Vibrations in 3 cylinders engines

Three-cylinder engine

If you have ever driven a car with a 4 cylinders engine and 3 cylinders one, maybe you felt that in the second case more vibrations are transmitted from the engine to the car; furthermore, the engine torque is less smooth. On older three-cylinders engines this difference can be also eared.

Of course, a part of this issue is due to one cylinder less respect to a four-cylinder engine, with a more variable engine torque as result.

In this post I would like to focus on another aspect, maybe less intuitive than fire spacing, but as much important: engine balancing, strictly related to engine vibrations.

First and second-order forces and moments

Forces and vibrations

Let’s start with the more simple forces to visualize. Looking at the picture and imagine the dynamic mechanism, we can guess that a centrifugal force acts on the connecting rod big end.

Without talking about mathematical details, it is shown that alternative forces generated during the combustion phase can be expressed with the following mathematical expression:


This formula means that the generic alternative force is a function of crank angle $\theta$, so its module is variable. In particular, it can be thought as a sum of two forces (of which we take only the projection on cylinder axis): the first one variable as the crank angle, the second one as the double of the crank angle. They are respectively first order and second-order forces, that create first order and second-order moments.

Why are they so important? Because if not balanced, vibrations are transmitted to the chassis.

First-order forces and moments on three cylinders engine

balancing masses vibrations in three-cylinder crankshaft

Let’s analyze in-depth the forces in using the image above. Cylinders are all in line and cranks are equally spaced each other by 120°. If we consider centrifugal forces, it is easy visualized that they have the same intensity and form a closed triangle: this means that are equilibrated themselves. Also first-order reciprocating forces are in the same condition, so another closed polygon of force is created and they are self equilibrated. In the following picture we can see this condition, where cylinder n°1 is taken as reference.

Primary forces

The same result is obtained if crank angles are calculated each one respect to the corresponding cylinder axis. In order to repeat the analysis on second-order forces, we just need to double the angle values, obtaining the following scheme.

secondary forces

As we can see forces on cranks n° 2 and n°3 are inverted, so the polygon remains closed and forces are self equilibrated.

Vibrations reduction: moments balancing

I order moments

The analysis of moments needs more attention. If we evaluate the equilibrium respect to point 2, we obtain the following scheme, more readable if we have a look also to the initial engine scheme:

Primary moments

Force $F_{1,p}$ create a moment $F_1C$ around point 2; force $F_{3,p} $ create a moment $F_3C$. The balancing of this moment needs an additional moment $\sqrt{3}FC$. How is it possible to create this? One solution is the use of two additional masses on the crankshaft, spaced by 180°, with a double effect: the total balance of centrifugal forces, the moment of which points in the same direction as the first-order one, and balance the last one. This solution has a problem: consider cylinder n°1 for simplicity. The intensity of reciprocating forces (that generates the moment) is a function of crank angle, instead the intensity of the balancing moment is always the same. It means that a part of the balancing moment became an imbalance! If we accept to balance only a part of the first-order moment the solution is to add the masses in order to balance totally centrifugal forces and only half of first-order moments. This is a compromise solution between balancing and simplicity.

Alternative balancing

Another (more efficient) solution is the following: If we consider the compromise solution previously analyzed, it is possible to add a countershaft rotating at the same angular speed of the crankshaft but in opposite direction, and adding two additional masses on it is possible to balance the remaining half part of the unbalancing moment without any additional negative effect. Of course, this is a more complicated solution, in terms of engineering and production.

II order moments

The analysis is the same as the previous, so we can calculate moments respect to point 1. Also this system needs a balancing moment $\sqrt{3}Fc$.

Secondary moments

Despite the previous case, now is impossible to try to balance second-order moments using the crankshaft in anyway, because they change direction as twice the crank angle. A solution is to add two countershafts with balancing masses, rotating at twice the angular speed of the crankshaft, counter-rotating respect each other.

There are many disadvantages in the use of this solution. It is an important complication in the engine design, friction is increased (organic efficiency reduced) and the balancing of the secondary moment is less important than the primary moments one, because the intensity is lower.

The four cylinders engine, for example, needs to be balanced only respect to first-order reciprocating forces, using two countershafts with the same angular speed of the crankshaft.

Vibrations balance in four-cylinder BMW

The six-cylinder engine is inherently self-balanced, both statically and dynamically; in this way no vibrations are transferred to the chassis.

The following video shows how countershafts are composed and where are mounted in a four cylinders engine.

