The NorEaster Engine/Power System

architectgeorgeMechanics

Oct 31, 2013 (3 years and 5 months ago)

53 views

1

O’Neill Power Systems Proprietary Information



The NorEaster
Engi
n
e
/
P
o
w
e
r

System

D
if
f
e
r
e
n
t
ia
t
ing

O
tto

c
y
c
l
e

(
or

C
l
e
rk

c
y
c
l
e)

I
C

en
g
ines

from

tur
b
ines,

as

p
re
s
en
t
ed

in

t
h
e

i
n
tr
o
du
c
t
io
n
,
is

a

s
tr
a
i
g
htf
o
r
w
a
r
d

m
a
t
t
e
r

and

a
l
r
eady

the

o
b
je
c
t

o
f

m
y
riad

t
rade

s
tud
i
es

th
a
t

h
a
v
e

se
g
m
en
t
ed

the

po
w
e
r
s
y
s
t
em

m
a
r
k
et

and

l
ed

to

t
urbi
n
e

app
l
i
c
a
t
ion

f
o
r

h
el
i
c
opt
e
rs

abo
v
e

a
b
out

2
5
0
0
l
b
s

and

p
is
t
on

en
g
ines

f
o
r
he
l
ico
p
te
r
s<2
5
00l
b
s.

C
on
s
eque
n
tl
y
, the

o
b
jec
t
i
v
e of

t
his
s
ec
t
ion

sh
a
ll

b
e
t
o

in
t
r
o
duce
t
he

N
or
E
as
t
er

in
t
h
e
con
t
e
xt

of

i
ts

f
e
a
t
u
res

a
n
d

be
n
e
f
its

r
e
l
a
ti
v
e

to

pi
st
on

en
g
in
e
s

a
nd

to

d
e
m
ons
t
r
a
t
e

how

i
ts

uni
q
ue
cha
r
ac
t
e
r
i
s
ti
c
s

a
ll
o
w

for

a

l
i
g
hter

p
o
w
er

s
y
s
t
e
m
,

supe
r
ior

p
e
r
for
m
ance,

and

lo
w
er

l
i
fec
y
c
l
e

c
o
s
t
,

ena
b
li
n
g
pra
c
t
i
cal

ap
p
l
i
ca
t
ion
o
f s
m
a
l
l
e
r
r
ot
o
r
c
ra
f
t

UAV
s.

A

con
v
en
t
i
on
a
l

c
ran
k
-
con
r
od

en
g
ine

of

any

s
t
ro
k
e
-
c
yc
l
e

has

t
h
ree

ba
s
ic

m
o
v
ing

pa
r
ts

p
er

c
y
lin
d
e
r
:
c
r
an
k
,

con
n
e
c
ting

rod

(co
nr
od),

a
n
d

p
i
s
t
o
n.

T
he

con
r
o
d

in
t
rod
u
ces

a

s
t
rong

se
c
ond

ha
r
m
onic

(
and

s
m
a
l
l
er
fou
r
th,

s
i
x
th,

a
n
d

o
t
her

e
v
en

ha
r
m
oni
c
s)

in
t
o

a
ll

the

ine
rt
ial

fu
n
c
t
ion
s
:

f
or
c
e,

t
o
rque,

and

m
o
m
ent

(
w
i
t
h
m
ultiple

c
yl
ind
e
r
s
).

T
h
ese

ha
r
m
onics

c
a
n

cau
s
e

v
ibra
t
ion

in

en
g
in
e
s

w
ith

s
m
a
l
l

nu
m
be
r
s

of

c
y
lind
e
rs

o
r
odd

c
y
lind
e
r

co
n
fi
g
u
r
a
t
io
n
s.

T
h
e

t
rans
v
e
r
se

co
m
pon
e
nt

of

wr
i
s
t
-
pin

force

from

the

co
n
ro
d
’s

an
g
u
l
a
r
ity
in
t
rodu
c
es

s
i
d
e
f
o
rce

on
t
he

pi
s
ton s
ki
rt

a
nd c
y
l
i
nder

w
a
l
l,

w
hich

can

ca
u
se
i
nc
r
ea
s
ed
f
r
i
c
t
i
on and

w
ear.



T
he

N
or
E
a
s
ter

cam

en
g
ine

has

only t
w
o

basic

m
o
v
ing pa
r
ts

per

c
y
lind
e
r:

c
am

and

pis
t
o
n
-
rod
asse
m
bl
y
.

T
h
e

p
i
s
t
o
n
-
rod

asse
m
bly

is

in

pu
r
e

t
ra
n
s
l
a
ti
on,

th
u
s

i
n
t
rodu
c
es

n
o

ad
di
tio
n
al

ha
r
m
oni
c
s,

and

i
t
a
l
so

adds

no

tra
n
s
v
e
r
se

f
o
rce

b
e
t
we
en

p
is
t
on

a
n
d

c
y
lin
d
e
r
.

T
w
o

con
c
en
t
r
i
c

ca
m
s

on

nested

co
n
ce
n
t
r
ic
sha
f
ts

a
re

d
ri
v
en

by

pa
i
r
s

of

r
o
l
l
e
r
s

a
r
r
an
g
ed

on

e
i
t
h
er

s
ide

o
f

each

pi
s
ton

rod

such

t
hat

the

do
w
n
w
a
r
d
m
otion

of

t
h
e

p
i
s
t
on

d
ri
v
es

one

c
am

C
W

and

the

oth
e
r

CC
W.

