Bevel Gears

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Introduction

This article provides a comprehensive look at bevel gears, include the following information:

• What is a Bevel Gear?
• Efficiency of Bevel Gears
• Bevel Gear Types
• Geometry and Terminologies
• Manufacturing Processes
• Applications of Bevel Gears
• And much more…

Chapter 1: What is a Bevel Gear?

A bevel gear is a toothed rotating machine element used to transfer mechanical energy or shaft power between shafts that are intersecting, either perpendicular or at an angle. This results in a change in the axis of rotation of the shaft power. Aside from this function, bevel gears can also increase or decrease torque while producing the opposite effect on the angular speed.

A bevel gear can be imagined as a truncated cone. On its lateral side, teeth that have been milled interlock with other gears with their own sets of teeth. The gear transmitting the shaft power is called the driver gear, while the gear where power is being transmitted is called the driven gear. The number of teeth of the driver and driven gear is usually different to produce a mechanical advantage. The ratio between the number of teeth of the driven to the driver gear is known as the gear ratio, while the mechanical advantage is the ratio of the output torque to the input torque. This relationship is shown by the following equation:

\begin{equation} \ MA = \frac{T_b}{T_a} = \frac{r_b}{r_a} = \frac{N_b}{N_a} \end{equation}

MA is the mechanical advantage, τb and τa are the torques, rb and ra are the radii, and Nb and Na are the numbers of teeth of the driven and driver gears, respectively. From the equation, it can be seen that increasing the number of teeth of the driven gear produces a larger output torque.

On the other hand, producing a larger mechanical advantage decreases the driven gear's output speed. This is expressed by the equation:

\begin{equation} \ MA = \frac{W_a}{W_b} \end{equation}

ωª and ωb are the driver and driven gears‘ angular speeds, respectively. In general, a gear ratio of 10:1 is recommended for a bevel gear set. For increasing the speed of the driven gears, a gear ratio of 1:5 is suggested.

Note that bevel gears are usually a paired set and should not be used interchangeably. Bevel gears are assembled in a specific way due to their inherent transmission of both thrust and radial loads, in contrast with spur gears which mostly transmit radial loads only. All bevel gears are assembled at the optimum position for best performance.

Chapter 2: Efficiency of a Bevel Gear

Efficiency is defined as the ratio of the output power to the input power. Note that this is different from mechanical advantage, which is concerned with amplifying of forces or torques by sacrificing speed. When it comes to bevel gears, loss of power during transmission is attributed to friction due to sliding between teeth surfaces and loads applied to the bearings or housing. The efficiency of different types of bevel gears compared with other types is summarized by the table below.

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Chapter 3: Types of Bevel Gears

There are different types of bevel gears as categorized by their tooth profile and orientation. The more complicated types, such as the spiral and hypoid bevel gears, resulted from the further development of manufacturing processes like CNC machining.

Straight Bevel Gears

A straight bevel gear is the simplest form of a bevel gear. The teeth are in a straight line that intersects at the axis of the gear when extended. The teeth are tapered in thickness, making the outer, or heel part of the tooth larger than the inner part, or toe. Straight bevel gears have instantaneous lines of contact, permitting more tolerance in mounting. A downside to using this type is the vibration and noise. This limits straight bevel gears to low-speed and static loading applications. CA common application of straight bevel gears is differential systems in automotive vehicles.

Straight bevel gears are the easiest to manufacture. The earliest manufacturing method for producing a straight bevel gear is by using a planer with an indexing head. More efficient manufacturing methods have been made following the introduction of Revacycle and Coniflex systems, employed by Gleason Works.

Spiral Bevel Gears

A spiral bevel gear is the most complex form of bevel gear. The teeth of spiral gears are curved and oblique, in contrast to the teeth orientation of straight bevel gears. This results in more overlap between teeth, which promotes gradual engagement and disengagement upon tooth contact. This improved smoothness results in minimal vibration and noise produced during operation. Also, because of higher load sharing from more teeth in contact, spiral bevel gears have better load capacities. This allows them to be smaller compared to straight bevel gears with the same capacity.

A disadvantage of spiral bevel gears is the larger thrust load exerted, which requires more expensive bearings. A rolling element thrust bearing is usually required for spiral bevel gear assemblies. Also, spiral bevel gears are made in matched sets. Different gear sets with the same design are not interchangeable unless built to be interchangeable on purpose. Spiral bevel gear sets are made either right-hand or left-hand.

Spiral bevel gear teeth are typically shaped by gear generating machines, which will be discussed in depth later. This process creates high accuracy and finish. Also, lapping is done to finish the teeth and further obtain the desired tooth bearing.

