When a moving engine is on screen :
F3..F6 : Alter watch point.
F2 : Standard watch
point.
PAGE
UP / PAGE DOWN : Zoom. HOME : Standard zoom.
F7 :
Axes On / Off. F8 / F10 : Standard Data / New
Data.
CTRL
and F1 : Strange Arrangements. SPACE BAR : Counterweights.
CURSOR : Rhythm (LEFT : Standstill,
RIGHT : Standard, UP / DOWN :
Change).
CTRL
and one of CURSOR LEFT or CURSOR RIGHT or END : Plan views.
CTRL
and one of F8, F9 / F7: Alter / Standard step of rotation with F3..F6.
When a diagram is on screen:
F /
FF : Fourier Analysis of Bright / Dark curve (then C to recompose).
SHIFT or ALT and one of F1..F10 : Save shown curve or Recall saved
curve.
Moment or Torque around an axis is regarded
positive if a right hand thread screw, under its action, proceeds to said axis
positive direction.
EXAMPLES
**** Case of six cylinder in 60 degrees
Vee: With the standard data proceed
until Multicylinders in Vee and then give: 6 (for six cylinders), 135 (mm distance from cylinder axis to
next cylinder axis on same bank), 120 (degrees angle from crank pin No1, of
first bank, to No2, of first bank), 240 (angle distance from crank pin No1 of 1st bank to No3 of 1st
bank), 45 banks offset, 60 (degrees for the angle between the two cylinder
banks) and -120 (degrees for the angle
after TOP DEAD CENTER of first
piston of bank 2 when first piston of bank 1 is at TOP DEAD CENTER). See the
moving engine and the diagrams of inertia loads. Then press SPACE BAR to enter
"Counterweights". Make array seem like:
|
1 |
-135 |
150 |
.866 |
1 |
0 |
0 |
|
2 |
0 |
270 |
.866 |
1 |
0 |
0 |
|
3 |
135 |
30 |
.866 |
1 |
0 |
0 |
Then press END key and you will see again the
engine but with the selected counterweights secured to its crank. Look
the difference of inertia loads on the engine block (diagrams) compared to the case without counterweights
on crankshaft. Reenter "Counterweights" and add two more rows:
|
4 |
-165 |
90 |
.041 |
-2 |
0 |
90 |
|
5 |
165 |
270 |
.041 |
-2 |
0 |
90 |
Now press END key and you will see the engine
rotating with the selected counterweights secured to crankshaft and with a
balancing shaft located into the Vee and
rotated in opposite direction with twice crankshaft speed. As you can see again
in diagrams, this countershaft cancels the inertia moments that couldn't be
canceled with counters secured to crank..
**** Case of Vee 90, eight cylinder: When in Multicylinders in Vee,
give the next data: 8, 100, 90, 270, 180, 20, 90 and -90. See
the engine in motion and then
the diagram of the inertia loads
on the engine block. There is a great inertia moment. Now press SPACE BAR to enter "Counterweights"
and then make the array seem like:
|
1 |
-170 |
180 |
.5 |
1 |
0 |
0 |
|
2 |
-130 |
180 |
.5 |
1 |
0 |
0 |
|
3 |
-70 |
270 |
.5 |
1 |
0 |
0 |
|
4 |
-30 |
270 |
.5 |
1 |
0 |
0 |
|
5 |
30 |
90 |
.5 |
1 |
0 |
0 |
|
6 |
70 |
90 |
.5 |
1 |
0 |
0 |
|
7 |
130 |
0 |
.5 |
1 |
0 |
0 |
|
8 |
170 |
0 |
.5 |
1 |
0 |
0 |
and press END key to see the engine moving with the counterweights
secured to crankshaft.