G-Vectoring Control Plus

Mazda GVC+
Mazda GVC+


In this post, we’ll have a closer look to a new control technology announced by Mazda few months ago. Its name is G-Vectoring Control Plus (GVC+), also known as G-Vectoring Moment Plus Control (GVC Moment Plus), an extension of the widely used GVC in Mazda vehicles.

Furthermore, we will explain why the car is easier and more safety to drive for the driver in terms of vehicle dynamics behaviour.

G-Vectoring Control (GVC) as the basis

Mazda G-Vectoring Control

The basic control technology is the already used GVC. It helps the driver to use less steering wheel angle in turn-in and turn-out using the engine torque in order to change the vertical loads on front/rear tires.

When we push or release the throttle pedal on our car we change the amount of torque produced by the engine; the effect is a change in longitudinal acceleration and so a longitudinal load transfer. When we approach a corner (especially mid-speed corner) and we start to move the steering wheel, the system recognizes we are in turn-in and cut a little of engine torque, transferring more vertical load on the front axle. The effect is a higher lateral force on front tires and a less understeering vehicle. The driver’s feeling is a more direct/precise steering wheel. In turn-out, when the steering wheel angle starts to reduce, the system works in the opposite way and the vehicle becomes more stable, i.e. more understeer on turn exit. It is able to recognise in which of the two states the vehicle is.

G-Vectoring Control Plus

On the GVC Plus a direct yaw rate control system is added using brakes.

In this evolution the systems work together: the “old” one during turn-in, and the new one during turn-out, applying brake torque on the front outer wheel in order to generate a yaw moment that enhances the vehicle attitude to follow a straight line path.

Also in this case the effect on driving is a more direct steering wheel feeling and a more safety driveability. The latter aspect is visible also during emergency manoeuvres, for example, a fast line change or double line change, where the effect of GCV Plus allows a faster e more safety trajectory change associated to a lower amplitude of the steering wheel angle. This means that to the driver more reaction time is allowed.

Because the system generates longitudinal and lateral accelerations, it works also to allow a smoother transition, with the feeling of more fluid driving experience.

Grip – European tire label


In the previous post we have looked at some aspects related to tire rolling resistance, strictly related to fuel consumption.

The same phenomena are also strictly related to the tire ability to generate grip, although their influence takes two opposite directions in these two cases. So, the more is the tire hysteresis, the more is the grip, but at the same time the fuel consumption of the car is higher.

Just to clarify: the grip class on the European tire grip is an information about the grip on wet surface.

How grip is created?

As already described, in the post about the influence of the tire on fuel consumption hysteresis was described. Because it is the main reason of grip generation, it can be useful revise the concept avoiding repeating it now.

Grip is composed by three phenomena:

  • Local deformation;
  • Adhesion;
  • Wear.
grip tire


First contribute: let’s imagine a rubber block sliding on a surface perfectly lubricated with some roughness. If we could see the interaction between rubber and surface we would see the picture highlighted as “deformation” known also as “indentation”. Due to hysteresis the pressure distriubution around the obstacle is not symmetrical, so a force opposite the motion direction is created. The relation between grip and rolling resistance is direct: the greater is the hysteresis, the greater are grip and rolling resistance.

Second contribute: let’s imagine now the same rubber block sliding on a surface perfectly dry without roughness. In this case the rate to grip is given by adhesion, i.e. the molecular interactions between rubber and the surface, better known as Van der Waals. The nature of these forces is the same of that ones that maintain a solid body as such but with a very lower intensity, giving however a significant contribution to grip generation.

The last contribute not always is highlighted. Maybe it is significant when we talk about racing tires, where a locally excessive compound deformation generate its laceration and so an increased energy dissipation whith an increasing on grip.

What is the grip influenced by?

Many factors affect tire grip, so there is no a single friction value. The following parameters affect mainly the grip:


The molecular structure of tire tread can assume two configurations: glassy if molecules behaves like the glass (stiff but fragile); or amorphous (the compound is soft and flexible). We can guess that at low temperatures the compound behaves like the glossy state, at high temperatures it behaves as amorphous. There is a big difference between these two configurations in terms of mechanical characteristics, and in the transition region (very narrow) the grip is maximum (and the maximum hysteresis). From that we can guess why is not recommended to use a summer tire in winter, because the tire wear would be excessive, and the vice-versa, because the grip would be too low than the one generated by a summer tire.


The understanding of the influence of this phenomenon is less immediate. Fortunately there is a mathematical relationship between it and temperature, in fact at the same temperature if the frequency is higher the molecular structure of the compound moves toward the glossy state and vice versa.

Type of road surface

The road roughness, divided in macro and micro, modify the way in which the compound moves between unevenness, modifying the grip level. The adhesion level is influenced by the road condition, id it is dry or wet, as already mentioned.

