder jetting offers unprecedented design and material freedom

to manufacture such complex geometries made of lattice structures.

For the purpose of evaluating the different designs, the following loading scenarios were considered based on McDonald’s

work [8] to simulate rotor deformations by static structural analyses in ANSYS (Fig. 6 depicts the coordinate system used in

rotor analysis):

1. Gravitational loading. A gravitational force of 9.81m/s

2

acting in the negative Z direction accounts for the worst-case

5

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axial deflection due to ground transportation.

2. Maxwell stress. The normal component of the Maxwell

force acting radially outward between the rotor magnets and

stator coils determined by:

σmaxwell =

Bˆ2

g

2μ0

(1)

3. Centripetal force. The high torque induces a centripetal

force that acts along the circumference of the rotor in the +Y

direction (a maximum shear stress of 40 kPa was assumed).

Other forces exist, such as the shear component of the air-gap

force, thermal expansion, and forces and moments of the five

other degrees of freedom for the turbine system. However, it is

assumed that all nontorque forces are transferred via the bearings, to the bed plate, and into the tower. Therefore, these forces

were assumed to be negligible. Additionally, adequate cooling

was assumed so that deformation from thermal expansion was

small enough to be ignored.

FIGURE 6. Coordinate system for loading criteria

Topology Optimization Using ANSYS

ANSYS provides an FEA topology optimization approach

that removes material under specified boundary conditions and

a constraint function. Selecting the required percent mass reduction results in the solver removing structurally unnecessary

material until the desired mass reduction is achieved. For each

additive-manufacturing-catered design in this study, topology

optimization was applied to determine further areas of mass reduction. The mesh was refined for topology optimization to give

a clearer picture of where material is removed. Although this was

computationally expensive, it aided in developing new geometries. Also, the optimizer was unable to resolve inertia loading as

the mass changed each iteration. A first-order approximation of

the weight-reduction potential is given through Topology Optimization of two conventional rotor designs (spoke arm and disk

arm) for a 5-MW generator.

1. Spoke-arm design

Running the 5-spoke-arm design through topology optimization forcing a 60% mass reduction suggests greater opportunity for structural optimization of the rotor. 60% was

chosen based on iteration until the most material could be

removed while maintaining the base shape. Figures 7 and 8

depict the topology optimization results.

FIGURE 7. Topology optimization results for spoked-arm design: (a)

preoptimization, where red depicts areas to be removed, and (b) postoptimization showing removed material

2. Disk design

Running the disk rotor design through ANSYS topology optimization forcing a 60% mass reduction indicates the optimization’s directional dependence. The optimized design

spokes are offset from the normal position in the direction

of the stress.

FIGURE 8. Topology optimization results for disc design: (a) preoptimization, where red depicts area to be removed, and (b) postoptimization showing removed material

6

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Designing for Rotor Eccentricity

Deflection of the rotor in the radial direction as a result of

loading conditions can cause one side of the rotor to be closer to

the stator coils than the other. As a result, there is an unbalanced

magnetic pull, which is stronger in the location of decreased air

gap. Variables influencing the maximum normal stresses experienced by the rotor for the 5-MW spoked-arm rotor design are

given in Table 3.

TABLE 3. THE MAIN DESIGN DIMENSIONS AND THE PARAMETERS OF THE BASELINE GENERATOR WITH Br = 1.1

Tesla

Symbol Description Unit Value

rs Air-gap radius m 3.376

ls Core length m 1.489

s Number stator slots – 1128

p Number of magnet pole pairs – 188

m Number phases – 3

q Number slots per pole phase – 1

Br Remnant flux density Tesla 1.2

τp Pole pitch mm 58.00

τs Stator slot pitch mm 19.30

hm Magnet height mm 8.53

hyr Rotor yoke height mm 45.00

hys Stator yoke height mm 71.36

Bs Stator slot width mm 8.70

Bso Stator wedge width mm 5

γs Air-gap correction factor – -0.0409

g Air-gap length mm 6.90

ge f f Effective air-gap length mm 14.40

μrm Relative permeability – 1.06

μ0 Permeability of free space – 4 πx10−7

Kcs Carter factor for stator slots – 0.9693

Bˆ

pm Peak magnet flux density Tesla Varies

Bˆ

g Peak air-gap flux density Tesla Varies

σmaximum Maximum normal Maxwell stress MPa Varies

An air-gap correction factor with the Carter factor for stator

slots (to account for the slot geometry) was used to calculate an

average effective air gap [6].

