Bevel gears have been made for over 50 years. There have been several incremental improvements to the initial methods, but the fundamental principles of machining these gears remain the same. Historically, there were two main ways to make a bevel gear.
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One method used specialized equipment and tooling; the other one used very simple tools (endmills) and required a solid model of the gear. It was a compromise either way. For the first method, customers had to wait for the right tooling to arrive and/or have special skills to prepare/modify the tooling. For the solid model-based method, the solid models were never right or complete enough to get good surfaces and contact patterns, and the productivity of the process was lower. Additionally, the two methods required completely different machines, operator skillsets, and programming software.
In last five to six years, things have changed significantly. Development of multi-tasking machines and new programming software combined with the newly-developed machining processes have created an opportunity to give a new glamour to gear machining and usher in 21st century advances. In short, gear manufacturing is reinventing itself.
This article focuses on how these advances are enabling new business plans for customers and on the indirect effects of these technologies.
To explain what I mean by the “indirect effects” of a technology, let’s take the example of a cell phone. People started using cell phones because they could call from anywhere—they no longer had to be in the office or carry the change for payphone. Parents then gave their children cellphones because that was safer. Improving safety became an indirect benefit of having cellphones. This was not the original motive, but a nice and important indirect benefit nonetheless. Similarly, the multi-tasking machines combined with new processes give several indirect benefits as outlined in the article.
Multi-tasking machines are machines with milling and turning capability, a sort of lathe and milling machine combined into one. They could be considered as two main types: Turn-Mill and Mill-Turn. Turn-Mill machines are typically suitable for longer parts (e.g. pinions) while Mill-Turn machines are suitable for larger diameter parts (e.g. gears). These are 5-axis machines that can do many manufacturing processes, machine all sides of the parts, and, in many cases, machine a part to completion. DMG/Mori Seiki already has machines of both these types in their broad portfolio. These machines are used in wide variety of industries including aerospace, medical, industrial, tooling, and now gear manufacturing.
For these new manufacturing processes, the tools are simple (end mills or disc cutters) with no special geometry for any specific gear form or tooth. No special option is required on the machines to make them produce gears. The key here is to generate the toolpath and create the gear geometry. This is where the programming software is so vital to the process.
The programming software gearMILL effectively handles the complexity of bevel gear geometries by making it visual. It does not need a solid model, and will create a surface using analytical data provided in gear data sheets. This way, customers can continue to use the gear design software that they currently use.
The software can currently program cylindrical gears, bevel gears, and worm wheels. It primarily uses two types of processes—one with flank milling (5-axis machining) and other using disc cutters (InvoMillingR). This means that same gear can be programmed in two different ways, using two different methods, while using the same machine and gear input data.
The software not only defines the geometry of the gear tooth but can also program the contact patterns. Under conventional processes, adjustment of this contact pattern is a skillful task—one has to do it either by lapping or by modification of the tool. The software makes it visual and easy to adjust. It makes the contact pattern adjustment more of a science than an art.
The quality of the gears produced by these methods is very good. Quality, as always, is proportional to cycle time. The more cycle time that one can spend the better the quality one can get. By definition, the above processes are milling processes. Hence, the quality of the gear tooth depends on milling process characteristics—stepover and feed rate. The stepover will affect the profile of the gear while the feedrate will affect the lead. Profile and lead errors on the tooth form will be shown on the quality charts from CMM measurement data. The methods allow machining of pre-heat treated and post-heat treated parts on the same machines.
All of the commentaries about “how well you can do the gears” or “how fast/slow you can produce them” or “how easy it is to program” are necessary prerequisites to consider, but not sufficient conditions to use these processes. But the case falls apart if the economics of the process do not justify. Readers of this article are very familiar with traditional bevel gear machining process costs (tooling costs, total times for machining, etc.). So here is an idea of what a cost-per-part would be for a part machined using multi-tasking machines.
I would first like to explain the key economic differentiators between the two processes. These are the “indirect” benefits that I explained earlier. Direct benefits are, of course, the ability to use standard tools, and the ability to program and adjust the parts just as needed. Now to the indirect benefits.
Reduced work-in-process, minimal idle resources (tools, machines, labor, etc.), reducing points of failures (single-point of failure is the best), and eliminating bottlenecks are all important aspects of lean manufacturing. By combining operations and including gear milling operations in the same setup as turning + milling, a leaner manufacturing process can be achieved.
Turning machine + milling machine + hobbing machine, as a sequential operation, will need a larger workforce and significantly more floor space. The need for buffers at each of these machines means significant work-in-process. Combining all operations into one machine with only one operator reduces work-in-process inventory. Additionally, this machine is the single point of failure—which is ideal. If any of the turning, milling, or hobbing machines go down, the whole line is affected. This is measured as production efficiency.