What happen on wet road?

The ability of the tire to maintain a good grip on wet road is due to the capability of the tread to drain the wates as well as possible in order to offer a drain contact between the road and thread blocks, allowing the adhesion forces to work properly.

When we drive on a wet road the tires of the car push forward the water on the road. At first a small “wall” of water is created that counteract the motion of the tire. A certain amount of over pressure is generated proportional of the vehicle speed. If that pressure is the equal o greater than tire inflation pressure, the last one tend to be lifted, the phenomenon is known as aquaplaning.

How increase tire wet grip

Reducing the aquaplaning risk means increase the vehicle speed at which it starts, behalf some design method of tire tread.

The first point is that is useful to have an oval contact patch instead a rectangular, in order to drain the “wall” of water in a better way. In the second phase tread sipes (transversal channels) are useful to drain the water outward.

The residual water is finally removed by tread blocks and grooves that work in synergy: blocks push the water to go inside the grooves. Tread blocks dimensions should be the correct compromise between the ability to drain water and maintain enough stiffness. Furthermore, the role of the edges of the blocks is important because destroy the surface tension of the drops, ensuring the contact with the road as dry as possible.

In the reference legislation the tire grip on wet road is divided in 7 classes, from G (the worst) to A (the best). Just to quantify the difference, from the last to the first class the braking distance is reduced up to 30%.


Should be better to have a look at the European tire label ad think about what the classes mean, avoiding buying too cheap tires…first of all safety! Keep in mind that all the forces that act on your car are applied also on the road through tires. Sometimes few centimeters on braking distance are enough to avoid a crash.

Fuel consumption – European tire label


fuel consumption

In the previous post we talked about tire noise, we have deepened the causes and some solutions to reduce it.

Today we talk about the second mark in the European tire label, in particular how tires affect fuel consumption; this parameter is related with tire rolling resistance.

What is the origin of this resistance? Which parameters affect it? Let’s have a closer look.


Let’s go immediately to the central point: when the tire touches the ground (enters the contact patch), it is deformed by the reaction force of the ground. When it leaves the contact patch not all the energy received is released. This behavior is named as hysteresis of the material.

Hysteresis and fuel consumption

How can we imagine this behavior? What does this concept, maybe still conceptually empty, means? The secret is the viscoelastic origin of the material. Let’s imagine the tire compound as a dish of spaghetti; these are glued each other in some contact points. When an external force is applied to spaghetti, these tend to stretch, but being glued each other a total stretch is not allowed, so the external energy is stored as elastic one.

If gluing points were perfect, when external force is released all the elastic energy would be released too; but in the reality this in not like that because every spaghetto slides respect others and a part of energy is dissipated as heat. This is the reason why the material is called visco-elastic.

So when this dish of spaghetti touches the ground, part of energy is stored and then released, another part is lost as heat. Due to this effect the pressure distribution on the contact patch is not a symmetrical parabola, but the peak is slightly translated onward respect to the wheel rotation axis. The resultant vertical force generates a moment opposite to the driving torque.

Rolling resistance and fuel consumption

The main parts of the tire where energy dissipation is concentrated are:

– Thread: about 70%;
– Sidewalls: about 15%;
– Beads: about 15%.

In order to give some additional information, compared the global vehicle motion resistance, the rolling one has the following influence:

– 20% on highway;
– 25% on backroad;
– 30% on city road;

Parameters that influence fuel consumption

We can distinguish two categories: intrinsic parameters and the ones that can be controlled by the driver.

First group

In the first group of course we can find the compound “recipe”, that with its ingredients represented by natural rubber, styrene, butadiene, carbon black, silica, sulfur and so on, defines the hysteresis level for the finished product, also function of temperature and frequency of road unevenness.

Another important parameter is the thread thickness and void ratio that is related to tire grooves dimensions: the bigger are the channels, the greater are tread blocks deformations, so the more energy is dissipated as heat.

The tire diameter is another influent parameter because the bigger is it, the smaller is the tire bending on the contact patch at leading edge, having as consequence less deformation.

It is not possible work with these parameters, the only thing that we can do is look carefully the European tire label. In order to reduce fuel consumption we can buy “green” tires; working with some data we can consider that if we use a green tire instead “black” ones, we can reduce up to 30% of rolling resistance with a real fuel consumption up to 6%. These numbers are not the truth, but are useful to understand better the phenomena.

Second group

In this group we can find tire pressure, because if it is constantly maintained in the optimal range allows reducing fuel consumption.

Vertical load increase also the rolling resistance, at the same tire pressure. So if for example we take our car for a holiday with our family, and we put on it 2 bicycles, a canoe and the car is full of baggage the fuel consumption is higher also because the tire rolling resistance is higher.