ge f f = Kcs(g+

hm

μrm

) (2)

where the Carter factor, Kcs, is given by

Kcs =

τs

τs −γ(g+

hm

μrm

)

(3)

γs = ( 4

π

)

0.5bs0

g+

hm

μrm

tan−1(

0.5bs0

g+

hm

μrm

)−lns1+ ( 0.5bs0

g+

hm

μrm

)

2

(4)

The effective air gap was used to calculate the peak permanentmagnet flux density:

Bˆ

pm =

Brhm

μrmge f f

(5)

The peak air-gap flux density was calculated using:

Bˆ

g = Br(

hm

μrmge f f

)( 4

π

)sin(

π

2

Bm

τp

) (6)

Solving for the peak air-gap flux density provided a Maxwell

normal stress of 0.1976 MPa that matched data from NREL’s

Generator SE [26]. However, the magnet remnant flux density

is assumed constant in these calculations. In reality, the remnant flux density may range from 1.1 to 1.4 Tesla depending on

the magnet manufacturer and quality control. Additionally, to

account for rotor eccentricity and radial deformations, the maximum Maxwell stress is found for the case where the air gap reduces to 0 mm (i.e., the rotor and stator are touching) and plotted

visually for various remnant flux densities shown in Fig. 9.

The maximum Maxwell stress as a function of air-gap

distance is plotted in Figure 10. The maximum Maxwell stress

possibly achieved in the rotor is in the case when g tends to

0; therefore, the worst-case loading scenario occurs with this

maximum Maxwell stress.

σminimum(Br = 1.1) = 0.196 MPa (7)

σmaximum(Br = 1.4)= 1.104 MPa (8)

Because this maximum Maxwell stress occurs in regions

where the air gap is closer to 0, it must be distributed around the

circumference of the rotor decaying toward zero on the opposite

7

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FIGURE 9. Magnetic flux density as a function of air-gap distance for

various remnant flux densities

FIGURE 10. Normal component of Maxwell stress as a function of

air-gap distance for various remnant flux densities

side. This is because if the deflection causes a smaller air gap on

one side of the rotor, it can cause a similar increase in air gap on

the opposite side. Because there will be a large air gap increase

directly opposite of this point load of maximum Maxwell stress,

it is assumed the Maxwell stress is 0. To simulate this loading

condition, the maximum stress with either Br=1.1 or Br=1.4 is

computed. Next, the circumferential direction is divided into

N subcomponents, which yield the angular step in degrees:

δθ =

2∗180o

N

; assuming 100 subdivisions yielded an angular

step of 3.6 degrees. Next, the maximum stress was distributed

over the circumference evenly on both sides using the cosine

relationship:

σ(θ) = 0; π

2 < θ <

3π

2

(9)

σ(θ) = σmaximum cos(θ); θ <

π

2

or θ >

3π

2

(10)

Note that because of coordinate system notation, this pressure is applied as a negative pressure in ANSYS to ensure proper

outward orientation as the Maxwell stress is an attractive stress.

This model is an inherent upper-bound estimation of the absolute

maximum stress, as it is spread over a 50-degree range, or 5π/18

range of angular values. In reality, the maximum stress will be

localized to a much smaller angular range.

Both Maxwell conditions are applied for each subsequent

design to determine the deflections associated with each case.

It should be noted that the maximum deflection is computed in

the case in which the maximum Maxwell stress is applied (i.e.,

if the rotor were to touch the stator). The deflection from this

loading situation is computed and compared against allowable

deflections. A successful design is one where the computed deflections from this maximum loading case is below the allowable

deformation limits.

ALLOWABLE DEFORMATION LIMITS

The allowable deformation limits of the rotor provide the

basis of the structural evaluation of each new design. Each limit

shown below is given for a 5-MW machine based on disk-arm

design from NREL’s GeneratorSE [26].

