Diametral change sensor for a cylindrical member

A sensing device for determining diametral changes of a cylindrical member which includes a clamp member having a body adapted to be positioned around the periphery of the cylindrical member and removably attached in at least partially spaced relationship to a portion of the cylindrical member. A proximity sensor attached to the body senses diametral changes in the cylindrical member and generates signals responsive to and representative of the sensed diametral changes. A computation unit connected to the proximity sensor receives the signals therefrom and determines the axial load on the cylindrical member, based on the diametral changes. Temperature sensors may be provided on the cylindrical member and the body for generating signals indicative of the respective temperatures of the cylindrical member and the body, which signals are transmitted to the computation unit and which, in response thereto, compensates for any temperature changes of the cylindrical member and the body in determining the axial load on the cylindrical member.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an improved device for measuring diametral 
changes in a cylindrical member and, more particularly, to such a device 
which measures diametral changes in a cylindrical member whereby axial 
loads on the cylindrical member may be determined. 
2. Description of the Related Art 
In many industries, it is important to measure the variable dynamic axial 
loads imposed on a work piece such as a cylindrical member. This is 
particularly true in the nuclear power industry where Motor Operator 
Valves (MOV's) are extensively used. It is important that these valves are 
set and maintained correctly at all times since correct operation is 
critical to health and safety as well as to proper operation of the system 
in which the MOV's are used. MOV's typically include a valve, a motor 
operator attached to the valve through a stem and yoke means extending 
partially around the valve stem for connecting the operator housing and 
the valve housing. The best measure for accurately monitoring the dynamic 
events within an MOV is by the direct measurement of the valve stem axial 
load. 
It is possible to determine the axial load or strain in a valve stem or any 
other generally cylindrical member from changes in the stem or cylindrical 
member diameter. The ratio of diametral change to axial elongation for a 
material, referred to as Poisson's ratio, is known. Therefore, by 
measuring the diametral change on the valve stem or other cylindrical 
member, axial strain and therefore valve stem axial load can be 
determined. 
There has long been need for a device which can accurately monitor and 
measure the dynamic operation of valves or other thrust bearing 
cylindrical members continuously during operation thereof. 
One current device for determining the axial load on a valve stem is a 
device which senses the changes in clamp means attached around the valve 
stem. As diametral changes occur in the valve stem, the clamp portion 
moves in response to diametral changes in the clamped portion of the stem. 
A sensor is provided to sense movement of the clamp portion of the device 
in response to the diametral changes. The sensed changes in the clamp 
means may be bending in the clamp portion of the device or distance 
changes between parts of the clamp portion of the device. A signal storage 
device, which also may be a computer, stores the signals from the sensor 
for real time or delayed determination of axial loading in the stem or 
other cylindrical member. Such a device is shown, for example, in Leon et 
al. U.S. Pat. No. 4,911,004. 
One disadvantage of the clamp type sensor such as that shown in Leon et al. 
U.S. Pat. No. 4,911,004 is that the clamp is quite bulky and cannot 
continuously travel with the stem during substantially the length of 
travel thereof. Moreover, the clamp can only be used to initially measure 
the stem load and this measurement is then used to calibrate another 
measuring device mounted on the yoke of the valve whereby the stem load is 
indirectly measured based on the strain in the valve yoke. This leads to 
many inaccuracies such as those caused by bending moments in the yoke, the 
fact that the yoke response is non-linear and can vary over the valve 
stroke and that the yoke load measuring device is sensitive to flow 
induced yoke vibration and valve stem harmonic imbalance. Additional 
inaccuracies in using a clamp type sensor can occur as a result of the 
fact that a stem has a normal stiffness and when the clamp is securely 
attached thereto, the normal stiffness changes. 
A further problem with a method for determining valve stem load by 
measuring yoke strain is that the yoke sensor must be calibrated to a 
direct stem sensor prior to each use. Moreover, the yoke sensor must be 
permanently installed with one sensor per valve. Such sensors also can be 
difficult and time consuming to install. 