Let us assume that uptime for each machine is 90%. In the sequential operations, if any one machine fails, the whole machining cell is shutdown/operates at lower efficiency. Hence, the net uptime of such a cell is 0.9 x0.9 x 0.9 = 0.729 or 73%. A multi-tasking machine performing all operations and producing a part complete will have an uptime of 90%. Machining the part in a single setup has many other advantages. For example, the concentricity between gear pitch circle diameter and OD/ID of the gear is inherently ensured and that will improve the noise quality of the bevel gear.
Traditional methods use specialized tooling where the gear form is built in the tool profile. Customers need to maintain a large inventory of hobs and bevel gear tooling (depending on the variety of parts they machine), because they don’t know what they will need to machine next. This large inventory of tools really adds to the “tied-up capital” necessary for running the business. For example, if you have a $1 million-cost of tools in your inventory, though you are just keeping them there without using much, it is equivalent of having a $1 million-dollar machine sitting idle without doing anything—and you will still need to pay interest on it. At 10% cost of capital (conservative estimate) this is equivalent of having $13,215/month carrying cost. For one shift operation (12 hours) 20 days in a month, this accounts for 55$/hr. The individual inventory cost and cost of capital may be different, but this is a number that cannot be ignored. (Please note that this does not include the cost of ordering new tooling or regrinding the tooling, which is about 2.7% of the total operating cost for an average job shop ($16-million revenue) which accounts for about $450,000. These are costs incurred only when machining the parts and depend on how many parts are actually machined.)
Sometimes it may be justifiable to carry this large tooling inventory, e.g. a large-volume manufacturing plant that makes just a few types of parts and uses carbide tooling. Additionally, the individual inventory value and cost of capital may be different—but again, the bottom line cannot be ignored.
When comparing two processes, it is common practice to compare their cycle times. However, what really matters is the total processing time. This includes setup time and cycle time. Setup time is not just the time to setup a job—it’s the actual time required to get a first good part. The smaller the batch size, the larger the influence of setup time on the overall time. Practices like overruns are common ways to increase the batch size to reduce the impact of setup time. These increase the capital tied up in the inventory. As each part is different, and the context in which it was made is different, it is very difficult to compare the two processes and determine which is the best. However, I would encourage the readers to compare the total cycle times when you compare two processes.
Multi-tasking machines have multiple options for process automation. Barfeeders and vacuum extractors are all standard options. It is not too foreign to imagine a machining cell making bevel gear parts with a single machine, without an operator. The machine feeds a bar, the main spindle machines the part, and machines the bevel gear. The part is then cutoff and transferred to the 2nd spindle, the back end of the part is finished, and then the part is vacuum extracted out or dropped out into the parts catcher bucket. The machining process uses carbide inserts and can be stable. The machine will automatically select “the next tool” in the tool group (a set of similar tools in tool magazine) when the life of one tool expires. This machine can be remote monitored, and the only thing operator is required to fill up the barfeeder and collect the machined parts from parts bin. There is no robot, no sequential stack of tolerances, no machine sitting idle because another machine is down. It is a very lean operation. It is always possible to add a robot to the machining cell, but there are many things that can be done even without it.
Many readers will be running their production facilities on a per-hour cost basis, which is what we would like to use to essentially define the shop rate of a machine cutting gears on a multi-tasking machine.
While isolating a machine to calculate the cost of electricity and cost of leasing the facility (per machine) is slightly difficult, this exercise can quickly yield the cost of owning and operating the machine. Interestingly enough, the tooling costs in this process are only incurred if you are actually machining the part (there is little or no cost of carrying tooling when you are not making any parts. It’s the same case with electricity). The labor cost of $50/hour, at 8 hour/day, 20 days/month and 12 months equals $96K. This includes salary & benefits and is a conservative estimate.
Now compare this $101/hour cost to the $55/hour tooling carrying cost. Numbers tell the story themselves. One can clearly see the importance of considering these “indirect benefits”. Truly, the numbers will be different on a case-by-case basis, but I believe the range will be the same.
Overall, it is beneficial to make bevel gears on multi-tasking machines. While many debate about what is the best way to make a bevel gear on multi-tasking machines, my opinion is that no one process is best. Every single process has its benefits, challenges, and limitations. Multi-tasking machines offer a choice of the process that lets customer select the process. This optimizes the whole gear-making operation and increases profits. Finally, while considering these machines as gear-making machines, one should not forget that these are very good milling + turning + 5 axis machines in the first place—so you will have less opportunity to turn down a customer request for machining a part.
The standard definition of a Bevel Gear is a cone-shaped gear which transmits power between 2 intersecting axels.