**** The balance of the four in line conventional engine: Proceed
until the Multicylinders "in
Line" and give: 4, 100, 180, 180, 0. The four in line appears moving on
the screen, but as you can see in inertia loads diagrams, the engine suffers
from inertia Forces and Torques. Press SPACE BAR to
enter "Counterweights" and make the array seem like:
|
1 |
-150 |
180 |
.0668 |
-2 |
100 |
0 |
|
2 |
150 |
180 |
.0668 |
-2 |
100 |
0 |
|
3 |
-150 |
180 |
.0668 |
2 |
-100 |
157.2 |
|
4 |
150 |
180 |
.0668 |
2 |
-100 |
157.2 |
and
press END key to see again the engine moving with two shafts rotating in opposite direction with twice the speed of
crankshaft. As
you see in inertia loads diagrams, the mounts of the engine are now
substantially free from inertia loads...
**** Small single balancing: Proceed until Multicylinders in
Line and give 1 and ENTER. Then see the inertia loads diagrams. When you
see the "Total Torque on block" curve, press SHIFT and F1 key together to save
curve. Then press SPACE BAR and give:
|
1 |
-20 |
180 |
.25 |
1 |
0 |
0 |
|
2 |
20 |
180 |
.25 |
1 |
0 |
0 |
and
press END key to see the engine with the counterweights on it. See the inertia
loads diagrams. At "Total Torque on block" diagram press ALT and F1 keys. As you
can see, Torque on block is unchanged. Press SPACE BAR key to reenter
"Counterweights" and add one more row:
|
3 |
0 |
180 |
.5 |
-1 |
60 |
0 |
and then
press END key. Now you see the typical balancing of small single. When on Total
Torque diagram, press ALT and F1 together. As you see, there is a significant Torque
increase instead Force is decreased...
STRANGE
ARRANGEMENTS
****
Radial, even firing, five cylinder engine: When at Multicylinders press CTRL key
together with F1 function key. Make the array seem like:
|
1 |
-20 |
0 |
0 |
0 |
1 |
0 |
|
2 |
-10 |
0 |
0 |
0 |
1 |
144 |
|
3 |
0 |
0 |
0 |
0 |
1 |
288 |
|
4 |
10 |
0 |
0 |
0 |
1 |
72 |
|
5 |
20 |
0 |
0 |
0 |
1 |
216 |
and
press END key to see the engine moving. Then see inertia loads diagrams and then
press SPACE BAR to select two counterweights like:
|
1 |
-40 |
180 |
1.25 |
1 |
0 |
0 |
|
2 |
40 |
180 |
1.25 |
1 |
0 |
0 |
and see engine and diagrams...
****
Analysis of crankshaft main journals torsional inertia loads of the four in
line: At in
Line arrangement enter: 1. At Total Torque on Block Diagram save curve (SHIFT
together with F1 keys). With B go back to in Line engines and give: 2, 100,
180. At Total
Torque on Block Diagram save curve (SHIFT and F2). Go back to in Line engines.
Give: 3, 100, 180, 180. Save the Total Torque on Block curve (SHIFT and F3). Get
back to in Line engines and give: 4, 100, 180, 180, 0. At Total Torque on Block
press ALT and F3, ALT and F2, ALT and F1. On screen are shown the torsional inertia
loads of all loaded crankshaft's main journals. Inertia torsional loads of the
main journals of crankshaft for any cylinder arrangement can similarly be
computed...
Case of
V-10 in 90 degrees V-angle:
With the standard data proceed until Multicylinders in Vee
and then give: 10 (for ten cylinders), 100 (mm distance from cylinder axis to next
cylinder axis on same bank), 72 (degrees angle from crank pin No1, of first
bank, to No2, of first bank), 288 (angle distance from crank pin No1 of 1st
bank to No3 of 1st bank), 144 (angle distance from crank pin No1 of 1st
bank to No4 of 1st bank), 216 (angle distance from crank pin No1 of 1st
bank to No5 of 1st bank), 20 (for 20 mm bank to bank offset along crankshaft
axis), 90 (degrees for the angle between the two cylinder banks) and -72
(degrees for the angle
after TOP DEAD CENTER of first piston of bank 2 when first piston of bank
1 is at TOP DEAD CENTER, in order to have even firing). See the moving engine,
the offset of the crankshaft throws and the diagrams of inertia loads.