Another device for measuring valve stem load is shown in Charbonneau et al. 
U.S. Pat. No. 4,542,649 which employs a system that measures displacement 
of a spring pack associated with the motor actuator of a MOV as an 
indicator of forces in the valve system. This spring pack deflection type 
device suffers from the disadvantage of being time consuming to install 
and calibrate. Moreover, spring pack deflection is proportional to motor 
torque and does not measure stem thrust. In addition, the spring pack 
deflection type devices can introduce errors of plus or minus 50% due to 
factors such as spring pack non-linearity, spring pack rate of loading and 
mechanical loss issues, the assumption that the spring pack deflection per 
unit thrust is the same in both directions and the fact that a spring pack 
device is calibrated in the out direction only into a load cell having a 
different stiffness than the valve seat. 
Another device for measuring valve stem thrust loads in a cylindrical 
member such as a valve stem is disclosed in Branam et al. U.S. Pat. No. 
4,856,327 wherein valve stem thrust loads in an MOV are monitored and 
measured by the use of load cells installed directly between the valve and 
the operator of the MOV. Again, however, this type of device does not take 
measurements directly on the valve stem and inaccuracies can occur as a 
result of vibration, temperature changes, etc. 
Accordingly, there is still a need for an improved device for accurately 
and continuously directly monitoring and measuring the axial load in a 
cylindrical member such as a valve stem throughout a substantial portion 
of the length of travel of the cylindrical member and which as well may 
rotate with the cylindrical member. There is a further need for such a 
device which also can compensate for temperature changes in the 
cylindrical member as well as in the measuring device itself. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a device for 
determining diametral changes of a cylindrical member. 
It is another object of the present invention to provide a device for 
continuously and directly measuring and determining the axial load on a 
movable valve stem throughout a substantial portion of its length of 
travel. 
It is yet another object of the present invention to provide a device for 
continuously and directly determining the axial load on a movable valve 
stem which is capable of moving with the stem throughout a substantial 
portion of its stroke and as well may rotate with the stem while still 
continuously measuring the axial load thereon. 
It is a further object of the present invention to provide such a device 
which also is capable of compensating for temperature changes in the 
cylindrical member as well as in the measuring device itself. 
It is yet another object of the present invention to provide such a device 
which is relatively simple in construction and may be easily installed on 
a cylindrical member for movement therewith to continuously measure the 
axial load on the member during use. 
It is another object of the present invention to provide such a device 
which employs proximity sensing means to determine diametral changes in 
the cylindrical member in order to determine axial loads thereon. 
It is still a further object of the present invention to provide a gauging 
device for measuring the diameter of a cylindrical member whereby the 
device may be slid along the length of the cylindrical member to measure 
any diametral changes in the cylindrical member along its length. 
The present invention achieves the above and other objects by providing a 
sensing device for measuring diametral changes of a cylindrical member 
comprising a clamp member having a body adapted to be positioned around 
the periphery of the cylindrical member. Means are provided for removably 
attaching the body of the clamp member in at least partially spaced 
relationship to a portion of the cylindrical member. Proximity sensing 
means are attached to the body of the clamp member for sensing diametral 
changes in the cylindrical member and for generating signals responsive to 
and representative of the sensed movement. Computation means are connected 
to the proximity sensing means for receiving the signals therefrom to 
determine the axial load on the cylindrical member. 
In one embodiment, one of the parts of the body is rigid and the other part 
is elastic with the proximity sensing means being mounted on the rigid 
part. In another embodiment the body of the clamp is ring-shaped and each 
of the parts is semi-cylindrical in configuration. In still another 
embodiment one of the parts is U-shaped, having two spaced apart legs 
forming an open end and another of the parts is a connecting member 
mounted in the open end and attached to the legs with the proximity 
sensing means being mounted on the connecting member. 
The device further includes spacer means mounted on the body of the clamp 
for maintaining at least the portion of the body having the proximity 
sensor means thereon in spaced relationship to the cylindrical member. The 
spacer means may be adjustable to accommodate different size cylindrical 
members. The spacer means also may be rigid on one side of the body and 
elastic on an opposite side of the body containing the proximity sensing 
means. 
