DOING THE TWIST
Jake Venter looks at torsional vibration

Let's start by asking what at first seems to be a daft question. If your car's engine idles smoothly at 800rpm, what speed is the crankshaft doing? No, it's not 800rpm, except perhaps for a millisecond or two. The rev counter only reads 800rpm because it only registers an average value. The real instantaneous speed fluctuates, in the case of the four-cylinder engine graphed in on the right, between about 710 and 860rpm, during the course of one revolution.

Why does this variation happen? One of the reasons is that the flywheel cannot do a perfect job. It has been designed to smooth the individual firing pulses and speed variation as much as possible, but can only be successful within certain limits, as dictated by its dimensions. Another reason is torsional vibration, the winding and unwinding of the crankshaft caused by the varying forces acting on it. At certain speeds, the crankshaft even writhes like a snake in the free space between the main bearings, causing eventual bell-mouthing of the main bearings.

 These graphs show the deviations from (1) the theoretically correct angle. (2) the engine speed (measured on a re counter) and (3) the average angular acceleration of the crankshaft while a four-cylinder engine idles at 800rpm.

The design of a flywheel starts with a graph of the torque variation during the course of the two revolutions that it takes to complete one cycle of events, using the average engine torque at the chosen speed as a base line. With a four-cylinder engine, there will be four peaks, corresponding to the four power strokes. At these points the areas between the curves and the base line are called positive, to denote the fact that the combustion process inputs energy into the system. Between these peaks the curves will dip below the base line, sinking lowest during the compression stroke. These areas are labelled negative because energy is being withdrawn from the system. Adding up all the positive values and subtracting all the negative ones from the total will give the work done by the crankshaft in two revolutions.

At some of the points the graphs cross the base line from positive to negative - the torque input changes from positive to negative. These points correspond to maximum crankshaft speeds, whereas other crossover points where the torque changes from negative to positive, represent minimum crankshaft speeds. These speeds, and their fluctuation, as well as the fluctuation of energy, can be calculated from the graph, enabling the dimensions of a flywheel that will keep the speed fluctuations within certain limits to be chosen.

 An easy way to show how the torsional twist varies along the length of a crankshaft is to represent each crankpin assembly by a disc that has the same deflection properties. These curves show the amplitude of relative twist between the various crankpins during the course of one revolution. Note that the greater portion of the crank twists from clockwise to anticlockwise, while the flywheel and small portion of crank at the rear twist in the opposite direction. The node is the point of zero twist, ie it is the weakest point, and this is where a crankshaft usually breaks.

Since the amount of energy a flywheel can absorb - and hence give out - depends mainly on its diameter or more precisely, on the amount of material near the outer rim, a large diameter flywheel would seem to be more effective than a smaller one. Unfortunately, space and weight considerations come into the picture so that the dimensions of the average flywheel, like everything else on a car, are largely a matter of compromise. The speed variation results from the choice of a non-ideal flywheel is not enough to bother even the most fastidious motorist, but some of the effects, such as gear rattle, and even body boom, are subjects for continuing study by clutch and transmission engineers.

The dual-mass flywheel fitted to a number of upmarket engines, introduces extra mass into the system without increasing the flywheel diameter, in such a way that it also helps to dampen the torsional vibrations. Furthermore, the flywheel/starter/alternators that we will soon see on some luxury models will also help to curb unwanted vibration.

But let's return to torsional vibration, not only because it is such an interesting subject, but also because it is a phenomenon that can destroy or shorten the life of components. If we return to our engine idling at 800rpm we find that this speed is equivalent to 13.33r/sec, which means one revolution takes about 75 milliseconds.

Now for a look at what is happening in cylinder number one. The intake valves are open for about 240 degrees, or 50 milliseconds, during which time the flywheel inertia keeps the crank turning, and the major resistance to motion is the drag of the piston and rings. The compression stroke lasts for about 28 milliseconds, and the increasing force from the mixture being compressed slows the crank down considerably.

