analysis of gear wear of vertical mill

simulation analysis of helical gears in the gear box of the rolling mill | atlantis press

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how to analyze gear failures

When an important gear failure occurs, someone becomes responsible for analyzing the failure, determining its cause and recommending a solution. A company can select its own engineer, an outside consultant or both. If a consultant is called in, this should be done as early in the process as possible.

Ideally, the engineer conducting the analysis should inspect the failed components as soon after failure as possible. If an early inspection is not possible, someone at the site must preserve the evidence based on instructions from the analyst.

The failure conditions can determine when and how to conduct an analysis. For example, if the gears are damaged but still able to function, the company may decide to continue their operation and monitor the rate at which damage progresses. In this case, samples of the lubricant should be collected for analysis, the reservoir drained and flushed and the lubricant replaced.

If gearbox reliability is crucial to the application, the gears should be examined by magnetic particle inspection to ensure that they have no cracks. The monitoring phase will consist of periodically checking the gears for damage by visual inspection and by measuring sound and vibration.

In some situations, the high cost of shutting down equipment limits the time available for inspection. Such cases call for careful planning. For example, dividing tasks between two or more analysts reduces the time required.

Request a skilled technician to disassemble the equipment under your direction. But, make sure that no work is done on the gearbox until you arrive. This means no disassembly or cleaning. Otherwise, a well-meaning technician could inadvertently destroy evidence.

Now, its time to assemble your inspection equipment, including items such as a magnifying glass, measuring tools, felt tip markers, lubricant sampling equipment and photographic equipment. A well-designed set of inspection forms for the gearbox, gears and bearings should be at the top of your priority list.

Before starting the inspection, review the background information and service history with the contact person. Then interview those involved in the design, installation, operation, maintenance and failure of the gearbox. Encourage them to tell everything they know about the gearbox even if they feel it is not important.

After completing the interviews, explain your objectives to the technician who will be working with you. Review the gearbox assembly drawings with the technician, checking for potential disassembly problems.

Before disassembling the gearbox, thoroughly inspect its exterior. Use an inspection form as a guide to ensure that you record important data that would otherwise be lost once disassembly begins. For example, the condition of seals and keyways must be recorded before disassembly. Otherwise, it will be impossible to determine when any damage may have occurred to these parts. Gear tooth contact patterns should be taken before completely disassembling the gearbox.

After the external examination, disassemble the gearbox and inspect all internal components, both failed and undamaged. Examine closely the functional surfaces of gear teeth and bearings and record their condition. Before cleaning the parts, look for signs of corrosion, contamination and overheating.

After the initial inspection, wash the components with solvents and re-examine them. This examination should be as thorough as possible because it is often the most important phase of the investigation and may yield valuable clues. A low-power magnifying glass and pocket microscope are helpful tools for this examination.

Gear tooth contact patterns. (Complete this step before disassembling gearbox components for inspection). The way in which mating gear teeth contact indicates how well they are aligned (Figure 1). If practical, record tooth contact patterns under either loaded or unloaded conditions. For no-load tests, paint the teeth of one gear with marking compound. Then, roll the teeth through mesh so the compound transfers the contact pattern to the unpainted gear. Lift the pattern from the gear with scotch tape and mount it on paper to form a permanent record.

For loaded tests, paint several teeth on one or both gears with machinists layout lacquer. Run the gears under load for a sufficient time to wear off the lacquer and establish the contact patterns. Photograph the patterns to obtain a permanent record.

Describe all important observations in writing, using sketches and photographs where needed. Identify and mark each component (including gear teeth and bearing rollers), so it is clearly identified in the written description, sketches and photographs. It is especially important to mark all bearings, including inboard and outboard sides, so their location and position in the gearbox can be determined later.

During the inspection, you will begin to formulate hypotheses regarding the cause of failure. With these hypotheses in mind, select specimens for laboratory testing. Take broken parts for laboratory evaluation or, if this is not possible, ensure that they will be preserved for later analysis.

Oil samples can be very helpful. But, an effective lubricant analysis depends on how well the sample represents the operating lubricant. To take samples from a gearbox drain valve, first discard stagnant oil from the valve. Then take a sample at the start, middle and end of a drain to avoid stratification. To sample from the reservoir, draw samples from the top, middle and near the bottom. Examine the oil filter and magnetic plug for wear debris and contaminants.

Have you got it all? Before leaving the site, make sure that you have everything needed (completed inspection forms, written descriptions and sketches, photos and test specimens) for completing the failure analysis.

Several failure modes may be present and you need to identify which is the primary mode, and which are secondary modes that may have contributed to failure. Table 1 lists six general classes of gear failure modes, of which the first four are the most common. An understanding of these four common modes will enable you to identify the cause of failure.

As a fatigue crack propagates, it leaves a series of beach marks (visible to the naked eye) that correspond to positions where the crack stopped (Figure 2). The origin of the crack is usually surrounded by several concentric curved beach marks.

Most gear tooth fatigue failures occur in the tooth root fillet (Figure 3) where cyclic stress is less than the yield strength of the material and the number of cycles is more than 10,000. This condition is called high-cycle fatigue. A large part of the fatigue life is spent initiating cracks, whereas a shorter time is required for the cracks to propagate.

Stress concentrations in the fillet often cause multiple crack origins, each producing separate cracks. In such cases, cracks propagate on different planes and may join to form a step, called a ratchet mark (Figure 2).

2. Contact fatigue. In another failure mode, called contact or Hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface (Figure 4). The most common types of surface fatigue are macropitting (visible to the naked eye) and micropitting.

Based on the type of damage, macropitting is categorized as nonprogressive, progressive, spall or flake. The nonprogressive type consists of pits less than 1 mm diam in localized areas. These pits distribute load more evenly by removing high points on the surface, after which pitting stops.