The device further may include temperature measuring means on one or both 
of the cylindrical member and the body of the clamp for generating signals 
indicative of the temperatures of the cylindrical member and/or the body 
and means for transmitting the temperature signals to the computation 
means whereby the computation means compensates for any temperature 
changes in the cylindrical member and/or the body in determining the axial 
load on the cylindrical member. 
One embodiment of the invention also constitutes a gauging device for 
measuring the diameter of a cylindrical member. The gauging device 
comprises a clamp member having a body adapted to be positioned around the 
periphery of the cylindrical member and includes means for removably 
attaching the body in at least a partially spaced relationship to a 
portion of the cylindrical member. The body is comprised of a rigid 
portion and an elastic portion in one embodiment and a rigid body held in 
place by an external support fixture in another embodiment. Proximity 
sensing means mounted on the rigid portion sense any diametral changes in 
the cylindrical member. The proximity sensing means generates signals 
responsive to any sensed diametral changes. Computation means are provided 
for receiving the signals from the proximity sensing means to determine 
any diametral changes in the cylindrical member. The body further may be 
slid along the length of the cylindrical member to sense any diametral 
changes therein, i.e., variations in diameter along the axial length of 
the body. Temperature measuring means also may be mounted on one or both 
of the cylindrical member and the body and signals indicative of the 
temperature fed to the computation means for compensation therefor. 
These, together with other objects and advantages, which will be 
subsequently apparent, reside in the details of construction and operation 
as more fully hereinafter described and claimed, reference being made to 
the accompanying drawings forming a part hereof, wherein like numerals 
refer to like parts throughout.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to the drawings, shown in FIG. 1 is a motor operated valve 
assembly generally comprised of a motor operator 12 and a valve 14 
connected by a yoke 16. The yoke extends partially around, and defines a 
spatial envelope 21 surrounding, a valve stem 18 which connects the valve 
14 to the motor operator 12. Only a portion of the axial length of the 
valve stem is accessible, i.e., the portion within the spatial envelope 
21. The valve 14 has a valve gate 20 which is connected to the valve stem 
so as to be movable between a closed or seated position in which it is 
engaged with the valve seat and an open or back seated position in which 
it engages a valve back seat. The valve gate 20 is shown in a closed or 
seated position in FIG. 1. The motor operated valve 10 is of a type which 
is generally well known and is readily commercially available. 
A sensing device 22 is mounted on the valve stem 18 as shown in FIG. 1 for 
measuring diametral changes in the valve stem under various load 
conditions. The sensing device 22 is of minimal axial length, comprising 
only a small fraction of the axial length of the valve stem which is 
accessible within the spatial envelope 21, and may be mounted either on 
the threaded portion or the smooth portion of the stem. The sensing device 
generates signals responsive to the sensed diametral changes and the 
signals are transmitted via suitable means such as cable 24 to a signal 
conditioning means 26 from where they are sent to computation means 28. 
The computation means may be programmed to determine axial load from the 
diametral changes in the stem. A read out device 30 is connected to the 
computation means to provide an indication of the axial load on the stem 
as it is moving. The indication can be a simple numeral read out or a plot 
of axial load verses time or axial load verses valve position. 
In the embodiment of the sensing device 22 shown in FIG. 2, the device 
includes a generally cylindrical or ring shaped clamp member 32 having a 
clamp body 34 comprised of two semi-cylindrical halves 36 and 38 fastened 
together by any suitable means such as threaded screws 40 mounted in 
threaded internal passageways 42 in the clamp body. The clamp body is 
shown in FIG. 2 mounted around the periphery of a cylindrical member 42, 
representing, for example, the valve stem 19 in FIG. 1. The clamp body may 
be made of any suitable material such as steel, aluminum or fiber 
reinforced plastic. As illustrated in FIG. 2, the axes A.sub.VS and 
A.sub.CM of the valve stem 42 and clamping member 32, respectively, are 
preferably substantially aligned in a non-loaded state of the cylindrical 
member/valve stem 42 and thus the assembled valve stem 42 and clamping 
member 32 are in substantially coaxial relationship, with their respective 
diameters D.sub.VS and D.sub.CM aligned with each other and with a radial 
measurement axis A.sub.MA transverse to the axes A.sub.VS and A.sub.CM ; 
the respective radial components, i.e., R.sub.VS1 and R.sub.VS2 likewise 
are aligned with R.sub.CM1 and R.sub.CM2. 
