Gear MCQ Quiz - Objective Question with Answer for Gear - Download Free PDF

Explanation:

Rack and Pinion Gear

Definition: A rack and pinion gear system is a type of linear actuator that comprises a circular gear (the pinion) engaging a linear gear (the rack). This system converts rotational motion into linear motion and is widely used in various mechanical applications.

Working Principle: In a rack and pinion system, the pinion rotates, and its teeth engage with the teeth on the rack. As the pinion turns, it moves the rack in a straight line. This conversion of rotational motion to linear motion is precise and efficient, making the rack and pinion system an essential mechanism in many engineering applications.

Advantages:

• Provides precise control of linear motion.
• Simple design and easy to manufacture.
• High efficiency in converting rotational motion to linear motion.

Disadvantages:

• Wear and tear of gears can affect the accuracy over time.
• Requires lubrication and maintenance to ensure smooth operation.

Applications: Rack and pinion systems are commonly used in steering mechanisms of vehicles, CNC machines, and other industrial equipment where precise linear motion control is required.

Explanation:

Circular Pitch in Gears

• Circular pitch is a term used in gear design that refers to the distance along the pitch circle between corresponding points on adjacent teeth. It is an essential parameter that helps in the analysis and design of gears, ensuring proper meshing and smooth transmission of motion and power between gears.

Formula: Circular pitch is mathematically defined as:

Circular Pitch (P_c) = π × Module

Here,

• π is a constant (approximately 3.14159).
• Module is the ratio of the pitch diameter to the number of teeth in the gear. It is a measure of the size of the teeth in a gear.

Working Principle:

• In gears, the pitch circle is an imaginary circle that represents the point of contact where two gears mesh. The circular pitch is the arc length of this pitch circle, measured between corresponding points on adjacent teeth. It plays a crucial role in determining the spacing and size of gear teeth to ensure proper meshing and efficient transmission of motion. The relationship Circular Pitch = π × Module is derived from the geometry of the pitch circle and the definition of the module.

Explanation:

Terms used in the specification and design of the gear:

Pitch circle: It is the imaginary circle on which two mating gears seem to be rolling. And the diameter of this circle is known as pitch circle diameter (D).

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. 

\({P_c} = \frac{{\pi ~ × ~D}}{T}\)

Module: It is the ratio of the pitch circle diameter (D) to the number of teeth (T).

 \(m=\frac DT\) .................. (1)

Diametral pitch: It is the ratio of numbers of teeth (T) to the pitch circle diameter (D). 

\({P_d} = \frac{T}{D}\) ................... (2)

\(∴ {P_d} .\ {P_c}=\frac{{\pi ~ × ~D}}{T} ×\frac{T}{D}=\pi\)

\(\Rightarrow {P_d}=\frac{\pi}{P_c}\)

∵ b = Diametral pitch, c = Module

∴ From (1) & (2)

b × c = 1

Additional Information

Other terms used in gear are

• 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 bottomland 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 depthITotal 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:

In gear systems, the module (m) is a measure of the size of gear teeth and is defined as:

\(m = \frac{d}{z}\), where d is the pitch circle diameter and z is the number of teeth.

Rearranging the formula, the pitch circle diameter is:

\(d = m \cdot z\)

Calculation:

For two meshing spur gears with pitch diameters d₁ and d₂, and modules m and tooth counts z₁, z₂, we have:

\(d_1 = m \cdot z_1\)  and  \(d_2 = m \cdot z_2\)

The center distance between the two gears is:

\(C = \frac{d_1 + d_2}{2} = \frac{m(z_1 + z_2)}{2}\)

If the module m is increased while keeping z₁ and z₂ constant, the center distance C will increase proportionally.

Concept:

Addendum: 

• It is the radial distance between pitch circle and the addendum circle.
• The addendum is the height by which a tooth of a gear projects beyond (outside for external or inside for internal) the standard pitch circle or pitch line.
• Also the radial distance between the pitch diameter and the outside diameter
• In the gear drive Standard Addendum = 1 module
• But we know that addendum (a) \(a=\frac{1}{DP}=\frac{CP}{\pi }=0.318~CP\)

Additional Information

• 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 CP. Mathematically

• Circular pitch \(CP = \frac{{\pi d}}{T}\)

• Diametral Pitch: It is the ratio of the number of teeth to the pitch circle diameter in millimetres. It is denoted by DP. Mathematically

• \(DP = \frac{T}{d}= \frac{\pi}{CP}\)

• Dedendum: It is the radial distance between the pitch circle and the root circle.
• Working depth: This is the distance of engagement of two mating teeth and is equal to the sum of the addendums of the mating teeth of two gears.
• Whole depth: This is the height of a tooth and is equal to the addendum plus dedendum.
• Face width: This is the width of the gear and it is the distance from one end of a tooth to the other end.
• Face of a tooth: This is the surface of the tooth between the pitch circle and the outside circle.
• Flank of tooth: This is the surface of the tooth between the pitch circle and root circle.
• Clearance: This is the radial distance between the top land of a tooth and the bottom land of the mating tooth.