Then
press SPACE BAR to enter "Counterweights". Make the array seem like:
|
1 |
-200 |
-153 |
1.230 |
1 |
0 |
0 |
|
2 |
200 |
27 |
1.230 |
1 |
0 |
0 |
|
3 |
-200 |
153 |
0.195 |
-1 |
0 |
100 |
|
4 |
200 |
-27 |
0.195 |
-1 |
0 |
100 |
Then
press END key and you will see the engine rotating with the selected
counterweights secured to crankshaft and with a balancing shaft located into the
Vee and rotated in opposite direction. Why this specific arrangement of
crankshaft throws? Because with this arrangement result the minimum second order
inertia moment.
Case of
V-10 in 72 degrees V-angle:
With the standard data proceed until Multicylinders in Vee
and then give: 10 (for ten cylinders), 100 (mm distance from cylinder axis to next
cylinder axis on same bank), 72 (degrees angle from crank pin No1, of first
bank, to No2, of first bank), 288 (angle distance from crank pin No1 of 1st
bank to No3 of 1st bank), 144 (angle distance from crank pin No1 of 1st
bank to No4 of 1st bank), 216 (angle distance from crank pin No1 of 1st
bank to No5 of 1st bank), 20 (for 20 mm bank to bank offset along crankshaft
axis), 72 (degrees for the angle between the two cylinder banks) and -72
(degrees for the angle after TOP DEAD CENTER of first piston of bank 2
when first piston of bank 1 is at TOP DEAD CENTER). See the moving engine (now
the two banks share common crankpins and the engine is even firing) and the
diagrams of inertia loads.
Then
press SPACE BAR to enter "Counterweights". Make the array seem like:
|
1 |
-200 |
-162 |
1.245 |
1 |
0 |
0 |
|
2 |
200 |
18 |
1.245 |
1 |
0 |
0 |
|
3 |
-200 |
162 |
0.385 |
-1 |
0 |
100 |
|
4 |
200 |
-18 |
0.385 |
-1 |
0 |
100 |
Then
press END key and you will see the engine rotating with the selected
counterweights secured to crankshaft and with a balancing shaft located into the
Vee and rotated in opposite direction. Compare the inertial forces, torque and
moment to them of the V-10 in 90 degrees V-angle.
Case of
conventional I-5 (crank pins at 0, 144, 216, 288 and 72 degrees):
With the standard data proceed until Multicylinders in Line
and then give: 5 (for five cylinders), 100 (mm distance from cylinder axis to next
cylinder axis), 144 (degrees angle from crank pin No1 to No2), 216 (angle
distance from
crank pin No1 to No3), 288 (angle distance from crank pin No1 to
No4), 72 (angle distance from crank pin No1 to No5). See the moving engine
and the diagrams of inertia loads.
This arrangement is used in VOLVO five cylinders, in
Mercedes Diesels, in AUDI Diesels, in Alfa Romeo Diesels, in MAN Diesels
etc.
Now
press SPACE BAR to enter "Counterweights". Make the array seem like:
|
1 |
-200 |
126 |
0.057 |
1 |
0 |
0 |
|
2 |
200 |
-54 |
0.057 |
1 |
0 |
0 |
|
3 |
-200 |
-126 |
0.057 |
-1 |
100 |
0 |
|
4 |
200 |
54 |
0.057 |
-1 |
100 |
0 |
Now press END key and you will see the engine rotating with
the selected counterweights secured to crankshaft and with a balancing shaft
rotated in opposite direction. This arrangement is used in FIAT (Coupe etc).
Case of
conventional Straight Six:
With the standard data proceed until Multicylinders in Line
and then give: 6 (for six cylinders), 100 (mm distance from cylinder axis to next
cylinder axis), 120 (degrees angle from crank pin No1 to No2), 240 (angle
distance from
crank pin No1 to No3), 240 (angle distance from crank pin No1 to
No4), 120 (angle distance from crank pin No1 to No5) and 0 (angle distance
from crank pin
No1 to No6). See the moving engine and the diagrams of inertia loads. The six in
line is not so good as regards its inertial torque (remember: the inertia torque
of a straight six mounted along vehicle axis has the same direction with the
inertia moment of a transversely mounted straight five).