T
h
i
s

g
i
v
es

s
i
m
ultaneous,

con
c
en
t
r
i
c
coun
t
e
r
ro
t
a
t
ion,
w
h
ich

is

i
d
e
a
l

for

r
o
to
r
c
r
a
ft.

I
f

the

cam

fun
c
ti
o
n

u
s
ed

is

s
i
m
ple

h
a
r
m
onic

m
otion

(
S
H
M)

wi
th

no

d
we
l
l
s,

t
hen

for

e
a
ch

c
a
m
,

the
r
e
w
ill

b
e

only

a

p
r
i
m
a
r
y

ha
r
m
onic

co
m
ponent

in

a
ll

t
h
e

in
e
r
t
ia

f
u
nc
t
io
n
s

ex
c
ept

t
orque.

B
u
t

i
n
e
r
ti
a
l

t
o
rq
u
e
of

t
h
e

cou
n
t
e
rr
o
t
a
ting

cam

is

of

o
ppo
s
i
t
e

s
i
g
n

and

c
anc
e
ls

t
he

i
n
e
r
t
i
al

tor
q
ue

as

f
e
lt

at

the

r
ot
o
rs

a
nd
a
i
r
f
r
a
m
e.

W
i
th

o
t
her

c
am

fun
c
tio
n
s

t
h
at

co
n
t
a
in

hi
gh
er

ha
r
m
oni
c
s,

the

a
r
r
an
g
e
m
ent

of

the

N
orE
a
s
t
e
r

s
pi
s
tons

in

opp
o
sed

p
a
i
r
s

c
anc
e
ls

a
l
l

h
a
r
m
onics

o
f

i
n
e
r
t
ia

f
o
rce

i
nc
l
uding

the

fi
rs
t
,

m
a
k
ing

it

p
e
r
f
ec
t
ly
for
c
e
-
ba
l
ance
d
.

I
f

the

pis
t
o
ns

a
r
e

a
ll

co
p
la
n
a
r
,

as

i
s

t
r
ue

in

the

N
or
E
as
t
er

en
g
in
e
,

then

th
e
re

i
s

a
l
so

z
e
r
o
ine
rt
ial

sha
k
ing

m
o
m
en
t
.

I
n

e
i
th
e
r

en
g
ine,

th
e
re

wil
l

s
t
i
ll

be

h
i
g
her

h
a
r
m
onics

o
f

t
h
e

g
as

fo
r
ce

a
nd

g
as
torq
u
e

fu
n
c
t
io
n
s,

and

th
ei
r

in
e
r
t
ia

tor
q
ues

c
an

ha
v
e

non
z
e
r
o

e
v
en

ha
r
m
oni
c
s.

A
g
a
i
n,

coun
t
e
r
r
ot
a
t
i
on
canc
e
ls

the

r
e
a
c
tion

t
o
rq
u
e

on

t
h
e

a
i
r
f
r
a
m
e.

O
nly

the

ca
m
shaft

exp
e
r
i
enc
e
s

t
he
s
e

os
c
i
l
la
t
io
n
s

i
nt
e
rn
a
ll
y
.
T
he

eq
u
a
t
ions

for

t
h
is
a
na
l
y
s
i
s

a
r
e

a
l
l

d
e
ri
v
ed

in
r
e
f
e
re
n
ce

i
v
.

T
he

g
eo
m
e
t
ry

of

a

v
ee

or

o
pposed

m
ul
t
i
-
c
y
lind
e
r

en
gi
ne

is

d
e
f
i
ned

as

shown

in

F
i
g
ure

4

(
f
rom

ref

i
v
,

p. 730).

T
h
is
g
eo
m
e
t
ry

is val
i
d for

e
i
th
e
r a cr
a
nk

en
g
ine
(
as s
h
o
w
n) or

a cam

en
g
ine. The r
e
f
e
ren
c
e
X
-
ax
i
s
is

ta
k
en

in

the

m
id

p
l
ane

be
t
w
e
e
n

the

c
y
lin
d
e
r
s

a
n
d

the

Y
-
ax
i
s

is

o
r
tho
g
on
a
l

t
h
rou
g
h

t
h
e

c
rank

o
r

c
am

cen
t
e
r
.

U
n
i
t

v
ec
t
ors

r
-
hat

a
nd

n
-
hat

a
re

d
e
f
ine
d
,

r
es
p
e
c
t
i
v
e
l
y
,

a
long

a
n
d

n
o
r
m
al

t
o

t
h
e

p
i
s
ton

ax
i
s

o
f

t
h
e

ri
g
ht

ban
k
,

and

v
ectors

l
-
hat

and

m
-
hat

a
r
e,

r
es
p
ec
t
i
v
e
l
y
,

a
l
ong

and

nor
m
al

to

the

pi
s
ton

ax
i
s

of

t
h
e

l
ef
t
ban
k
.

