WO2000029809A9

WO2000029809A9 - Laser-based system for measuring cylindrical objects

Info

Publication number: WO2000029809A9
Application number: PCT/US1999/022895
Authority: WO
Inventors: Lloyd R Lawrence; Mark A Mistretta
Original assignee: Stowe Woodward Company; Lloyd R Lawrence; Mark A Mistretta
Priority date: 1998-11-17
Filing date: 1999-09-30
Publication date: 2000-10-26
Also published as: AU6283099A; WO2000029809A1

Abstract

Systems for determining the shape and roundness of cylindrical bodies are disclosed, along with computer program products for determining these properties. The systems utilize lasers which contact the surfaces of the cylindrical bodies such that laser beams reflect therefrom. The systems also include means for manipulating the laser beams to ultimately determine the shape and roundness of the cylindrical bodies.

Description

LASER-BASED SYSTEM FOR MEASURING CYLINDRICAL OBJECTS

Field of the Invention

The invention relates generally to measuring physical properties of cylindrical bodies and, more particularly, to measuring physical properties of cylindrical bodies using non-contact devices such as lasers.

Background of the Invention

Industrial rolls, such as those formed from metal or rubber, are used in a wide variety of applications. As an illustration, rolls covered with polymeric and/or composite materials can be used in papermaking processes to transport a web sheet of paper stock that eventually becomes paper and to process the web itself into a finished paper product. Calender rolls may also be employed to improve the smoothness, gloss, printability, and thickness of the paper product.

The covers for such rolls are typically somewhat deformable, and are usually formed from a variety of materials such as, rubber, polyurethane, or epoxy. These materials may be unreinforced or reinforced with a filler material. The roll and cover are often constructed so that the outer surface of the, roll includes a "crown", i.e., it is slightly narrower at its ends and is somewhat thicker at its axial center to improve the interaction with, and thus the processing of, the web that is passing over it. Understandably, the dimensions of the crown profile can impact the interaction of the roll with the web upon which it acts, with small differences in dimensions having the potential for causing significant differences in product properties. Conventionally, the profile of a roll cover has been measured with some type of mechanical device, such as a micrometer, that contacts the surface of the roll cover in order to measure the diameter of the roll at given locations. The use of mechanical devices to measure the profile of a roll cover may suffer from various drawbacks. For example, the force required to ensure contact between the measuring device and the roll may excessively compress or deform the polymeric material which makes up the roll cover. Additionally, mechanical measuring devices conventionally employ a contact surface having a specific geometry. Because of the constraints associated with a specific geometry, mechanical devices may be incapable of measuring cylindrical bodies having geometries smaller than that of the contact surface of the measuring device.

The shape of a roll may also be determined by a linear transducer. Conventional linear transducers are usually equipped with a tip having a convex surface. Tips with convex surfaces may be able to function adequately with rolls having coarse geometries, but, unfortunately, may slide over smaller variations in surface geometry. Accordingly, the shape of the roll may be inaccurately determined.

Roll shape is also often determined by employing diameter tapes such as, for example, a pi tape. A diameter tape is wrapped around the roll, and the individual carrying out the testing then takes measurements which are eventually used in determining a roll crown profile. Notwithstanding any potential advantages this technique may have, employing diameter tapes may be unreliable in that this measuring method is dependent on the tester.

In view of the above, there is a need in the art for a measuring system that can accurately determine various physical properties of a cylindrical body, such as an industrial roll, including shape and roundness, without employing a mechanical device which contacts the substrate. Summary of the Invention

In view of the above, it is an object of the present invention to facilitate accurately measuring physical properties, such as shape and roundness, of various physical bodies. It is also an object of the present invention to facilitate accurately measuring physical properties, such as shape and roundness, of various physical bodies without requiring physical contact therewith.

These and other objects and advantages are provided by systems, methods and computer program products for determining physical properties, such as shape and roundness, of a body, such as a cylindrical industrial roll, using laser beams reflected from the body surface onto sensors adjacent thereto. According to one aspect of the present invention, shape (i.e., crown) of a longitudinally extending, cylindrical body, can be determined by obtaining and storing a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the body. For the purposes of the invention, shape (i.e., crown) is defined as the variation in cylindrical body surface height along the longitudinal axis of the body relative to a reference (typically at the end of the cylindrical body). Each measurement of relative displacement distance represents surface height from the body surface relative to a reference.