As shown in FIG. 2, the top half 36 of the clamp body has a pair of spaced 
inserts 44 which are embedded in the clamp body whereby a portion of the 
periphery of each insert protrudes inwardly from the inside of the clamp 
to serve as a contact point with the cylindrical member 42. The inserts 
preferably are each spaced at an angle .theta. of approximately 20.degree. 
from a line passing through the center of the clamp body. The inserts may 
be made of hardened steel and function to center the clamp around the 
cylindrical member. 
The other half 38 of the clamp body is provided with an elastic means such 
as elastic layer 46 on the inner surface thereof with the layer being 
centered in the middle of the body half 38 at a point directly opposite 
the side of the clamp member in which the inserts 44 are embedded. The 
elastic layer may be comprised of any suitable elastic material such as 
rubber. Other suitable elastic means may also be used such as spring 
pusher members or Bellville washers. The dimensions of the clamp body do 
not change with the diametral changes in the cylindrical member because 
the elastic means moves (i.e., resiliently compresses, or yields, and 
expands) with the diametral changes of the valve stem, or cylindrical 
member 42 (i.e., expansion or contraction, respectively). 
The elastic layer has an opening 48 therein defining a measurement gap MG 
between the exterior cylindrical surface to permit proximity sensing means 
50 to sense diametral changes in the cylindrical member 42. The exterior 
surface 42' of the cylindrical member/valve stem 42 and the interior 
surface 32' of the clamp member 32, at the effective intersections thereof 
with the commonly radially aligned measurement axis A.sub.MA and diameters 
D.sub.VS and D.sub.CM (and their corresponding radial components), define 
a measurement gap MG. While shown as extending between the surfaces 42' 
and 32', the measurement gap MG in fact may be considered as extending 
along the radially aligned measurement axis A.sub.MA from the surface 42' 
to any desired, pre-established reference position, or portion, of the 
member 38--e.g., in the embodiment of FIG. 2, the proximity sensing means 
50, later discussed. The proximity sensing means may be any suitable 
distance measuring device such as a Linear Voltage Differential 
Transmitter (LVDT), a proximity capacitive or inductive probe, a laser or 
other suitable optical means or a strain gauge displacement transmitter. 
The proximity sensing means 50 may be mounted in the clamp body by being 
threadably inserted through an opening 52 in the clamp body half 38 and 
may be further secured in the opening by a set screw 54 threaded into an 
opening 56 in the clamp body half. Signals generated by the proximity 
sensing means 50 are transmitted to the signal conditioning means 26 by 
cable 24 in the manner set forth with respect to FIG. 1. 
An advantage of this embodiment is that the inserts 44 provide rigid 
contact points on one side of the clamp and the elastic layer provides a 
non-rigid surface on the sensor side in contact with the cylindrical 
member to guarantee that the clamp won't deform to any significant extent 
in response to diametral changes in the cylindrical member. Thus and for 
example, as the cylindrical member 42 expands, contact points 44 will 
cause the top half 36 of the clamp body 32 to move therewith, producing a 
displacement (upward, in the plan view of FIG. 2) of the clamp member axis 
A.sub.CM from the cylindrical member/valve stem axis A.sub.VS by an amount 
which is linearly proportional to .DELTA.R.sub.VS1 (i.e., to take into 
account the angle .theta.) while maintaining alignment of the diameters 
D.sub.CM and D.sub.VS and producing a first component of change of the 
measurement gap MG. The measurement gap MG will change by a total amount 
equal to the sum of that first component, linearly proportional to 
.DELTA.R.sub.VS1, and a second component comprising .DELTA.R.sub.VS2. 