Looking at bevel gears from the differences in helix angles, they can be generally classified into straight bevel gears, which do not have helix angles, and spiral bevel gears (including zerol bevel gears), which do have helix angles. However, because of the fact that manufacture facilities for straight bevel gears are becoming rare and the fact that straight bevel gears teeth cannot be polished, making spiral bevel gears which can be polished superior in terms of noise reduction, spiral bevel gears are likely to become more common in the future.
Bevel gears can be generally classified by their manufacturing methods, namely the Gleason method and Klingelnberg method, which each have differing teeth shapes, and presently most gears use the Gleason method. Incidentally, all gears manufactured by KHK use the Gleason method.
Furthermore, there are also variations in gears in terms of teeth pitch (modules, etc.), whether polished or not, and materials used. For example in the case of materials, S45C of machine structural carbon steel, SCM415 of machine structual alloy steel and MC901 of engineering plastic, etc. are often used, and duracon, etc. are used for plastic molded parts.
Please enter part number here for a price and a drawing of the gear
NOTICE: Use of CAD Drawings
The tooth profile detailed in the CAD drawing differs from that of the actual gear.
Also, please note that the details of any chamfer, fillet, or slotted groove on the CAD drawing may differ from the true values or shape on the actual product.
This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.
The gears used when two shafts intersect are based on two cones in rolling contact with apexes meeting at the point of intersection of the two axes and having teeth at the same distance from the apexes. These are called bevel gears. Above mentioned cones are called pitch cones and their half peak angles are called pitch cone angles.
Figure 8.1 Pitch Angles of Bevel Gears
In Figure 8.1, assume the shaft angle to be Σ, the respective numbers of teeth zi (i = 1, 2 ), angular speed ωi, and pitch cone angle (or simply pitch angle) ɣ0i , then consider the rotating speed of a point on the common contact line of the cones at distance K from the apex :
ω1 K sin ɣ01= ω2 K sin ɣ02
ɣ01 + ɣ02 = Σ, angular speed ratio ω1/ω2 = z2/z1
Therefore,
tan ɣ01 = sin Σ / [(z2/z1) + cos Σ ] , tan ɣ02 = sin Σ / [(z1/z2) + cos Σ ]
Normally, Σ = 90° so that :
tan ɣ01 = z1/z2, tan ɣ02 = z2/z1 and ɣ01 + ɣ02 = 90°
In particular, when ɣ01 + ɣ02 = 45°, the bevel gear is called a miter gear. Furthermore, when Σ ≠ 90°, as shown in Figure 8.2, it is called an angle gear.
Figure 8.2 Angle Gear
When the large gear has a pitch angle of 90°, it is called a crown gear. It is equivalent to a rack in spur gear and becomes the base for tooth form and tooth cutting.
Bevel gears have been made for over 50 years. There have been several incremental improvements to the initial methods, but the fundamental principles of machining these gears remain the same. Historically, there were two main ways to make a bevel gear.
One method used specialized equipment and tooling; the other one used very simple tools (endmills) and required a solid model of the gear. It was a compromise either way. For the first method, customers had to wait for the right tooling to arrive and/or have special skills to prepare/modify the tooling. For the solid model-based method, the solid models were never right or complete enough to get good surfaces and contact patterns, and the productivity of the process was lower. Additionally, the two methods required completely different machines, operator skillsets, and programming software.
In last five to six years, things have changed significantly. Development of multi-tasking machines and new programming software combined with the newly-developed machining processes have created an opportunity to give a new glamour to gear machining and usher in 21st century advances. In short, gear manufacturing is reinventing itself.
This article focuses on how these advances are enabling new business plans for customers and on the indirect effects of these technologies.
To explain what I mean by the “indirect effects” of a technology, let’s take the example of a cell phone. People started using cell phones because they could call from anywhere—they no longer had to be in the office or carry the change for payphone. Parents then gave their children cellphones because that was safer. Improving safety became an indirect benefit of having cellphones. This was not the original motive, but a nice and important indirect benefit nonetheless. Similarly, the multi-tasking machines combined with new processes give several indirect benefits as outlined in the article.
Multi-tasking machines are machines with milling and turning capability, a sort of lathe and milling machine combined into one. They could be considered as two main types: Turn-Mill and Mill-Turn. Turn-Mill machines are typically suitable for longer parts (e.g. pinions) while Mill-Turn machines are suitable for larger diameter parts (e.g. gears). These are 5-axis machines that can do many manufacturing processes, machine all sides of the parts, and, in many cases, machine a part to completion. DMG/Mori Seiki already has machines of both these types in their broad portfolio. These machines are used in wide variety of industries including aerospace, medical, industrial, tooling, and now gear manufacturing.