Concept:

Power transmitted from pinion = Power gain by gear 

\(\therefore {{\rm{T}}_{{\rm{P\;}}}}{{\rm{\omega }}_{\rm{P}}} = {\rm{\;}}{{\rm{T}}_{{\rm{G\;}}}}{{\rm{\omega }}_{\rm{G}}}\)

Calculation:

Given:

No. of teeth on pinion, Z_P = 40, No. of teeth on gear, Z_G = 120, Rotational speed of pinion, N_P = 1200 rpm,, Torque, T_P = 20 Nm

As we know,

\(\frac{{{{\rm{N}}_{\rm{P}}}}}{{{{\rm{N}}_{\rm{G}}}}} = {\rm{\;}}\frac{{{{\rm{Z}}_{\rm{G}}}}}{{{{\rm{Z}}_{\rm{P}}}}}\)

\({{\rm{N}}_{\rm{G}}} = {\rm{\;}}\frac{{{{\rm{Z}}_{\rm{P}}}}}{{{{\rm{Z}}_{\rm{G}}}}}{\rm{\;}} \times {{\rm{N}}_{\rm{P}}}\)

\({{\rm{N}}_{\rm{G}}} = {\rm{\;}}\frac{{40}}{{120}}{\rm{\;}} \times 1200 = 400{\rm{\;rpm}}\)

Since the power transmitted by the two mating gears will be equal.

Thus, \({{\rm{T}}_{{\rm{P\;}}}}{{\rm{\omega }}_{\rm{P}}} = {\rm{\;}}{{\rm{T}}_{{\rm{G\;}}}}{{\rm{\omega }}_{\rm{G}}}\)

\({{\rm{T}}_{{\rm{G\;}}}} = {\rm{\;}}{{\rm{T}}_{{\rm{P\;}}}}\left( {\frac{{{{\rm{N}}_{\rm{P}}}}}{{{{\rm{N}}_{\rm{G}}}}}} \right)\)                                  \(\left(\because {{\rm{\omega }} = {\rm{\;}}\frac{{2{\rm{\pi N}}}}{{60}}} \right)\)

\({{\rm{T}}_{{\rm{G\;}}}} = {\rm{\;}}20\left( {\frac{{1200}}{{400}}} \right)\)

\({{\bf{T}}_{{\bf{G}}\;}} = 60\;{\bf{Nm}}\)

Explanation:

Undercutting:

• It happens when the dedendum portion of gear falls inside the base circle.
• The profile of the tooth inside the base circle is radial.
• If the addendum of the mating gear is more than the limiting value, it interferes with the dedendum of the pinion, and the two mating gears are locked. This will remove that portion of the pinion tooth which would have interfered with the gear as shown.
• This phenomenon of removal of material is known as undercutting.
• This weakens the tooth, however, when actual gear meshes with the undercut pinions, no interference occurs.
• Undercutting will not take place if the teeth are designed to avoid interference.

Methods of elimination of Gear tooth Interference:

• Use of a larger pressure angle results in a smaller base circle. As a result, more of the tooth profiles become involute.
• Increasing the number of teeth on the gear can also eliminate the chances of interference.
• Increasing slightly the center distance between the meshing gears would also eliminate interference.
• Tooth profile modification or profile shifting i.e. gears with non-standard profiles can also be an option to eliminate interference. In profile shifted meshing gears, the addendum on the pinion is shorter compared with standard gears.
• Under-cutting of the tooth as mentioned above.

∵ none of the given option matches as a remedy to avoid interference or undercutting, option (d) will be the correct answer.

Concept:

Speed ratio (or velocity ratio) of the gear train:

• Speed ratio (or velocity ratio) of the gear train is the ratio of the speed of the driver to the speed of the driven or follower.

Speed ratio = \(\frac{N_{driver}}{N_{driven}}=\frac{N_{1}}{N_{2}}=\frac{T_{2}}{T_{1}}\)

Where N and T are the speed and teeth of the gear. T₂ and T₁ are the numbers of gear teeth on the driven and driver gears.

