GATE Agricultural Engineering Farm Machinery Syllabus

Write the torsion equation for a shaft transmitting torque.

$$\frac{T}{J} = \frac{\tau}{r} = \frac{G\theta}{l}$$ where $T$ = torque, $J$ = polar moment of inertia, $\tau$ = shear stress at radius $r$, $G$ = modulus of rigidity, $\theta$ = angle of twist, and $l$ = shaft length. For a solid circular shaft $J = \frac{\pi d^{4}}{32}$.

Give the relationship between power, torque, and rotational speed for a rotating shaft.

$$P = T \cdot \omega = \frac{2\pi N T}{60}$$ where $P$ = power (W), $T$ = torque (N·m), $\omega$ = angular speed (rad/s), and $N$ = speed in rpm.

For a solid circular shaft subjected to pure torsion, express the diameter in terms of torque and allowable shear stress.

From $T = \frac{\pi}{16}\,\tau\, d^{3}$: $$d = \left(\frac{16\,T}{\pi\,\tau}\right)^{1/3}$$ where $\tau$ is the allowable (permissible) shear stress of the shaft material.

What is the function of a coupling, and how do rigid and flexible couplings differ?

A coupling connects two shafts to transmit power and motion. A rigid coupling (e.g. sleeve, flange) joins perfectly collinear shafts with no allowance for misalignment. A flexible coupling (e.g. bushed-pin, gear, Oldham) accommodates small angular, lateral, or axial misalignment and absorbs shocks/vibration.

What is the function of a key in a shaft-hub connection, and name the main types of sunk keys.

A key is inserted between a shaft and hub to prevent relative rotation and transmit torque. Main sunk keys: rectangular/square (flat) keys, gib-head key, feather key (allows axial sliding), and Woodruff (semicircular) key. Keys are designed to fail before the shaft to act as a safety element.

A rectangular key fails by shearing or by crushing. Write the torque-resisting equations for each mode.

Shearing: $$T = l \cdot w \cdot \tau \cdot \frac{d}{2}$$ Crushing: $$T = l \cdot \frac{t}{2} \cdot \sigma_c \cdot \frac{d}{2}$$ where $l$ = key length, $w$ = width, $t$ = thickness, $d$ = shaft diameter, $\tau$ = shear stress, $\sigma_c$ = crushing stress.

Classify bearings by the nature of contact and the direction of load supported.

By contact: sliding-contact (journal/plain) bearings and rolling-contact (ball/roller) bearings. By load direction: radial bearings (load perpendicular to shaft axis), thrust bearings (load along the axis), and angular-contact bearings (both radial and axial loads).

Define the basic dynamic load rating ($C$) and basic rating life ($L_{10}$) of a rolling bearing, and give the life equation.

$C$ is the constant radial load a group of bearings can endure for one million revolutions ($L_{10}$ life). The rating life: $$L_{10} = \left(\frac{C}{P}\right)^{k}$$ in millions of revolutions, where $P$ = equivalent dynamic load, $k = 3$ for ball bearings and $k = \frac{10}{3}$ for roller bearings.

What is a knuckle joint and what type of load is it designed to carry?

A knuckle joint connects two rods (links) whose axes are collinear and subjected to axial tensile (or compressive) loads, while permitting a small angular movement (hinge action) about the pin. Its parts are the eye (fork) end, the single eye, and the connecting pin. Used in tie rods, tractor link/hitch connections, and bracing.

List the modes of failure that must be checked when designing a knuckle joint pin.

The pin is checked for: (1) shear failure (double shear) $P = 2 \cdot \frac{\pi}{4} d^{2} \tau$; (2) bending failure (treated as a beam); and (3) crushing/bearing failure between pin and eye. The rods and eyes are also checked for tension, shear, and crushing.

Name the common sensors/transducers used to measure displacement and acceleration on machine elements.

Displacement: LVDT (Linear Variable Differential Transformer), potentiometers, capacitive and optical encoders, dial gauges. Acceleration: piezoelectric and piezoresistive accelerometers, and MEMS accelerometers. Velocity is often obtained by integrating acceleration or with tachogenerators.

What is a strain gauge and on what principle does it measure force or stress?

A strain gauge is a thin resistive grid bonded to a surface whose electrical resistance changes when it deforms. It works on the principle that resistance change is proportional to strain: $$\frac{\Delta R}{R} = G_f \,\varepsilon$$ where $G_f$ is the gauge factor. Strain is converted to stress via $\sigma = E\varepsilon$ and used in load cells (often a Wheatstone bridge).

Which instruments/methods are used to measure rotational speed of farm-machine shafts?

Mechanical and contact tachometers, magnetic and optical (photoelectric) non-contact tachometers, stroboscopes, and shaft encoders/proximity (Hall-effect) pickups counting pulses per revolution. Speed (rpm) is computed from pulse frequency and pulses per revolution.

How is torque on a rotating shaft commonly measured?

With a torque transducer (torque cell) using strain gauges bonded at $45^{\circ}$ on the shaft surface to sense torsional shear strain, connected through slip rings or telemetry. Alternatively by measuring the angle of twist over a known length, by torsion-bar/strain-ring dynamometers, or by reaction (cradle) dynamometers (e.g. PTO dynamometer).

Define tillage and state its primary objectives.