For these new manufacturing processes, the tools are simple (end mills or disc cutters) with no special geometry for any specific gear form or tooth. No special option is required on the machines to make them produce gears. The key here is to generate the toolpath and create the gear geometry. This is where the programming software is so vital to the process.
The programming software gearMILL effectively handles the complexity of bevel gear geometries by making it visual. It does not need a solid model, and will create a surface using analytical data provided in gear data sheets. This way, customers can continue to use the gear design software that they currently use.
The software can currently program cylindrical gears, bevel gears, and worm wheels. It primarily uses two types of processes—one with flank milling (5-axis machining) and other using disc cutters (InvoMillingR). This means that same gear can be programmed in two different ways, using two different methods, while using the same machine and gear input data.
The software not only defines the geometry of the gear tooth but can also program the contact patterns. Under conventional processes, adjustment of this contact pattern is a skillful task—one has to do it either by lapping or by modification of the tool. The software makes it visual and easy to adjust. It makes the contact pattern adjustment more of a science than an art.
The quality of the gears produced by these methods is very good. Quality, as always, is proportional to cycle time. The more cycle time that one can spend the better the quality one can get. By definition, the above processes are milling processes. Hence, the quality of the gear tooth depends on milling process characteristics—stepover and feed rate. The stepover will affect the profile of the gear while the feedrate will affect the lead. Profile and lead errors on the tooth form will be shown on the quality charts from CMM measurement data. The methods allow machining of pre-heat treated and post-heat treated parts on the same machines.
All of the commentaries about “how well you can do the gears” or “how fast/slow you can produce them” or “how easy it is to program” are necessary prerequisites to consider, but not sufficient conditions to use these processes. But the case falls apart if the economics of the process do not justify. Readers of this article are very familiar with traditional bevel gear machining process costs (tooling costs, total times for machining, etc.). So here is an idea of what a cost-per-part would be for a part machined using multi-tasking machines.
I would first like to explain the key economic differentiators between the two processes. These are the “indirect” benefits that I explained earlier. Direct benefits are, of course, the ability to use standard tools, and the ability to program and adjust the parts just as needed. Now to the indirect benefits.
Reduced work-in-process, minimal idle resources (tools, machines, labor, etc.), reducing points of failures (single-point of failure is the best), and eliminating bottlenecks are all important aspects of lean manufacturing. By combining operations and including gear milling operations in the same setup as turning + milling, a leaner manufacturing process can be achieved.
Turning machine + milling machine + hobbing machine, as a sequential operation, will need a larger workforce and significantly more floor space. The need for buffers at each of these machines means significant work-in-process. Combining all operations into one machine with only one operator reduces work-in-process inventory. Additionally, this machine is the single point of failure—which is ideal. If any of the turning, milling, or hobbing machines go down, the whole line is affected. This is measured as production efficiency.
Let us assume that uptime for each machine is 90%. In the sequential operations, if any one machine fails, the whole machining cell is shutdown/operates at lower efficiency. Hence, the net uptime of such a cell is 0.9 x0.9 x 0.9 = 0.729 or 73%. A multi-tasking machine performing all operations and producing a part complete will have an uptime of 90%. Machining the part in a single setup has many other advantages. For example, the concentricity between gear pitch circle diameter and OD/ID of the gear is inherently ensured and that will improve the noise quality of the bevel gear.
Traditional methods use specialized tooling where the gear form is built in the tool profile. Customers need to maintain a large inventory of hobs and bevel gear tooling (depending on the variety of parts they machine), because they don’t know what they will need to machine next. This large inventory of tools really adds to the “tied-up capital” necessary for running the business. For example, if you have a $1 million-cost of tools in your inventory, though you are just keeping them there without using much, it is equivalent of having a $1 million-dollar machine sitting idle without doing anything—and you will still need to pay interest on it. At 10% cost of capital (conservative estimate) this is equivalent of having $13,215/month carrying cost. For one shift operation (12 hours) 20 days in a month, this accounts for 55$/hr. The individual inventory cost and cost of capital may be different, but this is a number that cannot be ignored. (Please note that this does not include the cost of ordering new tooling or regrinding the tooling, which is about 2.7% of the total operating cost for an average job shop ($16-million revenue) which accounts for about $450,000. These are costs incurred only when machining the parts and depend on how many parts are actually machined.)
Sometimes it may be justifiable to carry this large tooling inventory, e.g. a large-volume manufacturing plant that makes just a few types of parts and uses carbide tooling. Additionally, the individual inventory value and cost of capital may be different—but again, the bottom line cannot be ignored.
When comparing two processes, it is common practice to compare their cycle times. However, what really matters is the total processing time. This includes setup time and cycle time. Setup time is not just the time to setup a job—it’s the actual time required to get a first good part. The smaller the batch size, the larger the influence of setup time on the overall time. Practices like overruns are common ways to increase the batch size to reduce the impact of setup time. These increase the capital tied up in the inventory. As each part is different, and the context in which it was made is different, it is very difficult to compare the two processes and determine which is the best. However, I would encourage the readers to compare the total cycle times when you compare two processes.
