From the December 1945 Issue of Motorcyclist magazine
Note: We are reprinting this article by Uncle Frank from our April, 1937, issue due to the demand we have had for back issues of this particular copy. Extra copies of this reprint are available by writing The Motorcyclist, 947 Bendix Building, Los Angeles 15, enclosing 15¢ for each copy. The April, 1937, issue is definitely a collector s’ item due to no extra copies remaining in our files.
This subject is so deep in mathematics and theory we would have to wade in with hip boots to understand it. We will try, however, to give you the elements of motor balancing as simply as possible. You need never worry about your stock motor balance as it was received from the factory because the motor was balanced for best all around service. However, if the pistons are replaced with lighter pistons, then rebalancing might be in order. We might add that pistons two or three ounces lighter than original pistons may be fitted to a motor without rebalancing the wheels and still the motor would run quite smoothly. If we do need to rebalance a motor, then we have formulae and set rules to follow for satisfactory results.
The service for which a motor is intended has much to do with the plans adopted for balancing flywheels. We would not balance a standard type of motor as we would a very high r.p.m. racing or hillclimbing motor. The standard type motor must run reasonably smooth at both extremes of speed, low and high. Whereas the racing motor functions more or less at full open throttle its low speed balance need not be considered. In fact, racing singles actually gallop at the lower speeds.
Inherent Forces Which Make Balancing Necessary
Due to the complex nature of the working members in an internal combustion motor we must consider four things when balancing such a motor.
1. The unbalanced rotating parts
2. The unbalanced reciprocating parts
3. Torque reaction
4. Torsional flexibility of flywheels (crankshaft)
The object in balancing a motor is to try and cancel out the forces which would make excessive and objectionable vertical and horizontal vibration. It is impossible to balance any motor perfectly! This is an impossible feat because of the complex forces which vary with the two extremes in a motor’s speed, setting up vibration harmonics. Vibration occurs when a mass in motion is interrupted or varied.
Engineers can, however, strike a happy medium in balance which will give a very satisfactory motor with out objectionable vibration.
The crankpin, nuts, washers, rollers, roller retainers and the lower half of the connecting rod make up the rotating mass in a motor. Naturally this revolving mass creates much centrifugal force. It would be rather easy to provide a counterweight to offset such a mass by adding weight on the opposite side of the crankpin. Thus, mechanical balance could be perfected. But we have more than rotating mass to deal with. The constantly varying force of the reciprocating mass sets up a harmonic that must be balanced to reduce vibration so that it is not objectionable. Since the lengths of the connecting rod, the stroke of the motor and the maximum r.p.m. all have to do with balance, these must be considered along with the weight of the reciprocating parts. Compression ratio is also a factor considered in balance formulae.
The pistons, rings, pins, locking rings and the upper half of the rods are considered as reciprocating parts. These parts make up a mass weight that is difficult to off set because this weight moves inward and outward (to and fro) and at varying speeds from zero to maximum and back to zero again, twice for each revolution of the flywheels. The pistons actually stop at both top and bottom dead centers, then change their direction of travel. Their rate of travel is, therefore, constantly variable. A motor that is running 3000 r.p.m. would cause each piston and rod to make 6000 strokes per minute. Where one revolution of the flywheel would require but 1/50 second, each piston stroke would be only 1/100 second of time in duration. We can appreciate that this terrific reciprocating action must be offset by balance by some opposite force, else the motor would jump out of the frame.
Since only the upper half of the connecting rod is considered as reciprocating mass, then the lower half tends to revolve with the crankpin and add weight to the rotating mass creating more centrifugal force. The action of the connecting rod is peculiar in that it starts from zero (dead center in the cylinder and crankshaft plane) and reaches a maximum speed of travel when it is at right angles (90°) to the crank throw. If we were to plot a curve of the mass movement of the rod we would develop a sort of pear-shaped design with the weight or body increasing toward the crankpin rotation. The center of the rod describes an elliptical orbit in its motion.
Most formulae call for balancing one half of the reciprocating mass. In practice, however, this may vary from .45 to .82 of the reciprocating mass weight. As already mentioned, the actual balancing weight selected depends upon the purpose for which the motor was designed.
By studying the figures in Illustration No. 2, you will get a fair idea of how the mass weight of pistons and rods is acted upon by the revolving mass weight of the flywheels. Note, especially, the position of the pistons when either rod is at right angles with the crank throw.
Besides the to-and-fro motion of pistons and rods and the revolving flywheel counterweight, we have the side thrust of the pistons against the cylinder walls on explosion and compression strokes to consider. When pressure is exerted on the piston head due to the combustion in the power stroke, the piston is forced violently against the side of the cylinder. At the same time, there is the outward force on the rod, driving the flywheels. The tendency of these torque reactions is to cause the cylinders to sway back and forth, vibrate. To check torque reaction we must have strong crankcases and heavy cylinders securely mounted in a rigid frame. Thus the motor mounting has much to do with controlling vibration
Torsional Flexibility of Flywheels
This means simply the tendency of flywheels to weave or flex under the extreme pressure of combustion and compression. These rapid changes, however, set up a sort of vibrating couple, lateral in its action. Only very strong flywheels will minimize this torsional force. Excessive vibration at this point will tend to break the flywheels or crankpin.