Tillage is the mechanical manipulation of soil to provide favourable conditions for crop growth. Objectives: to prepare a seedbed, loosen and aerate the soil, control weeds, incorporate crop residues and manure, conserve moisture, and improve soil-water-air relationships.

Differentiate between primary tillage and secondary tillage with examples of implements.

Primary tillage is the first, deep, vigorous soil-cutting operation that leaves a rough surface—implements: mouldboard plough, disc plough, subsoiler, chisel plough. Secondary tillage is shallower, finer pulverizing and levelling after primary tillage—implements: harrows (disc, tine), cultivators, rollers, and puddlers.

Name and define the three mutually perpendicular force components acting on a tillage tool.

Using a right-handed coordinate system: (1) Draft — the horizontal force component in the direction of travel (the useful pull resisted by soil); (2) Vertical force — the component perpendicular to the soil surface (downward suction or upward); (3) Side force — the lateral (transverse) component perpendicular to the direction of travel.

Define draft and unit draft (specific draft) of a tillage implement.

Draft is the horizontal component of pull required to move an implement in the direction of travel. Unit (specific) draft is draft per unit cross-sectional area of the furrow slice: $$\text{Unit draft} = \frac{\text{Draft}}{\text{width} \times \text{depth}}$$ expressed in N/cm² or kPa; it characterizes soil resistance independent of furrow size.

What is soil reaction on a tillage tool and how does the rake (approach) angle affect draft?

Soil reaction is the resultant force the soil exerts on the moving tool, opposing its motion. The rake angle is the angle of the tool's cutting surface to the horizontal; increasing the rake angle generally increases the vertical lifting/penetration action but also increases draft, while too small an angle reduces soil inversion. An optimum rake angle minimizes draft for required soil disturbance.

Name the main functional parts of a mouldboard plough and the function of each.

Share — cuts the furrow slice horizontally and penetrates the soil. Mouldboard — lifts, inverts and pulverizes the furrow slice. Landside — resists the side thrust and stabilizes the plough against the furrow wall. Frog — the base to which share, mouldboard, and landside are attached. Together they form the plough bottom.

What is a hitch system and what are the three main categories of tractor hitching?

A hitch system connects an implement to the tractor to transmit the pull. Categories: (1) Trailed (drawbar) hitch — single-point pull, implement carried on its own wheels; (2) Semi-mounted — partly supported by tractor and partly by its own wheels; (3) Fully mounted (three-point) hitch — implement carried entirely by the tractor's three-point linkage.

Describe the three-point linkage (3-point hitch) and name its links.

The three-point linkage attaches a mounted implement to a tractor using two lower links (draft links) and one upper (top) link. The lower links carry the draft and are raised/lowered by the hydraulic lift; the top link controls the implement's pitch/angle. The three links converge to a virtual hitch point, giving stable control of depth and weight transfer.

What is weight transfer in a mounted-implement hitch system and why is it beneficial?

Weight transfer is the transfer of part of the implement's working reaction (and soil resistance) onto the tractor's rear driving wheels through the three-point linkage. It increases traction (reduces wheel slip) and improves the tractor's pulling ability, especially with draft control raising the implement when soil resistance rises.

Distinguish between draft control and position control in a hydraulic hitch system.

Position control maintains the implement at a constant set height/depth relative to the tractor regardless of soil resistance. Draft control automatically adjusts implement depth to keep the draft (pull) constant—sensed through the top or lower links—raising the implement when draft increases, thereby maintaining steady engine load and traction.

State the functional requirements that any well-designed farm equipment should satisfy.

It should: perform the intended operation efficiently and to the required quality; be matched to the power source (manual, animal, or engine); be safe and easy to operate and adjust; be durable, light, and low-cost; require minimal energy/draft; and be easily maintained and repaired with locally available resources.

Compare manual, animal-operated, and power-operated farm equipment in terms of power source and typical capacity.

Manual (human-powered) equipment uses about $0.05$–$0.1$ kW of human effort, suited to small areas and low capacity. Animal-operated (bullock/buffalo) equipment delivers roughly $0.4$–$0.75$ kW per pair, for medium holdings. Power-operated (engine/tractor) equipment provides several to many kW, giving high field capacity and timeliness for large areas.

Define effective field capacity and field efficiency of a farm implement.

Effective field capacity is the actual area covered per unit time, $C_e = \frac{\text{area covered}}{\text{time taken}}$ (ha/h). Field efficiency is the ratio of effective to theoretical field capacity: $$\eta_f = \frac{C_e}{C_t} \times 100\%$$ where $C_t = \frac{w \cdot v}{10}$ (ha/h) with width $w$ in m and speed $v$ in km/h. It accounts for turning, overlap, and idle time.

What is the principle of working of a seed drill, and name its main components?

A seed drill meters seeds from a hopper and places them in furrows at a controlled rate and uniform depth, then covers them. Main components: seed hopper (box), seed-metering mechanism (fluted roller or cup-feed), seed tubes, furrow openers, covering device (drag/press), and ground (drive) wheel that powers the metering mechanism.

What are the functional requirements and working principle of a sprayer used in farm operations?

A sprayer must break the liquid (pesticide/fertilizer) into fine, uniform droplets and distribute them evenly over the target at a controlled rate. Working principle: liquid is pressurized (by a pump or compressed air) and forced through a nozzle that atomizes it into a spray; main parts are tank, pump, agitator, pressure regulator, cut-off valve, lance/boom, and nozzles.