Multi-tasking machines have multiple options for process automation. Barfeeders and vacuum extractors are all standard options. It is not too foreign to imagine a machining cell making bevel gear parts with a single machine, without an operator. The machine feeds a bar, the main spindle machines the part, and machines the bevel gear. The part is then cutoff and transferred to the 2nd spindle, the back end of the part is finished, and then the part is vacuum extracted out or dropped out into the parts catcher bucket. The machining process uses carbide inserts and can be stable. The machine will automatically select “the next tool” in the tool group (a set of similar tools in tool magazine) when the life of one tool expires. This machine can be remote monitored, and the only thing operator is required to fill up the barfeeder and collect the machined parts from parts bin. There is no robot, no sequential stack of tolerances, no machine sitting idle because another machine is down. It is a very lean operation. It is always possible to add a robot to the machining cell, but there are many things that can be done even without it.
Many readers will be running their production facilities on a per-hour cost basis, which is what we would like to use to essentially define the shop rate of a machine cutting gears on a multi-tasking machine.
While isolating a machine to calculate the cost of electricity and cost of leasing the facility (per machine) is slightly difficult, this exercise can quickly yield the cost of owning and operating the machine. Interestingly enough, the tooling costs in this process are only incurred if you are actually machining the part (there is little or no cost of carrying tooling when you are not making any parts. It’s the same case with electricity). The labor cost of $50/hour, at 8 hour/day, 20 days/month and 12 months equals $96K. This includes salary & benefits and is a conservative estimate.
Now compare this $101/hour cost to the $55/hour tooling carrying cost. Numbers tell the story themselves. One can clearly see the importance of considering these “indirect benefits”. Truly, the numbers will be different on a case-by-case basis, but I believe the range will be the same.
Overall, it is beneficial to make bevel gears on multi-tasking machines. While many debate about what is the best way to make a bevel gear on multi-tasking machines, my opinion is that no one process is best. Every single process has its benefits, challenges, and limitations. Multi-tasking machines offer a choice of the process that lets customer select the process. This optimizes the whole gear-making operation and increases profits. Finally, while considering these machines as gear-making machines, one should not forget that these are very good milling + turning + 5 axis machines in the first place—so you will have less opportunity to turn down a customer request for machining a part.
The standard definition of a Bevel Gear is a cone-shaped gear which transmits power between 2 intersecting axels.
Looking at bevel gears from the differences in helix angles, they can be generally classified into straight bevel gears, which do not have helix angles, and spiral bevel gears (including zerol bevel gears), which do have helix angles. However, because of the fact that manufacture facilities for straight bevel gears are becoming rare and the fact that straight bevel gears teeth cannot be polished, making spiral bevel gears which can be polished superior in terms of noise reduction, spiral bevel gears are likely to become more common in the future.
Bevel gears can be generally classified by their manufacturing methods, namely the Gleason method and Klingelnberg method, which each have differing teeth shapes, and presently most gears use the Gleason method. Incidentally, all gears manufactured by KHK use the Gleason method.
Furthermore, there are also variations in gears in terms of teeth pitch (modules, etc.), whether polished or not, and materials used. For example in the case of materials, S45C of machine structural carbon steel, SCM415 of machine structual alloy steel and MC901 of engineering plastic, etc. are often used, and duracon, etc. are used for plastic molded parts.
Please enter part number here for a price and a drawing of the gear
NOTICE: Use of CAD Drawings
The tooth profile detailed in the CAD drawing differs from that of the actual gear.
Also, please note that the details of any chamfer, fillet, or slotted groove on the CAD drawing may differ from the true values or shape on the actual product.
This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.
The gears used when two shafts intersect are based on two cones in rolling contact with apexes meeting at the point of intersection of the two axes and having teeth at the same distance from the apexes. These are called bevel gears. Above mentioned cones are called pitch cones and their half peak angles are called pitch cone angles.
Figure 8.1 Pitch Angles of Bevel Gears
In Figure 8.1, assume the shaft angle to be Σ, the respective numbers of teeth zi (i = 1, 2 ), angular speed ωi, and pitch cone angle (or simply pitch angle) ɣ0i , then consider the rotating speed of a point on the common contact line of the cones at distance K from the apex :
ω1 K sin ɣ01= ω2 K sin ɣ02
ɣ01 + ɣ02 = Σ, angular speed ratio ω1/ω2 = z2/z1
Therefore,
tan ɣ01 = sin Σ / [(z2/z1) + cos Σ ] , tan ɣ02 = sin Σ / [(z1/z2) + cos Σ ]
Normally, Σ = 90° so that :
tan ɣ01 = z1/z2, tan ɣ02 = z2/z1 and ɣ01 + ɣ02 = 90°
In particular, when ɣ01 + ɣ02 = 45°, the bevel gear is called a miter gear. Furthermore, when Σ ≠ 90°, as shown in Figure 8.2, it is called an angle gear.
