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This thesis describes a method for analyzing and designing a continuously variable transmission (CVT). The analysis process is implemented in a software package that can be used to tune a CVT for a given application. The analysis is accomplished through the use of kinematic principles as well as equations developed from basic energy balances. Although the theory developed can be applied to any CVT, this thesis focuses on a case study using the Team Industries brand CVT applied to the Virginia Tech Mini Baja Team. The work was motivated by the team's need to have a reliable and inexpensive method for CVT tuning. Previous approaches to CVT tuning were strictly empirical and involved mechanical component replacement in a slow and expensive trialand- error optimization loop. The tuning software is intended to be a first step in the process of properly tuning a CVT for a specific application and not a complete replacement for the empirical methods employed previously. / Master of Science

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In recent years the increasing demand for fuel efficient and less pollutant vehicles has stimulated the development of hybrid and electric vehicles. These vehicle platforms often incorporate drivetrains which utilize multiple power sources for vehicle propulsion in an effort to increase fuel mileage and reduce emissions. Coupling multiple power sources, such as an internal combustion engine and electric motor(s), has new challenges in drivetrain design. Understanding the torque and rpm relationships within the power transmission device used to combine power sources is fundamental to overcoming the design challenges associated with hybrid and electric vehicle platforms. Results from this research include the fundamental torque and rpm relationships that exist in a multiple-input, single-output power transmission device. These results were deduced from a test that incorporated two separate power inputs into a differential which combined to produce a single output. Testing displayed that a differential has the ability to function as an infinitely variable transmission (IVT). Additionally, the challenges associated with using a differential as a multiple-input, single-output device were identified. Recommendations for overcoming these challenges are also presented herein. This work provides the basis for future work in powertrain optimization for multiple-input, single-output transmission devices.

Rubber V-belt Continuously Variable Transmissions (CVT's) are commonplace in the Baja SAE collegiate design competition, and are also used widely in the power sports industry. These transmissions offer benefits of simplicity in mechanical design, consisting of only two pulleys, and are easy to use. While most teams in the competition use commercially available designs, custom designs are becoming more common, and the Baja team at Virginia Tech has used custom CVT's since the 2014 season. The design of these CVT's has relied heavily on trial and error, requiring significant adjustments to be made during the testing phase. In addition, only qualitative information is known for the relationship between efficiency and design parameters, such as sheave angle. The goal of this thesis is to create an improved V-belt model that may be used as a design tool. This model provides quantitative information about efficiency that can be used to make more informed design decisions. The belt model also provides insight into the magnitude and relationship between the axial forces in the pulleys. This can be used to create an initial design that is more accurate, and possibly reduce the time required for tuning. A CVT dynamometer was constructed to validate the analytical results for efficiency, and this will also serve as a tuning tool for future Baja teams at Virginia Tech. This thesis will advance the state of the custom CVT design and testing process at Virginia Tech, and hopefully lead to improved results at competition in the future. / Master of Science / Baja SAE is an annual collegiate competition where students design and build an off-road vehicle. Many teams choose to use Continuously Variable Transmissions (CVT’s) in order to maximize the efficiency of the vehicle’s transmission. By continually shifting ratios, CVT’s allow internal combustion engines to always run at peak performance. There are several types of CVT’s, but the most common one used in Baja SAE and the power sports industry is a rubber V-belt design that is controlled mechanically with springs and flyweights. While these devices are used extensively, the underlying dynamics are not well-documented in literature. The Baja team at Virginia Tech builds a custom CVT every year for the vehicle, but the success of the design relies heavily on tuning through trial and error. A better understanding of the dynamics of the belt will result in better initial designs, and will help to reduce the amount of tuning required for the success of the design. This thesis offers an improved dynamic model for a CVT belt, and validates the results of this model through testing on a custom-built dynamometer. This model is also able to predict the efficiency of the transmission, and these results may be used to influence design decisions by predicting their effects on performance. The results of this research will improve the design process for a rubber V-belt CVT and hopefully lead to improved results at competition for the Baja team at Virginia Tech.

With gas prices on the rise, the demand for high-mileage and low pollution vehicles has taken on an unprecedented role in our society. The production and implementation of electric and hybrid-electric vehicles has recently been a large focus of all major automobile manufacturers. Although these new vehicles have begun to solve much of the expensive fuel consumption and air pollution problems that our economy faces, the initial cost of these vehicles has proven to still be too expensive to capture a significant portion of the market. The further advancement of this technology must not only continue to focus on better fuel efficient and decreased pollution producing vehicles, but also decrease the cost of these vehicles to make them more available and enticing to the general public. Results from this research include one potential solution to reduce the cost of electric and hybrid-electric vehicles. Previous research performed in this area has led to the investigation and bench-top testing of a special type of mechanical system known as a Planetary Differential (PD). An exploration of the functionality of this system has shown that the PD can simplify expensive and complex electronic control systems for electric and hybrid-electric vehicles, thus reducing the cost to the consumer. In this study, fundamental speed, torque and power relationships for the PD were developed and tested under various loading conditions. Advantages and disadvantages of the PD, as compared to other similar mechanical systems, are identified and outlined. Recommendations for future work and implementation of the PD in electric and/or hybrid-electric vehicles are presented herein.