While preferred, the initial coaxial relationship of members 42 and 32, 
and thus the alignment of the axes A.sub.CM and A.sub.VS, is not critical; 
instead, what is important is the alignment of the diameters D.sub.CM and 
D.sub.VS (and the corresponding radial components thereof) with the radial 
measurement axis A.sub.MG and that at least a part of the interior surface 
32' of the clamp member 32, which part includes the reference portion 50 
defining the measurement gap MG, is spaced from the corresponding portion 
of the interior surface 42' of the cylindrical member/valve stem 42 such 
that the part of the clamp member which defines the radius R.sub.CM2 does 
not deform to any significant extent as a result of the diametral 
deformation of the member 42--i.e., R.sub.CM2 is a fixed value. As will 
also be apparent, the fixed radius R.sub.CM2 must be greater than the 
variable radius R.sub.VS2 of the cylindrical member/valve stem 42 (i.e., 
that radius being variable due to the diametral deformations of the member 
42, caused by axial loading thereof) so as to maintain a minimum finite 
value of the measurement gap MG. Moreover, the elastic layer serves to 
dampen vibrations and therefore increase the accuracy of the measurement. 
The elastic layer also permits use with different sized diameter 
cylindrical members. Moreover, the sensing device shown in FIG. 2 is 
relatively simple in construction and compact in size and when used in 
connection with a valve stem, is capable of being mounted on the stem and 
travel with the stem throughout the length of the stroke of travel thereof 
and as well may rotate with the valve stem to continuously measure the 
axial load in the stem during travel thereof. 
In the embodiment shown in FIG. 2, means may be provided for compensating 
for temperature variations in the cylindrical member and the body of the 
clamp sensing device. This may be accomplished by attaching temperature 
measuring devices 58 to the surface of the cylindrical member and to the 
surface of the clamp body. The temperature measuring device also could be 
embedded within the clamp body. Suitable temperature measuring devices 
include a resistance temperature detector, a thermistor and a 
thermocouple. The readings from the temperature measuring devices are sent 
to the signal conditioning means 26 and from there are sent to the 
computation means 28 whereby compensation may be made for any temperature 
change in the cylindrical member and the body of the clamp. 
The embodiment of the sensing device shown in FIG. 3 is similar to the 
sensing device shown in FIG. 2 in that it also includes a generally 
cylindrical ring shaped clamp member 32 having a clamp body 34 comprised 
of two semi-cylindrical halves 36 and 38 fastened together by any suitable 
means such as threaded screws 40 mounted in threaded internal passageways 
42 in the clamp body. The clamp body is shown mounted around the periphery 
of a cylindrical member 42 and likewise to define a measurement gap MG. 
The clamp body may be made of any suitable material such as steel, 
aluminum or fiber reinforced plastic. 
As shown in FIG. 3, the top half 36 of the clamp body has an adjustable 
threaded clamping screw 60 threadably mounted in opening 62 with the screw 
having a V-shaped contact surface 64 on the inner end thereof whereby the 
ends of the V each come to a point and function to help center the clamp 
on the cylindrical member. The point contacts of the V-shaped contact 
surface 64 define angles .theta.', which may be smaller than the angles 
.theta. of the FIG. 2 structure. The bottom half 38 of the clamp body has 
a pair of spaced screw inserts 66 threadably mounted therein in openings 
68. Each of the inserts 66 has a spring biased pusher member 70 on its 
inner end thereof for contacting the cylindrical member to assist in 
holding the clamp on the cylindrical member and center the clamp thereon. 
Each of the inserts is spaced at an angle .alpha. of approximately 20 from 
a center line passing through the clamp body. The screw inserts with the 
spring biased pusher members permit the device to be used with different 
sized diameter cylindrical members. In operation, the cylindrical member 
is placed inside the joined clamp body and fixed between the clamping 
screw 60 and the screw inserts with the spring loaded pusher members 70. 