Figure 8.2 Angle Gear
When the large gear has a pitch angle of 90°, it is called a crown gear. It is equivalent to a rack in spur gear and becomes the base for tooth form and tooth cutting.
Bevel gears are divided into straight bevel gears and spiral bevel gears based on their tooth lines at the pitch cone. Conical gears and face gears can also be considered as belonging to the spiral bevel gear group. Because they are not based on a pitch cone and rely on a specialized tooth cutting method however, they are discussed separately from spiral bevel gears.
Because most bevel gears are intersecting shaft gears, their mesh is almost always rolling contact, therefore their general efficiency is high, typically 98-99%.
Bevel gears are cone shaped gears which transmit motion between two intersecting shafts. Straight bevel gears are the simplest of these bevel gears with their teeth being straight and pointing toward the apex of the cone. They are easier than spiral bevel gears to make and do not produce inward thrust (in the minus direction), simplifying bearing construction. On the other hand, they have the disadvantage of not being able to grind teeth after heat treatment.
Straight bevel gears are divided into two groups: profile shifted Gleason type and non-profile shifted ones called standard type or Klingelnberg type. Over all, the Gleason system is presently the most widely used. In addition, the Gleason Company’s adoption of the tooth crowning method called Coniflex gears produces gears that tolerate slight assembly errors or shifting due to load and increases safety by eliminating stress concentration on the edges of the teeth.
Straight bevel gears are generally used in relatively slow speed applications (less than 2m/s circumferential speed). They are often not used when it is necessary to transmit large forces. Generally they are utilized in machine tool equipment, printing machines and differentials.
Bevel gears are cone shaped gears which transmit motion between two intersecting shafts. Spiral bevel gears are one type in which the teeth are curved spirally. Unlike straight bevel gears, these teeth contact each other gradually and smoothly from one end to the other. The meshing of teeth are, as in straight bevel gears, rolling contacts on the pitch cone surface.
With regard to design and gear cutting, just as in straight bevel gears, the Gleason type is most widely used in spiral bevel gears. However, in Germany, the Klingelnberg type with equal toe and heel tooth depth is still deeply rooted in use.
Spiral bevel gears have the advantage of being able to grind teeth after heat treatment, making it possible to produce high precision gears. Also, because the teeth contact ratio is higher than with straight bevel gears, noise and vibration are reduced and they are better suited for high speed applications. For example, noise and vibration are markedly reduced at high operating speed (more than 10m/s). They are also stronger and more durable than straight bevel gears allowing for higher load operations. On the other hand, it is more difficult to manufacture
spiral bevel gears and needs attention regarding change in thrust directions depending on the rotation and twist angle. These are some of the disadvantages.
In use, the right-hand spiral is mated with the left-hand spiral. As for their applications, they are frequently used in automotive speed reducers and machine tools.
This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.
Spiral bevel gears are gears that have the teeth arranged on a pitch cone along curved lines which produces a quiet operation even at high speed. Especially when the peripheral velocity exceeds 5 m/s, it is difficult to achieve a quiet operation and use of spiral bevel gears are considered desirable.
(a) Straight / (b) Circular Arc / (c) Involute
Figure 8.13 Types of Spiral Bevel Gears (Tooth Lines of Crown Gear)
The tooth form line is determined based on the standard crown gear tooth form (the intersection of the crown tooth surface and pitch surface). If this is considered as the logarithmic swirling line, the tilt angle of the tooth form is constant regardless of the radius which is most desirable from a tooth meshing consideration. However, for tooth cutting, it is not convenient and several curves more suitable for cutting are in actual use. As shown in Figure 8.13, these are tilted straight line (Reinecker form) [these are sometimes called helical bevel gears], circular arc (Gleason form), and involute (Klingelnberg form). Besides these, there are trochoid (Oerlikon form, Fiat form) and Archimedes spiral, etc.
In particular, as shown in Figure 8.14, when the tooth form is a circular arc and at the midpoint of the tooth form, the tilt angle is 0 is called Zerol gear. While the loading of the Zerol tooth is similar to the straight tooth, the meshing is smoother. All the circular arc gears other than Zerol gears are sometimes called helical bevel gears.