The case
of the I-5 with crank pins at 0, 72, 288 144 and 216 degrees:
It is exactly the order of the crank pins that makes the
difference.
With the standard data proceed until Multicylinders in
Line and then
give: 5 (for five cylinders), 100 (mm distance from cylinder axis to next
cylinder axis), 72 (degrees angle from crank pin No1 to No2), 288 (angle
distance from
crank pin No1 to No3), 144 (angle distance from crank pin No1 to
No4),216 (angle distance from crank pin No1 to No5). See the moving engine
and the diagrams of inertia loads. The first order inertia moment is heavy and
the second order is very weak.
Then
press SPACE BAR to enter "Counterweights". Make the array seem like:
|
1 |
-200 |
-162 |
0.6225 |
1 |
0 |
0 |
|
2 |
200 |
18 |
0.6225 |
1 |
0 |
0 |
|
3 |
-200 |
162 |
0.6225 |
-1 |
100 |
0 |
|
4 |
200 |
-18 |
0.6225 |
-1 |
100 |
0 |
Now
press END key and you will see the engine rotating with the selected
counterweights secured to crankshaft and with a balancing shaft rotated in
reverse. Compare the inertial forces, torque and moment to them of the best V-10
and to the conventional I-5.
Case of
V-90 degrees six cylinder (30 degrees offset of crank throws for even firing)
with a first order counterbalancing shaft (Mercedes etc).
With the standard data proceed until Multicylinders in Vee
and then give: 6 (for six cylinders), 100 (mm distance from cylinder axis to next
cylinder axis on same bank), 120 (degrees angle from crank pin No1, of first
bank, to No2, of first bank), 240 (angle distance from crank pin No1 of 1st
bank to No3 of 1st bank), 25 banks offset, 90 (degrees for the angle between the
two cylinder banks) and -120 (degrees for the angle after TOP DEAD
CENTER of first piston of bank 2 when first piston of bank 1 is at TOP DEAD
CENTER). See the moving engine and the diagrams of inertia loads.
Then
press SPACE BAR to enter "Counterweights". Make the array seem like:
|
1 |
-100 |
165 |
0.966 |
1 |
0 |
0 |
|
2 |
0 |
285 |
0.966 |
1 |
0 |
0 |
|
3 |
100 |
45 |
0.966 |
1 |
0 |
0 |
Then
press END key and you will see again the engine but with the selected
counterweights secured to its crank. Look the difference of inertia loads on the
engine block (diagrams) compared to the case without counterweights on
crankshaft. Reenter "Counterweights" and add two more rows :
|
4 |
-100 |
-15 |
0.22 |
-1 |
0 |
100 |
|
5 |
100 |
165 |
0.22 |
-1 |
0 |
100 |
Now
press END key and you will see the engine rotating with the selected
counterweights secured to crankshaft and with a balancing shaft located into the
Vee and rotated in opposite direction.
As you
can see again in diagrams, this countershaft cancels the 1st order inertia moment that couldn't be canceled with
counterweights secured to crank. What is left is the 2nd order inertia moment, making the engine worse than
the straight six.
Case of
V-60 degrees six cylinder, even firing.
With the
standard data proceed until Multicylinders in Vee and then give: 6 (for six
cylinders), 100
(mm distance from cylinder axis to next cylinder axis on same bank), 120
(degrees angle from crank pin No1, of first bank, to No2, of first bank), 240
(angle distance from
crank pin No1 of 1st bank to No3 of 1st bank), 40 banks offset, 60
(degrees for the angle between the two cylinder banks) and -120 (degrees for the
angle after TOP
DEAD CENTER of first piston of bank 2 when first piston of bank 1 is at TOP DEAD
CENTER). See the moving engine and the diagrams of inertia loads.
