The efficiency of the original Toroidal continuously variable transmission (CVT) is limited due to the spin losses caused by the different speed distribution in the contact area. To overcome this drawback, this paper replaces the original working surface with a new surface derived from a differential equation and proposes a novel Logarithmic CVT. Equations and ranges of the transmission ratio range, half-cone-angle, and conformity ratio, which are essential geometrical parameters of the Logarithmic CVT, are derived. A set of geometrical parameters is further recommended. With such geometrical parameters, the transmission ratio range of the Logarithmic CVT is as wide as that of the Half-Toroidal CVT. The two types of CVTs are compared with each other in terms of efficiency based on a widely accepted computational model. The results show that efficiency of the Logarithmic CVT is higher than that of Half-Toroidal CVT except for some particular situations because of the thrust bearing losses.
Researchers have proposed various solutions for Internal Combustion (IC) engine vehicles to satisfy the increasing strict emissions standards [
The two Toroidal CVTs’ geometries: (a) full-Toroidal CVT, (b) half-Toroidal CVT.
So far, researchers have exerted much efforts in parameter optimizations and structural innovations to reduce the spin losses of the Toroidal CVTs. Delkhosh [
In this paper, the differential equation method is presented in detail. Equations for transmission ratio range, half-cone-angle, and conformity ratio, which are essential geometrical parameters of the proposed CVT, are derived and their relationship is also expressed in an equation. After analysis of the relationship equation, we also recommend the ranges of the parameters. A design case for the Logarithmic CVT is carried out which enables us to determine a set of the geometrical parameters. The performances of the two types of CVTs are compared with each other in terms of efficiency based on a widely accepted EHL model [
Efficiency losses of the Toroidal CVTs consist of bearing losses, spin losses, churning losses, and slip losses [
As shown in Figure
To totally eliminate spin losses of the Toroidal CVTs, it is necessary to redesign the working surface of the disc. Suppose the new disc to be designed is located in a plane coordinate system
An ideal curve with no spin.
According to the zero-spin condition,
The tangent equation of the curve
As shown in Figure
As shown in Figure
As shown in Figure
The novel CVT using the new disc generatrix.
As shown in Figure
The transmission ratio
According to (
The half-cone-angle
The relationship of the half-cone-angle, conformity ratio, and transmission ratio range.
From Figure
In this section, we will present a method of determining the values of the three parameters which can maintain the performance of the Logarithmic CVT similar to that of the Half-Toroidal CVT.
Firstly, determine the transmission ratio range. Due to the limitations in size and users’ requirements, the transmission ratio range of the CVT is nearly 4.0–6.0 as mentioned in Section
Secondly, determine the values of
Finally is the collision checking. The discs of the Logarithmic CVT need axial motion [
The relationship of the half-cone-angle, conformity ratio, and transmission ratio range.
With such adopted geometrical parameters (
The solid geometry model of Logarithmic CVT.
For the original Toroidal CVT, the calculation of the efficiency is based on the EHL theory. Because of the high pressure in the contact area, accurate calculation of the efficiency is difficult [
Firstly the calculations of the spin ratio need to be adjusted [
Figure
The free body diagram of the discs and roller.
According to the force balance of the roller, the following kinetic equation of equilibrium is obtained:
The input and output torque coefficients
Because the Half-Toroidal CVT has been proved to be more efficient than the Full-Toroidal CVT, it is only necessary to compare the efficiency of the Logarithmic CVT with that of the Half-Toroidal CVT in this section. The adopted geometrical and operating parameters of the two types of CVTs are shown in Table
CVTs’ geometrical and operating data.
Half-Toroidal |
Logarithmic | |
---|---|---|
Cavity radius | 40 mm | 40 mm |
Roller radius | 32 mm | 20 mm |
Conformity ratio | 0.8 | 0.5 |
Half-cone-angle |
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|
Number of cavities | 2 | 2 |
Number of rollers’ set | 2 | 2 |
Transmission ratio range | 4 | 4 |
The fluid properties of the traction oil.
Absolute viscosity at the atmospheric pressure | 3.25 × 10−3 Pa s |
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|
Viscosity-pressure index | 0.85 |
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|
Pressure-viscosity coefficient | 1.71 × 10−8 Pa−1 |
|
|
Limiting shear stress at the atmospheric pressure | 0.02 × 109 Pa |
|
|
Limiting shear stress constant | 0.085 |
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|
Pole pressure constant of Roelands viscosity model | 1.96 × 108 Pa |
|
|
Pole viscosity of Roelands viscosity model | 6.31 × 10−5 Pa s |
Figures
The efficiency of the CVTs as a function of the input traction coefficient
The efficiency of the CVTs as a function of the input traction coefficient
The efficiency of the CVTs as a function of the input traction coefficient
As shown in Figure
In this paper, we proposed a mathematical method for eliminating the spin losses in Toroidal traction drives. The following conclusions can be drawn: By replacing the original generatrix of the Toroidal CVT with a Logarithmic curve derived from a differential equation, the spin losses have been eliminated theoretically. Relationship equation of transmission ratio range The relationship of the The ranges of A comparison of Logarithmic CVT with Half-Toroidal CVT in terms of efficiency based on a widely accepted computational model has been carried out. The results have shown that the efficiency of the Logarithmic CVT is higher than that of the Half-Toroidal CVT except for some particular situations.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the Applied Basic Research Programs of Sichuan Province (Grant no. 2012JY0085).