Fundamentals of Hybrid Power Trains Equipped with Planetary Transmission

Fundamentals of Hybrid Power Trains Equipped with Planetary Transmission

DOI: 10.4018/978-1-4666-4042-9.ch008
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Chapter 8 describes the most advanced hybrid power trains, which were generally depicted in Chapter 1. The presented figures consist of the two degrees of freedom planetary gears. It seems to be the best system of energy, split between the Internal Combustion Engine (ICE), the battery, and the electric motor, but unfortunately, it is also the most costly solution for its manufacture. This type of hybrid power train should be preferred as the best drive architecture composition from the technical point of view. For this reason, this chapter, in a detailed way, describes the features and the modeling approach to the planetary hybrid power train. Certainly, most attention is paid to the planetary two degrees of freedom gears, yet not only to them. Cooperating with the planetary gears, additional and necessary devices are considered. The role and modeling auxiliary drive components, such as the automatic clutch-brake device and mechanical reducers are discussed in this chapter. The design of electromechanical drives related to the planetary gear of two degrees of freedom controlled by the electric motor can be transformed to the purely electromagnetic solution. An example of the mentioned gear is given in the chapter. It is a complicated construction with the rotating stator of a complex, electrical machine requiring multiple electronic controllers. The increasing output torque of the electromechanical converter and its connection with the mechanical two degrees of freedom planetary gears are depicted as well.
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1. Planetary Gear Power Modeling

The scheme of the planetary gear is shown in Figure 1. As it is exemplary, the sun wheel can be connected with an Internal Combustion Engine (ICE), through auxiliary transmission, whilst the ring is connected with the motor shaft and carrier through the drive reducer, which is connected with the axles of road wheels. Angular velocities of gear shafts, according to the assumed descriptions, fulfill the constraint equation:

Figure 1.

The kinematic scheme of planetary gear


  • : The base gear ratio,

  • z1: Number of teeth of the sun wheel,

  • z2: Number of teeth of the crown wheel,

  • ω1, ω2, ω3: Angular velocity of sun, crown and yoke wheels, respectively.

The motion equation has the following form:

(2) where:

  • J1: Total moment of inertia of sun wheel and connecting elements reduced to sun shaft;

  • J3: Total inertial torque obtained from a reduction of the vehicle mass, road wheels and gears reducer, and inertial torques to the carrier shaft;

    • M1: External torque acting on the sun shaft;

    • M2: External torque acting on the ring shaft;

  • M3: External torque acting on the carrier and corresponding to the vehicle motion resistance reduced to the appropriate shaft;

  • η1, η2, η3: Substitute coefficients of internal power losses.

Internal power losses in the planetary gear (in practice to about 98%) can be neglected and the Equation (2) is simplified to the form:


If torque from inertial forces is considered as external torque, it is possible to write:


For this reason, the model changes form:


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