In one type, called spelling, the pits coalesce and form irregular craters over a large area. In flake macropitting, thin flakes of material break out and form triangular pits that are relatively shallow, but large in area.

Micropitting has a frosted, matte or gray stained appearance. Under magnification, the surface is shown to be covered by very fine pits (< 20 mm deep). Metallurgical sections through these pits show fatigue cracks that may extend deeper than the pits.

3. Wear. Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. The three major types of wear are adhesion, abrasion and polishing. Adhesion is the transfer of material from the surface of one tooth to that of another due to welding and tearing (Figure 5). It is confined to oxide layers on the tooth surface. Adhesion is categorized as mild or moderate, whereas severe adhesion is termed scuffing (described later).

Typically, mild adhesion occurs during gearset run-in and subsides after it wears local imperfections from the surface. To the unaided eye, the surface appears undamaged and machining marks are still visible. Moderate adhesion removes some or all of the machining marks from the contact surface. Under certain conditions, it can lead to excessive wear. Abrasion is caused by contaminants in the lubricant such as sand, scale, rust, machining chips, grinding dust, weld splatter and wear debris. It appears as smooth, parallel scratches or gouges (Figure 6).

Abrasion ranges from mild to severe. Mild abrasion consists of fine scratches that dont remove a significant amount of material from the tooth contact surface, whereas moderate abrasion removes most of the machining marks.

Severe abrasion, which removes all machining marks, can cause wear steps at the ends of the contact surface and in the dedendum. Tooth thickness may be reduced significantly, and in some cases, the tooth tip is reduced to a sharp edge.

Finally, polishing is fine-scale abrasion that imparts a mirror-like finish to gear teeth (Figure 7). Magnification shows the surface to be covered by fine scratches in the direction of sliding. Polishing is promoted by chemically active lubricants that are contaminated with a fine abrasive.

Polishing ranges from mild to severe. Its mild form, which is confined to high points on the surface, typically occurs during run-in and ceases before machining marks are removed. Moderate polishing removes most of the machining marks.

4. Scuffing. Severe adhesion or scuffing transfers metal from the surface of one tooth to that of another (Figure 8). Typically, it occurs in the addendum or dedendum in bands along the direction of sliding, though load concentrations can cause localized scuffing. Surfaces have a rough or matte texture that, under magnification, appear to be torn and plastically deformed.

Severe scuffing occurs on significant portions of a gear tooth (for example, the entire addendum or dedendum). In some cases, surface material is plastically deformed and displaced over the tooth tip or into the tooth root. Unless corrected, it is usually progressive.

In many cases, failed parts and inspection data dont yield enough information to determine the cause of failure. When this happens, gear design calculations and laboratory tests are usually needed to develop and confirm a hypothesis for the probable cause.

Gear design calculations. The gear geometry data collected earlier aids in estimating tooth contact stress, bending stress, lubricant film thickness, and gear tooth contact temperature based on transmitted loads for each gear. These values are calculated according to American Gear Manufacturers Association standards such as ANSI/AGMA 2001-B88 for spur and helical gears.

Laboratory examination and tests. A microscopic examination may confirm the failure mode or find the origin of a fatigue crack. Both light microscopes and scanning electron microscopes (SEM) are useful for this purpose. An SEM with an energy dispersive X-ray is especially useful for identifying corrosion, contamination or inclusions.

If the primary failure mode is likely to be influenced by gear geometry, check for any geometric or metallurgical defects that may have contributed to the failure. For example, if tooth contact patterns indicate misalignment or interference, inspect the gear for accuracy on gear inspection machines. Conversely, where contact patterns indicate good alignment and the calculated loads are within rated gear capacity, check the teeth for metallurgical defects.

When all calculations and tests are completed, you need to form one or more hypotheses for the probable cause of failure, then determine if the evidence supports or disproves the hypotheses. Here, you need to evaluate all of the evidence that was gathered including:

Finally, after thoroughly testing the hypotheses against the evidence, you reach a conclusion about the most probable cause of failure. In addition, you may identify secondary factors that contributed to the failure.

A failure analysis report should describe all relevant facts found during the analysis, the inspections and tests, weighing of evidence, conclusions and recommendations. Present the data succinctly, preferably in tables or figures. Good photos are especially helpful for portraying failure characteristics.

detection of gear wear and faults in spur gear systems using statistical parameters and univariate statistical process control charts | springerlink

In this study, the detection of wear faults in spur gears was examined using vibration analysis, statistical process control method, and statistical parameters. For this purpose, a closed-loop test rig with a power transmission system was established. Defect-free gears were attached to the test assembly, and the system was operated at a specific torsional load and number of cycles until the gears were worn. Vibration amplitudes at vertical and horizontal directions, received via sensors on the bearings, were transferred to the computer with a digital-analog converter. The control charts were plotted by sampling 30 data points per hour. Upper and lower control limits were determined by using the data obtained from the defect-free gears. The gears are worn in the process due to the effect of applied torque and the operation conditions suitable for the formation of defects. As a result, the vibration amplitudes were increased. The accuracy and convergence of the statistical process control method were verified by the statistical parameters root mean square, kurtosis value, skewness value, crest factor, and peak-to-peak values. It was emphasized that great convergence and accuracy between the statistical process control results and statistical parameters results are achieved. The present study showed that the detection of abrasion of a robust gear could be graphically demonstrated through a real-time experimental study. The statistical process control method is convenient and easily applicable, which allows constructing a real-time early warning system detecting malfunctions at the start.

