Resistor Grid Data (Form 9D)

The dynamic braking system of a rapid transit vehicle is used to decelerate the vehicle when it is operating at speeds greater than about 15 mph, with the change in the kinetic energy of the vehicle being converted into thermal energy in resistor grids mounted under the vehicle. This thermal energy is

released in turn to the subway environment and represents the major source of heat in a subway system.

The conventional resistor grid is a collection of electrical resistance elements in the form of metallic coils or tubes which are arranged in banks located beneath the vehicle. The grid elements have a high surface to mass ratio to facilitate heat dispersal. A set of grids in the propulsion system (acceleration grids) are primarily used to control the current passing through the propulsion motors during acceleration. In cam- controlled vehicles, resistor grids are an integral part of both the propulsion and dynamic braking

systems, but in a thyristor (chopper) controlled vehicle they are found only in the dynamic braking system.

The SES program has the capability of computing the instantaneous magnitude and location of heat rejected by the resistor grids of subway trains operating in a given system, accounting for the thermal inertia of the grid mass. The program computations for a given train in the system are based on the following assumptions: (1) each powered car of a cam-controlled subway train has two distinct sets of resistor grids, acceleration and deceleration, (2) each powered car of a chopper-controlled train only has deceleration resistor grids and the heat released during acceleration will be instantaneous, (3) the

8-33

acceleration resistor grids in all cars of a train type are alike, and (4) the deceleration resistor grids in all cars of a train type are alike.

As a consequence of the above assumptions, the program computes the instantaneous grid average temperatures and heat rejection rates for one pair of acceleration (if any) and deceleration grids and uses these values for the remaining grids on the train.

Input Requirements

The program user is required to supply the program with information which describes the physical characteristics of a train's acceleration and deceleration grids. These include the mass, specific heat, emissivity, effective diameter, effective convective surface area and effective radiative surface area of both grids for each type of train to be simulated.

The value used for the total weight of resistance elements per car represents the mass of all the resistor grid elements which actually resist current flow in the grid circuit, but excludes the weight of any of the supporting structure. The weight of the supporting frame and even the ceramic supports within each resistance element are not included in the weight entry. Typically, the weight of an individual resistance element may be on the order of 5 to 10 pounds, while the total weight of resistance elements per car for the braking resistor grid will be on the order of 300 to 400 pounds. If the grid mass is entered as zero, grid thermal inertia calculations are omitted and the energy which would normally enter the grid is instantaneously released to the tunnel air. (Note: Since a chopper-controlled train does not require acceleration grids, their mass must be entered as zero.)

The effective diameter of an element represents the characteristic length dimension of a resistor grid element. For the circular cross-sectional type of grid element, the effective diameter is simply the diameter of the outer surface of the element (see Figure 8.13). For a grid with rectangular cross-section, the effective diameter is equal to the hydraulic diameter of the cross-section.

The effective surface area for convection of a grid is the sum of the effective surface areas of the individual grid elements. For the circular cross-sectional type of grid element, this area is defined as the cylindrical surface area at the outer surface of the element (see Figure 8.13). For a grid element with rectangular cross-section, this area is defined as the area enclosing the element at its outer surface, not including its end.

EFFECTIVE AREA = EFFECTIVE DIAMETER = Dg

Dg

π* D L_g

B

A

EFFECTIVE AREA = 2(A+B)L

4(AB) EFFECTIVE DIAMETER = 2(A+B)

Figure 8.13 Effective Convective Area and Diameter of Resistor Grid Element

L

L

8-35

The effective surface area for radiation of a grid may be approximated by considering a resistor grid to be enclosed in an imaginary rectangular box (see Figure 8.14). Since the projected surface area of the grid is essentially equal to the projected surface area of the box as seen from any point outside the grid, the surfaces of the box can be considered as the effective radiating surfaces of the grid. The shape factor of the box with respect to its surroundings is equal to 1. Therefore, the effective radiative surface area of the grid is equal to the sum of the surface areas of the box.

The values used for the emissivity of the resistance element surface and the specific heat of the resistance element material should be evaluated at the average operating temperature of the grid. If this temperature is not known, the user should assume the deceleration grids to be operating in the

temperature ranges of 500-1000°F and the acceleration grids in the range of 200-400°F.

The program user must supply an initial grid temperature for each type. The grids are assigned these temperatures at the time the trains are dispatched onto their respective routes. If this initial grid temperature is entered as zero (0.), the grid is initialized at ambient temperature.

User Suggestions. Studies with the SES program indicate that heat released from train resistor grids at a given location in a subway is very much dependent on the history of train operation up to that location. The temperature history of deceleration grids (initialized at ambient temperature) as a train traverses a system shows that the resistor grid temperature builds up or cascades over several station stops, eventually leveling out to a repetitive cyclic pattern as the train continues through the system. The result is that a substantial portion of the kinetic energy dissipated during braking is retained by the resistor grid as stored thermal energy after the first station stop, but after several such stops the heat released from the grid during a train travel-dwell cycle approaches the kinetic energy dissipated during braking.

When the latter occurs, the grids are said to be operating in a state of thermal equilibrium; that is, the average temperature profile of the grid becomes repetitive from station to station. The grid thermal inertia phenomenon is illustrated graphically by Figure 8.15, which shows a typical SES-computed cascading of resistor grid heat release as a train undergoes several successive travel-dwell cycles.

L1

L2

L3

EFFECTIVE RADIATION SURFACE AREA = 2(L1 * L2 + L2 * L3 + L3 * L1)

Figure 8.14 Effective Radiation Surface Area for Resistor Grids

1

NOTE: The deceleration resistors were initially at ambient temperature.

THERMAL EQUILIBRIUM

Grid Heat Rejection Rate

Figure 8.15 Example of Deceleration Resistor Heat Rejection History

2 3 4 5 6 7 8 9 10 Station Stop

8-37

8.10 Flywheels