ABSTRACT
Next, estimate the distance the load will descend during its deceleration due to braking by integrating a=d2x/dt2 twice, subject to the initial conditions that x(0)=0 and dx(0)/dt=0 under the assumption that the deceleration is constant. From the resulting formulas,
it follows that if the load is to stop 2.0 seconds after the brake is applied, the values of acceleration a and distance s must be
Now that distance s is known, we can calculate the potential energy change for the rope as it extends from y1=y0−s to y2=y0 by integrating over this length to get
(84)
The potential energy for the load is given by
(8-
The kinetic energies may be found from
where m1 through m4 are the masses of gears 1 through 4, respectively, and r1g through r4g are their respective radii of gyration. Thus,
Addition of these gives
So upon adding this to the total potential energy of
the torque required may be found from
(8-
in which the average motor speed during braking was taken to be ωm/2. The braking requirement of 813.9 N-m may be met by using a variety of brakes, such
as band, external linear, annular caliper, and annular disk brakes. To choose among these, recall equation (1-10) from Chapter 1, equation (2-1) from Chapter 4, and equations (17) and (3-5) from Chapter 5 corresponding to the foregoing order, and let the internal
radius, r0, for both the annular caliper and annular disk be given by equation. Accordingly, evaluate the formulas
(8-
for a band brake,
(8-
for either two opposing internal or external linearly acting brake shoes,
(8-
for two opposing disc brake pads, each subtending angle φ0, and
(8-
for two complete annular pads in which φ0=2π in equation (8-9). We shall also consider an external pivoted drum brake with a leading and trailing shoe
that may be evaluated by invoking the program used in Chapter 3. In all of these calculations assume a friction coefficient of 0.3, and set the width for the band, the linearly acting drum brake, and the externally pivoted brake to 5 cm. Limit the maximum lining pressure for the band brake and for the externally pivoted brake to 2.0 MPa, and limit the pressure for the other linings to 3.0 MPa, which may be either formed or solid. Lining pressure for the externally pivoted brake was taken to be 2.0 MPa, merely for comparison with the band brake.