Pan, L.; et al.: Gear fault diagnosis method based on wavelet-packet independent component analysis and support vector machine with kernel function fusion. Adv. Mech. Eng. 10(11), 11036 (2018)

Hartono, D.; Halim, D.; Roberts, G.W.: Gear fault diagnosis using the general linear chirplet transform with vibration and acoustic measurements. J. Low Freq Noise Vib. Active Control 38(1), 3652 (2019)

Ahuja, A.S.; Ramteke, D.S.; Parey, A.: Vibration-based fault diagnosis of a bevel and spur gearbox using continuous wavelet transform and adaptive neuro-fuzzy inference system. In: Soft Computing in Condition Monitoring and Diagnostics of Electrical and Mechanical Systems, pp. 473496. Springer (2020)

Andrade, F.; Esat, I.; Badi, M.: A new approach to time-domain vibration condition monitoring: gear tooth fatigue crack detection and identification by the Kolmogorov-Smirnov test. J. Sound Vib. 240(5), 909919 (2001)

Zhan, Y.; Mechefske, C.: Load-independent condition assessment of gears using kolmogorov-smirnov goodness-of-fit test and autoregressive modeling. In: Engineering Asset Management, pp. 237252. Springer (2006)

Guo, P.; Fu, J.; Yang, X.: Condition monitoring and fault diagnosis of wind turbines gearbox bearing temperature based on kolmogorov-smirnov test and convolutional neural network model. Energies 11(9), 2248 (2018)

Parey, A.; et al.: Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect. J. Sound Vib. 294(3), 547561 (2006)

Mara, S., Arslan, H. & Birgren, B. Detection of Gear Wear and Faults in Spur Gear Systems Using Statistical Parameters and Univariate Statistical Process Control Charts. Arab J Sci Eng (2021).

analysis of reasons about failure of raymond mill gear transmission-sbm industrial technology group

SummaryIn the grinding process of Raymond mill, failure of gear transmission is one of the frequent problems. Once the Raymond mill gear transmission fails, it will seriously affect the grinding production and delay the efficiency of the whole production plant.

In the grinding process of Raymond mill, failure of gear transmission is one of the frequent problems. Once the Raymond mill gear transmission fails, it will seriously affect the grinding production and delay the efficiency of the whole production plant. What are the reasons about failure of Raymond mill gear transmission?

1. In the working process of Raymond mill, the working environment of gear transmission is poor, and the gear is serious polluted because of the serious influence of dust particles. In addition, the lubricating oil of the gear transmission part is not added in time, the lubricating oil is seriously polluted, etc., will both cause the failure of Raymond mill gear transmission.

2. After a period of operation of the gear transmission, the axis of the pinion and the axis of Raymond mill classification drum may become non-parallel, resulting in the local contact of gear mesh. If the gear is unevenly stressed across the entire tooth width, it is easy to cause bending and torsion deformation of the gear shaft. In addition, if the structure of the gear transmission material is uneven, there are slag inclusions, gas holes and hard particles, etc., the local shear stress of the surface or subsurface layer is too large, resulting in the failure of gear teeth.

3. There is stress concentration on the gear of Raymond mill. When the tooth tip of the gear enters meshing state, initial cracks are formed in the surface layer under the action of excessive equivalent contact shear stress. During the operation process of gear, the high pressure oil wave generated by contact pressure enters the crack at a high speed, and has a strong fluid impact on the crack wall. At the same time, the surface of the gear pair can close the crack opening, so that the oil pressure in the crack further increases, and forces the crack to expand in the direction of depth and tooth surface, and the material falls off from the tooth surface, forming pitting corrosion.

4. In the transmission, the time for the single tooth of the gear pair to bear the load is greatly extended, which is an important reason for the rapid wear of the gear. The decrease of the coincidence degree will inevitably lead to the increase of the gear backlash, so that some impurities, floating objects and dust in the air are easier to enter between the meshing surfaces of the gear pair, causing abrasive wear.

three causes of gearbox failure - mro magazinemro magazine

Gear reducers can be complex machines that apply the science of gearing and mechanical advantage to run thousands of complex operations in many different industries. Gearbox manufacturers have designed a variety of gearboxes in multitudes of different configurations and gear ratios. When failures happen it is critical to understand how to repair the failed units and how to prevent future failures in order to keep production up and running.

Lubrication is critical for both bearing and gear life. Important aspects of lubrication are the volume of lubricant that is delivered to each gear mesh and bearings, as well as the properties of the lubricant. The lubricant forms a thin film that prevents metal-to-metal contact between gears and between bearing components. Modern industrial gears use an involute tooth form and tooth engagement, which is a combination of rolling and sliding. The oil film is a thin barrier between moving parts that allows the rotating force to turn the gears easily without damage to the metal surfaces. Contamination in the lubricant can result in scuffing and much faster wear for both the bearings and the gearing in a gearbox, so it is imperative that maintenance mechanics check gearbox lubricant for contamination periodically, once for year as a minimum. Each gearbox would have a recommended oil level as well as a method to lubricate both the bearings and the gear set. With bath lubrication, all moving components dip down below the oil level. With splash lubrication, oil is splashed around inside the gearbox housing by fast moving components, covering all moving parts. With pressure lubrication, oil is pumped to each gear mesh and bearing through spray nozzles or oil passages from the gearbox oil sump or from and external reservoir.

Gears are designed to mesh with either parallel or right angle shafts and with a specific backlash between gear teeth. The alignment of the gears in the gearbox housing is critical, and assessment of the alignment of the gearbox housing bores is very important when a rebuild is being done. In mining applications, where gear reducers are in heavily loaded applications, we sometimes see firsthand that reducer housings can get distorted or bent. Even a small amount of misalignment can cause premature gear wear and failure. The gear teeth will not mesh the way they were designed to, resulting in excessive loads in the weaker parts of the teeth. Bearings rotating in their bores can also cause wear in the bores, in turn causing misalignment and gear damage.

