Wankel engine

Centenaro Stefano – stefano.centenaro.90@gmail.com – Degree in Mechanical Engineering

Furlan Ismaele – f.ismaele@gmail.com – Degree in Mechanical Engineering


The Wankel engine, presented for the first time by Felix Wankel in 1957, was conceived as an alternative to the traditional Otto engine based on the crank mechanism: it uses the eccentric rotation of its rotors to create the well known thermodynamic cycle of a four-stroke engine.

At the beginning Wankel engine seemed to be lighter and more powerful with respect to the same displacement, and less expensive as well; however, through the years problems of sealing, fuel consumption and reliability of its seal segments negatively influenced this technological application.

For these reasons nowadays few automotive companies (especially the Japanese Mazda and Toyo Kogyo) are still concerned with developing this engine. Nonetheless, the Wankel engine represents an interesting case of study since its operation is less intuitive than how it could be expected.


After a preliminary sizing of the main geometrical dimensions of a 1300cc Wankel engine (some industrial prototypes of cars has already tested this solution) the aims of this project are:

  • to model a two-rotor Wankel engine capable of reaching the real ones rotation velocities;
  • to reproduce the effect of the combustion cycle on the mechanical structure of the engine;
  • to perform faithfully direct kinematics and dynamics analysis with particular attention to rotor motion, contact’s normal and tangential forces between rotors and stators, torque and power transmission to the shaft.

Mechanism description ([1]-[3])

In order to understand the functioning of the Wankel engine correctly, a preliminary description of its main components can be useful. Real components of a Wankel engine have more complex geometry than those presented below in terms of fillets and chamfers but, for the purposes of this analysis, simplified geometries are acceptable.

The stator is a “fixed to the ground” component of the Wankel engine unit. The thermodynamic cycle takes place inside of it and for this reason in precise locations of its inner lateral edge are drilled holes to insert the mixture of air and fuel, to eject the exhaust gases and to house the sparks plug.






The rotor is the most stressed part of the Wankel engine: it can reach up to 3000 rpm rotation velocities (in fact, it is possible to demonstrate [1]-[2] that the angular velocity of the rotor is one third of the angular velocity of the shaft, that in these engines goes up to 9000 rpm), the combustion occurs between its three outer lateral surfaces and the stator and, above all, its three peripheral corners are in sliding contact with the inner surface of the stator. Three apex seals are necessary to preserve the insulation of the chambers.




The shaft has a disk for every rotor of the Wankel engine: the rotation axis of the rotor is the same of the geometrical axis of the disk but the shaft axis and the disk one are spaced by a distance equal to the eccentricity e.




The wheel is a component of the Wankel engine whose function is to drive the movement of the rotor along its trajectory to avoid every type of sliding between rotor and disk: it’s a motionless pinion.





The middle housing plate is the separation component between the two groups  of combustion made by a rotor, a stator, a motionless pinion and a part of the shaft. Its functions are basically the dissipation of the heat generated by the thermodynamic cycle and the seal of the chambers.






The video below shows how the Wankel engine is assembled, its spacial configuration and how it works:


The fundamental unit of a rotary engine is composed by a rotor moving inside a housing (stator): the space left between the two bodies describes three chambers, where the thermodynamic cycle takes place. During every rotor round the periodic variation of the volume of each chamber, due to the eccentricity between the rotor axis of rotation and the shaft one, is responsible for the steps of compression-combustion-expansion of the gasses.

           Compression                                        Combustion                                    Expansion

Observing only one fundamental unit of the studied Wankel engine the three chambers volume’s variations during the time is periodical and their phase displacements are clearly reported in the graph below:

The rotor is connected to the shaft’s disk through a shape coupling (the hole of the rotor with the disk of the shaft), while a gear between the rotor and the inner wheel drives it along its eccentric orbit. It is important to point out that the inner wheel of the gear does not rotate but it is motionless (fixed to the case of the engine) and its only function is to guide the rotor’s motion; the transfer of the torque from the rotor to the shaft is committed to their connection through the disk. In the picture below the spatial configuration of the engine.

                                    Left side                                                     Right side

Actual Wankel engines often present two, three or four rotors, rotating out of phase in order to contrast imbalance forces, that become important with high rotation velocities. Peripheral radial corner blades, also known as apex seals, are needed to prevent gas leakages between the three different chambers; side seals between the flat rotor sides and the end/intermediate housing side walls are also necessary to avoid engine oil reaching the combustion environment; sealing and its wear are one of the critical aspects of this type of engines.