Figure 8.14 Zerol Bevel Gear
At the point on the tooth line where it intersects the pitch cone generating line at angle β, if the perpendicular cross section is drawn, then the equivalent spur gear’s number of teeth zvi is
z vi = zi / cos ϓ 0i cos 3 β
and the normal to tooth surface pressure angle αn relates to the spherical surface pressure angle αs as
tan αs = tan αn / cos β
The twist direction of the teeth is, when looking from the small end of the teeth, if the teeth curve clockwise, it is a right spiral and if the teeth curve counterclockwise, it is a left spiral. For mating curved bevel gears, if one gear is right spiral, the opposite gear is left spiral.
This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.
The combination of helical racks which move straightly using crown gears, or cone shape gears guided through helical rack are called conical gear. Each gear is thought to be similar to helical gear in pic 8.27, whose addendum modification changes are oriented in the axial direction. It makes point-contact where contact lines of the mediating rack and each gear cross. Conical gearing is sometimes used instead of bevel gearing when the load is small because they can be cut by modified hob machinery or gear shavers, or by attaching auxiliary equipment. In case of parallel axes, it becomes a conical shifted gear (see p.93) and makes point-contact.
Pic 8.27 Conical gear
1) Cut edge of tooth by pitch cylinder
Important points for assembling bevel gear are :
Tolerances shown above are commonly expected values and can be referred as a rough guide.
Prevent strong edge contact along tooth trace direction within 10% of tooth trace length from both edges of tooth trace
Prevent strong contact along tooth depth near peak or bottom of gear tooth
Tooth contact should include the center of working depth
Too short mounting distance
Too long mounting distance
When adjusting backlash with mounting distance, tooth contact deteriorates if you move only one gear
Too large shaft angle
Too small shaft angle
When there is shaft axis error (offset error or shaft misalignment), tooth contact becomes diagonal
As every gear has pressure angle, the force going away from another gear acts when load is applied. This force then elastically deforms shaft, gear box, bearing and eventually deteriorates tooth contact when load is applied.
No load1. Bring tooth contact near inner side when no load
Loaded2. When load is applied, tooth contact moves towards outer end because of shaft flexure. Tooth contact becomes large as tooth surface is elastically deformed.
No load
LoadedWhen load is applied, shaft angle error and offset error occur simultaneously because of shaft flexure
If rigidity of shaft is low, tooth contact is prone to deteriorate when load is applied even if tooth contact is good when assembled
1. Thick shaft / both sides support / projected part from bearing is short
Related links :
锥齿轮
Types of Gears - A detailed description of Types of Gears
Miter Gears - A detailed description of miter gears
Zerol Bevel Gears - A detailed description of zerol bevel gears
Hypoid Gears - A detailed description of hypoid gears
Equivalent tables of each standard relating to raw materials and precision grades of gears
Ground Gears
Bevel gears are divided into straight bevel gears and spiral bevel gears based on their tooth lines at the pitch cone. Conical gears and face gears can also be considered as belonging to the spiral bevel gear group. Because they are not based on a pitch cone and rely on a specialized tooth cutting method however, they are discussed separately from spiral bevel gears.
Because most bevel gears are intersecting shaft gears, their mesh is almost always rolling contact, therefore their general efficiency is high, typically 98-99%.
Bevel gears are cone shaped gears which transmit motion between two intersecting shafts. Straight bevel gears are the simplest of these bevel gears with their teeth being straight and pointing toward the apex of the cone. They are easier than spiral bevel gears to make and do not produce inward thrust (in the minus direction), simplifying bearing construction. On the other hand, they have the disadvantage of not being able to grind teeth after heat treatment.
Straight bevel gears are divided into two groups: profile shifted Gleason type and non-profile shifted ones called standard type or Klingelnberg type. Over all, the Gleason system is presently the most widely used. In addition, the Gleason Company’s adoption of the tooth crowning method called Coniflex gears produces gears that tolerate slight assembly errors or shifting due to load and increases safety by eliminating stress concentration on the edges of the teeth.
Straight bevel gears are generally used in relatively slow speed applications (less than 2m/s circumferential speed). They are often not used when it is necessary to transmit large forces. Generally they are utilized in machine tool equipment, printing machines and differentials.
Bevel gears are cone shaped gears which transmit motion between two intersecting shafts. Spiral bevel gears are one type in which the teeth are curved spirally. Unlike straight bevel gears, these teeth contact each other gradually and smoothly from one end to the other. The meshing of teeth are, as in straight bevel gears, rolling contacts on the pitch cone surface.
With regard to design and gear cutting, just as in straight bevel gears, the Gleason type is most widely used in spiral bevel gears. However, in Germany, the Klingelnberg type with equal toe and heel tooth depth is still deeply rooted in use.
