Linear magnetic braking system with nonuniformly wrapped primary coil producing constant braking force on secondary coi

Kosmahl, H. G.

English

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https://ntrs.nasa.gov/search.jsp?R=19710008177 2020-03-17T02:45:43+00:00Z
LENEAR MAGNETIC BRAKE WITH TWO WINDINGS 
Fi led  Dec. 12, 1966 
INVENTORS 
United States Patent 86 3,493,797 ce Patented Fe, , ,970 
3,493,797 
LINEAR MAGNETIC BRAKE WITH 
TWO WINDINGS 
Heinrich G. Kosmahl, Olmsted Falls, Ohio, assignor to the 
United States of America as represented by the Ad- 
ministrator of the National Aeronautics and Space 
Administration 
Filed Dec. 12, 1966, Ser. No. 601,228 
Int. Cl. H02k 49/00 
U.9. Cl. 310-93 8 Claims 
ABSTRACT O F  THE DISCLOSURE 
The coil 1 con~prises a conductor 10 having a large di- 
ameter dl which is wrapped about a hollow tubular core 
14  as shown in the drawing. The coil 1 has one of several 
configurations which will be described later in greater 
detail. The coil 2 likewise comprises a large diameter 
conductor 12 which is uniformly wrapped about a cylin- 
drical core 16, and the ends of the conductor 12 are short 
circuited by a line 18. 
A payload 20 is rigidly mounted on one end of the coil 
2 and is preferably magnetically noninteractive. The coil 
2, core 16 and payload 20 comprise a test package 22 
which is free to fall towards the fixed primary coil 1 in 
the direction of the arrow shown in the drawing. The path 
~i~~~~ magnetic braking using a pair of inductively of movement of this test package 22 is alongthe axis of 
coupled circuits. A primary coil is nonuniformly wrapped 15 the 'Ore 14. 
about a tubular core with a winding density which pro- The interaction of the two coils 1 and 2 can best be 
duces a constant force on a secondary coil. described by their mutual inductance M in henries. The 
primary coil 1 is connected to a power source 24 which 
~rovides a load voltage Vn in volts and has an impedance 
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ORIGIN OF THE INVENTION 20 kg in ohms which is much smaller than the impedance R1 of the coil 1. The bottom end 26 of the coil 1 away 
The invention described herein was made by an em- from the coil 2 represents the origin of a coordinate sys- 
ployee of the United States Government and may be man- tem in which the axial coordinate is z. The test package 
ufactured and used by or for the Government for govern- 22 moves only in the z direction. 
mental purposes without the payment of any royalties 25 The payload 20 has a given mass ,no while the coil 2 
thereon or therefor. together with its core 16 have a mass Inz. The total mass 
BACKGROUND OF THE INVENTION r11 in kilograms of the test packase 22 is mo+m2. 
Prior to any interaction between the primary coil 1 and 
This invention is concerned with the controlled deceler- secondary coil 2 a steady-state current il,o from the power 
ation of a moving mass. The invention is particularly 30 source 24 flows in the conductor 10. As the test package 
directed to an improved magnetic brake system for stop- 22 moves in the direction its momentary distance from ping a falling body. the bottom end 26 of the coil 1 is z. The instantaneous 
A controlled stopping of a falling mass presents some velocity i [ z ( t )  11 of the coil 2, where z is the first deriva- 
difficult braking problems. In many applications the rate tive, is determined from the following equations in which 
of deceleration must not exceed a very low maximum to 35 L~ is the self inductance in henries of the coil 1 and j z  
avoid damage to the payload. Also, the amount of energy is the current flow in the second coil 2 in kiloamperes. 
which can be excended in decelerating the object should 
be kept to a minimum. 