B
ank

a
n
g
le

γ

de
f
i
n
es

the

a
n
g
ular

o
ff
s
et

o
f

e
ach

c
y
lin
d
er

b
a
nk

from

t
he

X
-
ax
i
s.

A
n

oppo
s
ed

con
f
i
g
ura
t
ion has γ =

±90
°
.
T
he an
g
le θ
i
s
t
h
e crank

or

cam

an
g
l
e
, and
i
s def
i
ned,

for any

c
y
linder
, as ωt



φ
i

,

w
he
r
e

φ
i

is

the

p
hase

an
g
le

of

the

i
t
h

c
y
li
n
de
r
,

n

is

the

n
u
m
ber

of

c
yl
i
n
de
r
s,

ω

is

s
ha
f
t

an
g
u
la
r
v
e
l
oc
i
t
y
,

m
B

is
t
he
m
o
v
ing

m
ass,

r
is
c
rank

r
a
di
u
s, and

t

is

t
i
m
e.

2

O’Neill Power Systems Proprietary Information




Figure

4
:

G
e
o
m
e
t
ry

o
f

a

Vee

o
r

o
p
p
o
s
ing

c
y
li
n
der pi
s
t
o
n

engine

3

O’Neill Power Systems Proprietary Information





T
he

ex
p
re
s
s
i
o
n
s
f
or

in
e
r
t
ial

sha
k
ing

for
c
e
F
s

in
r
i
g
ht

a
n
d l
e
ft

b
an
k
s can
b
e sho
w
n

t
o be:








































T
h
e
se

v
e
c
tors

in

the

pl
a
n
e
s

of

the

c
y
lind
e
r

b
a
n
k
s

a
r
e

co
m
bined

v
ect
o
r
i
a
l
ly

to

obt
a
in

t
he
i
r

v
ec
t
or
co
m
ponen
t
s

in
t
he

X
Y

p
l
a
n
es
wi
th:


T
h
e
se

eq
u
a
t
ions

as

s
h
o
w
n

a
r
e

ta
k
en

out

o
n
ly

to

the

s
e
cond

ha
r
m
onic

of

t
he

d
r
i
v
ing

f
unc
t
ion,

b
u
t

they
can

be

exp
a
nded

t
o

in
c
l
u
de

any n
u
m
ber

of

ha
r
m
onics

a
s

de
s
ire
d
.

A

su
f
f
ic
i
en
t
,

b
u
t

not

ne
c
es
s
a
r
y
,
cond
i
t
i
on for
z
e
r
o in
e
r
t
i
a
l

s
ha
k
ing

for
c
e
i
s
t
h
a
t

the su
mm
a
t
ions

o
f
t
he
t
ri
g
ono
m
e
t
r
i
c

f
u
nc
t
io
n
s

o
f the pha
s
e
an
g
les

a
s sho
w
n

in

the
e
qu
a
tio
n
s

m
ust

a
l
l

b
e
z
e
r
o:


4

O’Neill Power Systems Proprietary Information





E
v
en

absent

t
h
is

co
n
d
i
ti
on
,

the

bank

an
g
le

γ

can

ca
u
se

ce
r
t
a
in

co
m
ponen
t
s

o
f

s
ha
k
ing

force

to

be
z
e
r
o:

T
h
e

X

c
o
m
ponen
t
s

w
ill

a
ll

be

z
e
r
o

w
hen

γ

=

90
°
.

The
s
e

e
q
ua
t
io
n
s

c
a
n

be

s
ho
w
n

to

g
i
v
e

z
e
r
o
sha
k
ing

fo
r
ce

for

a
ll

h
a
r
m
o
nic

co
m
ponen
t
s

i
n

an

en
g
i
n
e

wi
th

a
ny

nu
m
ber

of

opp
o
sed

p
a
i
rs

of

c
y
lin
d
e
r
s
(
γ

=

90
°
),

a
r
ran
g
ed

r
ad
i
a
l
ly

at

equ
i
an
g
ul
a
r

sp
a
c
i
n
g
.

A
ny

pe
r
i
od
i
c

fun
c
t
i
on

can

be

a
p
proxi
m
a
t
ed

by

a

Four
i
e
r
se
r
ies

c
a
r
ri
e
d

o
ut

to

a

de
s
i
r
ed

nu
m
ber

of

t
e
r
m
s

(ha
r
m
onic
s
)
.

Thus,

any

cam

func
t
ion

s
e
le
c
ted

to

d
r
i
v
e

t
h
e

N
orEa
s
ter

cam

en
g
ine wi
l
l

res
u
lt

in

the
o
r
e
t
i
ca
l
ly

exa
c
t

for
c
e b
a
la
n
ce.

I
n

a

con
v
en
t
ional

in
l
ine

o
r

v
ee

c
r
ank

en
g
ine,

t
h
e

c
y
li
n
de
r
s

m
ust

be

s
pa
c
ed

ap
a
rt

a
l
ong

the

c
r
a
n
k
sh
af
t
ax
i
s,

as

s
ho
w
n

in

F
i
g
ure

4
,

to

a
llow

the

v
a
r
ious

c
r
ank

thro
w
s

to

p
a
ss

by

one

ano
t
h
e
r
.