When receiving a reducer from a mine for rebuild, repair shops should understand all of the application details, including input forces, output requirements, suspected cause of failure, maintenance history, vibration analysis results and oil sample analysis results. Once the reducer is in the shop, a full disassembly will take place with photo documentation and labelling of parts. Gear inspection will include an MPI of the teeth and any wear patterns will be documented. Not all rebuilds will require replacement of gears, in most cases only bearings and seals will be required unless the failure is more catastrophic or if contamination or misalignment has been in place for a longer time. The millwrights will make a full report on every detail so that parts can be ordered or manufactured to complete the rebuild. An engineer will then measure and reverse engineer any gearing so that they can be replaced, if required. Some of the larger and older reducers are no longer available from the original manufacturer, so OEM supply of parts would be impossible. Even if the OEM can supply parts, the lead-time may be prohibitive, especially when an emergency repair is required.

Each reducer is rebuilt after full cleaning, part replacements and housing alignment inspection. Housings can be re-machined if bores are worn or misaligned. The gearbox then has backlash, and bearing clearances measured and documented, and is test run under no load to check for vibration, noise or leakage. Finally, the gearbox is relabelled and painted to look new.

We often see reducers that are pushed to the limits and beyond. Conveyers are set to speed up, heavier loads are applied to the outputs and emergency stops and or cold starts can add shock loads to the reducers beyond their design ratings. In older reducers, just the normal wearing of parts can change the internal clearances and cause problems. Once a critical limit is reached, failure can occur quickly.

It can be difficult for mines to know how much extra loading a reducer can take. When a reducer starts to heat up, it draws more power to run, has an increase in noise and vibration levels and time for a rebuild becomes critical. It may take years for the first signs of damage or component failure to appear, but once that initial damage occurs, the progression of damage is accelerated and will ultimately lead to a catastrophic failure. Repairing a gearbox in the initial stages of failure may involve changing only bearings and seals, but repair of a gearbox that has suffered a catastrophic failure will likely involve much more cost as well as a longer lead time.

It is wise for any large facility to have spare bearings, seals or even full gear reducers on site to get back up and running quickly after a failure. If a spare reducer is installed to replace a failed gearbox, the failed reducer can be rebuilt and become the new spare without being rushed, avoiding overtime fees during the repair process. In very large reducers, the parts, such as bearings and gears, can be very expensive, reflecting not just the cost to purchase the components, but also the lead times that cause excessive downtime costs.

Smart monitoring, careful inventory of critical parts and preventative maintenance programs that check the oil temperature, oil contamination and monitor vibration levels will all help minimize downtime. Having a good partnership with a rebuild shop that offers full service and turnkey repairs will also ensure quality rebuilding. As more and more facilities outsource rebuilding services, understanding what suppliers can and cant do is critical.

Rapid Gear is an OEM supplier of custom gearing and precision machined parts. As part of our MRO services as a full turnkey supplier, Rapid Gear also offers full rebuilding services, including reverse engineering for any make or brand of gear reducer. Renato Foti, director of business development, Rapid Gear, Kitchener, Ont., can be reached @[email protected] For more information, visit

Are you looking at how to have Effective Asset Management? According to Leonard Middleton, Consultant, Asset Management Solutions, it Starts with Good Assets. WATCH HERE: #assetmanagement #solutions #maintenance #manufacturing #assets

PLANT TALK podcast is now LIVE! In our first episode Greta Cutulenco, from @AcertaAnalytics Solutions, spoke with Plants Associate Editor, Maryam Farag, about the differences between the #automotive and tech industries. LISTEN NOW:

failure analysis of machine shafts - efficient plant

Fig. 1 The appearance of an overload failure depends on whether the shaft material is brittle or ductile. Whether related to motors, pumps or any other types of industrial machinery, shaft failure analysis is frequently misunderstood, oftenbeing perceived as difficult and expensive.For most machine shafts, however, analysis should be relatively straightforward. Thats because the failure typically provides strong clues to the type and magnitude of forces on the shaft and the direction they acted in: The failed parts will tell exactly what happened.

There are only four basic failure mechanisms: corrosion, wear, overload and fatigue. The first twocorrosion and wearalmost never cause machine-shaft failures and, on the rare occasions they do, leave clear evidence. Of the other two mechanisms, fatigue is more common than overload failure. (NOTE: Keep in mind that many times corrosion will act in conjunction with fatigue loading to cause a shaft failure.) This article will focus on failures resulting from overload and fatigue factors.

Overload failuresOverload failures are caused by forces that exceed the yield strength or the tensile strength of a material. As depicted in Fig. 1, the appearance of an overload failure depends on whether the shaft material is brittle or ductile.

No shaft materials are absolutely brittle or absolutely ductile. The shafts used on almost all motors, reducers and fans are low- or medium-carbon steels and relatively ductile. As a result, when an extreme overload is placed on these materials, they twist and distort. The bent shaft shown in Photo 1 has been grossly overloaded by a torsional stress.

In diagnosing which mechanism caused the failure, a critical point to remember is that overload failures are generally caused by a single load application, while fatigue failures are always the result of a load applied repeatedly over many cycles. This means if the shaft failed as a result of an overload, the force that caused the failure was applied the instant before the shaft broke. Conversely, if fatigue was the culprit, the initial force may have been applied millions of cycles before the final failure occurred.

There are occasional cases when a ductile shaft will fail in a somewhat brittle manner. Photo 2 shows an example of this situationi.e., what happened when a 200 hp, 3600 RPM motor suddenly stopped running. The result was a huge torsional stress and a cracked shaft. But because the material is ductile, the angle of the crack it is not at the 45 position shown in Fig. 1, and there is obvious distortion of the keyway. When ductile materials are grossly overloaded very rapidly, they tend to act in a brittle manner.

