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Transmitted Force for Helical Gear Smaller Than Spur

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• Know most gear transmission torque

i. Gear functions

Hither is the list of gear functions for machinery designs. (Tabular array three-1)

Tabular array 3-1 Gear functions

Characteristic functions of gears	Explanation
Change management of rotating shaft	(already explained)
Convert rotary motility to linear motility	(already explained)
Change rotational direction (clockwise / counterclockwise)	(already explained)
Modify the number of rotations (speed upwardly / down)	(already explained)
Modify turning strength (increment / decrease torque)	See this affiliate

You can increase or subtract a gear's torque (turning force) by changing the number of rotations.

2. Definition of torque (turning strength)

Torque is the turning forcefulness when load F (N) is applied at a distance L (mm) away from the center of rotation. Torque T is expressed every bit the following formula in N・mm (Newton millimeter). (Figure 3-1)

Figure 3-i Torque

Torque T becomes larger as L (the altitude from the heart of rotation) becomes longer even if load F is small. On the other hand, torque T becomes larger as load F is increased even if L (the distance from the center of rotation) is brusque.
In other words, torque T is the factor determined by L (the distance from the center of rotation) and load F.

3. How to determine torque transmission (without regard to machine efficiency)

A gear's transmission torque changes as it increases or decreases speed. Generally, by reducing the speed, a minor torque at the input side is transmitted as a larger torque at the output side. The calculation of torque depends on the number of teeth. Permit me explain with a diagram using pitch circle diameters.
The torque is calculated equally follows:

1. Obtain load F of the meshing betoken (at the radius of the pitch circle of Gear A) of the input torque.
2. Obtain torque of the output side from load F of the teeth'due south meshing signal (radius of the pitch circle of Gear B).

Condition
Rated torque of motor: TA=600N·mm (0.6N·m)
Gear A'southward pitch circle diameter φ20
Gear B's pitch circle diameter φ40

Torque transmission adding
Load of Gear A'S meshing indicate: F=TA/FiftyA=lx(Northward)
Output side's torque: TB=F×FiftyB=60(N)×twenty(mm)=1200(N·mm)

Figure 3-2 Diagram of gear's torque transmission adding

As you can see from Effigy 3-ii, by reducing the output shaft speed from the input shaft by 1/2, the output torque increases past a factor of two.

4. Consideration of car efficiency

Every bit shown in the previous affiliate, y'all can calculate a gear'due south number of rotations by the number of teeth.
However, you cannot summate a gear's manual torque only as shown previously because of the following reasons:

• Heat is produced by meshing teeth and energy is lost.
• Hammering sound is produced by meshing teeth and free energy is lost.

Therefore, the torque (turning forcefulness) is reduced by as much as the free energy is lost every bit to a higher place.
The ratio of input to output forces of gears is called "machine efficiency" and its judge value is known according to the gear type. (Table 3-ii)

Table 3-2 Gear'due south machine efficiency by blazon

Human relationship of two shafts	Gear name	Motorcar efficiency η (%)
parallel shaft	spur gear	98.0 - 99.5 * Efficiency of helical gear is less than spur gear as teeth are inclined and strength is created in the thrust direction.
	helical gear
	double helical gear
	internal gear
	rack
	helical rack
intersecting shaft	straight bevel gear	98.0 - 99.0
	spiral bevel gear
skewed shaft	worm gear	30.0 - 90.0
	screw gear	lxx.0 - 95.0

Note) The efficiency shown higher up is the transmission efficiency of gears without regard to the loss in bearings or agitation of grease.
The gear efficiency shown above are the values when gears are installed properly. If incorrectly installed, such equally deviation in the intersection signal of bevel gears, efficiency will decrease.

"Never forget nearly machine efficiency when computing torque !"

5. Transmission torque calculation (including machine efficiency)

Now, let's meet the torque calculation formula including motorcar efficiency η. (Figure 3-3)

When gear A's input torque is TA, and machine efficiency is η, torque TB that is transmitted to gear B increases every bit efficiency η rises.