Zerol Bevel Gears

This type is a modification of a straight bevel gear trademarked by Gleason Works. Zerol bevel gears have teeth curved in a lengthwise direction. These gears are also somewhat similar to spiral bevel gears in their profile. Their difference is the spiral angle; Zerol types have 0° spiral angles, while spiral types have 35°.

As with straight bevel gears, Zerol types do not produce excessive thrust loads. Thus, plain contact bearings can be used. Zerol types can be substituted with straight bevel gears without changing the housing or bearings. Moreover, due to their curvature, Zerol bevel gear teeth have a slight overlapping action similar to spiral gears. This makes the gears run smoother than straight bevel gears.

Zerol bevel gear teeth are generated by a rotary mill cutter. The curvature of this cutter creates the lengthwise curvature of the tooth. Zerol bevel gears are with high precision, often finished by lapping or grinding.

Hypoid Bevel Gears

A hypoid bevel gear is a special type of bevel gears in which the axes of the shafts are not intersecting nor parallel. The distance between the two gear axes is called the offset. The teeth of hypoid bevel gears are helical, similar to spiral bevel gears. A hypoid bevel gear designed with no offset is simply a spiral bevel gear. The manufacture and shaping of hypoid types are similar to spiral bevel gears.

Because of the offset, the spiral angle of the smaller gear (pinion) of a hypoid bevel gear set can be made larger than the spiral diameter of the larger gear. The ratio of the number of teeth of the gears is not directly proportional to the ratio of their pitch diameter or the theoretical operating diameter of the gear. This makes it possible to match larger pinions to a particular size of a driven gear, making the pinion stronger and allowing it a higher contact ratio to the larger gear. In turn, the hypoid gear is allowed to transmit more torque and operate at higher gear ratios. Also, with enough offset, bearings on both sides of the gears can be placed since their shafts are not intersecting. The trade-off, however, is the decrease in efficiency as the offset is increased.

Hypoid gears operate more smoothly with minimal vibration compared to spiral gears. However, the downside of using hypoid gears, aside from the aforemented efficiency issue, is the high amount of sliding that takes place across the face of the teeth. This means special lubricating oils must be used.

Miter Bevel Gears

This is a type of bevel gear with a gear ratio of 1:1, meaning the driver and driven gears have the same number of teeth. Because a miter gear does not produce any mechanical advantage, the function of this type is limited to changing the axis or rotation. Usually, miter gears have axes that intersect perpendicularly. In some assemblies, The shafts are aligned to intersect at any angle. These are known as angular miter bevel gears. Shaft angles of angular miter bevel gears can range from 45° to 120°. Miter bevel gear teeth cuts can be straight, spiral, or Zerol.

Chapter 4: Geometry and Terminologies

To better understand gears and gear systems, one must first look at the terminology. Below are some of the terms used to describe gears and their tooth profile. These are applicable for all types of gears, not only bevel gears.

Pinion

The smaller bevel gear in a bevel gear set.

Gear

The larger bevel gear in a bevel gear set.

Pitch

Also known as circular pitch, pitch is the distance from one point on a tooth to the corresponding point of the adjacent tooth on the same gear.

Pitch diameter

The diameter of the pitch circle. This is a predefined design dimension where other gear characteristics such as tooth thickness, pressure angles, and helix angles are determined.

Diametral pitch

The ratio of the number of teeth and the pitch diameter.

Pitch angle

The angle between the face of the pitch surface and the shaft axis.

Pitch surface

The imaginary truncated cone wherein the base diameter is the pitch circle.

Pressure angle

A predefined value that is described by the angle between the line of force of the meshing teeth and the line tangent to the pitch circle at the contact point. Gears must have the same pressure angle in order to mesh. The recommended pressure angle for straight bevel gears is 20°.

Shaft angle

A predetermined value that defines the angle between the driven and driver shafts.

Addendum

The upper outline of the gear teeth.

Dedendum

The bottom outline of the gear teeth.

Total depth

The radial distance between the addendum and dedendum circles of a gear. Note that the teeth of a bevel gear are slightly tapered, thus, the total depth is not constant along the tooth. Because of this, the addendum and dedendum angles are used to describe the teeth instead of the addendum and dedendum circles.

Addendum angle

The angle between the face of the upper surface of the teeth, or top land, and the pitch surface.

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The Top 4 Advantages of Spiral Bevel Gears for Engineers

The angle between the bottom surface of the teeth, or bottom land, and the pitch surface.

Depth of taper

The change in tooth depth along the face, measured perpendicular to the pitch surface.

Space width taper

The change of the space width along the face, measured on the pitch surface.

