During the passage of a bucket coil, a sinusoidal current flow described by the equation
will appear in each drive coil. The angular frequency,
of the flow will be
2
/period, where the period
equals 4
m
/V with m being the spacing between drive
coils and V being the bucket velocity. At any moment, there
will be four contiguous drive coils having a current flow within
them. Every current will be 30o
out of phase with that in each of the adjacent drive coils.
Figure 2 illustrates the
current flows in neighboring coils during the activation of a
particular reference drive coil (coil no. 4). The equations
describing the current flows with respect to that reference drive
coil current are as follows:
| Coil no.1 |  |
| Coil no.2 |  |
| Coil no.3 |  </</TD> |
| Coil no.4 |  |
| Coil no.5 |  |
| Coil no.6 |  |
| Coil no.7 | |
The force experienced by any two active coils will be given by the product of the instantaneous current in each coil multiplied by the gradient of their mutual inductance (dM/dx) at the distance of their separation:
This force will be attractive between coils with currents of the same sign, and repulsive between coil currents of opposite sign.
Refer again to figure 1 and
consider the forces acting on the reference coil no. 4. During its
first quarter-cycle (-
t - /2),
coil no.4 will interact repulsively with coil no. 1, repulsively
with coil no. 2, and attractively with coil no. 3. At exactly
t = - /2, a weakly felt coil no. 1(a
distance 3m away) will turn off and a much
closer coil (coil no. 5 only a distance m away) will be activated. Because
the force on coil no. 4 due to coil no. 5 is stronger than was the
force from coil no. 1, a discontinuity in the gradient of the force
acting on coil no. 4 will exist. During the second quarter-cycle (-
t 0), coil no. 4 will feel a repulsion from both
coils nos. 2 and 3, and an attraction to coil no. 5. Through
considerations of symmetry, the forces exerted on coil no. 4 in the
third quarter-cycle are the negative of those exerted during the
second quarter-cycle. Similarly, forces felt during the fourth
quarter-cycle are the negatives of those experienced during the
first quartercycle. Over the complete cycle, then, a drive coil
receives no net force from its neighboring drive coils.
The program listed below is designed to calculate the reaction force on a drive coil due to all other active drive coils in its neighborhood as a function of the time from which that coil was turned on. It is written to be run on a Hewlett-Packard HP-67/HP-97 calculator.
It is assumed that bucket velocity may be taken as constant
during the passage of the bucket through any four successive drive
coils (a distance of only a few centimeters). Hence the angular
frequency will be
constant.
The program is initialized by the input of three pieces of
information: key in the dM/dx between drive coils
separated by a distance m; ENTER; key in the mat a distance of
2m; ENTER;
key in the dM/dx for a distance of 3m (ref.4). Initiate the program by pressing the
button labeled [A]. Program execution will begin. Very quickly, the
program will pause for a second and the display will show "1.0."
During this pause, key in the maximum drive coil current. (this
value will default to 1.0 of no entry is made; in this case, all
final answers will actually be
F/iaib.)
The program will then loop, displaying a zero for a second and
then blurring for a second. At any instant when the machine has
paused with a zero showing, key in a value of t and the reaction force of the drive
coil at that instant will be calculated. The program accepts values
of t expressed in
degrees rather than radians. The range of values
-180o t
180o.
Once a force has been calculated, the answer, (in Newtons) is
displayed for 10 sec. the program then branches to the zero/blur
input mode, ready to have the next value of t keyed in.
| 001 | *LBLA | 034 | RCL5 | 067 | x |
| 002 | DEG | 035 | 9 | 068 | RCL3 |
| 003 | ST03 | 036 | 0 | 069 | x |
| 004 | R |
037 | - | 072 | ABS |
| 005 | STO2 | 038 | X<0? | 071 | x |
| 006 | R |
039 | GTOB | 072 | ABS |
| 007 | STO1 | 040 | GSBc | 073 | RTN |
| 008 | CF3 | 041 | STO |
076 | SIN |
| 009 | 1 | 042 | GSBb | 075 | RCL5 |
| 010 | STO4 | 043 | ST-0 | 076 | SIN |
| 11 | PSE | 044 | GSBa | 077 | X2 |
| 12 | PSE | 045 | ST-0 | 078 | RCL2 |
| 13 | F3? | 046 | GTO3 | 079 | x |
| 14 | X2 | 047 | *LBLB | 080 | RCL4 |
| 15 | ST04 | 048 | GSBc | 081 | x |
| 16 | CF3 | 049 | ENT |
082 | ABS |
| 17 | *LBL1 | 050 | + | 083 | RTN |
| 18 | CLX | 051 | CHS | 084 | *LBLc |
| 19 | PSE | 052 | STO |
085 | RCL5 |
| 20 | F3? | 053 | GSBb | 086 | SIN |
| 21 | GTO2 | 054 | ST-0 | 087 | RCL5 |
| 22 | GTO1 | 055 | *LBL3 | 088 | COS |
| 23 | *LBL2 | 056 | RCL0 | 089 | x |
| 24 | X<0? | 057 | F2? | 090 | RCL1 |
| 25 | SF2 | 058 | CHS | 091 | x |
| 26 | ABS | 059 | PRTX | 092 | RCL4 |
| 27 | STO5 | 060 | PRTX | 093 | x |
| 28 | 1 | 061 | GTO1 | 094 | ABS |
| 29 | 8 | 062 | *LBLa | 095 | RTN |
| 30 | 0 | 063 | RCL5 | 096 | *LBLe |
| 31 | - | 064 | SIN | 097 | CLX |
| 32 | X>0? | 065 | RCL5 | 098 | 1/X |
| 33 | GTOe | 066 | COS | 099 | RTN |
| 100 | R/S |
|
Curator: Al Globus If you find any errors on this page contact Al Globus. |
 |
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