Fortunately, brittle fractures of machine shafts are extremely rare. Like all brittle fractures, they are characterized by a relatively uniform surface roughnessthe crack travels at a constant rate, and surface features called chevron marks are evident. Photo 3 shows the brittle fracture of the input shaft of a large reducer that was dropped. The chevron marks are the fine ripples on the surface that all point just to the left of the keyway.

Occasionally, a portion of a machine shaft will be case-hardened to reduce the wear rate. (NOTE: Case-hardening is usually done solely for wear-resistance purposes.) Photo 4 shows the case-hardened splined section of a hydraulic pump shaft, including its hardened case, the ring around the circumference with a very different texture than the majority of the shaft and chevron marks that point to the origin of the damage. Based on how this fracture grew straight across the shaft, the cause could have been related to either bending or tension. Its relatively uniform surface, though, would indicate that this fracture is of a brittle naturewhich also means it was caused by a single force application. Furthermore, since its impossible to put significant tension on a spline, the analyst could safely say that a single bending force caused the failure.

Fatigue failuresFatigue is caused by cyclical stresses, and the forces that cause fatigue failures are substantially less than those that would cause plastic deformation. Confusing the situation even further is the fact that corrosion will reduce the fatigue strength of a material. The amount of reduction is dependent on both the severity of the corrosion and the number of stress cycles.

Once they are visible to the naked eye, cracks always grow perpendicular to the plane of maximum stress. Figure 2 shows the fracture planes caused by four common fatigue forces. Because the section properties will change as the crack grows, its crucial for the analyst to look carefully at the point where the failure starts to determine the direction of the forces. For example, while it is common for torsional fatigue forces to initiate a failure, the majority of the crack propagation could be in tension. Thats because the shaft has been weakened and the torsional resonant frequency has changed.

The condition or roughness of the fracture surface is one of the most important points to look at in analyzing a failure because of the difference between overload failures and fatigue failures. With overload failuresbecause the crack travels at a constant ratethe surface is uniformly rough. Fatigue-induced cracks, however, travel across the fracture face at ever-increasing speeds. As a result, the typical fatigue fracture face is relatively smooth near the origin(s) and ends in a comparatively rough final fracture.

A typical plain bending fatigue failure is depicted in Fig. 3. The crack started at the origin and slowly grew across the Fatigue Zone (FZ). When it reached the boundary of the Instantaneous Zone (IZ) the crack growth rate increased tremendously and the crack traveled across the IZ at approximately 8000 ft/sec. During the period of growth across the FZ, there may be changes in the loading on the shaft, which result in changes in the surface that appear as progression marks.

Rotational loads or plane bendingFor a fatigue failure to occur, the forces must have been applied many times. There are low-cycle failures but most industrial fatigue failures weve seen involve more than 1,000,000 load cycles. A valuable feature of fatigue-failure interpretation is that the crack growth, i.e., the surface appearance, tells how the load was applied. If the crack grows straight across the shaft (as shown in Fig. 3), the force that caused the failure must have been a bending load operating in a single plane.

Figures 4 and 5, however, show examples of rotating bending. The difference between these two failures is that the shaft in Fig. 4 has a single origin, while the fracture in Fig. 5 has multiple origins. Looking at the two sketches, we see the IZ of Fig. 4 is the larger of the twowhich indicates that the load on the shaft when it failed was greater than that on Fig. 5. The analysis also shows that, even though Fig. 5 was less heavily loaded, it had many more fracture origins, an indication of a high stress concentration, such as a shaft step with a very small radius. The ratchet marks are the planes between adjacent crack origins and grow perpendicular to the crack propagation.

Photo 5 shows a 200 hp, 1180 RPM motor shaft that failed in less than a day. No progression marks means the fatigue load was constant. The instantaneous zone is relatively large, indicating the shaft was heavily loaded. Cracking started at numerous locations around the shaft, pointing to rotating bending as the cause. So many ratchet marks concentrated on the top and bottom of the photo make us suspect the shaft may not have been straight. Inspection, though, would indicate the root cause was associated with the belt drive. In fact, the sheaves were worn so badly that the belts were riding in the bottom of the grooves. This situation approximately doubled the shaft bending stress.

The drive shaft in Photo 6 was on a steel-mill elevator. The surface is smoothest near the root of the keyway and became progressively rougher as the crack grew across the shaft. Numerous progression marks surrounding the tiny IZ and the change in surface condition about 40% of the way across the shaft from the IZ suggest something changed during the crack growth or that the elevator was not used for an extended period. These features are indicative of a slow-growing failureand the fact that fretting corrosion may have substantially reduced the fatigue strength.

Torsional fatigue failuresUntil the advent of variable speed drives (VSDs), torsional fatigue failures were rare: Equipment designers could anticipate operating speeds and excitation frequencies and engi-neer around them. The purpose of a VSD is to allow operation at a wide range of speeds. That, unfortunately, has led to many motor and driven-shaft failures due to torsional-fatigue factors. While the most common torsional fatigue cracks start at the sharp corner (stress concentration) at the bottom of the keyway when couplings are poorly fitted, another common appearance is the diagonal shaft crack (like that shown in Fig. 2).

Photo 7 reflects the battered end of a motor shaft with a terrible (loose) coupling fit that let the hub repeatedly drive the key against the side of the keyway until a fatigue crack developed. (Its not uncommon to see cases where the crack has propagated entirely around the shaft, leaving only a stub on the shaft.)

Photo 8 shows both halves of the torsional-fatigue failure of a fan shaft in a plant that had recently changed to a VSD. The 45 angle to the central axis is a sure sign of torsional stresses, and the change in surface roughness across the shaft indicates the cause was fatigue forces.