Thickness taper

The change of tooth thickness measured on the pitch surface.

Working depth

The total depth of the teeth plus the value of the clearance.

Clearance

The difference between the addendum of a gear to the dedendum of the mating gear.

Backlash

The amount of space that exceeds the thickness of a mating gear tooth. For bevel gears, there are different types of backlash depending on the orientation of the movement. These are:

Circular

The arc along the pitch circle

Normal

The space between the surface of the mating teeth

Angular

The described as the angular movement

Radial

The linear movement perpendicular to the axis

Axial

The linear movement parallel to the axis

Backlash is necessary to prevent the gears from jamming due to contact. This space allows for lubricants to enter and protect the surfaces of the mating teeth. Also, the backlash allows for thermal expansion during operation.

The relationship between these terms is shown in the table of equations below.

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Chapter 5: Manufacturing Processes

There are four main methods of manufacturing gears. These are metal cutting, casting, forming, and powder metallurgy. Metal cutting is the most widely used process because of its dimensional accuracy. The second two, casting and forming, are used in special circumstances- for example, producing a large gear through casting, which reduces machining expenses by casting closer to the final shape. Another form of casting, known as injection molding, is used to manufacture plastic gears. Forming, on the other hand, can take the form of cold drawing or forging. Cold drawing involves a stock pulled or extruded into a series of dies to form the shape of the gear. Forging presses the stock against dies with the desired tooth configuration. Because of work hardening through continuous deformation, the resulting gear is harder, with a more contoured grain flow.

Gear cutting can be divided into four more classifications summarized below.

• Rotating threaded tool: hobbing, generating
• Rotating and reciprocating tool: shaping, shaving, generating
• Rotating disc wheel: milling, form grinding, thread grinding
• Linear motion tool: broaching, punching

Because of the conical shape resulting in a depth and width taper, not all techniques can be applied for bevel gears. For bevel gear cutting, metal cutting techniques can be categorized in to two: face hobbing and face milling.

• Face Hobbing: Face hobbing is a continuous indexing gear generation process. This involves groups of cutting blades that cut all teeth gradually until the desired depth is achieved. As one blade group cuts one tooth, the next blade group enters the next tooth space. The cutting tool and the workpiece rotate simultaneously.

  
  

• Face Milling: Face milling is a single indexing method where the cutting wheel or tool is fed to cut one tooth space and is then indexed to the next tooth location. The cutting tool and the workpiece are synched together to perform the cut. Each tooth is milled until all teeth are cut to the required depth. Face milling can be done by a two-tool planer, double rotary blade, single row mill cutter, or five-axis CNC milling machines.

  
  
• Powder Metallurgy: Powder metallurgy is a process in which metal powders are formed into products or materials. In its most basic form, this is achieved by pulverizing the desired material into a powder, compacting the powder into a die, and then sintering. This manufacturing process is valued due to the fact that metal removal processes are often not needed for secondary finishing, which results in less waste and, therefore lower costs. Gears that are formed by this process are lighter and make less noise, due to their naturally porous nature.

Chapter 6: Bevel Gear Applications

The use of bevel gears is one of the simplest and most efficient methods of changing a drivetrains‘ axis of rotation. The type of bevel gear and the manufacturing and finishing processes used depend on the type of application. Below are some of the applications of bevel gear systems.

Bevel Gears in Automotives

The most popular application of bevel gears is in the differential of an automotive vehicle. The differential is the part of the front or rear axle assembly that allows the wheels to rotate at different speeds. This allows the vehicle to turn corners while maintaining handling and traction. The driveshaft is connected to the hypoid gear assembly, which consists of a pinion and a ring gear. The ring gear is mounted to the carrier with other bevel gears in a planetary gear train.

Bevel Gears in Heavy Equipment

Bevel gears are used by heavy equipment either for propulsion, the same as an automotive differential system, or for auxiliary units.

Bevel Gears in Aviation

Bevel gears are used in the aviation industry for power transmission systems of helicopters and aircraft accessory gearbox drivers.

Bevel Gears in Industrial Plant Equipment

An example of industrial plant equipment that uses bevel gears is cooling tower fans. The motor is usually mounted at the deck of the cooling tower with the shaft axis oriented horizontally. A gearbox assembly reduces the speed and increases the torque while also reorienting the axis of rotation vertically.

Bevel Gears in Marine Transmission

Bevel gears are commonly used in marine transmission as part of the stern drive. There are two bevel gear sets used between the engine and the propeller.

