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Exercise 1

(((50%)))

Figure 1 shows a transmission system that

transmits power from an electric motor to an

industrial machine by means of V-belt and gear

transmission. The gears have a straight-toothed

tooth profile. The electric motor is delivered with

a V-belt mounted on the shaft journal. The

following data are given for the electric motor:

Nominal power, P = 60 kW, speed n1 = 625 rpm.

Due to the tension wheel, it can be assumed that

the pull in the tight part (T1) of the belt on the

pulley is twice as large as the pull in the slack part

(T2) and that both act parallel to the z-axis (see

Fig. 1 (b)) . The intermediate shaft is made of steel

(E335) and carries a pulley and a gear. It is

supported by a single-row ball bearing and a

cylindrical roller bearing. The shaft of the

industrial machine and the intermediate shaft lie

in the same vertical plane.

a) What is the effective torque of the industrial

machine if the belt drive is assumed to have an

efficiency of 90%?

b) Assume module m = 5 and that there is

clearance engagement between the gears, and

determine the base circle diameter (db), number

of teeth (z1) and tooth thickness (s) on gears 1.

c) A simplified calculation model of the

intermediate shaft together with mounted pulley,

bearings and gears are shown in FIG. 1 (c) above.

Fig. 1 (c) Simplified calculation model for the

intermediate shaft

Based on the nominal power of 60 kW and the

dimensions given in the figure:

i) Draw the torque diagram for loading the

intermediate shaft in both x-y and x-z

planes. How big is the largest bending

moment? The weight of the shaft, gears and

pulley can be neglected.

ii) At a point on the intermediate shaft, the

voltages acting on a voltage element have

been calculated as shown next to it. Use

Mohr's circle and find the magnitude and

direction of the main voltages for this

voltage element. Enter the voltages on a

sketch of a main voltage element.

d) An examination shows that the machine runs at

almost full load for 75% of the operating time and

otherwise with half load. What will be the nominal

service life of bearing A, in number of hours, if you

choose bearing type 6310 which has the following

bearing capacities: C = 65.0 kN, C0 = 38.0 kN?

e) FIG. 1 (d) shows a curvature surface diagram

for the intermediate shaft (see also Fig. 1 (a))

calculated on a plane where the shaft is most

loaded. The diagram is based on a shaft with a

constant diameter (Ø50). Use the linker

(curvature surface) method and calculate the max.

the displacement C at end C of the shaft. Tip: the

weight of the shaft, gears and pulley is neglected.

Fig. 1 (d) Deformation image and curvature

surface diagram

f) The pulley is rigidly connected (mounted) to the

intermediate shaft by a single-shrink connection.

As shown in Fig. 1 (a), the connection is

dimensioned with fit tolerance Ø45H6 / p5. The

following data are given for the shrink connection:

- Diametral press nozzle in mounted condition:

min = 10 μm, max = 37 μm. - Influence

coefficients are calculated and specified as

follows: Shaft: a = 5.0 * 10-5 Belt pulley (hub):

n = 6.5 * 10-5. How large must the width of the

contact surface between the pulley and the

intermediate shaft be in order to transmit a torque

of 1.5 kNm?

Exercise 2

A design draft for a manual water pump is shown

in FIG. 2 below. In order to be able to optimize the

water flow, it is recommended that the piston has

a vertical speed of vs = 50 mm / s. The pumping

force F is assumed to be perpendicular to the

crank arm BD at all times.

a) Determine the number of instantaneous poles

for the mechanism, and state the location of these

at the moment shown in the figure on a sketch of

the mechanism to scale.

b) Use graphical method and find the angular

velocity 2 of the crank arm BD.

c) The column CE is made of aluminum alloy (E =

70 GPa, Rp02 = 160 MPa) with an outer diameter

of 20 mm and a wall thickness of 4 mm. i) Make

the necessary assumptions and assess whether

the column is in the Euler area. ii) How great is the

safety against buckling of the column with respect

to Euler voltage when the angle θ = 00?

Fig. 2 Design draft of manual water pump

Exercise 3

Figure 3 shows the calculation model for a wheel

suspension in a trolley. The axle is bolted to the

car body at A and is supported against the car

body by a helical spring at B. The axle cannot

rotate, but it can swing in the vertical plane, the

plane shown in the figure. The wheel, which is in

contact with the road surface at all times, is

mounted on the axle at C.

By a random check, an imbalance has been found

in the wheel which can be stated as if the wheel's

mass of m = 25 kg is placed eccentrically in

relation to its axis of rotation at a distance e = 2

mm. Due to the fact that the mass of the car body

is so large in relation to the mass of the wheel, one

can disregard vibrations in the car body.

a) Neglect the mass of the axle and critically

calculate the angular velocity of the wheel in the

axle suspension. Tip: By considering the

relationship between an arbitrary force F

(centrifugal force) acting in C and the deformation

at the same point, one can derive the resulting

spring constant indicated by:

b) How large is the deformation amplitude of the

helical spring at B when the wheel turns at an

angular velocity of = 120 rad / s. Also determine

the alternating force that is transmitted to the car

body via the coil spring due to. the unbalanced

mass of the wheel.

We now consider that the following data are

known about the helical spring:

Material: cold drawn steel wire with 2 mm

diameter

Number of active turns: n = 10

Spring length in unloaded condition: L0 = 56 mm

Spring index: C = 10. c) To avoid buckling in the

spring, its compression should not exceed 25 mm.

i) How large is then the largest shear stress in

the spring.

ii) Also determine the safety against tight turns in

this case.