Torsional fatigue stresses frequently go unnoticed (until too late) because personnel dont understand what theyre looking at. For example, both of the pump shafts shown in Photo 9 failed due to torsional fatigue aggravated by a reduction in strength caused by corrosion. Some might look at the fracture face of the shaft on the right and think it was caused by rotating bending. Closer examination of the many ratchet marks shows they are at a 45 angle to the centerline of the shafta positive indication of torsional fatigue stresses with numerous origins. (Note that the ratchet marks seen in Photo 5 have straight sides, an indication that they were caused by bending forces.)

Words of caution on interpreting the cluesWhile the oldest part of a fatigue failure typically has the smoothest surfaceat least 98% of the timeits still crucial to look carefully at the failed part in the area of the origin: The shaft surface will describe the force.

One of the greatest takeaways from this article is that a crack always grows perpendicular to the plane of maximum stress. Many times, weve seen shafts where the originating force was torsion with a short angular crack, but the majority of crack propagation was in bendingfooling inspectors into thinking that bending was the primary force. Dont let yourself be taken in this way. MT

Neville Sachs is a Senior Consulting Engineer with the Sachs Salvaterra & Associates division of Applied Technical Services, Inc., a firm specializing in nondestructive testing and technical support services for improved plant and equipment reliability. Email: [email protected]

safety measures to use while operating milling machines

These short lists in no way cover all the factors you must consider when implementing workshop safety for your CNC machinists and shop personnel. Instituting a culture of shop safety may require consulting with a specialty firm to help you comply with OSHA and state safety regulations for yourself, your personnel, and your shop. You may wish to require your employees to pass a safety quiz before allowing them on the shop floor in any capacity.

gear mesh misalignment | gear solutions magazine your resource to the gear industry

Gear mesh misalignment may result in shifts in the load distribution of a gear pair that results in increasing contact and bending stresses, moving the peak bending stresses to the edge of the face width, and might also increase gear noise. This paper will discuss the sources of misalignment and show some examples of how this misalignment affects load distribution. Analyses will show how lead crowning and/or end relief can reduce the harmful effects of misalignment and then will discuss some of the pitfalls in the use of contact patterns to evaluate load distribution.

Throughout this paper, the helical gear pairs defined in Table 1 will be used as examples. These gear pairs were part of a large test program of the Army and NASA [1] and have subsequently been analyzed and tested at The Ohio State University [2]. Figure 1 shows the transverse view of the helical gear pair with the superimposed line of action that is tangent to the base circles of the respective gears.Figure 2 shows a schematic of this line of action and also defines the coordinate systems to be used in this paper. Figure 2shows how this line of action extends to a plane of action that now shows the superimposed diagonal lines of contact for one contact position. This plane of action is bounded on the top and bottom by the respective outside diameters of the two gears and on the edges by the face widths. The diagram would indicate that, for this position, there are three pairs of teeth in contact. Since the contact ratio is 2.63 at other positions, there will be two pairs of teeth in contact.

All simulation results presented in this paper will use a program entitled Load Distribution Program (LDP) that starts with the input geometry, discretizes the contact lines, and then simultaneously solves torque equilibrium and motion continuity equations [3-4]. Essentially the analysis of this program may be thought of as a special-purpose finite element solution that has many analytical simplifications that allow extremely time-efficient solutions.

In the gear contact sense, mesh misalignment implies the axial shifting of the position of the meshing surfaces due to either deflections or errors in the manufacture of the gears and their housings. The occurrence of any of these actions typically alters the location of contact on the tooth flank and may lead to large stresses and increased noise of a gear pair. Mesh misalignment may be divided into three categories:

Parallel misalignment, whether along the plane of action or at right angles to the plane, essentially results in a change in center distance of the shafts. A change in center distance will result in a slight change in the intersection of the outside diameters with the plane, thus slightly altering the profile contact ratio of the gear pair. Figure 3shows this result for a contracting of the center distance, where a slight extension of the active contact area occurs, thus resulting in a slight increase of the profile contact ratio. For our gear pair, a contraction of 0.0002 inches results in the profile contact ratio shifting from 1.383 to 1.385, so this change is quite small and may usually be neglected in predictive analysis.

Unlike parallel misalignment, the effect of angular misalignment depends upon the plane that it acts in. Angular misalignment parallel to the plane of action tends to shift the load to the side of the tooth by increasing the separation at one side of the tooth and reducing the separation at the other side of the tooth. In this case, the shape and area of the theoretical active contact plane remains the same as the ideal shape of Figure 2. Figure 4 shows how this type of misalignment changes the load distribution from the aligned case to a case where the line of action misalignment is 0.002 inches across the face width (0.0016 in/in). We see that the load shifts sharply to the left, but that each contact line still has contact over its entire length.

However, when the angular misalignment is at a right angle to the plane of action, the outside diameters of the respective gears rotate as shown in Figure 5 in such a manner that the shape of the contact zone becomes skewed and the contact area is reduced. This reduction in contact area results in a reduction of total contact ratio. If this misalignment is severe enough, the effect on the contact lines will be similar to what would happen if two cylinders are skewed, where the contact line will change to elliptical contact as shown in Figure 6. This same skewing will occur for the lines of contact of both spur and helical gears.

There are many causes of misalignment; some of them directly cause line of action (LOA) or offline of action (OLOA) misalignment, and others cause misalignment in rather arbitrary directions. Figure 2shows a set of coordinate systems in which the shafts are aligned vertically in an x-y horizontal/vertical coordinate system. The appropriate gear mesh misalignment system is shown by the LOA and OLOA directions.