T
h
is

g
i
v
es

t
h
e
pote
n
t
i
al

f
o
r

u
nb
a
lan
c
ed s
h
a
k
ing

m
o
m
en
t
s
t
o ex
i
st

ab
o
ut

a
n

a
xis
t
ra
n
s
v
e
r
se to

t
he crank a
x
i
s
, as d
e
f
i
ned
i
n
equa
t
io
n
s

14.11

in

re
f
e
r
e
n
ce

i
v
.

The

cam

en
g
ine

do
e
s

not

h
a
v
e

th
i
s

l
i
m
ita
t
ion.

A
ll

c
y
l
i
nde
r
s

a
re

i
n

t
h
e
sa
m
e p
l
ane

and

c
o
nse
q
ue
nt
ly

do not

g
en
e
ra
t
e any

m
o
m
en
t
s about

t
rans
v
e
r
se a
xe
s.

T
h
e
re
w
i
l
l

a
lso
b
e an

in
e
r
ti
al

s
h
a
k
ing torq
u
e
i
n

e
i
th
e
r a

c
r
ank

or

cam

en
g
ine.
I
ts equa
t
ions

a
r
e
:

































T
h
e
se

show t
h
e
f
i
r
st

th
r
ee
h
a
r
m
onics
o
f i
n
e
r
t
i
al

to
r
que.

For
t
h
em

to be
z
e
r
o,

su
f
f
i
c
i
ent

c
ond
i
t
i
ons

a
r
e
:




5

O’Neill Power Systems Proprietary Information





For

a

c
r
ank

or

cam

en
g
ine

cons
t
ru
c
ted

o
f

p
a
irs

o
f

o
p
posed

c
yl
ind
e
rs,

f
or

e
a
ch

o
pp
o
sed

p
a
i
r,

a
l
l

o
d
d
ha
r
m
onic

t
e
r
m
s

of

ine
r
t
ia

t
orque

i
nc
l
uding

the

fu
n
d
a
m
en
t
al

w
ill

be

z
e
r
o,

b
u
t

a
l
l

e
v
en

ha
r
m
onics

m
ay

be
non
z
e
r
o

un
l
ess

the

c
am

func
t
ion

i
s

s
i
m
ple

h
a
r
m
onic

m
otion,

in

w
hi
c
h

ca
s
e

th
er
e

w
ill

b
e

only

a

se
c
ond
ha
r
m
onic

o
f

i
ne
r
t
i
a

tor
q
ue

as

s
h
o
w
n

in

Fi
g
ure

5.

B
u
t,

a
l
l

of

th
e
se

t
o
rque

co
m
ponen
t
s

a
r
e

c
anc
e
l
l
ed

by

t
h
e
coun
t
e
r
ro
t
a
t
ing

ca
m
.

T
his

i
s

a

s
i
g
n
i
f
i
ca
n
t

ad
v
an
t
a
g
e

o
f

the

c
am

en
g
ine

o
v
er

a

c
r
a
nk

en
g
ine

that

can

o
n
ly
g
i
v
e
counte
r
r
o
ta
t
ion

th
r
ou
g
h a
g
earb
o
x,

w
hi
c
h ad
d
s
i
ts

o
w
n ha
r
m
onics.




Figure

5
:

I
ner
t
ia

T
o
rque

f
o
r

a

On
e
-
L
o
be,

S
y
m
m
e
t
ric
a
l

SH
C
C
a
m

O
v
er

One

Re
vo
luti
o
n



A

c
r
ank

en
g
ine

has

p
i
s
ton

dis
p
la
c
e
m
en
t
,

v
e
l
oc
i
t
y
,

and

acc
e
l
e
ra
t
ion

fun
c
ti
o
ns

w
hose

s
h
apes

for

any
one

c
yl
ind
e
r, and thus
i
ts Fou
r
i
e
r

co
m
pone
n
ts, a
r
e co
m
ple
t
e
ly d
e
fi
n
ed

by
it
s

b
o
r
e
/
s
t
ro
k
e

r
a
t
io and
c
r
an
k
/
c
o
nrod ra
t
io.

A
n

ex
a
m
ple

of

these
f
un
c
t
i
ons

i
s

s
ho
w
n

in

Fi
g
ure

6

o
v
er

t
w
o re
v
olu
t
io
n
s

of

t
h
e

c
r
a
n
k
.
N
ote

the

d
i
s
to
r
ti
o
n

of

the

s
hapes

f
rom

t
h
e

la
r
g
e

sec
o
n
d

ha
r
m
onic

due

to

co
n
rod

osc
i
l
l
a
t
ion.

T
he

b
o
ttom
plot

shows

the

g
as

f
o
rce

f
or

a

t
w
o
-
s
t
ro
k
e

en
g
ine,

f
i
r
i
ng

once

per

re
v
olu
t
ion.

F
i
g
ure

7

shows

t
he

i
ne
r
t
i
a
torq
u
e

fun
ct
ion

f
o
r

a

t
w
o
-
c
y
linder

op
p
osed

c
rank

en
g
ine

o
v
er

t
w
o

re
v
olu
t
ions

of

the

c
r
an
k
.

A
s

shown

it
in
c
ludes

t
h
e
f
ir
s
t

th
r
ee h
ar
m
onics of

the

fun
c
ti
o
n,
a
ll

of
w
h
i
ch
a
re non
ze
ro.