The research presented in this thesis regards walking of quadruped robots, and particularly the walking of the Warp1 robot. The motivation for the robot is to provide a platform for autonomous walking in rough terrain. The thesis contains six papers ranging from development tools to actuation of robot legs. The first paper describes the methods and tools made for control development. These tools feature: programming of the robot without low level coding (C-code); that the controller has to be built only once for simulation and experiments; and that names of variables and constants are unchanged through the chain of software Maple -- Matlab -- Simulink -- Real~Time~Workshop -- xPC--Target. Three controllers, each making the robot walk are presented. The first controller makes the robot walk using the crawl gait. The method uses static stability as method for keeping balance and the instantaneous trunk motions are given by a concept using the so called weight ratios. A method for planning new footholds based on the positions of the existing footholds is also proposed and the controller experimentally verified. The second walking controller shows that the robot also can walk dynamically using the trot gait. The method proposed uses information from ground contact sensors on the feet as input to control balance, instead of, which is common, inertial sensors. It is experimentally verified that Warp1 can trot from level ground onto a slope and turn around while staying balanced. The main ideas of these two walking controllers are fused in the third which enables smooth transitions between crawl and trot. The idea of using the ground contact sensors from the first controller is here used to estimate the position of the center of mass. This controller uses weight ratios in the gait crawl as well as in the dynamic gait trot. Hence, the method of using weight ratios is not only useful for static stability for which it was originally intended. The controller is experimentally verified on Warp1. The Warp1 robot weighs about 60 kg, has 0.6 m long legs with three actuated joints on each. The speed and strength is sufficient only for slow walking, even though the installed power indicates that it should be enough for faster walking. The reason is that a walking robot often needs to be strong but slow when the feet are on the ground and the opposite when in the air. This can not be achieved with the motors and transmissions currently used. A transmission called the passively variable transmission (PVT) is proposed which enhance motor capabilities of robot joints. It is elastic, nonlinear and conservative. Some general properties for elastic transmissions are derived such that they can be compared with conventional transmissions. The PVT gives strong actuation at large loads and fast actuation at small loads. The proposed transmission is compared to a conventional transmission for a specific task, and the result is that a smaller motor can be used. / QC 20100831

Elastohydrodynamic lubrication (EHL) allows transfer of power and forces in gears and rolling bearings without surface-to-surface contact and is the basis for a continuously variable transmission studied in this report. Previous research constructed models and derived solution methods, but often lacked full explanations of the approach and was usually applied to limited and specific cases. This report precisely develops the numerical solution of EHL contact and includes the more general cases of elliptical contacts and side-slip. The model and numerical method are validated on known benchmark cases and test results. Side-slip is investigated and the results shown in this report. Finally, the model is used to determine the film thickness and pressure of a contact patch under identical conditions to that in a physical drive developed by Fallbrook Technologies in Austin, TX. A minimum film thickness of 0.8978 [mu]m is found, setting a benchmark for the maximum allowable surface roughness values to prevent surface-to-surface contact. Additionally, under normal drive conditions the film thickness to surface roughness ratio is in the range of ideal values for maximum life. / text

In this investigation, four coatings were tested for their ability to increase the wear life of A390 aluminum primary clutch sheaves used in continuously variable transmission (CVT). The coatings tested were: hard chrome, electroless nickel metal, hard coat anodizing and composite ceramic coating. The primary clutch sheave material is a die-cast A390 aluminum. A wear test stand was developed to duplicate wear found on CVTs currently in use. The wear was evaluated using four methods. First, the change in shift characteristics of the CVT while running on the wear test stand, second a change in performance using an ATV and chassis dynamometer, third the amount of material lost, through wear, was measured using a profilometer, and finally a scanning electron microscope which was used to identify the dominate mechanism of wear in the sheave material. All of the tests showed the hard chrome coating to have the lowest wear rates and the best wear characteristics. The electroless nickel metal coating did improve the wear life of the CVT but had very high variation. The hard coat anodized and ceramic composite coatings were eliminated early in testing because of poor performance.

Research in developing a Positively Engaged Continuously Variable Transmission (PECVT) has been underway at Brigham Young University for some time. The inherent problems associated with embodiments of this type of transmission, namely the Non-Integer Tooth Problem (NITP), have been identified. This research is focused on the development of a Positively Engaged Piecewise Continuous Transmission (PEPCT), which is a subset of the PECVT. This document describes the hypothesis and analysis of using non-circular gearsets to overcome the NITP. This proposed solution enables a varying angular output from a constant angular input. In this research two analytical methods were evaluated based on their theory, mathematics and simulated results. Haupt's concept is shown to have discrepancies between the theorized and mathematical results which produce a gearset that has velocity spikes in its output. The second method, proposed by Danieli, describes the behavior on an infinitesimal level and the theorized results match up with the mathematical result. As a result of the analysis, Danieli's method is declared to produce a varying output from a constant input. The method requires only the definition of an input function that defines the shape of the pitch line similar to the pitch circle for circular gears. Using this function an infinitesimal approach is used to describe the interaction of consecutive contact points on the tooth profiles. This interaction takes into consideration adapted principles that are derived from the Fundamental Law of Gearing and the Law of Conjugate Action. With these principles defined it is possible to design gearsets that are capable of producing a varying angular output from a constant angular input. With the validation of the second method, and the principles defined by which it is governed, the proposed gearset is achievable allowing a PEPCT to be conceived. The proposed transmission utilizes the non-circular gearset to accelerate a secondary shaft to the next desired ratio while maintaining constant engagement. This concept is then analyzed and recommendations are made for the development of a Positively Engaged Continuously Variable Transmission.