Bevel Gears in Hand Tools

• Drills - The use of bevel gears in drills is one of their most common uses. As the handle of the drill turns vertically, the bevel gear changes the direction to horizontal at the chuck. Additionally, bevel gears are used to control the rotation speed, making it possible to drill several types of material.
• Planers - Planers are used to shape a workpiece using linear motion. Bevel gears in planers allow for adjustments during the planing process and displacement caused by deflection.

Conclusion

• Bevel gears are rotating machine elements used to transmit mechanical power between two intersecting shafts, either perpendicular or at an angle. Aside from changing the axis of rotation, bevel gears can also produce a mechanical advantage by increasing the output torque.
• Producing a mechanical advantage, however, decreases the angular speed of the driven shaft. Thus, bevel gears can also be used as speed reduction mechanisms.
• Efficiency is the ratio between output power and input power. Power loss from bevel gears is mostly due to friction from sliding contact. This is then dissipated as heat, which is usually removed by lubricating oils.
• Bevel gears are classified according to the tooth profile and orientation. The types of bevel gears are straight, spiral, Zerol, and hypoid.
• Efficiencies of bevel gears range from 97-99.5%, except for hypoid bevel gears- with an efficiency of 90-98%. A larger offset of a hypoid gear causes a further decrease in efficiency.
• There are many terms used to describe gears. The most important for bevel gears are the pitch diameter, pressure angle, shaft angle, and number of teeth. These are the key values that will define the geometry of the gear.
• There are three main methods of manufacturing gears: cutting, casting, and forming. Among the three, cutting is the most widely used. Powder metallurgy is also used.
• Gear cutting is further broken down into several methods. One is by using a rotating threaded tool such as a hob. Next is by using a rotating or reciprocating cutting tool that mates together with the gear blank. Third is cutting using a rotating disc wheel as seen in milling processes. Lastly is gear cutting using a linear shaper or broaching tool.
• The most popular application of bevel gears is the automotive differential. This is seen not only in automotive vehicles, but also in light and heavy equipment. Other main uses are in the aviation and marine industries.

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A spiral bevel gear drive’s sophistication and superior performance offer the engineer many opportunities. In a typical right angle gear, the perpendicular alignment of the gear teeth can cause noise, unpredictable operating cycles, and other issues. Spiral bevel gears have teeth designed to mesh on the diagonal, making the transmission of force smooth, quiet, and powerful. 

A spiral bevel gear can also significantly reduce backlash when correctly calibrated. In most instances, this is achieved with a shim or retaining ring. MITRPAK spiral bevel gear drive features a unique locknut for faster, more precise adjustment.  Few gears outmatch a MITRPAK spiral bevel gear drive in performance, speed, and ingenuity.                             

Minimizing Noise In Right Angle Gear Drives

Spiral bevel gear drives are precisely fitted to minimize the distance between enmeshed gears. The reduced space between the gear teeth means less opportunity for backlash and noise during operation as the teeth connect. Thus, the quieter operation of spiral bevel gears is ideal to utilize in environments where noise reduction is a priority. 

Spiral Bevel Gear Drives for High-Torque and High-Speed Applications

Because spiral bevel gears have a greater tooth area, they can deliver more torque output than other gears of the same size. Spiral bevel gears, as a result, can move faster than other gears, producing greater output in less time. In industrial applications, spiral bevel gears offer strength and robust transmission of force.

Smooth Operation Keeps Gear Drives Cool 

Smooth operation comes naturally with the higher speed and precision of a spiral bevel gear. Equipment utilizing a spiral bevel gear drive benefits from reduced strain, less friction, and lower heat generation. This feature is essential in scenarios where heat and safety are a concern, especially in industrial applications requiring prolonged continuous operation. As the teeth of typical gears make contact, the impact and friction can cause a host of problems: heat output, backlash or recoil, and erratic operation cycles— just to name a few! On the other hand, spiral bevel gears minimize friction and impact between gear teeth with minimal backlash and consistent, predictable cycle times.

Spiral Bevel Gears Minimize Need for Repairs or Replacements

Spiral bevel gears are often higher in quality and last longer than other types of gears, requiring less need for maintenance repairs. While some may require frequent lubrication and calibration,  MITRPAK® spiral bevel gear drives have double-shielded, permanently lubricated and sealed bearings, an aluminum alloy housing, and hardened steel gears for optimal performance with minimal maintenance requirements.

Spiral Bevels Lead the Way in Right Angle Gears 

When it comes to right angle gear performance there’s no question about it— spiral bevel gears are the discerning engineer’s top choice. From sporting arena seating to heavy industrial equipment, spiral bevel gear drives offer enticing benefits for any operating scenario. Explore MITRPAK and discover the right angle gear drive to optimize your equipment design today. 

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