Just before top dead centre the spark occurs, initiating a rapid burning of the mixture that lasts for about 19 crank degrees, or four milliseconds. The crank feels this as a kick, delivered down the con-rod, which results in a distortion of the big-end journal and crank webs by a tiny fraction of a millimetre. The kick speeds up the motion of the crank, even before the steel has had a chance to spring back to its original state. The crank now accelerates, imparting fresh energy to the flywheel, and as the exhaust valve opens before bottom dead centre for about 50 milliseconds, the reduced resistance above the piston helps to shift more energy into the flywheel. The cycle of events now repeats itself in this cylinder.

 This is a Lanchester slipper-flywheel vibration damper, similar to the early Rolls-Royce damper.

Meanwhile, half a revolution, or 37.5 milliseconds, after number one cylinder has started down the intake strike, number three starts the same cycle of events, followed by cylinders number four and two at the same time intervals later. If the throttle is now opened wide, the size of the kicks will increase, as well as the frequency. As stated, at 800rpm the crank gets a kick every 37.5 milliseconds, but at 600rpm this changes to a kick every five milliseconds. The crank on a six-cylinder engine gets even less respite, being jerked every 3.33 milliseconds, at this speed.

But these are not the only shocks the crank has to endure. The crank also has to absorb the normal now-up now-down inertia loading due to the con-rods and pistons, which could easily amount to a ton on each cylinder. The net result is not only a speed variation in the crankshaft, but also the abovementioned distinction. The size of these crank movements depends to some extent on the shape of the crank, and the material used, but the length of the crank has by far the bigger influence on the torsional vibration. It is therefore no surprise that the phenomenon was first encountered on six-cylinder engines, and the cure was not easy to find.

The earliest cars had single-cylinder engines, but twins followed soon afterwards, and by the turn of the century a motorist could choose between one, two, three or four cylinders. Engine speeds were not much more than 1500rpm and engine smoothness was not a prime consideration. A low price and simplicity were the main selling points. Many motorists were against four cylinders, and the first sixes were considered ridiculously complicated, so much so that even eminent engineers were vociferous in their consideration of these complicated monsters.

The first six-cylinder car was exhibited in 1902 by the Dutch Spyker firm. It also had four-wheel drive and four-wheel brakes, but was never put into production. Soon after that, the sole selling agent for Napier cars, the never-reticent S F Edge, persuaded Montague Napier to build a six. Edge was thrilled with the prototype because of its smooth and even flow of torque, although he noticed a bad vibration at a certain speed, which he called a power-rattle to placate the customers.

 The figure shows the traces from a Summer's torsiograph, which records the angular speed variation as a change in radius; a vibration shows up as a wavy line. These readings were taken from the nose of a six-cylinder engine. Note that the bad vibration at 2025rpm is only 25rpm away from a smooth 2000rpm.

The first cars were sold in 1904, but the Napier engineers were not happy. They experimented with different ways to balance the engine, reduced the compression on the number six cylinder, and tried bigger diameter crank journals. Unfortunately, they never really stopped the power-rattle. Within a year other manufacturers were producing sixes, including Rolls-Royce, but it faced even worse - initially. One of the first cars produced broke a crank while out on test followed by two more within days, forcing Henry Royce to find a quick cure.

These early Rolls-Royce sixes had a normal flywheel at the rear as well as a smaller flywheel at the front, to curb a disturbing timing-gear rattle. Royce suspected that the crank was winding and unwinding between the flywheels, like a torsion bar. He realised that this constant reversing of the twist, or torsional oscillation, could easily break a crank in half. Royce lightened the crank by removing the balance masses, and reduced the front flywheel mass by half. This cured the problem, for the time being, by changing the critical speed of the assembly to a value greater than the speed the engine could attain.

During the experimentation, Royce had a wooden distance-piece made to fit between the crank and flywheel, which cured the timing gear rattle, but the steel production piece did not work. When Royce examined the wooden piece, he saw that the wood was charred on one side, which meant it was moving against the hold-down bolts. He immediately realised why it worked, and devised the slipper-flywheel vibration dumper, which was a feature of Rolls royce engines for many years. This incorporated two small flywheels that could move relative to a hub, mounted on the nose of the crank. Frictional material was introduced between the mating surfaces, so that any vibration of the crank would set the flywheels vibrating in opposition, forming an effective damper.

