# Calculating Hub Gear Efficiency ## Simplified method to calculate epicyclic transmission efficieny early in design

Standard methods for analyzing transmission efficiencies assume that all of the power flows through each gear in a sequence. In a hub gear, the planetary gear trains (PGTs) or epicyclic gear trains involve a number of planet gears transferring power in parallel. This requires special methods for efficiency analysis which are often time consuming to perform. This paper presents a simplified method. It has been validated against previously published results and may be useful for the evaluation of proposed designs.

The method in this paper only considers gear-mesh loses, caused by the sliding friction when the teeth mesh together, which normally provides a reasonably accurate calculation of efficiency. The procedure has the following steps:

1. List all fundamental circuits, consisting of two meshing geats and a carrier. For each, carry out kinematic analysis to solve for the angular speed of each link.
2. Find the idealized torque of each link, assuming there is no power loss.
3. Identify the direction in which power is flowing through each link
4. Add gear-mesh losses for each gear pair, giving the actual torque of each link
5. Sketch a power flow diagram and calculate the overall efficiency

The paper goes step-by-step through a method of calculating the efficiency of a hub gear system. If you want to perform the calculations you’ll need to read the full paper.

### Abstract:

#### Purpose

The analysis of power flow and mechanical efficiency constitutes an important phase in the design and analysis of gear mechanisms. The aim of this paper is to present a systematic procedure for the determination of power flow and mechanical efficiency of epicyclic-type transmission mechanisms.

#### Design/methodology/approach

A novel epicyclic-type in-hub bicycle transmission, which is a split-power type transmission composed of two transmission units and one differential unit, and its clutching sequence table are introduced first. By using the concept of fundamental circuits, the procedure for calculating the angular speed of each link, the ideal torque and power flow of each link, the actual torque and power flow of each link determined by considering gear-mesh losses, and the mechanical efficiency of the transmission mechanism is proposed in a simple, straightforward manner. The mechanical efficiency analysis of epicyclic-type gear mechanisms is largely simplified to overcome tedious and complicated processes of traditionally methods.

#### Findings

An analysis of the mechanical efficiency of a four-speed automotive automatic transmission completed by Hsu and Huang is used as an example to illustrate the utility and validity of the proposed procedure. The power flow and mechanical efficiency of the presented 16-speed in-hub bicycle transmission are computed, and the power recirculation inside the transmission mechanism at each speed is detected based on the power flow diagram. When power recirculation occurs, the mechanical efficiency of the gear mechanism at the related speed reduces. The mechanical efficiency of this in-hub bicycle transmission is more than 96 percent for each speed. Such an in-hub bicycle transmission possesses reasonable kinematics and high mechanical efficiency and is therefore suitable for further embodiment design and detail design.

#### Originality/value

The proposed approach is suitable for the mechanical efficiency analysis of all kinds of complicated epicyclic-type transmissions with any number of degrees of freedom and facilitates a less-tedious process of determining mechanical efficiency. It is a useful tool for mechanical engineering designers to evaluate the efficiency performance of the gear mechanism before actually fabricating a prototype as well as measuring the numerical data. It also helps engineering designers to cautiously select feasible gear mechanisms to avoid those configurations with power recirculation in the preliminary design stage which may significantly reduce the time for developing novel in-hub bicycle transmissions.

### Reference:

Computing the power flow and mechanical efficiency of in-hub bicycle transmissions

Wu, Yi-Chang; Cheng, Chia-Ho, 2014

In: Engineering Computations (Swansea, Wales) v 31, n 2