The modelling problem

Preliminary sizing and solid modelling

The first aspect to examine is the solid modelling of the system, since the characteristic dimensions are related to one another: the starting assumption was to examine a 1,3 liters two-rotor engine, a typical size of the few rotary engines in use. The cubic capacity is given by

where e is the eccentricity, R is the radius of the rotor’s circumscribed circle and b is the depth of the rotor, obtainable by multiplying the radius R by an empirical coefficient that was assumed equal to 0,5. Moreover, since the inner profile of the stator can be described by the trajectory of a vertex of the rotor, by writing the motion’s laws it is possible to demonstrate ([1], [2]) that the shaft angular velocity is three times greater than the rotor angular velocity; therefore, since the rotor’s motion is guaranteed by the gear, the ratio between the primitive radius of the pinion and the primitive radius of the crown must be 2/3, and it is possible to evaluate the eccentricity as the difference between them. The number of teeth of the crown must then be 1,5 times the one of the pinion, and by establishing these and the wheels modulus we can get the eccentricity and the value of R. Once known R, e, and the primitive radius of the crown it is possible to model the rotor. As for the stator, its shape can be defined from the geometrical procedure explained in [3].

Without an exact structural calculation of the gear, that exceeds the objectives of this work, we chose to give 48 teeth to the crown and therefore 32 to the pinion. The curvature of the sides can also be determined through an experimental formula from [1].

Contact model

At the beginning of the project, using a couple of Bracket Joint velocity driver, the real movements of the Wankel engine has been reproduced properly: this strategy has allowed to drive in a passive way every component of the engine separately from the others but not to analyze the model kinematics and dynamics effects caused by the real thermodynamics cycle in particular on the contacts between rotor and stator (apex seals). For this reason the contacts between the six apex seals with the two stator is reproduced through the Sphere to Extruded surface model: six identical spheres were modeled on the peaks of the two rotors in order to simulate the apex seals, whereas the extruded bodies of the contacts are the stators themselves. The spheres have a radius of 3 mm and a surface thickness of 2 mm.

instrumented rotor

The Hertzian contact model was used, with some damping added; the mechanical properties of the model come from the materials used for the different parts: stators are typically made of alluminiom-silicon alloys, with a hard chromium-molybdenum plating on the inner lateral surface; apex seals are made of hard carbon materials, and in recent years graphite has been used for its self-lubricant properties in order to maintain sealing capacity and to reduce friction at the same time. In the contact model there are also a restitution coefficient imposed as null and a friction coefficient equal to 0,15.

The parameters adopted for the contact model are summarized in the following list:

Sphere radius

5 mm

Young modulus 1 (stator)

2,1 ∙1010 Pa

Maximum penetration depth

20 mm

Poisson’s ratio 1 (stator)


Transition velocity

0,01 m/s

Young modulus 2 (seal)

1,2 ∙109 Pa

Radius of exclusion

0 mm

Poisson’s ratio 2 (seal)


Angle on sphere

Restitution coefficient


Infinite extrusion


Damping coefficient

10 kg/s

Circular profile


Friction coefficient


Road profile


Joints and constraints

In order to define a gear joint between rotor hole and the shaft’s disk, LMS Virtual Lab needs the user to set two revolute or cylindrical joints connecting each the gear bodies to a third common body: in this case it has been necessary to consider the disk as a different body from the shaft even if in reality they are a unique component, this expedient allows to define the two gearing bodies as the rotor and the pinion (disk), and the common body as the shaft, this is the only possible choice because the rotor’s motion does not give the chance to define a revolute or cylindrical joint between the rotor itself and a grounded body. Moreover, revolute joints are used to connect the eccentric disk to the shaft and to the rotor, and the shaft to the ground. The stators, the mid housing plate and the stationary pinions are set as fixed to the ground.

The only necessary constraint is the shaft velocity driver imposed to the revolute joint that connects the shaft to the ground: through the dimensioning and joining work previously described, the shaft velocity driver makes the whole system move correctly leaving zero degrees of freedom.

The combustion cycle and its forces

Next step of the modelling phase is to reproduce the thermodynamic cycle of the internal combustion engine and to use it to define the combustion forces to be applied to the three lateral faces of each rotor: once obtained the evolution of the volume of each chamber, the compression and expansion phases are defined as polytropic transformations with their exponents respectively equal to 1,2 and 1,3 (average values from the literature [2]); the maximum pressure, which common range was also read in literature, is set as a parameter and can be modified. It is also necessary to set appropriate boolean parameters to make the software recognize the compression phase from the expansion phase: to do this, an auxiliary angle was defined, so that it varies from 0° to 360° within a single rotation of the rotor; it is then sufficient to set the correct angular intervals for the compression and expansion phases in each of the six chambers of the two-rotor engine.The parameters adopted to model the thermodynamic cycle are:

patm = 1,01325 bar                       kcomp = 1,2

pmax = 20 bar                              kexp = 1,3

Combustion chamber volume = calculated from the model.

