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
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
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?
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
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
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
ii) Also determine the safety against tight turns in