The dimensions of the clamp body do not change with the diametral changes 
in the cylindrical member since the spring loaded pusher members move 
radially either outwardly or inwardly, adjusting to the diametral changes 
of the cylindrical member. The measurement gap MG of the FIG. 3 structure 
varies in the same manner as does the measurement gap MG of FIG. 2. 
Proximity sensing means 50 may be mounted in the clamp body by being 
threadably inserted through an opening 52 in body half 38. Although not 
specifically shown in FIG. 3, the proximity sensing means may further be 
secured in the opening 52 by a set screw in the same manner as shown with 
respect to the embodiment of FIG. 2. Signals generated by the proximity 
sensing means 50 may be transmitted to the signal conditioning means 26 by 
cable 24. Temperature measuring devices 58 may also be attached to the 
cylindrical member and the clamp body whereby the signals from the device 
are sent to the signal conditioning means in the manner as described with 
respect to the embodiment of FIG. 2. 
In the embodiment of the sensing device 22 shown in FIG. 4, the clamp body 
is comprised of a U-shaped member 72 having two spaced apart legs 74 
forming an open end in which a connecting member 76 is securely mounted by 
suitable means such as screws 78 passing through the ends of the legs and 
into the ends of the connecting member. A pair of clamping screws 80 are 
threadably mounted in openings 82 in opposite sides of the legs of the V. 
Similar to the clamping screw in the embodiment of FIG. 3, the clamping 
screws 80 each have a V-shaped inner contact surface whereby the ends of 
the V each come to a point and function to center the clamp body on the 
cylindrical member 42. In operation, the U-shaped member 72 and the 
connecting member 76 are securely joined together around the cylindrical 
member and the clamping screws 80 are then adjusted to contact the surface 
of the cylindrical member and securely hold the clamp body in place. 
The connecting member 76 has a proximity sensing device 50 threadably 
mounted in an opening 52 therein for sensing the diametral changes in the 
cylindrical body. Signals generated by the proximity sensing means may be 
transmitted to the signal conditioning means by cable 24 in the same 
manner as that described with respect to the embodiment of FIG. 2. 
Similarly, temperature measuring device 58 may be mounted on the 
cylindrical member and the clamp body whereby the readings from the 
temperature measuring device are sent to the signal conditioning means 26 
and from there to the computation means 28 whereby compensation may be 
made for any temperature change in the cylindrical member and the body of 
the clamp. 
It is noted that in this embodiment the cylindrical member is clamped and 
securely held at diametrally opposed positions on its circumferential 
surface, or periphery, by the clamping screws 80 and that therefore the 
proximity sensing means measures changes in the radius of the cylindrical 
member. Using the same nomenclature as in FIG. 2 but with prime 
indications, the measurement gap MG' in FIG. 4 between the exterior stem 
surface 42' and the reference portion 50 changes directly in accordance 
with .DELTA.R.sub.VS2'. Diametral changes in the cylindrical member can be 
accurately deduced by multiplying the radial changes by a factor of two. 
Since the original no load radius of the cylindrical member is known, the 
proximity sensing means can be calibrated and any changes in the radius 
measured by the sensor. The corresponding axial load on the member can 
then be calculated using known equations. 
In the embodiment of the sensing device 22 shown in FIG. 5, the clamp body 
is comprised of a rigid part 82 and an elastic part 84. The rigid part is 
semi-cylindrical in shape and may be made of steel, aluminum or fiber 
reinforced plastic. Mounted adjacent the ends of the rigid part 82 are a 
pair of oppositely disposed contact points 86 which contact the 
circumferential surface of the cylindrical member 42 and maintain the 
rigid part in spaced relation to the cylindrical member. As shown in FIG. 
5, the contact points 86 contact the cylindrical member at intersections 
of the surface thereof and a cord c which is of less length than the 
diameter of the cylindrical member. In this manner, the rigid part of the 
clamp body won't come into contact with the cylindrical member. The cord c 
preferably is between 0.8 and 0.95 the length of the diameter D of the 
cylindrical member. The ends of the elastic part 84 are connected to the 
ends of the rigid part 82 by any suitable means 88 such as bracket means, 
clamp means or the like. The elastic part may be made of any suitable 
elastic material such as rubber or coil springs. The elastic part 
maintains the clamp body in position around the cylindrical member. 