- 
di These problems encountered in decelerating a moving V~=il(t)  Rl+Ll ;ii- 7 
body have been solved by a magnetic brake system con- qo (1 
structed in accordance with the present invention. The d"(z) i l ( t )+n/ , ( z )  d i l ( t )  - -
mechanism of operation of this system is based on Lenz's O = i z ( t ) R ~ + L z ~ + ~  at (2)  
law which states that magnetic fields induced in one cir- 
cuit as a result of interaction with another circuit oppose 
each other. This system relies on the mutual inductance 
between two magnetically coupled and unconventionally 45 
wound circuits spaced from one another. One of these 
circuits has a primary magnetic coil whose configuration 
is such that the motion of a secondary magnetic coil 
through the fields of the primary coil is brought to a stop 50 
under controlled conditions requiring minimum primary 
energy. 
It is, therefore, an object of the present invention to 
provide a magnetic brake system which will bring a known 
mass to a full stop with a minimum expenditure of energy. 
A further object of the invention is to provide a mag- 55 
netic brake system in which the braking action is ac- 
complished in a precisely adjustable manner with respect 
to the desired degree of deceleration by simply vnrying 
the voltage and current of a primary circuit. 
The repelling magnetic force F, acting upon the turns 
12 of the falling payload is 
where z is the distance between defined points in coils 
1 and 2. In the following equation of motion of the pay- 
load 2 is the second derivative and the value of g is 9.81 
meters per second per second. 
Multiplication by 2, the first derivative, and integration 
between r=O and t = t  produces the following energy equa- 
tion in which 11 is the total distance in meters through 
which the test package 21, as fallen. 
These and other objects of  the invention will be a p  " 2 t= t  
parent i r o ~ n  the specification which foliows and from the ( 2  112 t=o  i r ( l ) ~ i , ( t )  d"(ili(l)di dz 
drawing in which like n~lmerals are used thro~lghout to 
identify like parts. (5) 
The drawing is a schematic illustration of a magnetic since ( 0 ) ,  the velocity z=,l, is zero. braking system constructed in accordance with the pres- fi5 The initial value conditions are i,(0)=io and iZ=O. 
ent invention. After M = M ( z )  has been computed, Equations 1, 2 Referring now to the drawing, the braking system util- 
izes a pair of magnetic coils 1 and 2. The primary coil 1 is and 5 are solved simultaneo~lsl~ for z ( t )  and z ( t ) .  The 
fixed in a desired position, such as at the bottom of a _ values ;(t,)=0 and z(t,) give the stopping time t, and 
drop tower in a zero gravity research facility. The second- ( 0  stopping position z(t,)=x, of the payload above the 
ary coil 2 forms a part of a movable structure, such as a ground level. 
drop tower experiment capsule. It is evident from these equations that the stopping 
3,493,797' 
3 4 
chaiacteristics can be altered by changlng the ~orifigiria in Table 7 ale for n sjstei;: having a piimalq coil w ~ t h  a
tion of the winding of the coil b Var~ous palameters for wrndlng density of 2 f l i  5 cos az/ll) Ths last foui 
three such configur ations aie shown in Tables 1 and 2 value\ i n  Tahlt: 2 ale for a s)ilein having a j;iiniarq coil 
These tables list the lengths li and l2 in meters of the with a winding density of 
coils 1 and 2, respectively. The diameter d2 of the con- 
ductor 12 in the coil 2 is glven in meters along with 2 [ l+b ( I ? )  
its specific resistivity p2 in ohms meter. 
As stated above the conductor 12 of the coil 2 is uni- In deciding which configulation is preferable over the 
formly wrapped, and the tables list the winding density o the~s  for a particular application the primary power 
IV of this coil in turns per meter. Two separate values in 10 must not be the sole criterion because of the presence 
meters for the radius b of the secondary coil 2 are also of retraining conditions and ease of constluction. Two 
shown. important conditions in diop tower applications are the 
TABLE 1 
dn, 111 a,, ( n )  (111) m, tulnsllll lb ,m $ 7 ,  111 VI, V 11 o kA G,,, , g x,, m P, hl\V T, ,  src 
TABLE 2 
dz, 111 on, ( 0 )  (m) w, turnslnl 11, m 12, m VI, V i1.0 kA G,,,,., p x., m P. 311%' TI.  see 
In addition to the aforementioned geometrical para- time constant r1 be as small as possible where the mag- 
meters these two tables contain the primary coil voltage netic field is unconstrained in order for the current il to 
V1,  the steady-state primary current il ,o at the beginning build up as close to its final value ilp0 as possible in a 
of interaction, the power P, the normalized force G in 45 time t which is less than or equal to approximately twice 
multiples of go, and the ~osition s, at  which the center the free fall time through a height h. By way of example, 
of the payload turns approaches zero velocity, measured where h=120 meters the time t=10 seconds is the maxi- 
from the bottom end 26 of the primary coil where z=0. mum period available for the build up of current in case 
The decelerating force persists even after z has reached 60 a two-way up-and-dOwn experiment. 