(((50%)))

Figure 1 shows a transmission system that

transmits power from an electric motor to an

industrial machine by means of V-belt and gear

transmission. The gears have a straight-toothed

tooth profile. The electric motor is delivered with

a V-belt mounted on the shaft journal. The

following data are given for the electric motor:

Nominal power, P = 60 kW, speed n1 = 625 rpm.

Due to the tension wheel, it can be assumed that

the pull in the tight part (T1) of the belt on the

pulley is twice as large as the pull in the slack part

(T2) and that both act parallel to the z-axis (see

Fig. 1 (b)) . The intermediate shaft is made of steel

(E335) and carries a pulley and a gear. It is

supported by a single-row ball bearing and a

cylindrical roller bearing. The shaft of the

industrial machine and the intermediate shaft lie

in the same vertical plane.

a) What is the effective torque of the industrial

machine if the belt drive is assumed to have an

efficiency of 90%?

b) Assume module m = 5 and that there is

clearance engagement between the gears, and

determine the base circle diameter (db), number

of teeth (z1) and tooth thickness (s) on gears 1.

c) A simplified calculation model of the

intermediate shaft together with mounted pulley,

bearings and gears are shown in FIG. 1 (c) above.

Fig. 1 (c) Simplified calculation model for the

intermediate shaft

Based on the nominal power of 60 kW and the

dimensions given in the figure:

i) Draw the torque diagram for loading the

intermediate shaft in both x-y and x-z

planes. How big is the largest bending

moment? The weight of the shaft, gears and

pulley can be neglected.

ii) At a point on the intermediate shaft, the

voltages acting on a voltage element have

been calculated as shown next to it. Use

Mohr's circle and find the magnitude and

direction of the main voltages for this

voltage element. Enter the voltages on a

sketch of a main voltage element.

d) An examination shows that the machine runs at

almost full load for 75% of the operating time and

otherwise with half load. What will be the nominal

service life of bearing A, in number of hours, if you

choose bearing type 6310 which has the following

bearing capacities: C = 65.0 kN, C0 = 38.0 kN?

e) FIG. 1 (d) shows a curvature surface diagram

for the intermediate shaft (see also Fig. 1 (a))

calculated on a plane where the shaft is most

loaded. The diagram is based on a shaft with a

constant diameter (Ø50). Use the linker

(curvature surface) method and calculate the max.

the displacement C at end C of the shaft. Tip: the

weight of the shaft, gears and pulley is neglected.

Fig. 1 (d) Deformation image and curvature

surface diagram

f) The pulley is rigidly connected (mounted) to the

intermediate shaft by a single-shrink connection.

As shown in Fig. 1 (a), the connection is

dimensioned with fit tolerance Ø45H6 / p5. The

following data are given for the shrink connection:

- Diametral press nozzle in mounted condition:

min = 10 μm, max = 37 μm. - Influence

coefficients are calculated and specified as

follows: Shaft: a = 5.0 * 10-5 Belt pulley (hub):

n = 6.5 * 10-5. How large must the width of the

contact surface between the pulley and the

intermediate shaft be in order to transmit a torque

of 1.5 kNm?

Exercise 2

A design draft for a manual water pump is shown

in FIG. 2 below. In order to be able to optimize the

water flow, it is recommended that the piston has

a vertical speed of vs = 50 mm / s. The pumping

force F is assumed to be perpendicular to the

crank arm BD at all times.

a) Determine the number of instantaneous poles

for the mechanism, and state the location of these

at the moment shown in the figure on a sketch of

the mechanism to scale.

b) Use graphical method and find the angular

velocity 2 of the crank arm BD.

c) The column CE is made of aluminum alloy (E =

70 GPa, Rp02 = 160 MPa) with an outer diameter

of 20 mm and a wall thickness of 4 mm. i) Make

the necessary assumptions and assess whether

the column is in the Euler area. ii) How great is the

safety against buckling of the column with respect

to Euler voltage when the angle θ = 00?

Fig. 2 Design draft of manual water pump

Exercise 3

Figure 3 shows the calculation model for a wheel

suspension in a trolley. The axle is bolted to the

car body at A and is supported against the car

body by a helical spring at B. The axle cannot

rotate, but it can swing in the vertical plane, the

plane shown in the figure. The wheel, which is in

contact with the road surface at all times, is

mounted on the axle at C.

By a random check, an imbalance has been found

in the wheel which can be stated as if the wheel's

mass of m = 25 kg is placed eccentrically in

relation to its axis of rotation at a distance e = 2

mm. Due to the fact that the mass of the car body

is so large in relation to the mass of the wheel, one

can disregard vibrations in the car body.

a) Neglect the mass of the axle and critically

calculate the angular velocity of the wheel in the

axle suspension. Tip: By considering the

relationship between an arbitrary force F

(centrifugal force) acting in C and the deformation

at the same point, one can derive the resulting

spring constant indicated by:

b) How large is the deformation amplitude of the

helical spring at B when the wheel turns at an

angular velocity of = 120 rad / s. Also determine

the alternating force that is transmitted to the car

body via the coil spring due to. the unbalanced

mass of the wheel.

We now consider that the following data are

known about the helical spring:

Material: cold drawn steel wire with 2 mm

diameter

Number of active turns: n = 10

Spring length in unloaded condition: L0 = 56 mm

Spring index: C = 10. c) To avoid buckling in the

spring, its compression should not exceed 25 mm.

i) How large is then the largest shear stress in

the spring.

ii) Also determine the safety against tight turns in

this case.

Answered 121 days AfterMay 17, 2021

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