6

O’Neill Power Systems Proprietary Information






Figure

6
:

Fr
o
m

t
o
p

to

bott
o
m
:

P
i
s
t
o
n

Di
s
plac
e
m
ent,

Vel
o
cit
y
,

Acceler
a
tion,

a
nd

G
a
s

F
o
rce

in

a

Cr
an
k

E
ngine





Figure

7
:

I
ner
t
ia

Sh
a
k
ing

T
o
r
q
ue

in

a

T
w
o
-
C
y
li
n
der

Op
p
o
s
ed

Cr
a
n
k

E
ng
i
ne

7

O’Neill Power Systems Proprietary Information






T
he

N
orE
a
s
t
er

cam

en
g
ine,

on

t
h
e

o
th
e
r

ha
n
d,

c
an

t
a
il
or

t
hese

p
i
s
t
o
n

f
u
nc
t
io
n
s

w
ith

v
a
r
i
a
ti
o
n

i
n

t
h
e
cam

prof
i
le.

T
he

s
i
m
ple
s
t

a
r
r
an
g
e
m
ent

is

a

s
ym
m
e
t
r
i
cal,

s
i
m
ple
-
ha
r
m
oni
c
-
m
otion

r
i
se

and

f
a
ll

c
am

as
shown

o
v
er

one

re
v
ol
u
t
i
on

in

Fi
g
ure

8.

T
h
is

m
i
m
ics

a

S
c
ot
c
h
-
y
o
k
e

m
echan
i
s
m
,

w
hich

is,

i
n

e
f
f
ect,

a
c
r
ank

en
g
ine

wi
th

an

i
n
f
i
n
it
e
ly

long

co
n
rod.

B
o
t
h

o
f

t
h
ese

m
echan
i
s
m
s

ha
v
e

pure

ha
r
m
o
n
ic

m
otion.
Fi
g
ure

9

shows

t
hat

i
ts

f
u
nc
t
ions

a
r
e

s
ym
m
e
t
ric,

c
o
nti
n
uous,

p
u
re

h
a
r
m
onics

in

a
ll

d
e
ri
v
a
t
i
v
e
s
.

Al
l
de
r
i
v
a
t
i
v
es

c
on
t
a
i
n

only

t
he

fun
d
a
m
en
t
al

f
r
eque
n
c
y
,

w
hich

due

to

the

f
o
u
r
-
lobe

ca
m

is

four

t
i
m
es

the

cam
rot
at
ion
a
l

s
peed,

i
.
e,

p
i
s
ton

spe
e
d

wi
th

o
ne

p
i
s
ton

per

ca
m
.

Fi
g
ure

5

shows

t
h
e

ine
rt
ial

sha
k
ing

t
orq
u
e
fun
c
tion

for

a

o
n
e
-
lobed,

S
H
M

ca
m
,

w
hich

is

a

pure

s
econd

h
a
r
m
onic.

A

m
ult
i
-
l
obed

S
H
M

cam

such

a
s
the

one

in

Fi
g
ure

8

wi
ll

h
a
v
e

a

s
i
n
g
le

ha
r
m
onic

a
t

2X

t
h
e

nu
m
ber

of

fo
l
lo
we
rs

(pi
s
ton
s
)
,

i
.
e,

an

e
i
g
h
t
h
ha
r
m
onic

f
o
r

t
h
is

fo
u
r
-
lobed

ca
m
,

assu
m
ing

one

c
ylin
d
er

p
e
r

ca
m
.

A
g
a
i
n,

these

h
a
r
m
onics

w
i
l
l

b
e
canc
e
l
l
ed by

the

cou
n
t
e
rr
o
t
a
t
i
ng

ca
m
.




Figure

8
:

F
o
ur
-
L
o
be

S
y
m
m
e
t
ric
a
l

S
H
M

C
a
m

f
o
r

the

N
o
rEa
s
ter

E
ngine

8

O’Neill Power Systems Proprietary Information






Figure

9
:

Fr
o
m

t
o
p

t
o

bott
o
m
:

SHM

Di
s
plac
e
m
e
nt,

Vel
o
cit
y
,

Acce
l
er
a
tion,

a
nd

J
erk

in

a

C
a
m

E
ngine



I
f

desired,

t
h
e

N
orEa
s
t
e
r

p
is
t
on

m
otion

can

be

m
ade

asy
m
m
e
t
ric

a
nd

be

t
a
i
l
or
e
d

to

ta
k
e

m
ax
i
m
u
m
ad
v
an
t
a
g
e

of

f
la
m
e
-
front

tr
a
v
el

r
a
te,

f
lu
i
d

d
y
na
m
ics

of

the

i
n
ta
k
e

s
y
s
t
e
m
,

or

o
t
her

de
s
ir
e
d

p
a
ra
m
e
t
e
rs.

A
n
asy
m
m
e
t
ric

cam

is

s
h
o
w
n

i
n

Fi
g
ure

10
.