Each measurement of relative displacement distance is obtained by illuminating, via a laser beam, a portion of the cylindrical body at each location so that the laser beam reflects from the cylindrical body surface and contacts a spot position on a sensor positioned adjacent the cylindrical body. The distance between a zero position and a spot position on the sensor is measured at each location, and an electrical signal corresponding to each measurement of distance between a zero position and a spot position on the sensor is generated. Preferably, surface portions of the cylindrical body at each location are illuminated with first and second laser beams so that the first and second laser beams reflect from the cylindrical body surface and contact respective spot positions on respective first and second sensors positioned adjacent the body. Most preferably, the first and second laser beams are diametrically opposed (i.e., 180° apart). Measurements that are not within a predetermined tolerance range for a respective surface location are then removed from each stored set. This is accomplished by first determining a mean value of relative displacement distance for each stored set of measurements. Measurements in each stored set that exceed the mean value for the respective stored set by a predetermined amount are discarded. In addition, measurements in each stored set that were taken over an inconsistency, e.g., drill hole or other type of perforation, imperfection, or non-homogeneity in the cylindrical body surface, are also discarded. An average value of relative displacement distance for each stored set of measurements using measurements remaining within each respective stored set are then obtained. Using the average value of relative displacement distance for each respective stored set, the reference dimension of the cylindrical body at each of the plurality of surface locations can be determined. The reference dimension is defined as the distance from a measurement device (e.g., laser) to the surface location on the body contacted by a corresponding laser beam determined relative to a distance from the measurement device to a reference or "zero" surface location on the cylindrical body surface.

According to another aspect of the present invention, roundness of a longitudinally extending, cylindrical body, such as an industrial roll, can be determined by obtaining and storing a set of measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body. For the purposes of the invention, roundness can be defined as the variation in cylindrical body surface height relative to a reference along the circumference of the cylindrical body. To obtain measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body, a surface portion of the body at each circumferential location is illuminated with one or more laser beams so that each laser beam reflects from the cylindrical body and contacts a spot position on a respective sensor positioned adjacent the body. The distance between a zero position and a spot position on each sensor is determined at each location, and an electrical signal corresponding to each measurement of distance between a zero position and a spot position on the sensor is generated. Measurements in each stored set that exceed a predetermined value are identified and then replaced with linearly interpolated values obtained using measurements within each respective set that do not exceed the predetermined value. Preferably, a measurement that exceeds the predetermined value is replaced with a linearly interpolated value calculated from measurements on opposite, adjacent circumferential sides of the replaced measurement. An average value of relative displacement distance for each stored set of measurements is then obtained using measurements within each respective stored set that do not exceed the predetermined value. A reference dimension of the cylindrical body at each of the plurality of circumferential locations can then be determined using the average value of relative displacement distance for each respective stored set. The reference dimension is defined as the distance from a measurement device (e.g., laser) to the surface location on the body contacted by a corresponding laser beam determined relative to a distance from the measurement device to a reference or "zero" surface location on the cylindrical body surface.

The present invention is advantageous because the shape of virtually any type of object can be measured without requiring any contact with the object being measured. This is particularly advantageous for objects having deformable surfaces because measurements can be obtained without the risk of causing any damage in the surface thereof. In addition, because a narrow light beam, such as a laser beam, is utilized, relatively small surface geometries can be followed with good accuracy. Furthermore, because the present invention allows various shape or roundness measurements within each set that exceed a predetermined value to be replaced, objects, such as industrial rolls, can be measured with or without any inconsistencies being present in the surface. For the purposes of the invention, the term "inconsistency" is to be broadly construed to include, but not be limited to, any type of imperfection, perforation (e.g., a drilled hole), or other lack of homogeneity that may exist in the surface of the cylindrical body. Brief Description of the Drawings

FIG. 1 is perspective view of a mounted cylindrical body and laser and motion unit used for determining a physical property of a cylindrical body in accordance with the invention; FIG. 2 is a schematic diagram illustrating the laser of the system of

FIG. 1 positioned over a portion of a cylindrical body;

FIG. 3 is a schematic diagram illustrating the operation of a laser and sensor in detecting the reflection of a laser beam from a cylindrical body, according to the present invention; FIG. 4 is a schematic diagram illustrating the operation of a processing system for gathering and storing laser measurements;

FIGS. 5A-5C schematically illustrate operations for determining shape (i.e., crown) of a cylindrical body, according to the present invention. FIGS. 6A-6B schematically illustrate operations for determining roundness of a cylindrical body, according to the present invention.

FIG. 7 is a graph illustrating the theoretically-determined crown and the crown determined according to the invention at various locations along the length of a cylindrical body using the system illustrated in FIG. 1 ; and

FIG. 8 is a graph illustrating the theoretically-determined crown and the crown determined according to the invention at various locations along the length of another cylindrical body using the system illustrated in FIG. 1.

Detailed Description of Preferred Embodiments

The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the thickness of layers and regions are exaggerated for clarity. Like numbers refer to like elements throughout.

As described herein, the invention generally relates to determining physical properties of cylindrical bodies. For the purposes of the invention, the term "cylindrical bodies" is to be broadly interpreted to include bodies that have cross-sections formed from a variety of geometries. One example of a cylindrical body involves a body with a circular cross-section, however other cross-sectional geometries (such as, but not limited to, elliptical, rectangular, etc.) are certainly within the scope of the invention.

