Figure 11.19 Basic shape of bevel gears. Figure 11.20 Typical set of bevel gears. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 214 214 Maintenance Fundamentals Figure 11.21 Shaft angle, which can be at any degree. Figure 11.22 Miter gears, which are shown at 90 degrees. HELICAL Helical gears are designed for parallel-shaft operation like the pair in Figure 11.25. They are similar to spur gears except that the teeth are cut at an angle to the centerline. The principal advantage of this design is the quiet, smooth action that results fromthe sliding contact of the meshing teeth. Adisadvantage, however, is the higher friction and wear that accompanies this sliding action. The angle at which the gear teeth are cut is called the helix angle and is illustrated in Figure 11.26. It is very important to note that the helix angle may be on either side of the gear’s centerline. Or if compared with the helix angle of a thread, it may be either a ‘‘right-hand’’ or a ‘‘left-hand’’ helix. The hand of the helix is the same regardless Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 215 Gears and Gearboxes 215 of how viewed. Figure 11.27 illustrates a helical gear as viewed from opposite sides; changing the position of the gear cannot change the hand of the tooth’s helix angle. A pair of helical gears, as illustrated in Figure 11.25, must have the same pitch and helix angle but must be of opposite hands (one right hand and one left hand). Helical gears may also be used to connect nonparallel shafts. When used for this purpose, they are often called ‘‘spiral’’ gears or crossed-axis helical gears. This style of helical gearing is shown in Figure 11.28. WORM The worm and worm gear, illustrated in Figure 11.29, are used to transmit motion and power when a high-ratio speed reduction is required. They provide a steady quiet transmission of power between shafts at right angles. The worm is Figure 11.23 Typical set of miter gears. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 216 216 Maintenance Fundamentals Figure 11.24 Miter gears with spiral teeth. Figure 11.25 Typical set of helical gears. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 217 Gears and Gearboxes 217 Figure 11.26 The angle at which teeth are cut. Figure 11.27 Helix angle of teeth: the same no matter from which side the gear is viewed. Figure 11.28 Typical set of spiral gears. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 218 218 Maintenance Fundamentals Figure 11.29 Typical set of worm gears. always the driver and the worm gear the driven member. Like helical gears, worms and worm gears have ‘‘hand.’’ The hand is determined by the direction of the angle of the teeth. Thus, for a worm and worm gear to mesh correctly, they must be the same hand. The most commonly used worms have either one, two, three, or four separate threads and are called single, double, triple, and quadruple thread worms. The number of threads in a worm is determined by counting the number of starts or entrances at the end of the worm. The thread of the worm is an important feature in worm design, as it is a major factor in worm ratios. The ratio of a mating worm and worm gear is found by dividing the number of teeth in the worm gear by the number of threads in the worm. HERRINGBONE To overcome the disadvantage of the high end thrust present in helical gears, the herringbone gear, illustrated in Figure 11.30, was developed. It consists simply of two sets of gear teeth, one right hand and one left hand, on the same gear. The gear teeth of both hands cause the thrust of one set to cancel out the thrust of Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 219 Gears and Gearboxes 219 the other. Thus the advantage of helical gears is obtained, and quiet, smooth operation at higher speeds is possible. Obviously they can only be used for transmitting power between parallel shafts. GEAR DYNAMICS AND FAILURE MODES Many machine-trains utilize gear drive assemblies to connect the driver to the primary machine. Gears and gearboxes typically have several vibration spectra associated with normal operation. Characterization of a gearbox’s vibration signature box is difficult to acquire but is an invaluable tool for diagnosing machine-train problems. The difficulty is that (1) it is often difficult to mount the transducer close to the individual gears, and (2) the number of vibration sources in a multi-gear drive results in a complex assortment of gear mesh, modulation, and running frequencies. Severe drive-train vibrations (gearbox) are usually due to resonance between a system’s natural frequency and the speed of some shaft. The resonant excitation arises from, and is proportional to, gear inaccuracies that cause small periodic fluctuations in pitch-line velocity. Complex machines usually have many resonance zones within their operating speed range because each shaft can excite a system resonance. At resonance these cyclic excitations may cause large vibration amplitudes and stresses. Basically, forcing torque arising from gear inaccuracies is small. However, under resonant conditions torsional amplitude growth is restrained only by damping in that mode of vibration. In typical gearboxes this damping is often small and permits the gear-excited torque to generate large vibration amplitudes under resonant conditions. Figure 11.30 Herringbone gear. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 220 220 Maintenance Fundamentals One other important fact about gear sets is that all gear sets have a designed preload and create an induced load (thrust) in normal operation. The direction, radial or axial, of the thrust load of typical gear sets will provide some insight into the normal preload and induced loads associated with each type of gear. To implement a predictive maintenance program, a great deal of time should be spent understanding the dynamics of gear/gearbox operation and the frequencies typically associated with the gearbox. As a minimum, the following should be identified. Gears generate a unique dynamic profile that can be used to evaluate gear condition. In addition, this profile can be used as a tool to evaluate the operating dynamics of the gearbox and its related process system. Gear Damage All gear sets create a frequency component, called gear mesh. The fundamental gear mesh frequency is equal to the number of gear teeth times the running speed of the shaft. In addition, all gear sets will create a series of side bands or modulations that will be visible on both sides of the primary gear mesh fre- quency. In a normal gear set, each of the side bands will be spaced at exactly the 1X or running speed of the shaft and the profile of the entire gear mesh will be symmetrical. Normal Profile In a normal gear set, each of the side bands will be spaced at exactly the 1X running speed of the input shaft, and the entire gear mesh will be symmetrical. In addition, the side bands will always occur in pairs, one below and one above the gear mesh frequency. The amplitude of each of these pairs will be identical. For example, the side band pair indicated as À1 and þ1 in Figure 11.31 will be spaced at exactly input speed and have the same amplitude. If the gear mesh profile were split by drawing a vertical line through the actual mesh (i.e., number of teeth times the input shaft speed), the two halves would be exactly identical. Any deviation from a symmetrical gear mesh profile is indica- tive of a gear problem. However, care must be exercised to ensure that the problem is internal to the gears and induced by outside influences. External misalignment, abnormal induced loads, and a variety of other outside influences will destroy the symmetry of the gear mesh profile. For example, the single reduction gearbox used to transmit power to the mold oscillator system on a continuous caster drives two eccentrics. The eccentric rotation of these two cams is transmitted directly into the gearbox and will create the appearance of Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 221 Gears and Gearboxes 221 eccentric meshing of the gears. The spacing and amplitude of the gear mesh profile will be destroyed by this abnormal induced load. Excessive Wear Figure 11.32 illustrates a typical gear profile with worn gears. Note that the spacing between the side bands becomes erratic and they are no longer spaced at the input shaft speed. The side bands will tend to vary between the input and output speeds but will not be evenly spaced. FREQUENCY GEARMESH AMPLITUDE Figure 11.31 Normal profile is symmetrical. FREQUENCY GEARMESH AMPLITUDE Figure 11.32 Wear or excessive clearance changes side band spacing. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 222 222 Maintenance Fundamentals In addition to gear tooth wear, center-to-center distance between shafts will create an erratic spacing and amplitude. If the shafts are too close together, the spacing will tend to be at input shaft speed, but the amplitude will drop drastically. Because the gears are deeply meshed (i.e., below the normal pitch line), the teeth will maintain contact through the entire mesh. This loss of clearance will result in lower amplitudes but will exaggerate any tooth profile defect that may be present. If the shafts are too far apart, the teeth will mesh above the pitch line. This type of meshing will increase the clearance between teeth and amplify the energy of the actual gear mesh frequency and all of its side bands. In addition, the load- bearing characteristics of the gear teeth will be greatly reduced. Since the pres- sure is focused on the tip of each tooth, there is less cross-section and strength in the teeth. The potential for tooth failure is increased in direct proportion the amount of excess clearance between shafts. Cracked Or Broken Tooth Figure 11.33 illustrates the profile of a gear set with a broken tooth. As the gear rotates, the space left by the chipped or broken tooth will increase the mechan- ical clearance between the pinion and bull gear. The result will be a low ampli- tude side band that will occur to the left of the actual gear mesh frequency. When the next, undamaged teeth mesh, the added clearance will result in a higher- energy impact. The resultant side band, to the right of the mesh frequency, will have much higher amplitude. The paired side bands will have non-symmetrical amplitude that represents this disproportional clearance and impact energy. FREQUENCY GEARMESH CRACKED OR BROKEN TOOTH AMPLITUDE Figure 11.33 A broken tooth will produce an asymmetrical side band profile. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 223 Gears and Gearboxes 223 [...]... in machinery Helical gears also have a preload by design; the critical force to be considered, however, is the thrust load (axial) generated in normal operation; see Figure 11. 12 TF ¼ 126 , 000 à HP Dp à RPM 22 6 Maintenance Fundamentals STF ¼ TF à tan f cos l TTF ¼ TF à tan l where TF ¼ Tangential Force STF ¼ Separating Force TTF ¼ Thrust Force HP ¼ Input horsepower to pinion or gear ¼ Pitch diameter... produced by each stage of compression 23 1 23 2 Maintenance Fundamentals Configuration The actual dynamics of centrifugal compressors are determined by their design Common designs are overhung or cantilever, centerline, and bull gear Overhung or Cantilever The cantilever design is more susceptible to process instability than centerline centrifugal compressors Figure 12. 1 illustrates a typical cantilever... Figure 12. 2 illustrates the normal airflow pattern through a horizontal split-case compressor Inlet air enters the first stage of the compressor, where pressure and velocity increases occur The partially compressed air is routed to the second stage, where the velocity and pressure are increased further Adding Figure 12. 1 Cantilever centrifugal compressor is susceptible to instability Compressors 23 3 Figure.. .22 4 Maintenance Fundamentals If the gear set develops problems, the amplitude of the gear mesh frequency will increase and the symmetry of the side bands will change The pattern illustrated In Figure 11.34 is...    Overload    Process Induced Misalignment         Worn Bearings   Worn Coupling  Unstable Foundation Water or Chemicals in Gearbox Source: Integrated Systems, Inc      22 8 Maintenance Fundamentals Gear overload is another leading cause of failure In some instances, the overload is constant, which is an indication that the gearbox is not suitable for the application In other... failure modes for the gearbox Gears and Gearboxes 22 9 Figure 11.35 Normal wear pattern Figure 11.36 Wear pattern caused by abrasives in lubricating oil Abrasion Abrasion creates unique wear patterns on the teeth The pattern varies, depending on the type of abrasion and its specific forcing function Figure 11.36 illustrates severe abrasive wear caused by particulates in the lubricating oil Note the score... and other foreign substances in the lubricating oil supply also cause gear degradation and premature failure Figure 11.37 illustrates a typical wear pattern on gears caused by this failure mode 23 0 Maintenance Fundamentals Figure 11.37 Pattern caused by corrosive attack on gear teeth Figure 11.38 Pitting caused by gear overloading Overloading The wear patterns generated by excessive gear loading vary,... While this practice permits longer operation times, the torsional power generated by a reversed gear set is not as uniform and consistent as when the gears are properly installed Gears and Gearboxes 22 7 Table 11.1 Common Failure Modes of Gearboxes and Gear Sets High Vibration    Broken or Loose Bolts or Setscrews          Damaged Motor  Elliptical Gears Exceeds Motor’s Brake Horsepower... are cut straight and parallel to the axis of the shaft rotation No more than two sets of teeth are in 1X 1X 1X 1X 1X FREQUENCY Figure 11.34 Typical defective gear mesh signature 1X Gears and Gearboxes 22 5 mesh at one time, so the load is transferred from one tooth to the next tooth rapidly Usually spur gears are used for moderate to low speed applications Rotation of spur gear sets is opposite unless... compressed air is routed to the second stage, where the velocity and pressure are increased further Adding Figure 12. 1 Cantilever centrifugal compressor is susceptible to instability Compressors 23 3 Figure 12. 2 Airflow through a centerline centrifugal compressor additional stages until the desired final discharge pressure is achieved can continue this process Two factors are critical to the operation of these . symmetrical. FREQUENCY GEARMESH AMPLITUDE Figure 11. 32 Wear or excessive clearance changes side band spacing. Keith Mobley /Maintenance Fundamentals Final Proof 15.6 .20 04 7:38pm page 22 2 22 2 Maintenance Fundamentals In addition. Adding Figure 12. 1 Cantilever centrifugal compressor is susceptible to instability. Keith Mobley /Maintenance Fundamentals Final Proof 15.6 .20 04 7:42pm page 23 2 23 2 Maintenance Fundamentals additional. conditions. Figure 11.30 Herringbone gear. Keith Mobley /Maintenance Fundamentals Final Proof 15.6 .20 04 7:38pm page 22 0 22 0 Maintenance Fundamentals One other important fact about gear sets is