 A section through a modern Boge hydraulic vibration damper, which prevents the transmission of all kinds of vibrations. It is fitted between the engine-transmission unit and the chassis or floorpan.

Torsional vibration may have seemed mysterious to the pioneers, but it has been studied extensively since then. The preceding description details how the crank gets excited, but that is only a part of the picture. This excitation is harmful because of two other considerations. Firstly, the presence of a flywheel, so necessary to curb the normal speed fluctuation, actually accentuates the torsional vibration. The flywheel's inertia literally acts like a millstone towards the vibrating crank. The result can be imagined if you picture the crank as torsion bar, twisting hither and thither against the unyielding flywheel. It is no wonder that on most crankshafts the vicinity of the rear main bearing is the weakest point. When passenger car engines are adapted for trucks, the fitting of a heavier flywheel sometimes results in the crank twisting off just in front of the flywheel.

The second accentuating factor is that every object has a natural vibration frequency that depends on the material itself and shape, ie every object behaves like a tuning fork if a sudden force is applied to it. Most crankshafts are strong enough to withstand the torsional vibration, considered as a lone phenomenon. However, as soon as the frequency of the exciting force approaches the natural frequency of the crankshaft, the amplitudes - the magnitudes of the displacements - grow to such an extent that a breakage becomes almost inevitable. The phenomenon is known as resonance, and the engine speed where this occurs is known as the major critical speed.

 These curves show how effective a good damper can be, by contrasting an undamped vibration (1) with the effect of a rubber damper (2) and a viscous damper (3).

Resonance can be avoided by either damping the system, or by making sure that the engine cannot be run at the major critical speed. The shortness of four-cylinder cranks results in a major critical speed of well over 9000rpm, so that a torsional damper is not essential on a four. It is still sometimes fitted to take care of the minor critical speeds. These are the speeds at which resonance of a lower amplitude occurs because the forces involved are smaller, or are damped by other induced vibrations.

The straight-eight engine, used extensively for racing between the world wars, resonates at about 3100rpm, where the forces are low enough to be dealt with, either by making sure the crank is robust, or fitting a damper, or having the power take-off in the centre of the crankshaft. In the latter case, the crankshaft behaves like two four-cylinder cranks. V8s and V6s have shorter cranks, but modern designs are fitted with dampers. The six-cylinder engine is the difficult one, with a major critical near 5000rpm, where the forces are high enough to render a good damper essential.

Modern vibration dampers belong to one of four basic designs.
The Lanchester-type damper, uses the friction in two sets of multiple disc plates to curb the vibration. One set of discs is internally splined to the hub, and the other set is splined externally to a heavy inertia ring. The whole design looks very much like a multiple-plate motor cycle clutch. The friction discs are lightly squeezed together by six evenly spaced coil springs, and the assembly is submerged in oil. The relative slip between the many pairs of surfaces dissipates the vibrational energy.

The solid friction damper is very much like the Rolls-Royce damper. It uses the friction between two flywheels and the hub to dampen the vibration.

The viscous fluid damper uses a silicon fluid that changes very little with temperature, enclosed in a steel casing, to drag an annular ring with it when there is no vibration. When a vibration occurs, the shearing forces in the fluid damp it.

The tuned rubber vibration damper has a rubber mass interposed between an outer inertia ring and a central hub. The action is similar to what would happen were another mass attached to the crank by means of a rubber band. That is, the original vibration frequency is replaced by another (much smaller) vibration frequency, above and below the original frequency.

The critical aspects may cause a rumbling noise in an engine due to backlash in meshing gear teeth, or due to pistons pounding from side to side in their clearances. The noise may be suppressed when the engine is cold and the viscosity of the oil is high. When the oil is hot the reduced damping capacity of the oil permits the noise to become audible. If the engine is run up to a high speed and the fuel supply cut off, so that the engine has to run down over its speed range, amy vibration period it goes through may be due to resonant torsional vibration.

In the USA there are a number of aftermarket vibration dampers. Engine tuners are as fussy about choosing the correct damper for their particular application as they are about choosing the correct manifolds. A good damper will not only prolong engine life, but will also help the engine to deliver more power.

Author: Jake Venter
Source March 2002

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