zero because the time constant r2=L2/R2 of the secondary Other conditions for experiments conducted in the 
coil 2 prevents an instantaneous decay of j2 to zero. above drop tower are that the upper limit of decelera- 
Therefore, the repelling magnetic force F, remains finite tion G is smaller than 30 g's. The power requirements to 
over a period of a few constants, and a perfect stop is bri"g the payload 22 to a full stop can be reduced sub- 
possible. stantially if the condition G is equal to or less than 30 is 
Also listed in Tables and are two values of the disregarded because stopping action can be accomplished 
specific resistivity p2 for aluminum which are with a shorter primary coil. A study of Tables 1 and 2 indicates that the application 
3 x 10-8(ft) ( m )  of cryogenic cooling to the secondary turns reduces sub- 
at room temperature ~ = 3 0 0 0  K and 0 . 6 ~  10-8(~)  (,,,) stantially the primary power requirements in the case of 
at T=800 K. The primary current il is not absolutely d2=0.05 meter and only slightly in the case of d2=0.1 
constant; however, because of the relatively large time meter. Also, the primary Power requirement decreases 
constant the current il changes by less than per- r "31~ as the secondary coi! radius is increased fro= 
cent of the initial ilZo value. 0.75 to 1.0 meter and the primal-y coil radius is 1.5 
The parameters sho.rin in Tables I and 2 are applica." 65 meters. 
ble to a payload 20 having a mass nzo of 900 kilograms For- equzi! values of specific resistivity, conductor di- 
to which the mass of an aluminunn cundrrcior. 12 has been "DleteF. coil length. winding density, and coil radius of 
added. The diameter of the primary coil is three meters. the secondary coil 2 while keeping G equal to or less than 
The primary turns consist of 0.1 meter diameter copper 30 the power requirements of the three tabt~lated wind- 
wire 10 having a spcific resistivity pl of 1.8X 10-8 ohnts 70 ing configui-ations necessary to bring about a full stop 
meter. are approximately the same. However, the energy re- 
Parameters for three different winding configurations quirements are not equal. 
of the primary coil I are set out in Tables 1 and 2. The The primary coil configuration having a winding den- 
primary coil 1 of the system described in Table 1 has a sily of~~=conslant sll-(z/l)l  produces the shortest time 
winding density of lo(/--z/ll). The first six values listed 75 constant 1-,=2.3 seconds. This configuration also requires 
5 6 
the Smallest nt~mber of turns to bring ;rboilt a ful l  stop What i s  clain7ed is: 
of the payload. 1" P,pparaius for stopping a freely falling body with a 
The meaning of the terrll full stop refers to a motion mininluln expenditure of electrical energy and a pvedeler- 
in wllicl? the  locit city decays directly to zero ~,xiithor:t mi!;ed amo.i?i-it of d-celci-ation comprising 
oscillations in the sign of the deceleration. That is, there a tubular core being rigidly ~nourited iit the path of 
is no acceleration. The position of the stop in all sym-  the freely falling body and having a diameter greater 
lnetrically wound coils lies above the coil center where than said body to enable thz same to enter said core, 
2=11/2. This occurs because in symmetric coils the mu- a first constant diameter conductor forming a single 
tual inductance M has a maximum and primary coil wrapped about said tubular core, 
clild- a power supply connected to said primary coil for pass- 
-- ing a predetermined current through said primary 
clz coil to create a first magnetic field therein, 
at the center of the coil. Thus dM/clz reverses its sign a cylindrical core mounted on the freely falling body, 
in going through the center. In the expression for the a second constant diameter conductor forming a sec- 
repelling force F, set forth above in Equation 3, i~(t) 15 ondary coil wrapped about said cylindrical core, and 
remains almost constant and the sign of i2 depends prl- means for short circuiting the ends of said secondary 
marily on that of dM/dz.  Because the time constant 7-2 is coil to enable an induced current to flow therein as 
rarely below 0.1 second a reversal in the sign of dM/dz  said secondary coil moves through the magnetic field 
in going through the center would preclude that oc- of said primary coil thereby creating a second mag- 
curring in i,. 20 netic field in opposition to said first magnetic field, 
Therefore, if the payload 20 moves over the center, a said primary coil being nonuniformly wrapped with a 
short period of acceleration will follow: the payload ve- winding which produces a constant force. 
