Preface

Vibrations are natural phenomena. Vibration frequencies and amplitudes that are observed in rotating machinery such as gearboxes and airplanes and in structures such as bridges and buildings (due to forced excitations) can be measured. Generally, the frequencies of these vibrations do not exceed 20 kHz. Their amplitudes in rotating equipment are in the range of 10 mils or less, whereas the amplitudes of structural vibrations may exceed a few inches. Vibrations are destructive whether they arise in rotating equipment or any structures. This book discusses gearbox vibration, which has detrimental effects on the life of the gearbox. Also presented are methods to reduce vibration.

A gearbox is a simple rotating piece of equipment that consists of a stationary housing and components such as gears and shafts mounted on bearings within the housing. As the gears rotate to transfer motion from one shaft to the other, the gearbox vibrates, even at low speeds under small loads. The vibrations are attributed to minor unbalances in the rotating components. The level of such vibrations is generally low; however, as the speed and load increase, the level of vibrations increases. In addition to the microunbalance of rotating components, an error in gear tooth geometry and the dynamic complexity of the rotating components are considered the primary causes for vibration-level increases. As the speed increases to 1525 m/min (5000 ft/min) and more, even at a moderate load intensity, it becomes difficult to maintain the vibration level on a gearbox below 10g, which is an acceptable level of vibrations. In general, gearboxes subjected to vibration above this limit fail before their expected lives. Gearbox failures may cause major breakdowns of a manufacturing operation, shutdown of power generation, and disruption in propulsion of naval ships, airplanes, and many other applications where gearboxes are a vital component. To eliminate failures, the vibration level of a gearbox can be reduced by changing its design.

To design a gearbox for reduced vibrations, it is important to ensure that the rotational frequency of the components does not excite the housing structure to its natural frequency, which can create a resonance. To ensure this, a detailed analysis of the housing structure is needed to produce an optimum design that not only eliminates resonance conditions but also maintains precise spatial relationships among rotating components for kinematic stability, even at high speeds.

In addition to housing, gear tooth geometric accuracy is considered a major source of gearbox vibrations. It is important to design gears with the high geometric accuracy achievable with the current manufacturing equipment. In addition to gear geometry, there are a number of other gear design parameters that influence the level of vibration.

These include selection of a minimum number of teeth in the gears and pinions, the pressure angle of the teeth, the number of teeth in the pinion and gear for hunting tooth combinations, suitable diametral pitch, helical gears with high contact ratio, and shaft misalignment. In addition to these gear parameters, bearings that support the shafts play a significant role in raising the vibrations of gearboxes. For low speed and load, ball or roller bearings are suitable. On the other hand, precision tilt-pad sleeve bearings with high stiffness are preferred for dynamic stability and reduced vibrations at high-speed and high-load applications. Furthermore, high-speed shafts that are used for mounting gears must be designed to avoid vibrations due to rotodynamic instability.

In some turbomachinery applications, gearboxes operating at high speeds of approximately 1525 m/min (5000 ft/min) exhibit the presence of nonsynchronous and spiking-type vibrations, which are found to limit the operation of turbines at partial loads. This is due to bearing instability at high speeds and high load. To overcome this type of instability, it is possible to redesign the bearings with a taper pressure dam, which makes the bearings stable and allows the high-speed equipment to operate satisfactorily under proper hydrodynamic lubrication.

In addition, most high-speed gearboxes experience subsynchronous vibrations. Experimental studies indicate that when the level of these low-frequency vibrations rises above 1 mil, the life of Babbitted sleeve bearings is significantly reduced. An improvement in bearing design alone is not always successful in reducing these vibrations below 1 mil. For this, an in situ balancing mechanism was developed that is useful in reducing the low-frequency vibrations, particularly for the epicyclic type of parallel-axis gearbox.

This book includes eight chapters. Chapters 1 and 2 discuss the basic vibration theory applicable to gearbox vibrations and their measurement fundamentals. In Chapter 3, experimental verification and an analysis of the various factors that cause gearbox vibrations are presented. Furthermore, it is shown how vibrations that arise are related to gear tooth geometry, particularly transmission error of gear teeth. Also given in this chapter is information on a new type of gear tooth error, tooth index variation form error, observed during package testing of high-speed turbomachinery, that increases the vibration level of a gearbox.

Chapter 4 is dedicated to establishing vibration limits for different classes of gearboxes. These are helpful to design engineers for the initial design of a gearbox. Chapter 5 discusses the occurrence of nonsynchronous and spiking vibrations during a turbomachinery package test. These types of abnormal vibrations were found to have a detrimental effect on the life of tilt-pad bearings, particularly when the packages run at partial load. To overcome this limitation, some new design guidelines were developed for the bearings after systematic analysis of test results from a number of turbomachinery packages. Guidelines are discussed that minimize such vibrations, allowing the packages to operate over the full-load spectrum without the loss of any unexpected bearing life.

Chapter 6 presents several gearbox field failures. An analysis for each type of these failures is presented, identifying the cause of failure. Recommendations are made regarding design modification to avoid future failures. Chapter 7 summarizes the various design considerations for reduced vibrations of high-speed gearboxes. A graphical presentation is developed to establish a gear quality for the level of vibration desired. Chapter 8 presents the step-by-step development of an epicyclic gearbox for high efficiency and reduced vibrations.

Finally, the author firmly believes that gearbox design development is essential for the success of future high-speed gearboxes.