T
he

v
e
l
o
c
i
ty

pro
f
ile

of

the

p
i
s
t
on

on

e
i
t
h
e
r

t
h
e

up

o
r

do
w
n

s
t
ro
k
e
can

b
e

v
a
r
i
ed

w
it
h
in

bro
a
d

l
i
m
its

u
s
i
ng

so
p
hi
s
t
i
c
a
t
e
d

m
otion

fun
c
ti
o
ns

such

a
s

B
-
sp
l
ines

as

shown

i
n
Fi
g
ure

11.

I
t

is

pos
s
i
b
le

t
h
a
t

k
nock con
t
r
o
l

in

a co
m
press
i
o
n
-
i
g
nition

en
g
ine

c
an

b
e

ef
f
e
c
ted

by

sha
p
ing of
the
p
is
t
on
v
e
l
o
c
ity

pr
o
f
i
le
n
ear

top d
e
ad ce
n
t
e
r
(
T
D
C
).

T
h
is w
i
ll

in
t
rod
u
ce
h
i
g
her

ha
r
m
onics

in t
h
e d
r
i
v
ing
fun
c
tio
n
,

t
h
e

e
v
en

m
e
m
be
r
s

of

w
h
i
ch

c
an

s
h
ow

up in

t
h
e

sha
k
ing

t
o
rque.

O
n
e

of t
h
e

g
oa
l
s

o
f

t
he

p
ropo
s
ed
s
t
udy

is

to

d
e
t
e
r
m
ine

t
he

e
f
f
ic
a
cy

of

v
a
r
i
a
t
ion

in

ca
m

pr
o
file

on

c
on
t
rol

of

p
o
w
er

d
e
li
v
e
r
y

f
rom

the
exp
l
o
d
ing

ch
a
r
g
e

to

t
he

m
oti
o
n

con
v
e
r
s
ion

m
echa
n
i
s
m

of

this

u
n
ique

and

v
e
r
s
a
t
i
le

cam

en
g
ine

and

i
t
s
e
f
f
ect

on
t
he en
g
i
n
e

s

sp
e
c
i
fic

fu
e
l

c
o
nsu
m
ptio
n
,

a
m
ong

other

f
a
c
to
r
s.

9

O’Neill Power Systems Proprietary Information






Figure

10
:

An

As
y
m
m
e
t
ric,

F
o
u
r
-
L
o
be

S
p
li
n
e

C
a
m

f
o
r

the

N
o
rEa
s
t
er

E
ngine




Figure

11
:

Fr
o
m

t
o
p

to

bott
o
m
:

P
os
ition,

v
el
o
cit
y
,

a
cceler
a
tion

a
nd

je
r
k

f
o
r

a
n

A
s
y
m
m
e
t
ri
c
,

F
o
u
r
-
L
o
be

S
p
li
n
e

C
a
m

10





I
n

add
i
t
i
on

to

i
ts

sup
e
r
i
or

ba
l
an
c
e

s
t
a
te

and

r
es
u
l
ti
ng

low

v
ibra
t
ion,

t
h
e

m
a
j
or

ad
v
an
t
a
g
e

of

the
N
orEa
s
ter

c
am

en
g
ine

is

i
t
s

a
l
l
o
w
an
c
e

of

s
i
m
ultan
e
o
u
s

coun
t
e
r
-
rot
a
ting

out
p
ut.

T
h
is

e
li
m
ina
t
es

t
he

ne
e
d
for a

t
a
il

r
o
tor

and

its

as
s
o
c
ia
t
ed

s
h
a
f
t,
g
ea
r
ing

and
a
i
rf
ra
m
e str
u
c
t
u
re.

T
h
is

con
s
t
it
utes

a
s
i
g
nif
i
ca
n
t

w
e
i
g
ht
sa
v
ing

as

w
e
l
l

as

a

r
edu
c
t
i
on

in

c
o
m
plex
i
ty

and

o
v
e
r
a
l
l

v
e
h
ic
l
e

s
i
z
e.

A
not
h
er

a
d
v
an
t
a
g
e

is

th
a
t

ha
v
ing
m
ultiple

lo
b
es

o
n

t
h
e

c
am

g
i
v
es

an

inh
e
re
n
t

g
ear

re
d
uc
t
ion

r
a
t
io

b
e
t
we
en

p
is
t
on

speed

and

out
p
ut

sh
af
t
rot
at
ion
a
l

s
p
eed.

T
h
e en
g
i
n
e
i
s

es
s
en
t
i
a
lly

an

i
nte
g
r
a
t
e
d po
w
er

sou
r
ce a
n
d s
p
eed

r
educ
t
ion

un
i
t.
I
t

does n
o
t
need

an

e
x
t
e
rn
a
l

g
earbox.

W
i
th

a

fo
u
r
-
lobe

ca
m
,

w
hich

can

a
c
co
m
m
oda
t
e

e
i
g
ht

c
y
linde
r
s,

p
i
s
t
on

spe
e
d
w
ill

b
e
f
o
u
r
t
i
m
es that

o
f c
a
m

rota
t
ion.

T
h
is
f
e
a
tu
r
e
i
s
p
a
r
t
ic
u
l
a
rly

w
e
l
l
-
su
i
t
ed
t
o

t
h
e
r
eq
u
i
r
e
m
en
t
s of

s
low
-

tur
n
ing

he
l
i
cop
t
er

r
ot
o
rs

a
n
d

pis
t
o
ns

t
ra
v
e
l
i
ng

at

opt
i
m
u
m

v
e
l
oc
i
t
i
es

f
o
r

po
w
er

g
enera
t
ion.

