Gear Terminologies MCQ Quiz in मल्याळम - Objective Question with Answer for Gear Terminologies - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Explanation:

Clearance:

It is the radial distance from the top of the tooth to the bottom of the tooth, in a meshing gear (the difference between the dedendum of one gear and the addendum of the mating gear). Clearance is the amount by which dedendum of a gear exceeds the addendum of its mating gear.

Backlash: 

Backlash is the difference between the tooth space and the tooth thickness, as measured along the pitch circle. Theoretically, the backlash should be zero, but in actual practice, some backlash must be allowed to prevent jamming of the teeth due to tooth errors and thermal expansion.

Flank: The flank of the tooth is the surface of the gear tooth below the pitch surface.

Tooth space:

Tooth space is the width of space between the two adjacent teeth measured along the pitch circle.

Tooth thickness: 

It is the width of the tooth measured along the pitch circle.

Important Points

Circular pitch

It is the distance measured on the circumference of pitch circle from a point of one tooth to the corresponding point on the tooth.

\({P_c} = \frac{{\pi ~ \times ~D}}{T}\)

Pitch circle: It is the imaginary circle on which two mating gears seem to be rolling.

Addendum Circle: It is the circle drawn through the top of the teeth and is concentric with the pitch circle. It is also called the Outside circle.

Dedendum circle: It is the circle drawn through the bottom of the teeth. It is also called the root circle.

Base Circle: It is the circle from which the involute tooth profile is developed.

Addendum: It is the radial distance of a tooth from the pitch circle to the top of the tooth (or addendum circle).

Dedendum. It is the radial distance of a tooth from the pitch circle to the bottom of the tooth (or dedendum circle).

Land: The top land and bottom-land are surfaces at the top of the tooth and the bottom of the tooth space respectively.

Working depth: This is the distance of the engagement of two mating teeth and is equal to the sum of the addendum of the mating teeth of the two gears. It is the radial distance from the addendum circle to the clearance circle.

Whole depth/Total depth: This is the height of a tooth. It is the radial distance between the addendum and the dedendum circles of a gear. It is equal to the sum of the addendum and dedendum.

Concept:

Pressure angle:

• The angle between the pressure line and common tangent to the pitch circle is called Pressure angle or angle of obliquity.

Pitch circle diameter:

• It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also known as pitch diameter.

Circular pitch: 

• It is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth. It is usually denoted by pc. Mathematically,

Circular pitch, \(p_c = \frac{{\pi d}}{T}\)

Diametral Pitch:

• It is the ratio of the number of teeth to the pitch circle diameter in millimetres. It is denoted by pd. Mathematically,

\(p_d = \frac{T}{d}= \frac{\pi}{p_c}\)

Module (m):  

• It is the ratio of the pitch circle diameter in millimetres to the number of teeth. It is usually denoted by m. Mathematically

\(m = \frac{d}{T}\)

Additional Information

Involute profile

• It is defined as the locus of the point on the line which rolls without slipping on the fixed circle.
• In involute gears, the pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant. It is necessary for smooth running and less wear of gears.
• But in cycloidal gears, the pressure angle is maximum at the beginning of the engagement, reduces to zero at pitch point, starts increasing and again becomes maximum at the end of the engagement. This results in less smooth running of gears.

Explanation:

Spur Gear: The teeth are cut parallel to the axis of rotation. The spur gears are used to transmit power between two parallel shafts.

In spur gear, the tooth profile starts from the base circle, covers the face and flank region and finally ends at top of the tooth.

Forms of teeth:

• Two curves of any shape that fulfil the law of gearing can be used as the profiles of teeth.
• An arbitrary shape of one of the mating teeth can be taken and applying the law of gearing the shape of the other can be determined. Such gear is said to have conjugate teeth.

Teeth that satisfy the law of gearing are:

1. Cycloidal profile teeth.
2. Involute profile teeth.

Concept:

The Law of gearing states the condition which must be fulfilled by the gear tooth profiles to maintain a constant angular velocity ratio.

According to the law of gearing:

• If it is desired that the angular velocities of two gears remain constant, the common normal at the point of contact of the teeth should always pass through the fixed point which is the pitch point. This pitch point is the point of contact of two pitch circles which divides the line of centers into the inverse ratio of the angular velocities. 
• If the tooth profiles are not designed as per the law of gearing. then the motion transfer will not be proper because of improper meshing which results in vibration and tooth damage.

Cycloid and involute profile

• A cycloid is a curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line.
• An involute toothed profile of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping or by a point on a taut string which is unwrapped from a reel.

• Both Involute and Cycloidal profiles are Conjugate profiles.
• Every Conjugate profile must satisfy the Law of gearing.