1. Radial Deflection: No more than 10% of the air-gap length

(0.10)(0.002rs) = 0.35 mm

2. Axial Deflection: No more than 2% of the axial length

0.02ls = 30 mm

3. Torsional Deflection: No more than 0.05◦angle of twist

0.05◦πrs

180◦ = 3 mm

ALTERNATIVE DESIGNS AND DESIGN PARAMETERS

1. Lattice design with hollow truss

To make a reasonable comparison and avoid changes to the

electromagnetic design, we chose to retain the thickness of

the rotor cylinder to be the same as the baseline rotor structural model. A high-strength structure in the form of a lattice design with hollow trusses (spokes) was created to fill

the space originally occupied by the spoke-arm design. The

lattice consisted of repetitions of support ribbon and trusses

8

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distributed radially around the rotor. For this study, the location of the ribbons was fixed and their thickness and width

allowed to change. This decision was made a from preliminary set simulations that indicated that a symmetric design

does indeed have the greatest structural strength. A parametric optimization was carried out to remove as much structural material while ensuring the lowest weight and maximum strength. The optimized solid design proved to be

heavier than the original spoked-arm designs. To attempt

to remediate this problem, the trusses in lattice were made

hollow with a variable wall thickness. A schematic of the

hollow truss design with optimization variables is shown in

Fig. 11.

FIGURE 11. Optimization parameters of a 5-MW lattice support with

hollow trusses showing a cross-sectional view

Table 4 indicates the design variables of the hollow truss

design as well as their optimized value.

TABLE 4. LATTICE DESIGN WITH HOLLOW TRUSS

MEMBERS-OPTIMIZED VALUES

Symbol Design Dimension Unit Value

wd Disk width mm 181.5

ds Truss diameter mm 92.41

ws Truss wall thickness mm 44.51

wr Ribbon width mm 209.00

tr Ribbon thickness mm 72.95

ntrusses Number of trusses – 19

2. Lattice design with U-beam truss

A mold analysis was carried out to examine the feasibility

of printing the various designs. Initial results suggested that

that the lattice design with hollow trusses was impossible to

make using AM powder-binder printing technology. This is

because the spoke necessitated a solid core floating in the

center of the spoke to ensure it casts hollow. However, this

design is impossible to create as the core must be supported

in the center. To solve this problem, a lattice design with a

U-beam truss was created, thereby changing the cross section of the trusses from a circle to a U-beam.

FIGURE 12. Optimization parameters of a 5-MW lattice support with

U-beam trusses

Highlighted design parameters in Fig.12 depict the optimization variables used in ANSYS to select the optimized

design. Table 7 indicates the design variables as well as optimized values.

RESULTS

1. Hollow truss lattice design

The lattice structure with a solid truss design exhibited

strong reduction in radial and torsional deformation. Therefore, creating hollow trusses facilitates mass reduction without sacrificing the deformation advantages.

(a) Mesh convergence

For the hollow truss design, mesh independence was

validated for the total deformation for three different

mesh sizes. The change in total deformation was less

than 5% indicating confidence in mesh sizing at the

lowest bound of 294,000 elements. However, care

should be taken in confirming this result for the torsional deflection as it was observed to vary by as much

9

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
as 10% with refinements to the mesh. Therefore, we

conducted parameter and topology optimization with a

coarser mesh to save computational resources as well

as performed static analysis using a fine mesh for more

accurate deformations. The mesh independence study

depicted a 7% change in total deformation with mesh

sizes from 294,000 to 2,146,000 elements.

(b) Parameter optimization

Results from the parameter optimization study in the

ANSYS workspace are presented in Table 5.

TABLE 5. HOLLOW-TRUSS DESIGN: PARAMETER OPTIMIZATION RESULTS (TORQUE LOADING)

Symbol Design Dimension Unit Valueoptimized

wd Disk width mm 181.5

td Disk depth mm 90

ds Truss diameter mm 92.41

tws Truss wall thickness mm 44.51

wr Ribbon width mm 209

tr Ribbon thickness mm 72.95

ntrusses Number of trusses – 19

Radial deformation mm 0.212

Axial deformation mm 1.71x10−3

Torsional deformation mm 5.404

Structural mass mT 18.27

Active mass mT 16.47

Total mass mT 34.74

Figures 13-15 present results for FEA deformations

found with ANSYS for the hollow-truss-lattice design.