Calculation:

Given:

T1 = 24, T2 = 8

N₂ = 36

Speed ratio = \(\frac{N_{driver}}{N_{driven}}\) = \(\frac{N_{1}}{N_{2}}\) = \(\frac{T_{2}}{T_{1}}\)

⇒ \(\frac{N_{1}}{N_{2}}\) = \(\frac{T_{2}}{T_{1}}\)

⇒ \(\frac{N_1}{36}~=~\frac{8}{24}\)

⇒ N₁ = 12

Explanation:

Undercutting:

• It happens when the dedendum portion of gear falls inside the base circle.
• The profile of the tooth inside the base circle is radial.
• If the addendum of the mating gear is more than the limiting value, it interferes with the dedendum of the pinion, and the two mating gears are locked. This will remove that portion of the pinion tooth which would have interfered with the gear as shown.
• This phenomenon of removal of material is known as undercutting.
• This weakens the tooth, however, when actual gear meshes with the undercut pinions, no interference occurs.
• Undercutting will not take place if the teeth are designed to avoid interference.

Methods of elimination of Gear tooth Interference:

• Use of a larger pressure angle results in a smaller base circle. As a result, more of the tooth profiles become involute.
• Increasing the number of teeth on the gear can also eliminate the chances of interference.
• Increasing slightly the center distance between the meshing gears would also eliminate interference.
• Tooth profile modification or profile shifting i.e. gears with non-standard profiles can also be an option to eliminate interference. In profile shifted meshing gears, the addendum on the pinion is shorter compared with standard gears.
• Under-cutting of the tooth as mentioned above.

Additional Information

Explanation:

Gear is a machine element which, by means of progressive engagement of projections called teeth, transmits motion and power between two rotating shafts. 

Gears can be classified on the basis of the relation between axes of power transmitting shafts:

• Parallel shafts: Spur gear. rack and pinion, helical gears, herringbone gears, etc. 
• Non-parallel and Intersecting shafts: Straight bevel gear
• Non-parallel and non-intersecting shafts: Worm gears

Worm gear:

• Worm gearing is essentially a form of spiral gearing in which the shafts are usually at right angles.
• The two non-parallel and non-intersecting, but non-coplanar shafts connected by worm gears.
• The worm shaft has spiral teeth cut on the shaft and worm wheel is a special form of gear teeth cut to mesh with the worm shaft.
• These are widely used for speed reduction purpose.

Additional Information

Helical Gear: 

• In a helical gear, the teeth are cut at an angle to the axis of rotation. It is used to transmit power between two parallel shafts.

• Types of Helical gears
  • Parallel Helical gears
  • Crossed Helical gears
  • Herringbone gears
  • Double Helical gears

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

Oldham Coupling is used to join two shafts which have a lateral misalignment. It consists of two flanges A and B with slots and a central floating part E with two tongues T1 and T2 at right angles. The resultant of these two components of motion will accommodate lateral misalignment of the shaft as they rotate.

This coupling is used when there is some lateral misalignment, that is, axes of both the shafts are parallel, but not co-axial.

Torque is transmitted through the pressure between the slot and tongue. The pressure is the maximum at the outer periphery and zero at the centroid.

Explanation:

Forms of teeth:

Two curves of any shape that fulfil the law of gearing can be used as the profiles of teeth i.e. 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.

The Involute profile of teeth is preferred over the cycloidal profile of teeth because of the benefits we have in Involute teeth as compared to Cycloidal profile as mentioned in the given table.

Concept:

Contact ratio is given by:

\(Contact~ratio = \frac{{Arc~of~contact}}{{Circular~pitch}} \)

Arc of contact is given by:

\(Arc~of~contact = \frac{{path~of~contact}}{{\cos \left( ϕ \right)}}\)

where ϕ = pressure angle

Circular pitch = πm

where m = module

Calculation:

Given:

m = 3.5 mm, \(Length~of~path~of~contact = 11\sqrt 3 ~mm\), ϕ = 30°

\(Arc~of~contact = \frac{{path~of~contact}}{{\cos \left( ϕ \right)}} = \frac{{11\sqrt 3 }}{{\cos \left( {30^\circ } \right)}} = 22~mm\)  

\(Contact~ratio = \frac{{Arc~of~contact}}{{Circular~pitch}} = \frac{{Arc~of~contact}}{{π \times m}} = \frac{{22}}{{π \times 3.5}} = 2\)

Explanation:

The involute profile of teeth is preferred over the cycloidal profile of teeth because only one curve is required to cut. 

Involute teeth have a number of benefits as compared to the Cycloidal profile as mentioned in the given table.

Concept:

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 pitch point. This pitch point is the point of contact of two pitch circles which divides the line of centres 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.

Explanation:

Interference is a phenomenon in which the addendum tip of gear undercuts into the addendum or base circle of a pinion.

This tooth interface can be reduced by increasing the number of teeth above a certain minimum number.