Concept:

Circular pitch: It is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth. It is usually denoted by pc. Mathematically,

If the circular diameter is D, and No. of teeth is T

Circular pitch, \(p_c = \pi m=\frac{{\pi D}}{T}\)

where m is the module of gear. (m = D/T)

Calculation:

Given:

D = 28 cm = 280 mm, T = 40

\({p_c} = \frac{{22}}{7} \times \frac{{280}}{{40}} = 22\;mm/tooth\)

Explanation:

The module of spur gear is defined as:

• It is the ratio of the pitch circle diameter to the number of teeth.

  m = \(\frac dt\)

• Dedendum minus addendum.
• The ratio of the pitch circle diameter to the number of teeth.
• The inverse of the number of teeth.
• \(P_d=\frac{ T}{D}=\frac{1}{m}\)
• The inverse of the module.

Additional Information

Concept:

Gear ratio:

It is the ratio of teeth in driving gear to teeth in driven gear.

\(\rm Gear\;Ratio=\frac{Teeth\;of\;Driving\;Gear}{Teeth\;of\;Driven\;Gear}=\frac{Load\;Gear}{Effort\;Gear}\)

Load gear is the driven gear, and effort gear is the driving gear.

Calculation:

Given:

Tdriver = Tload = 160, Tdriven = Teffort = 32

\(\rm Gear\;Ratio=\frac{Teeth\;of\;Driving\;Gear}{Teeth\;of\;Driven\;Gear}=\frac{Load\;Gear}{Effort\;Gear}\)

\(\rm Gear\;Ratio=\frac{160}{32}=5:1\)

Terms Used in Gears:

Module (m): It is defined as the ratio of the pitch circle diameter to the number of teeth of a gear.

Pitch circle: It is the imaginary circle on which two mating gears seems to be rolling.

Circular pitch: It is the distance from the point of one tooth to the corresponding point of the adjacent tooth measured on the pitch circle.

Pitch circle diameter: It is the diameter of the pitch circle.

Addendum Circle: It is the circle drawn through the top of the teeth and is concentric with the pitch circle. It is also called the Outside circle.

Dedendum circle: It is the circle drawn through the bottom of the teeth. It is also called the root circle.

Base Circle: It is the circle from which the involute tooth profile is developed.

Addendum: It is the radial distance of a tooth from the pitch circle to the top of the tooth (or addendum circle).

Dedendum. It is the radial distance of a tooth from the pitch circle to the bottom of the tooth (or dedendum circle).

Land: The top land and bottom-land are surfaces at the top of the tooth and the bottom of the tooth space respectively.

Working depth: This is the distance of engagement of two mating teeth and is equal to the sum of the addendum of the mating teeth of the two gears. It is the radial distance from the addendum circle to the clearance circle.

Whole depth/Total depth: This is the height of a tooth. It is the radial distance between the addendum and the dedendum circles of a gear. It is equal to the sum of the addendum and dedendum.

Concept:

The path of contact and arc of contact are related as 

Path of contact = Arc of contact × cos ϕ

Where ϕ - Pressure angle;

The Path of contact is given by 

Path of contact = path of approach + path of Recess

\(= \left( {\sqrt {R_A^2 - {R^2}{{\cos }^2}\emptyset } - Rsin\emptyset } \right) + \left( {\sqrt {r_A^2 - {r^2}{{\cos }^2}\emptyset } - rsin\emptyset } \right)\)

R_a - addendum radius of Gear, r_a - addendum radius of pinion;

Explanation:

Given ϕ = 20°, T = t = 50, m = 10 mm;

\(R = r = \frac{{mT}}{2} = \frac{{10 \times 50}}{2} = 250\;mm\)

Arc of contact = 3 × circular Ritch

⇒  Arc of contact = 3 × πm

⇒ Arc of contact = 30 π mm

Now,

Path of contact = 30 π cos 20°

\(⇒ \left( {\sqrt {R_a^2 - {R^2}{{\cos }^2}ϕ } - R\sin ϕ } \right) + (\sqrt {r_a^2 + {r^2}{{\cos }^2}ϕ } - r{\rm{sin}}ϕ {\rm{\;}})\; = 30\;\pi \cos 20^\circ \)

\(⇒ 2(\sqrt {R_a^2 - {{250}^2}{{\cos }^2}20^\circ } - 250\sin 20^\circ ) = 30\;\pi \cos 20^\circ \)

∴ R_a = 268.39 mm

⇒ R_a – R = 18.39 mm

Explanation:

Circular pitch: It is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth. It is usually denoted by pc. Mathematically,

If the circular diameter is D, and No. of teeth is T

Circular pitch, \(p_c = \pi m=\frac{{\pi D}}{T}\)

where m is the module of gear. (m = D/T)