Spiral bevel gears have the advantage of being able to grind teeth after heat treatment, making it possible to produce high precision gears. Also, because the teeth contact ratio is higher than with straight bevel gears, noise and vibration are reduced and they are better suited for high speed applications. For example, noise and vibration are markedly reduced at high operating speed (more than 10m/s). They are also stronger and more durable than straight bevel gears allowing for higher load operations. On the other hand, it is more difficult to manufacture
spiral bevel gears and needs attention regarding change in thrust directions depending on the rotation and twist angle. These are some of the disadvantages.
In use, the right-hand spiral is mated with the left-hand spiral. As for their applications, they are frequently used in automotive speed reducers and machine tools.
This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.
Spiral bevel gears are gears that have the teeth arranged on a pitch cone along curved lines which produces a quiet operation even at high speed. Especially when the peripheral velocity exceeds 5 m/s, it is difficult to achieve a quiet operation and use of spiral bevel gears are considered desirable.
(a) Straight / (b) Circular Arc / (c) Involute
Figure 8.13 Types of Spiral Bevel Gears (Tooth Lines of Crown Gear)
The tooth form line is determined based on the standard crown gear tooth form (the intersection of the crown tooth surface and pitch surface). If this is considered as the logarithmic swirling line, the tilt angle of the tooth form is constant regardless of the radius which is most desirable from a tooth meshing consideration. However, for tooth cutting, it is not convenient and several curves more suitable for cutting are in actual use. As shown in Figure 8.13, these are tilted straight line (Reinecker form) [these are sometimes called helical bevel gears], circular arc (Gleason form), and involute (Klingelnberg form). Besides these, there are trochoid (Oerlikon form, Fiat form) and Archimedes spiral, etc.
In particular, as shown in Figure 8.14, when the tooth form is a circular arc and at the midpoint of the tooth form, the tilt angle is 0 is called Zerol gear. While the loading of the Zerol tooth is similar to the straight tooth, the meshing is smoother. All the circular arc gears other than Zerol gears are sometimes called helical bevel gears.
Figure 8.14 Zerol Bevel Gear
At the point on the tooth line where it intersects the pitch cone generating line at angle β, if the perpendicular cross section is drawn, then the equivalent spur gear’s number of teeth zvi is
z vi = zi / cos ϓ 0i cos 3 β
and the normal to tooth surface pressure angle αn relates to the spherical surface pressure angle αs as
tan αs = tan αn / cos β
The twist direction of the teeth is, when looking from the small end of the teeth, if the teeth curve clockwise, it is a right spiral and if the teeth curve counterclockwise, it is a left spiral. For mating curved bevel gears, if one gear is right spiral, the opposite gear is left spiral.
This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.
The combination of helical racks which move straightly using crown gears, or cone shape gears guided through helical rack are called conical gear. Each gear is thought to be similar to helical gear in pic 8.27, whose addendum modification changes are oriented in the axial direction. It makes point-contact where contact lines of the mediating rack and each gear cross. Conical gearing is sometimes used instead of bevel gearing when the load is small because they can be cut by modified hob machinery or gear shavers, or by attaching auxiliary equipment. In case of parallel axes, it becomes a conical shifted gear (see p.93) and makes point-contact.
Pic 8.27 Conical gear
1) Cut edge of tooth by pitch cylinder
Important points for assembling bevel gear are :
Tolerances shown above are commonly expected values and can be referred as a rough guide.
Prevent strong edge contact along tooth trace direction within 10% of tooth trace length from both edges of tooth trace
Prevent strong contact along tooth depth near peak or bottom of gear tooth
Tooth contact should include the center of working depth
Too short mounting distance
Too long mounting distance
When adjusting backlash with mounting distance, tooth contact deteriorates if you move only one gear
Too large shaft angle
Too small shaft angle
When there is shaft axis error (offset error or shaft misalignment), tooth contact becomes diagonal
As every gear has pressure angle, the force going away from another gear acts when load is applied. This force then elastically deforms shaft, gear box, bearing and eventually deteriorates tooth contact when load is applied.
No load1. Bring tooth contact near inner side when no load
Loaded2. When load is applied, tooth contact moves towards outer end because of shaft flexure. Tooth contact becomes large as tooth surface is elastically deformed.
No load
LoadedWhen load is applied, shaft angle error and offset error occur simultaneously because of shaft flexure
If rigidity of shaft is low, tooth contact is prone to deteriorate when load is applied even if tooth contact is good when assembled
1. Thick shaft / both sides support / projected part from bearing is short
Related links :
锥齿轮
Types of Gears - A detailed description of Types of Gears
Miter Gears - A detailed description of miter gears
Zerol Bevel Gears - A detailed description of zerol bevel gears
Hypoid Gears - A detailed description of hypoid gears
Equivalent tables of each standard relating to raw materials and precision grades of gears
Ground Gears
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