A proximity sensing means 50 is mounted in at the center of the rigid part 
82 by any suitable means such as a threaded connection. Signals generated 
by the proximity sensing means may be transmitted to the signal 
conditioning means 26 by cable 24 in the manner set forth with respect to 
FIG. 1. Temperature measuring devices 58 also may be mounted on each of 
the cylindrical member and the rigid part of the clamp body. Readings from 
the temperature measuring devices are sent to the signal conditioning 
means 26 and from there sent to the computation means 28 whereby 
compensation may be made for any temperature changes in the cylindrical 
member and the rigid part of the clamp body. 
In operation of the sensing device of FIG. 5, as the cylindrical member 
expands or contracts, the elastic part permits the rigid part of the clamp 
to move radially outwardly or inwardly (i.e., upwardly or downwardly, 
respectively, in the transverse axial cross-sectional view of FIG. 5) thus 
varying the distance between, the proximity sensing device and the opposed 
outer surface of the cylindrical member. By measuring the changes in this 
distance, the axial load in the cylindrical member may be calculated. The 
proximity sensing device measures the changes in a measurement gap A (the 
distance between the surface of cylindrical member along the measurement 
axis, as before-defined, and the reference portion of the rigid part of 
the clamp body) caused by the changes in the diameter of the cylindrical 
member. Gap A will change because as the diameter of the cylindrical 
member changes, the rigid portion of the clamp body is displaced such that 
contact points 86 engage the surface of the cylindrical member at points 
defined by intersections with another cord, since the aperture of the 
rigid part remains constant. 
The cord length c is related to the radius r by the following equation: 
##EQU1## 
where h is as defined in FIG. 5 as the distance along a center line, i.e., 
a portion of the radius of the cylindrical member 42 between cord c and 
the outer surface of the cylindrical member, aligned with the 
corresponding radius of the rigid part 82. Solving for h: and knowing 
from FIG. 5: 
EQU h=b-A 
A can be solved for in terms of b, r, c: 
##EQU2## 
Changes in gap length A are related to the radial changes by the following 
equation: 
##EQU3## 
where A.sub.o is the original gap length, and A is the gap length under 
axial load. 
The sensing device of FIG. 5 may also be applied to a range of different 
sized diameter cylindrical members because once the initial gap (A.sub.o) 
is calibrated, the relative changes can be recorded. 
The sensing device of FIG. 5 also has a significant general application as 
a gauging device for checking the diameter of any cylindrical member since 
it can be put on a cylindrical member and slid along the length thereof to 
check for any variations in diameter. The device could be used, or 
example, to check the constancy of the diameter of a fuel rod in a nuclear 
system. 
The embodiment of the sensing device of FIG. 6 is similar to the sensing 
device of FIG. 5 except the elastic part 84 has been removed and the 
sensing device held in place by an external support fixture 90 such as a 
robotic arm or other manufacturing fixture. The external support structure 
may be adapted to move the rigid body part 82 along the length of the 
cylindrical member. 
With the sensing device of FIGS. 5 and 6, as well as with the sensing 
devices shown in FIGS. 2, 3 and 4 it is no longer necessary to calculate 
the relationship between the changes in the clamp means corresponding to 
diametral changes in the cylindrical member and then calculate the axial 
load. The diametral changes may be taken directly. Also the sensing 
devices are not susceptible to bending moments in the cylindrical member 
and are relatively insensitive to errors in measuring the nominal diameter 
of the cylindrical member. 
Numerous alterations and modifications of the structure herein disclosed 
will suggest themselves to those skilled in the art. It is to be 
understood, however, that the present disclosure relates to the preferred 
embodiments of the invention which is for the purpose of illustration only 
and is not to be construed as a limitation of the invention. All such 
modifications which do not depart from the spirit of the invention are 
intended to be included within the scope of the appended claims.