Then
press SPACE BAR to enter "Counterweights". Make the array seem like:
|
1 |
-100 |
150 |
0.866 |
1 |
0 |
0 |
|
2 |
0 |
270 |
0.866 |
1 |
0 |
0 |
|
3 |
100 |
30 |
0.866 |
1 |
0 |
0 |
Then press END key and you will see again the engine but
with the selected counterweights secured to its crank. This engine also lacks
smoothness compared to I-6 (with a second order moment counterbalancing shaft it
could be equal in smoothness to the I-6).
When in
Multicylinder arrangements press CTRL and F1 keys together, and then make the
array seems like:
|
1 |
-150 |
0 |
0 |
-7.5 |
1 |
-7.5 |
|
2 |
-90 |
0 |
0 |
127.5 |
1 |
7.5 |
|
3 |
-30 |
0 |
0 |
232.5 |
1 |
-7.5 |
|
4 |
30 |
0 |
0 |
247.5 |
1 |
7.5 |
|
5 |
90 |
0 |
0 |
112.5 |
1 |
-7.5 |
|
6 |
150 |
0 |
0 |
7.5 |
1 |
7.5 |
The engine is not as smooth as the six in line. With a first
order countershaft it becomes smoother but again not as smooth as the straight
six, as there is a second order inertia moment.
When in
Multicylinder arrangements press CTRL and F1 keys together, and then make the
array seems like:
|
1 |
-170 |
0 |
0 |
0 |
1 |
39,5 |
|
2 |
-150 |
0 |
0 |
26 |
1 |
-24,5 |
|
3 |
-50 |
0 |
0 |
165 |
1 |
24,5 |
|
4 |
-30 |
0 |
0 |
191 |
1 |
-39,5 |
|
5 |
30 |
0 |
0 |
180 |
1 |
39,5 |
|
6 |
50 |
0 |
0 |
206 |
1 |
-24,5 |
|
7 |
150 |
0 |
0 |
-15 |
1 |
24,5 |
|
8 |
170 |
0 |
0 |
11 |
1 |
-39,5 |
Press SPACE BAR and make the counterweights array seem
like:
|
1 |
-150 |
-85,5 |
0,1695 |
1 |
0 |
0 |
|
2 |
150 |
94,5 |
0,1695 |
1 |
0 |
0 |
Two counterweights are secured to the crankshaft to
counterbalance partially the first order moment.
Press SPACE BAR again to add two second order
counterweights:
|
1 |
-150 |
-85,5 |
0,1695 |
1 |
0 |
0 |
|
2 |
150 |
94,5 |
0,1695 |
1 |
0 |
0 |
|
3 |
0 |
-11 |
0,140 |
-2 |
100 |
-50 |
|
4 |
0 |
191 |
0,140 |
2 |
100 |
50 |
Again it is not as smooth as the ordinary V-8.
When in
Multicylinder arrangements press CTRL and F1 keys together, and then make the
array seems like:
|
1 |
-160 |
0 |
0 |
-7,5 |
1 |
-43,5 |
|
2 |
-100 |
0 |
0 |
127,5 |
1 |
-28,5 |
|
3 |
-40 |
0 |
0 |
232,5 |
1 |
-43,5 |
|
4 |
20 |
0 |
0 |
247,5 |
1 |
-28,5 |
|
5 |
80 |
0 |
0 |
112,5 |
1 |
-43,5 |
|
6 |
140 |
0 |
0 |
7,5 |
1 |
-28,5 |
|
7 |
-140 |
0 |
0 |
4,5 |
1 |
28,5 |
|
8 |
-80 |
0 |
0 |
139,5 |
1 |
43,5 |
|
9 |
-20 |
0 |
0 |
244,5 |
1 |
28,5 |
|
10 |
40 |
0 |
0 |
259,5 |
1 |
43,5 |
|
11 |
100 |
0 |
0 |
124,5 |
1 |
28,5 |
|
12 |
160 |
0 |
0 |
19,5 |
1 |
43,5 |
Press SPACE BAR and make the counterweights array seem
like:
|
1 |
-150 |
57 |
0,182 |
1 |
0 |
0 |
|
2 |
150 |
-123 |
0,182 |
1 |
0 |
0 |
Two counterweights are shown, secured to the crankshaft, for
counterbalancing partially the first order moments.
PATTAKON