A Study in Counterweights
Referring to Fig.1, in the Illustration No.1, we see a ball “W” revolving at the end of a rod. This revolving ball is unbalanced in that no equal weight is located on the opposite side of the shaft center. Therefore, the centrifugal force sets up an outward pull with the consequent eccentricity of rotation. Vibration will result. In Fig.2, we see a flywheel with a counterweight “W” which would act the same as the ball just described in rotation. Such a weight must have a counter weight to balance it. Fig.3 shows two weights, “W” and “W1” mounted on opposite sides of a shaft center. Of the two weights, “W1” is the heavier. Naturally centrifugal force would be in favor of this heavier weight. This sketch may be likened to the flywheel, rod and piston shown in Fig.4 a simple single cylinder motor. In actual practice the piston, rings, pin and upper half of the rod do weigh more than the counterweight “W”. If revolved in the same plane, that is, just let fly around this mass would be considerably out of balance. We must remember, however, that part of the weight is reciprocating and part rotating and the two masses tend to cancel each other, anyway enough to effect fair running balance of the motor. The single-cylinder motor with its lack of power impulses, is the most difficult motor to balance. Only very high r.p.m. singles can be balanced nicely at top speeds.
The Vee-type Twin Engine
In the Vee twin motor we find two sets of reciprocating parts moving at almost right angles to each other. This angularity varies with the degree at which the cylinders are located from each other. While one set of parts is moving up and down vertically the other is more or less in a horizontal (back and forth) motion. Study Figs.2 and 3 in Illustration No.2 for graphic explanation. Thus, these dual reciprocating masses more or less combine to make a radial force (centrifugal force) which can be quite satisfactorily balanced by counterweights placed opposite the crank pin. With the unequal motions of the two sets of reciprocating parts in a Vee twin there is sort of dampening effect which is beneficial to smoothness of operation.
In Fig.1 we see both rods held halfway between the cylinder center lines. Thus, the pistons are not quite at top dead center. We can also see that at no time will both rods be in line with each cylinder center line. At this point the rotating mass is at its highest peak, both rods are practically stationary. The resultant force would, therefore, be in a horizontal plane. But this does not last long, for soon both reciprocating members are in motion, thus breaking up the horizontal vibration. In Fig.6, Illustration No.1, we see a series of arrows emanating from a common center. These arrows approximate the direction of forces set up in a Vee twin, the object being to cancel all vertical and horizontal forces, thus breaking up the vibration harmonics.
Referring again to Illustration No.2 Fig.2, we see the rear piston descending until its rod is at right angles (90°) with the crank throw. At this point the piston speed is greatest. The actual location of this point during flywheel rotation depends, of course, upon length of connecting rod and stroke, or throw of crank. Note that while the rear cylinder is pretty well down in its travel, the front cylinder rod and piston are lagging behind. In Fig.3, we see the same rod when it has reached right angles with the crank throw on the upward stroke. Again note the angle of the front cylinder rod. Lower dead center for both rods is approximated in Fig.4. Here again, the mass weight of the reciprocating parts is almost at zero. And in this particular position, the upper section of the rods is in motion against the rotation of the flywheel revolving weights. Here again, opposite forces tend to cancel out vibration.
The ideal balance would be theoretically obtained with a horizontally opposed (180° cylinders) motor with rods and cylinders in perfect alignment, in the same plane. Here outward and inward masses would be cancelled by the constant reverse motion of the pistons.
Balancing in Practice
In practice, we find it possible to balance a twin motor, or a single for that matter, by offsetting two-thirds of the reciprocating parts’ weight. Harley-Davidson motors have been balanced very satisfactorily with this method. This means that the pistons, rings, pins, locking rings, rods (with bushings), crankpin, rollers, retainers, nuts, locking washers and screws were weighed. One-third of this weight is taken and used to balance EACH of the flywheels. Thus, two-thirds of the reciprocating mass is balanced. The wheel with the determined weight, located in crankpin hole, is placed on true and level rails and the rim drilled at the proper point to allow the wheel to remain stationary in any position.
For very high speed motors, it is advisable to allow the counterweight side to be slightly heavier (2 or 3 ounces) than for stock motors. In other words, the reciprocating mass is lighter and the revolving mass is heavier.
Indian balancing may be done by using one rod with piston and rings, and one rod with piston removed, the flywheels then drilled to make this mass balance at any position on level test rails.
For a complete formula and illustration on flywheel balancing, we would refer you to the Question and Answer Book, pages 52 to 57 inclusive under Question No. 73. If you are interested in the mathematics of motor balancing, then refer to the work of Dalby’s “Balancing of Engines”, A.W. Judge’s “Automobile and Aircraft Engines”, or Ricardo’s “Internal Combustion Engine”. These are all English publications and may be obtained at larger libraries. End.