High speed increases rolling resistance because tire is affected by strong waves and vibrations. In addition to being a low efficiency condition, it is also dangerous for the integrity of the tire.

How to reduce fuel consumption

reduce fuel consumption

Going directly to the target, in order to reduce fuel consumption we should read carefully the European tire label when we buy a new tire set and take care of its state, having a periodical inspection in order to check tire pressure and wear, also for safety reasons.

A higher class on the label may mean a tire with a lower hysteresis, but if fuel consumption is reduced, on the other side also grip is reduced, because it depends on the hysteresis too.

The higher class may mean a compound with less percentage of fillers as carbon black, but also in this case in the other side tire wear gets worse.

As usual the optimum is a compromise between what we need.

Tire noise – European tire label

Tire noise - European tire label

Buying a new tire set you may have seen a label like this.

It is just a summary of informations about the characteristics of the tire we are buying, in terms of fuel consumption, wet grip and sound emission.
This label is subjected to European regulations, and tire manufacturer must declare  tire class on three fields, defined behalf standard tests.
The difference between the last and the first class can be summarized as follows:

  • Fuel consumption: tests define tire rolling resistance coefficient. From G class to A the consumption is reduced by 7,5%;
  • Wet grip: From G class to A the braking distance is reduced by 30%;
  • Sound emission: one black wave corresponds to a silent tire, 3 waves indicate a noise one, and there is always the value in dB.

Let’s explore the three categories, starting with the sound emission.

Tire noise

Who have driven an electric car, will have noticed that when the car stops there is no sound…is very difficult understand if it is on or off.
The “sound” changes when the speed increase, the driver is able to listen the aerodynamic and tire noise.
Why tires are noisy? Which are the main reasons?

Sidewall vibrations

Tire noise from sidewalls pumping

During wheel rotation, the tire portion that touch the ground entering the contact patch causes tire deformation.
One of the main parts involved in this deformation process are the sidewalls, due to their lower stiffness compared to the other parts of the tire.
When this region leaves the contact patch, the corresponding portion of the sidewall return to its undeformed shape.
This cyclic deformation create pressure waves in the air with a variable frequency in the range from 500 Hz and 800 Hz.

Horn effect

Tire noise horn effect

Let’s look the tire from the side, as if it were bidimensional. When the tire region enters the contact patch, pressure waves are generated and their propagation is toward the vehicle running direction, and due to the shape of the cavity between the tire and the ground, like a horn, the amplitude of wave pressure is increased.
The same effect is produced when the tire leaves the contact patch.

Tread pumping

Every tread has is own sculpture, created mainly to improve handling on every type of ground, dry, slippery or to drain in the best way the water behalf circumferential and lateral channels.
When the tire region touches the ground, tread blocks are deformed and as consequence also grooves. The air that fills the grooves is pushed out the tire and noise is generated. In proximity to the trailing edge of the contact patch the tire returns to its original shape and the air comes back to fill the grooves.
The amplitude of this phenomena is a function of:

Grooves dimensions, the bigger are, the more is the noise;
– The angle between lateral grooves and vehicle running direction, proportional to the noise generated;
Vehicle speed, also proportional to the noise generated.

Cavity noise

Tire noise - cavity

When the tire is radially deformed pressure waves propagate also inside the tire, in the area between the tread and the wheel rim, and noise is generated.


Tread blocks in contact with the road are subjected to cyclic stick and slip. In some conditions these vibrations enter in the hearing frequency range, so we can hear the typical tire screech. The frequency of these vibrations depends on blocks dimensions and stiffness.

Tire noise is also influenced by wheel torque, not as source itself but as a parameter that can modify the amplitude of the phenomena; the greater is the torque, the noisier is the tire.
Furthermore, it is influenced proportional to inflation pressure. For low wheel torque the trend can be reversed, so a tire with higher inflation pressure can be less noisy.

Tire noise reduction

Tire noise reduction

In order to reduce the noise produced by tread is useful optimize grooves dimensions and its angles, finding a compromise between noise and the need to have a good grip, also on wet.
It is possible also create a circumferential offset between internal and external tread blocks.
The internal noise can be reduced using foams (in the following image Contisilent) to damp carcass vibrations; it can be mounted also on the rim internal channel. The disadvantage of the first option is the increased moment of inertia of the wheel, so it needs more power to be accelerated or slowed, but foams are very light.

Another option to reduce sidewalls noise is change their stiffness using a different compound. Anyway, each of these solutions is a compromise between low noise level, a good grip and a low fuel consumption.