It is a step by step analysis of the reciprocating engines' mechanism.
An approximation of the unbalanced inertia loads (force, torque and moment) in typical (in line and in Vee) and strange (in star, in W etc) cylinder arrangements.
Easy 'Fourier' analysis and resynthesis of the loads mentioned.
Addition and modification of counterbalancing shafts (of any kind and speed) and check of their effectiveness in vibration reduction.
Actually a calculator specifically made for reciprocating engines, a tool for that one who needs to understand what is going on inside engine.
With a moving engine on screen use:
F3..F6 function keys of keyboard to change watch point.
F2 function key for standard watch point.
PAGE UP / PAGE DOWN keys for zoom.
HOME key for standard zoom.
F7 function key for Axes-On / Axes-Off.
F8 / F10 function keys for "Standard Data" / "New Data".
CTRL key together with F1 function key: Strange Arrangements.
SPACE BAR key: Counterweights.
ARROWS keys: Rhythm (LEFT : Standstill, RIGHT : Standard, UP / DOWN : Change).
CTRL key together with one of LEFT ARROW or RIGHT ARROW or END : Plan views.
When a diagram is on screen press F key once (or twice) for the "Fourier Analysis" of the Bright (or of the Dark) curve. Then press C key as many times as necessary to recompose the curve from its harmonics.
Use SHIFT key (or ALT key) together with one of F1..F10 keys to save in memory the selected curve (or recall a previously saved curve).
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:
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:
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 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:
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...
**** Case of four in line with crossplane crankshaft technology ( Yamaha re-invented this arrangement with its R1 2009 model ): Proceed until the Multicylinders "in Line" and give: 4, 100, 90, 270, 180. The four in line appears moving on the screen. There is a heavy unbalanced first order inertia moment. Press SPACE BAR to enter "Counterweights" and make the array seem like:
and press END key to see again the engine moving with balance-webs on its crankshaft and one 1st order counter-rotating balance shaft. Now the inertia balance of the unconventional four in line is better than the balance of a V-8 in 90 degrees. The absence of inertia torques (just like in the case of the four cylinder V-90 with crankpins at 0 and 180 degrees) leaves only "net" power pulses to pass through the gearbox to the rear tyre, and this makes the difference. The un-even firing is a side-effect.
**** Case of four cylinder boxer engine.: Proceed until the Multicylinders "in Vee" and give: 4, 120, 0, 180, and then 40, and then 180, and then 0. The boxer four appears moving on the screen. The forces are completely balanced. The unbalanced second order inertia torque is as high as in the conventional four inline. And there is an unbalanced second order inertia moment.
**** Case of Vee 90, four cylinder with crankpins at 0 and 180 degrees ( like some versions of Honda VFR ): When in Multicylinders in Vee, give the next data: 4, 120, 180, 20, 90 and -90. See the engine in motion and then the diagram of the inertia loads on the engine block. Now press SPACE BAR to enter "Counterweights" and then make the array seem like:
and press END key to see the engine moving with the counterweights secured to crankshaft. There is a significant unbalanced 2nd order inertia force (70% of the unbalanced inertia force of the conventional four in line). With significant 2nd order unbalanced forces and uneven firing, the absence of inertia torque leaves only "net" power pulses to arrive to the rear tyre, and this gives the feeling of like "turbine", as described by journalists, operation.
**** Case of Vee 90, four cylinder with crankpins at 0 and 360 degrees ( like some other versions of Honda VFR ): When in Multicylinders in Vee, give the next data: 4, 120, 0, 20, 90 and -90. See the engine in motion and then the diagram of the inertia loads on the engine block. Now press SPACE BAR to enter "Counterweights" and then make the array seem like:
and press END key to see the engine moving with balance webs secured to the crankshaft. There is a significant unbalanced 2nd order inertia force (70% of the unbalanced inertia force of the conventional four in line). There is also a relatively strong unbalanced 3rd order inertia torque (press F key for Fourier analysis when the inertia torque diagram is on screen) and a relatively strong 1st orded inertia moment.
**** Case of three cylinder in line: With the standard data proceed until Multicylinders "in Line" and then give: 3, 100, 120, 240. See the moving engine and the diagrams of inertia loads. Then press SPACE BAR to enter "Counterweights". Make array seem like:
Then press END key and you will see again the engine having the selected counterweights secured to its crank. Reenter "Counterweights" and add two more rows:
Now press END key and you will see the engine rotating with the selected counterweights secured to crankshaft and with a counter-rotating 1st order balance shaft.
**** Case of conventional Vee 90, eight cylinder ("crossplane" crankshaft): 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 make the array seem like:
and press END key to see the engine moving with the counterweights secured to crankshaft.
**** Case of Vee 90, eight cylinder with "flat" crankshaft (used in some sport and racing engines): When in Multicylinders in Vee, give the next data: 8, 100, 180, 180, 0, 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 unbalanced inertia force of 2nd order, vertical on the Vee bisecting plane. Now press SPACE BAR to enter "Counterweights" and make the array seem like:
and press END key to see the engine moving with two counter-rotating with double crank speed) balance-weights.