The normal convention in defining shaft misalignments would be to use the horizontal or vertical coordinate system in which x-direction misalignments would define changes along the centerline that are often called parallelism errors, and y-direction misalignments are at right angles to the centerline and are often referred to as skew misalignment. We shall refer to these misalignments as Mx and My, respectively. We will also assume that these misalignments are given in normalized units of mm/mm in Metric units or in/in in English units. Using these non-dimensional units, the values will be the same whether we consider Metric or English units. In order to compute the misalignments in the LOA and OLOA directions, we need to use the following formulas: MLOA = MxSin + MyCos , and MOLOA = MxCos + MySin

With regard to line of action misalignment, one finds that the y-axis skew misalignment is far more important than the parallelism misalignment. If one is given the misalignments in angular units as Mx and My, respectively, then the respective normalized misalignments along the x and y directions would be: Mx = Tanx and My = Tany

If the misalignments of a 23.45 degree pressure angle gear are 0.002 in/in in the x-direction and 0.001 in/in in the y-direction we get LOA and OLOA misalignments of: MLOA = 0.398*0.002 + 0.917*0.001 = 0.00171 in/in MOLOA= 0.917*0.002 + 0.398*0.001 = 0.00223 in/in

Check for Offline Action Misalignment Significance The theory of Hertz [Roark] will be applied to determine whether the major axis the ellipse length of Figure 6. If the ellipse diameter is less than the face width, then it should be factored into load distribution calculations. The equations for calculating the ellipse diameters are given as:

When the appropriate radii are inserted into the above equations, one gets the major radius to be about 15 in and the minor diameter is 0.007 in. The major diameter is obviously considerably larger than the face width of 1.25 in, hence the assumption of line contact of cylinders is upheld and there is no need to perform any special analyses. Even if the load is reduced by a factor of 10, the major diameter reduces to 5.5 in, which is still significantly larger than the face width.

Lead wobble. This error in lead slope results from an angular eccentricity that occurs when mounting the gear. This occurs either when it is placed on its manufacturing arbor or when it is mounted to its shaft, and it wobbles relative to the shaft. Figure 7shows sample lead charts for four teeth taken at 90-degree increments around a gear. The changing slopes of the four charts indicate lead wobble, and the average slope is the lead slope error listed above.

Bore parallelism and skew. Here the error is most likely to be defined in terms of the x and y misalignments defined in the previous section. Often prints are very clear about the parallelism misalignment, but are sometimes a bit hazy with regard to the skew misalignment. Yet skew misalignment will have a greater effect on LOA mesh misalignment.

Shaft bending deflections. For a single gear on a shaft, this deflection will be along the line of action, but when additional gears and other external forces are applied to the shaft, these deflections will take on a general direction. Also, for wide face width gears, this misalignment may have some curvature error as well as slope error. It is important to note that this misalignment is reasonably linear with load, so as load increases, the misalignment also increases .

Bearing and housing deflections. Since both of these deflections are at the shaft support, they may be added together. Bearing stiffness increases with load, so the increase in bearing deflection with load is not directly proportional. As with shaft deflections, bearing deflections are in the line of action direction if only a single gear is mounted on the shaft, but are more general when additional forces are applied to the shaft. Housing deflections, which can exceed those of the bearings, are usually quite linear with load, but may need to be measured or need a detailed finite element analysis in order to be determined with some certainty. One should also be aware that the stiffnesses at the bearing has five degrees of freedom; three in translation, and two in rotation. Thus, to account for them properly, a complete bearing stiffness matrix must be determined.

Gear blank deflections. The blanks of gears with thin rims tend to deflect away from the line of action on the overhanging section of the gear tooth. This deflection will tend to reduce the load carried in this region of the tooth.

Temperature gradients. These gradients are particularly apparent in helical gears, where the lubricant tends to be pushed along the helix and heats up as it progresses. The blank then heats up and expands, thus giving an apparent change in helix angle, as well as a slight change in all gear geometry parameters due to thermal expansion.

Centrifugal forces. In thin-rim gears that spin at high speed, the centrifugal forces may be great enough to cause a differential deflection across the tooth face width, hence creating a form of misalignment.

Fortunately for the gear designer, the values of many of these misalignments are quite small for their application, but they each should be investigated to be sure that they do not impact a given design.

Mounted gear runout. Mounted runout includes the effect of manufactured eccentricity as well as mounting eccentricity. These eccentricities have the effect of increasing and then decreasing the effective shaft center distance at a period of one shaft rotation per each gear.

Housing thermal expansion. This has the effect of increasing the center distance, but one must remember that the gear elements and shafts might also expand. If they are made of different materials, differential expansions must be considered.

When considering misalignment, one must take into account the quality level of the gears, tolerances placed on engineering drawings, and deflections due to load or temperature. Misalignments related to tolerances or accuracy are assumed to occur in a random fashion, while those due to load or temperature may be much more systematic. In the latter case, it may be possible to provide mean changes to the lead to compensate for these effects. However, in so doing, one should be reminded that these systematic changes in alignment change with load, so any lead change will be good only at that load.

In the example calculation, AGMA Q9 (old definition) lead tolerances will be used for each gear (this translates to roughly an AGMA A8 gear using the new definition), a bore tolerance of 0.005 inch will be applied in the x and y directions, and the simple shaft model of the Load Distribution Program will be used to analyze shaft deflections. The gear set will be mounted on the shafting that is configured in Figure 8, where the shaft diameters are 1 inch and the bearing radial stiffness is 1e6 lb/in. We shall also assume that the temperature of the left side is elevated 150F and the right side is elevated 100F.

Figure 9shows the shaft deflection and bearing deflection results of the LDP model when using a unit load (1.0 lb-in). The three different graphs indicate deflections if the mean load is placed at three different locations across the face width. In this case we shall assume the load is centered, so the middle trace will be used.