(c) Deformation with varied magnetic loading

Table 6 lists the deformation associated with the

hollow-truss design under the two extreme cases of

magnetic loading.

(d) Topology optimization of the design

Fig. 16 illustrates areas of further mass reduction of

the hollow-truss geometry. Results were extracted

from ANSYS after imposing 0.20 MPa of normal

stress and 40 kPa of shear stress. Topology optimization results suggested further mass reduction of the

5-MW hollow-truss design by:

FIGURE 13. Hollow-truss design: radial deflection

FIGURE 14. Hollow-truss design: torsional deflection

FIGURE 15. Hollow-truss design: axial deflection

(i) Creating an hourglass shape for the trusses

instead of a continuous circular cross section

(ii) Removing the two outermost ribbons.

The hollow-truss design resulted in a 13% structural

mass reduction as compared to the solid-truss design.

However, this is still 11% greater structural mass than

10 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
the conventional spoke-arm design, warranting further

study for mass reduction.

TABLE 6. MAXIMUM DEFORMATION OF THE HOLLOWTRUSS DESIGN UNDER DIFFERENT MAGNETIC LOADING

Direction Unit Br = 1.1 Tesla Br = 1.4 Tesla

Radial deformation mm 1.985 3.084

Torsional deformation mm 6.305 6.803

Axial deformation mm 2.06e−3 4.43e−3

FIGURE 16. Topology optimization results for hollow-truss-lattice

design: (a) pretopology optimization, and (b) post-topology optimization

2. Lattice design with U-beam truss

Owing to the challenges in printing a hollow-truss design, a

U-beam design was chosen for the cross section of the truss

and optimized. The U-beam was oriented along the radial

direction to provide the highest moment of inertia in the direction of twist to reduce torsional deformation.

(a) Mesh convergence

Because of a more complicated cross section, attention must be given to meshing parameters to determine mesh independence. Both the x and z directions

are readily mesh-independent, with less than a 2.5%

change in deformation with refinements from 135,000

to 4,308,000 elements. The torsional deformation was

considered mesh-independent, with a change in mesh

sizing of less than 5%. Therefore, we selected a middle

ground of a 592,000 element mesh arising from web

element sizes of 40 mm and general element sizes of

60 mm.

(b) Parameter optimization

Results from the parameter optimization study in the

ANSYS workspace are summarized in Table 7. Figures 17-19 indicate FEA deformations found with ANSYS for the U-beam-truss lattice design.

TABLE 7. U-BEAM-TRUSS DESIGN: PARAMETER OPTIMIZATION RESULTS (TORQUE LOADING)

Symbol Design Dimension Unit Value

wd Disk width mm 192.67

td Disk depth mm 90

wr Ribbon width mm 227.23

tr Ribbon thickness mm 78.73

ws Truss width mm 167.55

wa Truss arm width mm 42.68

hs Truss height mm 94.28

ntrusses Number of trusses – 27

Radial deformation mm 0.208

Axial deformation mm 3.29x10−5

Torsional deformation mm 2.87

Active mass mT 16.47

Structural mass mT 12.47

Total mass mT 28.95

FIGURE 17. U-beam-truss design: radial deflection

11 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
FIGURE 18. U-beam-truss design: torsional deflection

FIGURE 19. U-beam-truss design: axial deflection

(c) Maximum deformation associated with changes in

magnetic loading

The maximum deformations due to worst-case scenario Maxwell loading conditions with the smallest air

gap are shown in Table 8. It should be noted that the radial and torsional deformations increase above acceptable limits; however, as the worst-case scenario, actual

rotor forces will be below these bounds. Low deflections seen in the torque loading case are representative

of actual rotor operation.

