Power-split principles for a simple differential

It is clear that there are a number of limitations regarding the use of a variator device as a CVT. Some of these issues can be addressed by considering mechanical power-split transmissions (PSTs). These are achieved by using a differential gearing unit with 2 degrees- of-freedom to split the main power flow into two paths. The kinematic and torque relationships that exist between the branches of the differential allow the overall power flow to be controlled by controlling the power flow in one of the two power-split branches. Fundamental analysis of power-split transmissions has been performed for a range of configurations consisting of a variator and PGS [90-93]. The way in which the three branches of a PGS are connected in these transmissions affects the overall operation, but the general analysis method used by White [94] allows an analysis of the system to be performed for the generic differential unit shown in Figure 2-21.

Figure 2-21 – Description of generic differential gearing unit

The kinematic and ideal torque relationships for the generic differential illustrated in Figure 2-21 are shown in Equation 2-1 and 2-2 respectively.

2 1 2 3        R Or alternatively... 3 





These equations apply to any type of differential in any configuration. It has been shown [95] that the relationship between the ratio of ring to sun diameter of a planetary gearset (PGS) type differential and the value of R can be defined for each of the six possible configurations, as shown in Table 2-4 for a simple PGS and Table 2-5 for a PGS with idler planet gears. Branch: 1 3 2 R 0 1 3 2             R where

59

Table 2-4 – Relationship between R and simple PGS [95]

Table 2-5 – Relationship between R and PGS with idler planets [95]

It can be seen that once an appropriate value of R has been identified for a given application, the most appropriate PGS configuration can be deduced for these types of differential by referring to Figure 2-22.

Figure 2-22 – Possible range of R values for practical simple and idler PGSs [95]

This allows a power-split system to be analysed for a given application as follows; i. Analyse system using the equations for a generic differential,

(a) Basic ratios for a planetary gearset with idler planets (b) Basic ratios for a simple planetary gearset

60

ii. Identify an appropriate characteristic differential gear ratio for the application, iii. Identify the most practical differential type and branch connections in order to

achieve the required characteristic gear ratio

This is a powerful analysis method for understanding PSTs as it eliminates the need for an exhaustive study of all possible permutations of differential types and connection options. Simple variator-controlled PSTs can be classified as either input or output coupled, depending on whether the variator connects between the control branch and the power input or power output branch of the PGS. Analysis of these configurations shows that several operating regions are possible, as illustrated in Figure 2-23 for the case of an output coupled PST.

Figure 2-23 – Illustration of the possible operating regions for a variator-controlled ‘output coupled’ power-split transmission with arrows showing direction and magnitude of power flow

(adapted from [96])

It can be shown (see Chapter 5) that in order to achieve genuine power-split operation (with power flow through each of the two branches being less than the overall power flow) the ratio spread of the PST is always smaller than the ratio spread of the variator. This spread can only be increased by allowing power-recirculation to occur. As well as extending the ratio spread, the presence of power-recirculation also makes it possible to achieve a geared neutral condition (i.e. zero transmission output speed with a non-zero input speed) and reverse drive (i.e. negative output speed for positive input speed) – these are often described as infinitely

61

variable transmissions (IVTs). This however requires the variator to be able to handle large power flows, and limits the overall efficiency of the PST due to high power losses in the variator and gearing. This reduction in efficiency has been demonstrated analytically and experimentally for the two main types of simple (single regime) power-split operation [97- 99].

The compromise between ratio coverage and transmission efficiency has been investigated by Beachley et al. [93] for a flywheel hybrid passenger car application. The general hybrid power-train configuration used in the analysis is shown in Figure 2-24.

Figure 2-24 – Proposed flywheel hybrid power-train for passenger car [93]

A range of simple variator-controlled PSTs were considered for the CVT, with varying degrees of power-split and power-recirculation operation. The analysis focuses on the efficiency of the CVT rather than quantifying fuel savings. In order to produce general results that were independent of the control policy for the system, simulations were performed assuming a range of constant flywheel speeds. The results are therefore not useful in assessing the effect of factors such as energy storage capacity, flywheel self-discharge or the hybrid power-train control strategy on the overall FESS performance. They do however confirm that power-recirculation results in average CVT efficiencies considerably lower than average variator efficiencies. A ‘load factor’ (calculated assuming no transmission component losses and identical variator dimensions in all cases) was used to assess the relative variator size required for each case, which was shown to increase with the proportion of power flowing through the variator.