TB=η（ZB/ZA）× TA

When gear B'due south input torque is TB, torque TA that is transmitted to gear A decreases as efficiency η falls.

TA=η（ZA/ZB）× TB

Effigy 3-3 Adding formula of manual torque

Exercise problem for manual torque (1)

Calculate the torque transmitted to driven gear (B). Assume the gear type to be spur gears.
Symbolin Figure 3-4 represents the drive gear.

[Status]
Number of teeth: ZA=20, ZB=40
Drive gear A'south torque: TA=600 (N·mm)
Machine efficiency η: Gear up to 0.99 as spur gears are used.

[Answer]
Torque transmitted to gear B
TB=η(ZB/ZA)×TA
= 0.99(40/20)×600=1188(N·mm)

Figure 3-4 Exercise problem for transmission torque (one)

Exercise problem for manual torque (2)

Calculate the torque transmitted to worm wheel B. (Figure 3-5)

[Condition]
Number of teeth: ZA=1, ZB=30
Worm A'southward torque: TA=600 (N·mm)
Machine efficiency η: Set to 0.three as worm gears are used.

[Respond]
Torque transmitted to worm bike B
TB=η(ZB/ZA)×TA=0.iii(30/1)×600
= 5400(North·mm)

Effigy 3-5 Exercise trouble for manual torque (two)

Practice trouble for manual torque (three)

Calculate the torque transmitted to driven gear (C). Assume the gear type to be helical gears.
Symbolin Figure 3-half-dozen represents the drive gear.

[Condition]
Number of teeth: ZA=20, ZB=thirty, ZC=20
Drive gear A's torque: TA=500 (N·mm)
Automobile efficiency η: Set to 0.98 every bit helical gears are used.

[Respond]
Torque transmitted to gear B
TB=η(ZB/ZA)×TA
=0.98(30/xx)×500=735(Due north·mm)
Torque transmitted to gear C
TC=η(ZB/ZC)×NB
=0.98(20/xxx)×735=480.2(Due north·mm)

Figure three-half-dozen Exercise trouble for transmission torque (3)

"Just like the number of rotations, the number of teeth of the commencement and terminal gears determines the torque of a unmarried stage gear, but the torque is reduced as automobile efficiency is affected by the number of intermediate gears !"

Practice problem for manual torque (four)

Calculate the torque transmitted to driven gear (D). Presume the gear blazon to exist helical gears.
Symbolin Effigy 3-7 represents the drive gear.

[Condition]
Number of teeth: ZA=20, ZB=forty, ZC=20, ZD=30
Bulldoze gear A's torque: TA=400 (N·mm)
Machine efficiency η: Set to 0.98 every bit helical gears are used.

[Answer]
Torque transmitted to gear B
TB=η(ZB/ZA)×TA
=0.98(40/20)×400=784(N·mm)
Torque transmitted to gear C
TC=TB=784(N·mm)...equally beingness on the same shaft
Torque transmitted to gear D
TD=η(ZD/ZC)×TC
=0.98(30/20)×784=1152.five(Due north·mm)

Figure three-7 Exercise problem for transmission torque (four)

When starting a mechanism design using gears, it is important to be conscious of machine efficiency. The mechanism designed without because machine efficiency may not satisfy specifications because of torque shortage.
Nosotros discussed that machine efficiency influences gear'southward transmission torque depending on the gear types and the number of meshing.
Next we will explain parameters that determine gear shapes when designing gears.
(To exist continued...)

*Illustration: KAOSUN

DISCLAIMER

The purpose of writing this article was to educate the readers with the simple level of gear engineering science.
We promise that the actual design and manufacturing of gears and mechanism utilizing gears are washed with sufficient technical and specialized considerations under the user's full responsibility.
Nosotros disavow any liability and will non recoup for any straight or indirect damages caused by the gears designed by the users who read this article.

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Transmitted Force for Helical Gear Smaller Than Spur UPDATED

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