Spur Gears(4)

Determining backlash in Involute gears

Backlash is defined as the amount by which width of tooth space exceeds the tooth thickness of gear engaged that measured on pitch circle. Now it is clear that when this happens there is some gap left between the teeth which are engaged. This create a lot of noise when a gearbox runs at a low speed, another disadvantage is it might remove flank material of driven gear over a certain period of time, which will further increase the backlash. The backlash of a gear train equals the sum of the backlash of each pair of gears, so in long trains backlash can become a problem.

Backlash = Tooth space - Tooth thickness

Several methods are used for indicating and checking backlash. The common method i.e. particularly with spur gears is to place the mating gears on pins located at the correct center distance and then measure the backlash by the use of a feeler gage inserted between the teeth as shown at A in fig. Another method is to place the gears on pins and bring the teeth into intimate contact and then determine the difference between the standard and measured center distance, as shown at B in fig. This last check does not indicate backlash directly but the amount of backlash can be determined by the following formula,

B = 2tanφ * d

Where

B = Backlash in inches

Φ = Pressure angle

d = Difference between standard and measured center distances

Fig: Two methods of determining backlash between gear teeth.

Non-standard Spur gears; extended center distance system

There are two mostly used systems for non-standard gear

• Extended center distance system
• Long and short addendum system

In the extended center distance system cutter is withdrawn a certain amount from the blank so that the addendum of basic rack passes through interference point of the pinion when the pinion is being cut. When the pinion is mated with its gear, it will be found that the center distance has been increased because of the decreased tooth space and the pressure angle at which the gears operate increases.

The offset distance can be computed from

e = a + r_b cosΦ – r_p = a + r_p ( cos Φ) cosΦ- rp

= a- r_p sin²Φ

The tooth thickness is increased but the tooth space is decreased. So the center distance of mating gears has to be increased. The tooth thickness (t) of the pinion on its cutting pitch circle can be find out from tooth space of the rack on its cutting pitch line.

t = 2etan Φ + P_c/2

Methods of gear production

Gear production depend on machinery available, design specifications or requirements, cost of production with type of material from which gear is to be made.

There are many methods for production of gears. They are

• Metal removal processes (hobbing, shaping, milling, shaving, grinding, honing, and lapping)
• Different casting processes for both production of gear blanks and near-net shape gears
• Stamping and fine blanking
• Extrusion and Cold drawing
• Powder metallurgy
• Injection molding
• Gear rolling
• Forging for production of gear blanks and precision type forged near and net-shape gears

The production methodology involved for production of the given types of gears defines types of machines to be used. The various production methods for producing the above gears by machining are as follows.

1. Gear Milling: This is one of the initial and best known metal removal process for any type making gears. This method need the usage of a milling machine. It is also to be noted that this method can produce all types of gears and this method involves the use of a form cutter which is passed through the gear blank to create tooth gap. Currently this method used only for the manufacture of gears requiring very less dimensional accuracy.
2. b) Gear Hobbing: Gear Hobbing is a continuous generating process that the tooth flanks of the constantly moving work piece are formed from equally spaced cutting edges of the hob. The main benefits from this process is its versatility to produce a variety of gears including Spur, Helical, Worm Wheels and Splines etc. Another advantage of the method is the higher productivity rate of gears.
3. c) Gear Shaping: it is a generating process. The cutter used is virtually a gear provided with cutting edges. The tool is rotated at required velocity ratio relative to gear to be manufactured and any one manufactured gear tooth space is formed from one complete cutter tooth. This method used to produce cluster gears, internal gears, racks etc with the ease which may not have possibility to be manufactured in gear hobbing.
4. d) Bevel Gear Cutting: Bevel gear cutting is a very advanced area in the field of gear cutting. This involves a special type of machine for each variety type of bevel gear to be manufactured. Some of the bevel gear types along with the type of machines need are Gleason, Oerlikon, Hypoid and Zerol. Each type of bevel gear is always manufactured only on the corresponding type of machine against to its name. The tooling required also tends to vary based on the type of gear.

Advantages and Disadvantages of Gear Drive

The following are advantages and disadvantages of the gear drive as compared to belt, rope and chain drives.

Advantages

• It transmits exact velocity ratio.
• It may be used to transmit large power.
• It has high efficiency.
• It has reliable service.
• It has compact layout.

Disadvantages

• The manufacture of gears require special tools and the equipment.
• The error in cutting teeth may cause vibrations and noise during operation.

References:
1. H.H. Mabie and C. F. Reinholtz, “Mechanism and Dynamics of Machinery”, Wiley.
2. J.S. Rao & R.V. Dukkipati Mechanisms and Machine Theory, New Age International (P) Limited..
3. J.E. Shigley and J.J. Uicker, Jr., “ Theory of Machines and Mechanisms”, McGraw Hill.
4. B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice Hall.
5. C. E. Wilson, J.P. Sadler and W.J. Michels, “Kinematics and Dynamics of Machinery”, Harper Row.