For

e
xa
m
ple,
w
ith

a

fo
u
r
-
lobe

cam

dri
v
ing

rotors

at

10
0
0

rp
m
,

the

pi
s
tons

wi
ll

be

op
e
r
a
ting

at

an

e
f
fe
ct
i
v
e

4000

rp
m
,
thus
b
e
i
ng

in

a b
e
t
t
er

ran
g
e

for

th
e
r
m
od
y
n
a
m
ic ef
f
i
c
ie
n
c
y
, po
w
e
r
, and

t
o
rque
o
ut
p
ut.

I
n

s
u
m
m
a
r
y
,

the

t
r
ade

s
pa
c
e

for

p
i
s
ton

v
s.

t
u
rb
i
ne

p
o
w
er

s
y
s
t
e
m
s

is

a
l
r
eady

es
ta
bl
i
shed

a
nd

di
v
i
d
ed
into t
w
o

s
eg
m
en
t
s

w
h
e
re

t
u
rbi
n
es

a
re
t
he sup
e
ri
o
r

s
o
l
u
t
ion

f
or la
r
g
er

r
o
tor
c
r
a
ft,

w
h
ile p
i
s
ton en
g
i
n
es t
r
ade
fa
v
ora
b
ly

for

r
o
to
r
c
r
a
ft

<
2
500l
b
s.
T
h
e

N
o
rEa
s
t
e
r

p
r
o
v
ides

a

s
i
g
nif
i
ca
n
t

i
m
pro
v
e
m
ent

o
v
er

the

cu
r
re
n
t
pi
s
ton

en
g
ine

s
e
g
m
ent

on

a

s
t
a
n
d
-
a
l
one

ba
s
is

of

lo
w
-
v
ibra
t
ion

o
pe
r
a
t
ion,

po
we
r/
we
i
g
ht

by

re
m
o
v
al

of
g
ear

red
u
c
t
ion

t
ra
n
s
m
issio
n
,

and

o
v
e
r
a
l
l

s
i
m
p
lic
i
ty

of

desi
g
n.

Fu
r
th
e
r

ben
e
f
i
ts

ac
c
r
ue

a
t

t
h
e

s
y
s
t
em

le
v
el
from

ab
i
l
ity

f
o
r

co
u
nt
e
r
-
ro
t
a
t
i
on,

t
a
i
l

r
o
t
o
r

re
m
o
v
a
l
,

a
n
d

expe
c
ted o
v
e
r
a
l
l

p
ac
k
a
g
ing

e
f
fi
c
ie
n
cy and

i
m
pact
on

o
v
e
r
a
l
l

r
o
to
r
c
r
a
f
t

de
s
i
g
n.

C
onsequ
e
n
t
l
y
,

it

i
s

a
n
ti
ci
pa
t
ed

th
a
t

n
o
t

o
n
ly

w
ill

t
he

N
orEa
s
ter

ena
b
le

m
ore
pra
c
t
i
cal

a
pp
l
ic
a
t
i
on of s
m
a
l
l
e
r r
o
to
r
c
r
a
ft

in the 50
h
p r
a
n
g
e, but

a
l
so
t
h
at

i
t

m
ay
v
e
ry

w
e
l
l

ex
t
e
nd the
t
ra
d
e
space

for

p
i
s
ton

en
g
in
e
s

in

rot
o
rc
r
a
f
t

be
y
ond

the

25
0
0lbs

r
an
g
e

due

to

i
ts

i
m
pro
v
ed

po
w
e
r
/
we
i
g
ht

o
v
er
con
v
en
t
i
o
n
a
l

p
i
s
t
on

en
g
in
e
s

and
i
ts
o
th
e
r
a
sso
c
i
a
ted

s
y
s
t
em

bene
f
it
s
.




R
obert

L
.
N
o
r
ton

P
.
E
.,
C
onsu
l
tant

E
duca
t
ion:
B
S,

M
e
cha
n
i
c
al

En
g
in
e
e
r
ing

&

I
ndus
t
r
ial

T
e
chn
o
lo
gy
,
N
orthea
s
t
e
rn

U
ni
v
e
r
s
i
ty
MS, En
g
ine
e
ring

D
e
s
i
g
n, Tuf
t
s

U
ni
v
e
r
s
ity

Aw
a
r
ded Do
c
t
o
r of En
g
i
n
e
e
r
in
g
, W
o
r
c
es
t
er

P
o
l
y
tec
hn
ic
I
ns
t
i
t
ute

Prof
e
ss
i
onal

B
ac
k
ground

and

E
xperie
n
ce:

M
r.

N
orton

i
s

a

re
g
i
s
t
e
red

p
r
ofe
s
s
i
o
n
al

en
g
i
n
eer

i
n
Mas
s
ach
u
s
e
tts.