TABLE 8. DEFORMATION OF U-BEAM-TRUSS LATTICE DESIGN UNDER DIFFERENT MAGNETIC LOADING

Direction Unit Br = 1.1 Tesla Br = 1.4 Tesla

Radial deformation mm 2.61 4.22

Torsional deformation mm 4.24 5.10

Axial deformation mm 5.1x10−3 1.64x10−3

(d) Topology optimization of design

Following parameter optimization in ANSYS, topology optimization was performed on the U-beam-truss

design to determine additional opportunities for mass

reduction. Figure 20 presents the results of topology

optimization.

Further mass reduction from the U-beam-truss design

was possible by:

(i) Removing the outermost set of rings on the lattice

(ii) Decreasing the thickness of the inner disk.

The optimized U-beam-truss lattice design proved to

be at least 40% lighter than the solid-truss lattice design and 32% lighter than the hollow-truss lattice design. Additionally, the U-beam-truss lattice utilized

24% less structural mass than the conventional spokedarm design, resulting in a total rotor mass savings of

3.975 metric tons.

FIGURE 20. Topology optimization results for the 5-MW U-beamtruss design: (a) pretopology optimization, and (b) post-topology optimization

MASS AND STRUCTURAL DEFORMATIONS: A DESIGN COMPARISON

The ultimate goal of creating optimized rotor designs is to

decrease the structural mass, thereby resulting in overall system

cost savings due to lower engineering constraints for other wind

turbine components such as the tower. Figure 21 compares the

mass of each optimized design to conventional designs. A continual decrease in structural mass can be noted with each design

iteration.

Additionally, the final U-beam-truss lattice was the only design with a lower structural mass than the hollow-truss design,

with a 24% reduction. Therefore, it was identified as the optimal

design from this study. The radial and torsional deflections for

12 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
FIGURE 21. Structural mass comparison: conventional optimized

designs versus nonconventional optimized designs

these designs are given in Figure 22 and 23. The axial deformations were ignored as they were on the order of a few microns and

the machine is not expected to reach critical axial deformation

under given loading conditions. It should be noted that the radial

deformations of the new designs are more than 60% lower than

the conventional spoked-arm design. The torsional deformations

of the U-beam-truss lattice and solid-truss lattice designs are under the critical limit calculated earlier from the maximum angle

of twist of the rotor.

FIGURE 22. Radial deformation of 5-MW rotor designs

COST ANALYSIS OF SAND-CAST AM

Using additive manufacturing to create sand-cast molds has

the potential to save both costs and time, provided steps are taken

FIGURE 23. Torsional deformation of 5-MW rotor designs

to design for AM. These steps include mold optimization of minimizing unwanted volume as well as indirect tooling approaches

to create a “mold of a mold” to achieve multiple casts with the

same mold.

Cost Evaluation of Additive-Manufacturing-Catered

Geometries

Using powder-binder printing technology, a new costing

model must be developed that takes into account the substantially different manufacturing process. To accomplish this,

we developed a basic costing scheme for a sand-cast-printed

generator as shown in Eq. 11 and the constant bounds are given

in Table 9. To make a comparison, the costs for conventional

rotors made were obtained from a study by the Global Wind

Network [18].

Cost = VmoldC1 + MsteelC2 +SAdesignC3 +C4 (11)

where, Msteel = steel mass (mT)

C1 = printed material cost ($/m

3

)

C2 = steel casting cost ($/mT)

SAdesign = design surface area (m

2

)

C3 = finishing cost per surface area ($/m

2

)

C4 = transportation cost ($)

TABLE 9. COSTING MODEL PARAMETER BOUNDS

Cost Components Unit Low Bound High Bound

Printed material cost $/m

3 8,000 14,000

Steel casting cost $/mT 1,700 2,500

Finishing cost $/m

2 100 500

Transportation cost $ 6,000 18,000

Costing schemes for powder-binder printing can be split into

13 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
multiple cases, as represented in Fig. 24.

Case I: Pay for all sand/binder from manufacturer with no

optimized mold

Case II: Pay for all sand/binder from manufacturer with an

optimized mold

Case III: Amortized cost of optimized mold over 10 turbine

rotors.