**** Case of two cylinder in line, crank-pins at 0 and 180 degrees: With the standard data proceed until Multicylinders "in Line" and then give: 2, 100, 180. See the moving engine and the diagrams of inertia loads. Then press SPACE BAR to enter "Counterweights". Make array seem like:
Then press END key and you will see again the engine having the selected counterweights secured to its crank. Reenter "Counterweights" and add two more rows:
Now press END key and you will see the engine rotating with the selected counterweights secured to crankshaft and with a counter-rotating 1st order balance shaft.
**** Case of two cylinder in line, crank-pins at 0 and 360 degrees (like the old TDM of Yamaha) : With the standard data proceed until Multicylinders "in Line" and then give: 2, 100, 0. See the moving engine and the diagrams of inertia loads. Then press SPACE BAR to enter "Counterweights". Make array seem like:
Then press END key and you will see again the engine having the selected counterweights secured to its crank. Reenter "Counterweights" and add four more rows:
Now press END key and you will see the engine rotating with the selected counterweights secured to crankshaft and with a counter-rotating 1st order balance shaft.
**** Case of two cylinder in line, crank-pins at 0 and 90 degrees (like the new TDM of Yamaha) : With the standard data proceed until Multicylinders "in Line" and then give: 2, 100, 90. See the moving engine and the diagrams of inertia loads. Then press SPACE BAR to enter "Counterweights". Make array seem like:
Then press END key and you will see again the engine having the selected counterweights secured to its crank. Reenter "Counterweights" and add four more rows:
Now press END key and you will see the engine rotating with the selected counterweights secured to crankshaft and with a counter-rotating 1st order balance shaft. The small inertia torque of this arrangenet (similar to the inertia torque of the V-90 two cylinder) makes the difference. The un-even firing is a side-effect.
**** Case of two cylinder in Vee 90 degrees (like Ducati): With the standard data proceed until Multicylinders "in Vee" and then give: 2, 20, 90, -90. See the moving engine and the diagrams of inertia loads. Then press SPACE BAR to enter "Counterweights". Make array seem like:
Then press END key and you will see again the engine having the selected counterweights secured to its crank.
The un-even firing is a side-effect.
**** Case of two cylinder boxer engine.: Proceed until the Multicylinders "in Vee" and give: 2, 40, 180, 0. The two cylinder boxer appears moving on the screen. The forces are completely balanced. The unbalanced inertia torque equals to that of the conventional two cylinder inline with crankpins at 0 and 360 degrees. There is an unbalanced inertia moment (of first and second order). To balance the first order inertia moment, press SPACE BAR to enter "Counterweights", and make the array like:
**** Case of single cylinder: 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:
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...
**** 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:
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:
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:
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).
**** Case of six cylinder boxer engine.: Proceed until the Multicylinders "in Vee" and give: 6, 120, 120, 240 and then 40, and then 180 and then 0. The boxer six appears moving on the screen. The inertia forces are completely balanced. The inertia moments are completely balanced. There is an unbalanced inertia torque of third order, equal to the unbalanced inertia torque of the six in line. I.e. the boxer six is isentical, as regards its inertia vibrations, to the six inline.
**** Case of in line five (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:
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:
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 :
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 VR6 of VW
When in Multicylinder arrangements press CTRL and F1 keys together, and then make the array seems like:
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.
**** Case of W8 of VW.
When in Multicylinder arrangements press CTRL and F1 keys together, and then make the array seems like:
**** 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...
2. RoadLoad program
Click here and download/save all the files you see in a folder of your computer. With this program you can see the relation between the used gear ratio, the speed of the vehicle and the force which is applied to the vehicle and passengers from the road. You can compare the ROAD LOADS (as function of the used gear and of the vehicle velocity) of a number of vehicles all in the same graph.
You can compute the best point to change gear, the effect of hard use instead of soft use of the clutch etc, etc.
Keep always in mind: this is an effort to APPROACH reality.
3. Harmonic program
Click here to download the harmonic.exe program
An internal combustion engine having pure sinusoidal motion of its pistons. The balancing of the single cylinder prototype is so perfect that it can stand free on the ground operating from idling to top revs (24 m/sec mean piston speed) without any tend to leave its place.
The slow motion of the piston at TDC improves the combustion. The absence of thrust load on cylinder wall (and so the absence of piston skirt) is a characteristic. The short height compared to conventional of same stroke, is another one.
Photos of the single cylinder prototype (one with a beautiful blue flame coming out of the exhaust port) can be found in the Pulling Piston Engine Analysis.
The above applications were created using QuickBasic under MSDOS, around 1990. It is hoped they will help students, mechanics, engineers etc, to deeply and easily understand the way things work.
To Download or Open a program: mouse click on the relevant title.
To Quit a running program: press ESC key on keyboard.