locity would increase temsporarily before final decelera- 2. Apparatus as claimed in claim 1 wheren the primary 
tion could occur to cause the final stop. This two phase coil has a winding density of K ( I -z / l )  where K is a 
deceleration with a short acceleration period in between 23 constant, z is the distance from one end of the coil and 1 
produces a workable mode of operation requiring ap- is the length of the coil. 
proximately 10 percent less power than one phase stop- 3. Apparatus as claimed in claim 1 wherein the decele- 
ping. ration is smaller than 30 g's and the primary coil has a 
The effect of changing l2 on the power requirement indi- winding density of 10 (1-z/l) where z is the distance from 
cates an optimum length l2 is less than 11. This is be- 30 one end of the coil and 1 is the length of the coil. 
cause two competing factors produce a minimum power 4. Apparatus as claimed in claim 1 wherein the second- 
requirement. More particularly, increasing 12 increases ary coil is uniformly wrapped about the cylindrical core. 
the flux through the secondary coil which increases the 5. Apparatus as claimed in claim 1 wherein the primary 
braking force. However, the mass in, increases propor- coil is mounted at the bottom of a drop tower in a zero 
tionally with I2 and reduced the effect of the decelerating 35 gravity research facilily, and the moving body comprises a 
force in front of the integral in Equation 5. drop tower experiment capsule. 
A clear dip in power requirements occurs when the 6. Apparatus as claimed in clai~ll 5 wherein the drop 
winding density of the secondary coil 11,~ is changed as tower experiment capsule is free to fall toward the pri- 
shown in Table 1 .  This optimum occlns because of the mary coil from a predetermined height. 
competing effects between the secondary time constant 40 7. Apparatus as clainled in claim 5 wherein the drop 
7~ which prevents a rapid build-up of i, and the mutual tower experiment capsule includes the secondary coil, the 
inductance Because both 7 2  as well as  MI,^ increase cylindrical core within said secondary coil, and a payload 
with increasing T V ~ ,  a minimum in the required power rigidly mounted on one end of said core. 
occurs if the total interaction time is not substantially 8. Apparatus as claimed in claim 7 wherein the payload 
larger than 7,. 45 is magnetically noninteractive. 
Although several embodiments of a braking system 
constructed in accordance with the invention have been References Cited 
described, it will be appreciated that various structural 
modifications may be made without departing from the 
spirit of the invention or the scope of the subjoined 
claims. For example, the payload 20 in the system de- 
scribed is magnetically noninteractive. However, it is 
contemplated that certain installations may have pay- 
loads that are magnetically interactive with the primary 
-. . -
UNITED STATES PATENTS 
8/1932 Nartzell -------- 336-224 XR 
12/1934 Huse ---------------- 310-13 
1 /I935 Loughlin -------- 336-224 XR 
7/1966 Beach --------------- 310-14 
1/1967 Deutsch ------------- 310-14 
coil. It  is further contemplated that the magnetic field 55 ORIS L, RADER, Primary Exanliner 
mav be constrained to the inside of the tubular core bv 
placing a magnetically conducting membrane perpen- A. G. COLLINS, Assistant Examiner 
dicular to its axis. With such a modification the time 
constant r1 is of little importance, and the field can be U.S. C1. X.R. 
built up prior to the ejection of the payload. 60 310---I3 


Linear magnetic brake with two windings Patent

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