H
e

has

o
v
er

50

y
ear
s


e
x
pe
r
ie
n
ce

in

en
g
inee
r
ing

de
s
i
g
n

and

m
anu
f
a
c
t
u
ring

and

o
v
er

4
0
y
ears

exp
e
r
i
en
c
e

t
e
ac
h
ing

m
echan
i
c
a
l

en
g
ine
e
r
i
n
g
,

en
g
inee
r
ing

de
s
i
g
n,

co
m
p
uter

s
c
ien
c
e,

and

r
e
la
t
ed
su
b
j
e
c
t
s

at

N
o
r
the
a
s
t
e
r
n

U
ni
v
e
r
s
i
t
y
,

T
u
f
ts

U
ni
v
e
r
s
i
t
y
,

and

WP
I
.

N
orton

has

be
e
n

on

the

fac
u
lty

of

WPI
s
i
n
c
e

198
1
,

and

is

c
u
rre
ntl
y

the

M
i
l
ton

P.

H
i
gg
ins

I
I

D
is
t
in
g
uis
h
ed

P
r
o
f
e
ss
o
r

E
m
e
r
itus.

H
e

is

a
l
so

the
found
e
r a
n
d p
r
e
s
ide
n
t

of
N
orton

A
sso
c
i
a
tes

En
g
ine
e
r
i
ng

C
onsu
l
t
a
nts

s
i
nce
1
970.

A
t

Po
l
a
r
o
id

C
o
rp
o
ra
t
ion

for

10

y
ea
r
s,

he

d
e
s
i
g
n
e
d

ca
m
e
r
as,

r
e
l
a
ted

m
echan
i
s
m
s,

and

hi
g
h
-
speed
au
t
o
m
a
t
ed

m
ach
i
ne
r
y
.

H
e

spent

t
h
r
e
e

y
ears

at

J
e
t

S
p
r
ay

C
ooler

I
nc.,

d
e
s
i
g
ning

f
oo
d
-
hand
l
ing

m
achine
r
y
and

p
r
odu
c
ts.

For

fi
v
e

y
ears

he

h
e
l
p
ed

d
e
v
e
l
op

ar
t
i
fi
c
i
a
l
-
heart

and

n
o
nin
v
a
s
i
v
e

as
s
i
s
te
d
-
c
i
rc
u
l
a
ti
o
n
de
v
ices

a
t

the

T
u
fts

N
ew

En
g
land

Me
d
ic
a
l

C
en
t
er

a
nd

B
os
t
on

C
i
ty

H
osp
i
t
a
l.

Since

lea
v
ing

indu
s
try

to
j
oin

a
cade
m
ia

in

197
4
,

he

has

con
t
inu
e
d

as

an

in
d
e
p
ende
n
t

cons
u
l
t
ant

on

en
g
i
n
ee
r
ing

pr
o
j
e
c
t
s

r
an
g
ing
from

disp
o
sa
b
le
m
ed
i
c
a
l

p
r
oduc
t
s
t
o

hi
g
h
-
speed p
r
od
u
c
t
i
on
m
achin
e
r
y
.

H
e ho
l
d
s

th
i
r
t
een
U
.S.
p
a
t
e
nt
s
.

H
e

is

the

au
t
hor

of

nu
m
e
r
ous

tec
h
ni
c
al

pa
p
e
r
s

and

j
o
urn
a
l

a
r
ti
c
l
e
s

co
v
e
r
ing

k
ine
m
a
t
ics,

d
y
na
m
ics

of
m
achine
r
y
,

cam

desi
g
n

a
n
d

m
anu
f
act
u
rin
g
,

co
m
put
er
s

in

e
duc
a
t
i
on,

en
g
i
n
ee
r
i
n
g

educa
t
ion,

a
n
d

of

the
te
x
ts

D
es
i
gn

of

M
a
ch
i
n
er
y
,

K
inemat
i
cs

and

D
ynam
ic
s

of

Mac
h
in
e
ry,

M
a
ch
i
ne

D
esig
n
:

An

Int
e
gr
a
t
e
d
Approac
h
,

a
n
d

t
he

C
am

D
e
s
i
gn

and

Ma
n
uf
a
c
t
u
r
i
ng

H
andboo
k
.

H
e

is

a

F
e
l
low

o
f

t
he

A
m
e
r
i
c
an

S
o
c
i
e
t
y
of

Me
c
ha
n
ic
a
l

En
g
inee
r
s

and

a

m
e
m
ber

of

the

So
c
ie
t
y

of

A
uto
m
oti
v
e

En
g
ineers.

I
n

2007,

he

w
as
sel
e
c
t
ed

a
s

a

U
.

S.

P
ro
f
es
s
or

of

t
h
e

Y
e
ar

by

t
he

C
o
un
c
i
l

f
o
r

the

A
d
van
c
eme
n
t

a
n
d

Supp
o
rt

of

E
duc
a
ti
o
n

11





(
C
AS
E
)

and

the

C
arneg
i
e

Founda
t
ion

f
or

t
h
e

Adva
n
ce
m
ent

o
f

Tea
c
hin
g
,

w
ho

joi
n
tly

pr
e
se
n
t

the

o
n
ly
na
t
ion
a
l

aw
a
rds

for

t
e
ac
h
i
n
g

exce
l
l
ence

g
i
v
en
i
n t
h
e
U
ni
t
ed S
t
a
t
e
s
o
f
A
m
e
r
ica.