JNTU
JNTU B.Tech III DESIGN OF MACHINE MEMBERS - II Previous Question Paper (March - 2021 - R16)
Answer any five questions
All questions carry equal marks
Main
The following data is given for a 3600 hydrodynamic bearing:
Radial load = 2 kN; Journal diameter = 50 mm
Bearing length = 50 mm; Viscosity of oil = 20 m Pa s
Specify radial clearance that need be provided so that when the journal is rotating at 2800 rpm, the minimum film thickness is 30 microns. Evaluate the corresponding coefficient of friction. Also check for the Heat dissipation.
Answer
Given: Radial load W = 2000 N, Journal diameter D = 50 mm (Radius r = 25 mm), Bearing length l = 50 mm, Viscosity μ = 0.02 Pa.s, Speed N = 2800 rpm, Minimum film thickness h0 = 0.03 mm.
First, calculate the Sommerfeld number (S) using the minimum film thickness ratio. For l/D = 1, the ratio h0/c is related to the eccentricity ratio ε and the Sommerfeld number. Using Raimondi and Boyd charts for l/D = 1, at h0/c = 0.3, the eccentricity ratio ε is approximately 0.7. For ε = 0.7, the Sommerfeld number S is approximately 0.12.
The formula for the Sommerfeld number is:
Where P is the bearing pressure: P = W / (l * D) = 2000 / (50 * 50) = 0.8 N/mm2. Substituting the values:
The radial clearance required is 77.9 μm.
To evaluate the coefficient of friction (μf), use the Petroff's equation or the friction variable (r/c)f. For S = 0.12 and l/D = 1, the friction variable (r/c)f is approximately 3.2. Thus:
Finally, check for heat dissipation. The heat generated (Hg) is:
Heat dissipation capacity (Hd) is typically calculated using the formula Hd = k * A * (Tb - Ta). Assuming standard operating conditions, the bearing is capable of dissipating heat provided the temperature rise is within limits. Since Hg is relatively low (73.1 W), the bearing will operate safely under normal ambient conditions.
A 100 mm diameter shaft is supported by a bearing 100 mm long with a minimum oil-film thickness of 0.025mm and radial clearance of 0.0625 mm. It is lubricated by SAE 20 oil. The bearing carries a load of 10 kN of projected area at 900 rpm. Employing the design charts, determine the temperature of the oil film, the coefficient of friction and the friction power.
Answer
Given: Diameter d = 100 mm, Length l = 100 mm, Minimum oil-film thickness h0 = 0.025 mm, Radial clearance c = 0.0625 mm, Load W = 10 kN = 10,000 N, Speed N = 900 rpm, l/d ratio = 1.
1. Calculate the eccentricity ratio (ε):
ε = 1 - (h0 / c) = 1 - (0.025 / 0.0625) = 1 - 0.4 = 0.6.
2. Determine the Sommerfeld number (S):
For l/d = 1 and ε = 0.6, from standard Raimondi and Boyd charts, the Sommerfeld number S is approximately 0.12.
3. Calculate the operating viscosity (μ):
The bearing pressure p = W / (l × d) = 10,000 / (100 × 100) = 1 N/mm2 = 1 MPa.
Using the formula S = (μ × Ns / p) × (r / c)2, where Ns = 900/60 = 15 rps and r/c = 50/0.0625 = 800:
0.12 = (μ × 15 / 1) × (800)2 × 10-6 (adjusting units for MPa and seconds)
0.12 = μ × 15 × 0.64
μ = 0.12 / 9.6 = 0.0125 N-s/m2 = 12.5 cP.
4. Determine temperature:
For SAE 20 oil, a viscosity of 12.5 cP corresponds to an operating temperature of approximately 75°C based on standard viscosity-temperature charts for SAE 20.
5. Calculate coefficient of friction (μf):
From charts for l/d = 1 and S = 0.12, the friction variable (μf × r / c) is approximately 3.2.
μf = 3.2 × (c / r) = 3.2 × (0.0625 / 50) = 0.004.
6. Calculate friction power (Pf):
Pf = μf × W × v, where v = π × d × N / 60 = π × 0.1 × 900 / 60 = 4.71 m/s.
Pf = 0.004 × 10,000 × 4.71 = 188.4 Watts.
A ball bearing subjected to a radial load of 5 kN is expected to have a life of 8000 hours at 1440 rpm with a reliability of 99%. Calculate the dynamic load capacity of the bearing so that it can be selected from the manufacturer's catalogue based on a reliability of 90%.
Answer
Sign in to view the complete answer paper.
Derive the expression Equivalent cubic load as applied to rolling contact bearings subjected to variable load cycle of W1, W2, W3 … for the cycles N1, N2, N3….
Answer
Sign in to view the complete answer paper.
A 25 mm deep-groove ball bearing carries a combined load of 2 kN radially and 3 kN axially at 1500 rpm. The outer ring rotates and the load is steady. Determine the rating life in hours. Determine the expected rating life of the same bearing, if only a 5% probability of failure can be permitted at 1200 rpm.
Answer
Sign in to view the complete answer paper.
The following data is given for a four-stroke diesel engine:
Cylinder bore = 100 mm; Length of stroke = 125 mm;
Speed = 2000 rpm; Brake mean effective pressure = 0.65 MPa
Maximum gas pressure = 5 MPa; Fuel consumption = 0.25 kg per BP per h
Higher calorific value of fuel = 42 000 kJ/kg
Assume that 5% of the total heat developed in the cylinder is transmitted by the piston. The piston is made of grey cast iron and the permissible tensile stress is 40 MPa (k = 46.6 W/m/0C). The temperature difference between the centre and edge of the piston head is 2200C. Calculate the thickness of the piston head by strength and thermal consideration. Which criterion decides the thickness of the piston head?
Answer
Sign in to view the complete answer paper.
The following data is given for the cap and bolts of the big end of the connecting rod:
Engine speed = 1500 rpm; Length of connecting rod = 320 mm
Length of stroke = 140 mm; Mass of reciprocating parts = 1.75 kg
Length of crank pin = 54 mm; Diameter of crank pin = 38 mm
Permissible tensile stress for bolts and Cap = 120 MPa
Calculate the nominal diameter of bolts and thickness of cap for the big end.
Answer
Sign in to view the complete answer paper.
A helical compression spring of the exhaust valve mechanism is initially compressed with a pre-load of 350 N. When the spring is further compressed and the valve is fully opened, the torsional shear stress in the spring wire should not exceed 750 MPa. Due to space limitations, the outer diameter of the spring should not exceed 42 mm. The spring is to be designed for minimum weight. Calculate the wire diameter and the mean coil diameter of the spring.
Answer
Sign in to view the complete answer paper.
A pair of spur gears with 200 pressure angle consists of a 25 teeth pinion meshing with a 60 teeth gear. The module is 5 mm, while the face width is 45 mm. The pinion rotates at 500 rpm. The gears are made of steel and heat treated to a surface hardness of 220 BHN. Assume that dynamic load is accounted by means of the velocity factor. The service factor and the factor of safety are 1.75 and 2 respectively. Calculate wear strength of gears, the static load that the gears can transmit without pitting and rated power that can be transmitted by gears.
Answer
Sign in to view the complete answer paper.