The combustion cycle of every chamber is represented in the pressure-volume graph below:

pressure [N_m2] – Volume [m3]

While the pressures of the six chamber are out of phase as shown below:

Once represented the combustion cycle, it is necessary to convert the pressure that acts in every chamber into a force applied to the center of the corresponding lateral surface of each rotor. To do this, six Vector expression force “action-reaction” elements were defined: these feature allows the user to define a force or a torque acting between two bodies, which is exactly what is needed in this case since the combustion takes place within the space between the rotors and the stators, that were thus set as the two bodies involved. The Vector expression force requires also a reference axis system with respect to which the x, y, z force and torques must be defined: for this reason it has been created a specific axis system on each center of the lateral surfaces of the rotors, with the x axis oriented inwards and the force along x direction. The explained rotor loads configuration is reported in the figure below.

The time trend of the forces is obtained dividing the pressure trend of a chamber by one lateral rotor surface, the rotor is loaded with three forces out of phase as the pressure trends of the three chambers, each force has an the intensity reported in the graph below:

Simulations and analysis of results

In order to have not only a geometrical but also a kinematic and dynamic comprehension of Wankel engine behavior some analysis has been carried out about velocities, accelerations, transmission of power and torque, stress of apex seals.

Every analysis presented in this paragraph has shown reliable results compared to the literature ones demonstrating the quality of the project despite of its simplifications.

Kinematic analysis: rotor velocity and acceleration

For a constant speed of the Wankel engine in the graphs below there are the comparisons between theoretical [2] and measured (from the model) velocities and accelerations of a general apex seal element, represented in the model by a contact sphere. The velocity is given by [2]

Where “φ” is defined by [2]

The radial theorical acceleration is [2]

And the tangential acceleration [2]

The following are the comparison graphs:

Comparison between theoretical (blue) and measured (red) velocity of rotor apex

 Comparison between theoretical (blue) and measured (red) acceleration of rotor apex

Dynamic analysis: sealing contacts

The major problems of the Wankel engine reliability is the tearing of its apex seals, this phenomenon is mainly related to the forces that the combustion in every chamber releases on the contacts between rotor and stator. With an appropriate simulation it has been possible to quantify the normal and tangential forces magnitude, the results are strictly related to materials used and to the operating speed of the engine. In the graphs below are reported the trend of normal and tangential forces that the apex seal of the rotor have to bear for a rotor velocity of one thousand rpm.

    normal forces on a rotor apex seal

tangential forces on a rotor apex seal

As the graph shows the distribution of the three impulsive combustion forces on the apex seals causes some loss of contacts between rotor and stator: when this happens tangential and normal forces are up to zero but, when the contact begins to act again, in a very short time the forces, increases up to the maximum. This phenomenon causes lots of micro impacts that are damaging for the apex seals.

Dynamic analysis: shaft torque

The transmission of torque in the Wankel engine occurs between every rotor to the shaft through the connection of the rotor with the eccentric disk of the shaft, to observe this phenomenon is necessary to plot the torque measured by the shaft rotation velocity driver. This Wankel engine model does not give information about the performance coefficients of the real Wankel applications because the study of the real functioning complexities falls outside the aim of this work. For this reason every performance coefficient is taken equal to one and it is not possible to obtain the usual “torque-rpm” graph therefore the graph below shows the transmission of torque during the time with a constant engine speed of one thousand rpm due to the successive combustion of the engine cycle.

The torque transmitted to the shaft

The transmitted torque average value of about 220 Nm at one thousand rpm of the rotor (is supposed a perfect engine so the real value is lower) is in agreement with the theoretical studies that estimate about 300 Nm with the top rotor speed of 3000 rpm.


The aim of this project is to create a simplified model of a Wankel engine, a type of propulsion based on a rotation technology. The principal components of this application are: the rotor, that rounds inside a stator, having its rotation axis eccentric respect to the shaft one. The particular configuration of components in this engine does not help to define a correct stage of joints that allows to measure the principal sizes of interest. After the implementation of the thermodynamic cycle of this engine to examine the velocities, the accelerations and the stress acting at the sliding contact between rotor and stator (apex seals) are used the Hertian contact theory while some revolute joints and a gear joint (rotor-disk) manage to measure the transmission of power to the shaft.

The results of simulation are in agreement with the theoretical studies about Wankel engine.


[1]          R. F. Ansdale, The Wankel RC Engine, Iliffe Books Ltd., 1968

[2]          V. Quaggiotti, Il motore Wankel, Casa editrice prof. Riccardo Patron, Bologna, 1972

[3]          H. Heisler, Advanced Engine Technology, Edward Arnold, 1995<a type=”application/x-shockwave-flash” name=”allowscriptaccess” href=”http://

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