FIGURE 24. Costing schemes for sand-cast printing

Results indicate that an optimized mold is necessary to

achieve significant cost reductions in single-use molds. Mold optimization refers to removing all volume not needed for casting.

However, only indirect tooling (Case III) results in additive rotor

costs below that of conventional means. Indirect tooling refers to

creating a mold of a mold to spread out the cost of using additive

manufacturing to create a sand-cast mold. In this case, the additive manufactured mold is used to create a solid metallic mold

that can be used to directly cast the rotor design. In this manner,

the mold cost can be amortized over many rotors, resulting in

economic viability and lower lead times.

Costs for Printing Conventional Spoked-Arm Geometries

In order to compare AM sand casting with traditional approaches, we must compare the cost of creating the hollow

spoked-arm conventional design with the same design using AM.

Mold optimization is key to the analysis. As shown in Figure 25,

since there are few arms, it is unnecessary to create mold support

in areas in between the arms. As a result, the volume of the mold

is drastically reduced. Because of this reduced volume, the cost

to produce the conventional hollow spoked-arm design through

additive manufacturing greatly decreases. This cost model is dependent on assumptions of printing costs, labor costs, and limited knowledge of manufacturer costs and should be considered

a first-order approximation of the rotor cost; however, the AM

cost is significantly below the conventional cost shown in Figure

26.

FIGURE 25. Additive manufacturing sand-cast mold of a hollow

spoked-arm design

FIGURE 26. Costing cases for additive-manufactured hollow spokedarm design

CONCLUSIONS

Additive manufacturing offers unique potential in improving the design of conventional direct-drive generators by reducing structural weight with increased stiffness. By taking advantage of additive manufacturing’s ability to make complex parts

as cost-effective as simple parts, manufacturers can focus better

14 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
on designing for functionality and performance. The structural

and costing analyses in this study provide the following insights:

1. Design for additive manufacturing of generator rotors for a

permanent-magnet direct-drive machine has the potential to

reduce the structural mass by up to 24%.

2. Nonconventional lattice-based structures with U-beam truss

members elicit high structural strength resulting in 60% less

radial deformation with torsional deformation within critical

limits.

3. The nonconventional lattice-based designs are expected to

preserve their structural integrity under unbalanced magnetic pull arising from rotor misalignment, eccentricity, and

deflections.

4. A first-order AM rotor costing model developed during this

study suggests that the printed material volume is the greatest cost component. Using an optimized mold (removing

unnecessary volume) has the potential to decrease sand-cast

printing costs by 33%. However, printing single-use molds

can cost up to 38% more than conventional methods.

5. Indirect tooling (printing a mold of a mold) greatly reduces

the per-rotor cost well below that of conventional means.

Cost estimates for indirect tooling suggest that the casting

cost can be significantly reduced for an increased number of

rotors cast from one mold.

To reduce the mold volume, we envisioned printing only a mold

for the structural component of the lattice design and welding

this to the rotor to allow for greater structural complexity with

decreased cost. However, cost estimates need to be refined to

include labor and assembly to weld the lattices structures to the

rotor.

FURTHER WORK

Further analysis has been planned on using AM to:

1. Explore the structural design space for novel geometries and

conduct more detailed analyses of the entire generator including the stator.

2. Perform experimental validation creating the U-beam lattice rotor using additive manufacturing and testing structural

properties.

3. Refine the cost approximation of both conventional and additive manufacturing approaches.

ACKNOWLEDGEMENTS

This work was supported in part by the U.S. Department of

Energy under Contract No. DE-AC36-08GO28308 with the National Renewable Energy Laboratory, and the Office of Science,

Office of Workforce Development for Teachers and Scientists under the Science Undergraduate Laboratory Internships Program.

The authors acknowledge support from Jason Cotrell who

was instrumental in formulating this summer project and the

team at NREL. The results of detailed study by Mcdonald (2008)

shed insight into the elastic behavior of spoked arm designs.

Funding for the work was provided by the DOE Office of

Energy Efficiency and Renewable Energy Wind Energy Technologies Office.

The U.S. government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide

license to publish or reproduce the published form of this work,

or allow others to do so, for U.S. government purposes.

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