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

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Explanation:

What is Gear Backlash?

Gear backlash is a term used in mechanical engineering and design to describe the clearance or play between meshing gear teeth. It is an intentional gap or space that exists between the driving and driven gear teeth in a gear mechanism. This gap is necessary to ensure smooth operation, prevent binding, and allow for manufacturing tolerances. While backlash is essential for the proper functioning of gears, excessive backlash can lead to undesirable effects such as increased noise, reduced accuracy, and mechanical wear. Conversely, insufficient backlash can cause interference, overheating, and premature failure of the gear system.

The correct option in the given question is:

Option 2: The clearance or play between meshing gear teeth.

This definition accurately describes gear backlash, which is the slight gap or looseness intentionally left between the engaging surfaces of gear teeth to accommodate thermal expansion, manufacturing tolerances, and lubrication.

Understanding Gear Backlash in Detail:

Backlash is a critical parameter in gear design, and its magnitude depends on the application, the type of gear, and the operating conditions. In most mechanical systems, a certain amount of backlash is required for the following reasons:

• Thermal Expansion: During operation, gears may heat up due to friction and other factors. This heat causes the material of the gears to expand. Without sufficient backlash, the expanding gears may bind or interfere with each other, leading to mechanical failure or excessive wear.
• Manufacturing Tolerances: Perfectly machining gears without any dimensional variation is practically impossible. Backlash provides a margin to accommodate these small variations in gear dimensions.
• Lubrication: The gap created by backlash allows lubricant to flow between the meshing teeth, reducing friction and wear.
• Ease of Assembly: Backlash makes it easier to assemble gear systems by providing some flexibility in the alignment of components.

How Backlash is Measured:

Backlash is typically measured as the angular or linear distance that a gear can move without engaging the mating gear. In the case of spur gears, for example, it is measured as the gap at the pitch circle of the gears. The measurement can be performed using dial indicators or other precision instruments. The unit of backlash is usually expressed in millimeters or inches.

Effects of Excessive Backlash:

While some amount of backlash is necessary, excessive backlash can have the following negative effects:

• Reduced Accuracy: In precision applications such as robotics or CNC machining, excessive backlash can lead to errors in positioning and motion control.
• Increased Noise: Excessive backlash can cause noisy operation due to the impact or slap of the gear teeth during engagement.
• Mechanical Wear: The increased movement of gears with excessive backlash can lead to accelerated wear and tear of the gear teeth.

How to Control Backlash:

Controlling backlash is essential for maintaining the efficiency and reliability of gear systems. The following methods are commonly used to control or reduce backlash:

• Precision Manufacturing: High-precision machining techniques can minimize dimensional variations and reduce the need for excessive backlash.
• Preload Mechanisms: Springs or other preload mechanisms can be used to maintain constant contact between gear teeth, thereby reducing backlash.
• Gear Design: Designing gears with features such as helical teeth or double helical teeth can help reduce backlash by ensuring smoother engagement.
• Adjustment Mechanisms: Some gear systems include adjustable components that allow the user to modify the amount of backlash as needed.

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Explanation:

Simple Gear Train

A simple gear train consists of two or more gears in which the gears are mounted on separate shafts. In such a setup, the motion and power are transmitted from the driving gear (input gear) to the driven gear (output gear) through one or more intermediate gears, which are termed idler gears. The function of the idler gear is to transmit motion between the driving and driven gears without affecting the gear ratio.

In this problem, there are three gears in the gear train:

• Gear X: The driving gear with 48 teeth.
• Gear Y: The driven gear with 48 teeth.
• Idler Gear: The intermediate gear with 24 teeth, which transmits motion between gears X and Y.

The speed ratio (or velocity ratio) in a gear train is determined by the ratio of the number of teeth on the gears. The idler gear does not change the speed ratio but only reverses the direction of rotation.

Solution:

The given data is as follows:

• Teeth on gear X (T<sub>X</sub>): 48
• Teeth on gear Y (T<sub>Y</sub>): 48
• Teeth on the idler gear (T<sub>idler</sub>): 24 (not relevant for speed calculation)
• Speed of gear X (N<sub>X</sub>): 210 rpm (clockwise)

To find the speed of gear Y (N<sub>Y</sub>), we use the following relationship in a simple gear train:

Speed ratio (SR) = N<sub>X</sub> / N<sub>Y</sub> = T<sub>Y</sub> / T<sub>X</sub>

Substituting the values:

N<sub>X</sub> / N<sub>Y</sub> = T<sub>Y</sub> / T<sub>X</sub>

210 / N<sub>Y</sub> = 48 / 48

210 / N<sub>Y</sub> = 1

Hence, N<sub>Y</sub> = 210 rpm.

Since the idler gear only reverses the direction of rotation without affecting the speed, the direction of rotation of gear Y will be the same as gear X. Therefore, gear Y rotates at 210 rpm in the clockwise direction.

Correct Option Analysis:

The correct option is:

Option 2: 210 rpm clockwise

This is the correct answer because the speed of gear Y matches the speed of gear X (210 rpm), and the direction is clockwise due to the effect of the idler gear reversing the rotation twice (restoring the original direction).

Additional Information

Analysis of Other Options:

Option 1: 840 rpm clockwise

This option is incorrect because the speed of gear Y cannot exceed the speed of gear X in a simple gear train with equal teeth on gears X and Y. The speed ratio (1:1) ensures that both gears rotate at the same speed.

Option 3: 210 rpm counter-clockwise

This option is incorrect because the idler gear reverses the direction of rotation twice (restoring the original direction). Therefore, the direction of gear Y remains clockwise, not counter-clockwise.

Option 4: 420 rpm counter-clockwise

This option is incorrect because the calculated speed of gear Y is 210 rpm, not 420 rpm. Additionally, the direction is clockwise, not counter-clockwise.

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Concept:

The contact ratio of gears is the ratio of the length of the arc of contact to the base pitch.

It is calculated using the formula,

Calculation:

Given:

Pinion teeth, , Gear teeth,

Pressure angle, , Module, , Addendum,

Pitch circle radii:

,

Base circle radii:

Addendum circle radii:

Length of path of contact:

Base pitch:

Contact ratio:

Concept:

Sliding velocity at the beginning of engagement in external gear meshing is given by,

Where,  and  are angular velocities of the pinion and gear respectively.

Calculation: 

Given:

Pinion speed, = 150 rpm , Gear speed, = 100 rpm

Distance from point of engagement to pitch point = 20 mm = 0.02 m

Step 1: Convert rpm to rad/s

Step 2: Use sliding velocity formula at the beginning of engagement:

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.

Concept:

Power transmitted from pinion = Power gain by gear 

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,

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

Thus, 

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 = 

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 =  =  = 

⇒  = 

⇒ 

⇒ 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:

Arc of contact is given by:

where ϕ = pressure angle

Circular pitch = πm

where m = module

Calculation:

Given:

m = 3.5 mm, , ϕ = 30°

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.

Explanation:

Spur gear:

• Spur gears are those gears in which teeth are straight and parallel to the axis of the shaft.
• These types of gear are noisy, more fatigue, and have less life.
• Spur gears are used for very low power transmission.

Stalling torque

Stalling torque is the torque produced by the spur gear tooth at zero pitch line velocity and it is the torque that produces maximum stress in the arm and teeth.

Design of arm of gear is done on the basis on stalling torque.

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.