Shaft, bearing, and housing deflections. The data from the center of the teeth in Figure 9 is used. Since the data is for the line of action, it must be converted to center distance coordinates using the sine function and the values must be doubled since the identical shafts will have the same deflections.

Mounted gear runout. Like bore parallelism, runout has a mean of zero, but will have minimum and maximum values that must be added for the two gears to get the maximum extremes. The AGMA Q9 runout is 0.002 in per-gear. Since this is a peak-to-peak value, one would expect the plus or minus values to be 0.001 in per-gear with the changes in center distance being twice this value or 0.002 in (two gears doubles the error).

The final center distance change will have 0.003 in (0.001 + 0.002) of random error and +0.00532 in giving a center distance range of: 0.00532 0.003 in. Using the maximum center distance increase of 0.00832 in gives a reduction in the profile contact ratio of the gear pair from 1.383 to 1.328, and the backlash increases from 0.006 in to 0.0138 in.

Again, both random and systematic errors exist. Values will be calculated in normalized units of in./in, but may easily be converted to inches across the face width by multiplying by the face width of 1.25 in.

Lead slope error.The AGMA Q9 lead error is 0.00048 in. Since this is the total span of the error, we shall divide it by two so that it gives the plus minus error of 0.00024 in. We must multiply this by two to take into account the possibility of both gears having maximum lead error at the same time and divide by the face width to get its value in normalized form. This random error then becomes:

Bore parallelism and skew. Here we are going to assume that the tolerance on the bore locations in both the x and y directions are the same, so the tolerance of the bores along the line of action will be the same as the bore misalignment. This will be a random error that must be divided by the distance between the bearings to give a normalized value:

Here one could correct for the systematic error by putting a slope deviation of 0. 001461 in/in on the engineering drawing of the part, or one could treat this value as random misalignment in which case the worst-case misalignment would be 0. 000979 in/in. In the subsequent analyses we will assume the latter, and apply a worst-case misalignment of 0.002 in.

Angular OLOA misalignment: Could be calculated, but for now assume to be of the LOA misalignment = 0.15 degrees. This is very similar to the earlier calculation that concluded that the cylindrical contact used in the LDP calculation is extremely adequate.

Fortunately for the gear designer, the values of many of these misalignments are quite small for their application, but they each should be investigated to be sure that they do not impact a given design.

In addition to the load distributions of Figure 4, LDP also allows one to evaluate the contact stresses, transmission error, root stresses, and many other design evaluation parameters. Figure 10shows the contact stresses for both the aligned and misaligned perfect involute helical gears whose load distribution is shown in Figure 4.

Table 2summarizes the contact stress levels at several locations in the contact region. At both the entering and leaving corners of tooth contact, the stress levels get extremely exaggerated due to what is called corner contact [6]. This corner contact may be harmful or may simply get polished out so that the stress reduces closely to the surrounding values. If one wishes to eliminate this corner effect, the application of tip relief (removal of material at the tips of the teeth) is required. One notes that when the tooth pair is misaligned, the contact still covers most of the face width, yet the values of contact stresses that exclude the corners increase from 157 ksi to 242 ksi.

In order to compensate for misalignment, one often uses lead crowning or end relief [7] so that the loads and hence, stresses, do not rise at the tooth edges. We will next use the LDP program results to show the effects of both tip relief, circular lead crowning, and end relief on various gear design parameters. Selection of modification level and shape are such that transmission error the main noise excitation is minimized, while at the same time extreme levels of stresses and flash temperature are avoided for both the aligned and misaligned cases. Analysis is run at design load of 4000 lb-in.

Corner contact: We have avoided quoting values for corner contactstresses, since they are estimates at best and, depending upon thesimulation method, one can obtain a large range of values. However,the amount of corner contact is reported in a qualitative manner.

Sum-of-forces [8]: This is a more complete noise metric that takesinto account not only transmission error, but also friction forces andthe axial shuttling of the mean tooth force that results from the movementof the contact lines across the tooth.

Surface temperature: This is a metric that has been used to evaluatethe sensitivity of a design to scoring and other surface damage. Itaccounts for contact stresses as well as sliding velocity in the contactregion.

2) Profile crown only (Case I): In order to minimize peak-to-peak transmission error of the aligned set, 0.0011 in a circular tip modification is applied. Note that tip relief alone results in a large reduction in the noise excitations and flash temperature, even when misaligned, but results in increases in both contact stresses and root stresses. These increases result because any removal of material tends to centrally focus the loads, hence increasing stresses.

3) Profile crown and lead crown (Case II). 0.0120 in of circular lead crown was applied to the tip relieved gear. Since we are further focusing the load, both contact stresses and root stresses of the aligned part increase further. However, the lead crown lowers stresses for the misaligned gears. It is interesting that the noise excitations increase, but are still less than those of the perfect involute.

4) Combinations of tip relief and lead relief (Case III). Here we apply end relief and a more complex shape of profile modification that is shown in Figure 11. The resulting contact stresses plot for the aligned and misaligned gear pair are shown in Figure 12.

In situation 2, for instance, if there is lead wobble in the matingpart, the contact will move back and forth across the face width.The resulting contact pattern will superimpose each of the individualpatterns, and the result will be that the measured patternextends on both sides to the extremes of the individual patterns.Figure 10 illustrates this very well. The contact pattern for both thealigned and misaligned gears are shown in Figure 12.

Gear misalignment comes from a number of sources that have been identified in this article. Techniques such as lead crowning can assist the designer in minimizing the effects of misalignment, but requires some compromises by the designer. This paper has quantified some of the compromises that need to be made and has shown the value of load distribution analysis in assessing the effects of misalignment on key design parameters such as root and contact stresses, transmission error, and surface temperature.