I. Laser Measurement System

In one aspect, the invention relates to a system for determining a physical property of a cylindrical body. The system is described in detail with reference to FIG. 1 , and is denoted by the number 10. In particular, the system may be used to measure shape (i.e., crown), roundness, or surface finish of a cylindrical body 11. In this embodiment, the cylindrical body 11 appears in the form of a paper roll formed from conventional materials known to one skilled in the art. For the purposes of the invention, it is to be appreciated, however, that the cylindrical body may encompass industrial rolls that may be covered by a polymeric material such as, but not limited to, rubber, polyurethane, or epoxy. The surface of the rolls thus may be deformable or non-deformable. For the purposes of the invention, the term "deformable" is to be broadly interpreted as a cylindrical body surface which is capable of alteration upon the application of pressure or stress. The deformation may be temporary (as in the case of rubber, for example) or permanent. The cylindrical body 11 preferably has a radius r ranging from about 0.001 inches to about 1000 inches, and a length I ranging from about 1 inch to about 10,000 inches. Not depicted in FIG. 1 , a unit is employed to mount the cylindrical body

11 , the unit being known to one skilled in the art such as, for example, a grinder unit which includes a carriage and grinder bed. Two parallel rails (e.g., ways) 14a and 14b are present and extend in a collinear fashion with respect to the longitudinal axis I of object 11. The ways 14a and 14b function to define the motion of the grinder carriage such that the grinder bed is square. The configuration of the cylindrical body, ways, and grinder is conventional.

Positioned at a first distance di (preferably from about 1 inches to about 100 inches, more preferably from about 2 inches to about 25 inches, and most preferably 80 mm) from the cylindrical body 11 is at least one laser 15. The laser 15 is described in greater detail with reference to FIG. 2. An exemplary laser 15 is presented in U.S. Patent No. 5,617,645 to Wick et al., the disclosure of which is incorporated herein by reference in its entirety, and also in W.P. Kennedy, "The Basics of Triangulation Sensors", Sensors: The Journal of Applied Sensing Technology (May 1998). A commercially preferred laser is a Keyence Laser sold by Keyance, Inc of Woodcliff Lake, New Jersey. Preferably, a pair of lasers 15 are utilized. Most preferably, the lasers are diametrically opposed (i.e., 180° apart) as illustrated. Although not wishing to be bound by any theory of operation, it is believed that the positioning of the diametrically opposed lasers is advantageous in that accurate measurements may be taken from the cylindrical body surface irrespective of the alignment of platform 13 to which the lasers 15 are ultimately attached, or misalignment of cylindrical body 11. Operation of each laser 15, in accordance with the present invention, will now be described in greater detail with reference to FIG.2. As shown, each laser 15 includes a housing 16 that surrounds a semiconductor laser and drive circuit 17. A laser emitting lens 18 is positioned collinearly with the semiconductor laser and drive circuit 17, as illustrated. The laser emitting lens 18 and semiconductor laser and drive circuit 17 are generally perpendicular to the longitudinal axis I of the cylindrical body 11 , as illustrated. Located within housing 16 is a sensor 19 for receiving a laser beam 20 reflected from the cylindrical body 11. The sensor 19 may be one which is conventionally known to one skilled in the art. The sensor 19 serves as means for converting a reflected laser beam 20 to an electrical signal.

FIG. 3 illustrates in greater detail the detection of a reflected laser beam 20 by sensor 19. In general, a laser beam 20 may reflect from a reference point b on the cylindrical body 11 so as to contact sensor 19 at a reference spot position o. As shown in FIG. 3, during operation, each of the diametrically opposed lasers are capable of directing a laser beam 20 towards the cylindrical body 11 at locations a and c, for example, that correspond to varying distances from the surface of the cylindrical body 11 to the laser 15. As a result, the reflected laser beams corresponding to locations a and c contact sensor 19 at different spot positions, o' and o" respectively.

Distances d' and d" are then determined corresponding to the distance along the sensor from spot positions o' and o" to the reference zero position o. Electrical signals are generated by sensor 19 corresponding to these relative displacement distances that are representative of the distances from positions a and c on the cylindrical roll 11 to laser 15. FIG. 3 also depicts a conventional receiver lens 21 which may be used in a manner known and appreciated by one skilled in the art.

Referring now to FIG. 4, an electrical signal produced by sensor 19 is transmitted to a laser interface 22 in electrical communication with sensor 19. The laser interface 22 serves to amplify and filter the signal received from the sensor 19. The amplified and filtered signal is then transmitted to a processor 23 in electrical communication with the laser interface 22. The processor 23 performs various operations for determining physical properties of the cylindrical body 11 using the electrical signals received from each sensor 19. These operations are described below with respect to FIGS. 5A-5C and FIGS. 6A-6B. Results from the processor 23 may be downloaded to a printer 24, if so desired.

II. Operations for Measuring Shape of a Cylindrical Body Referring now to FIGS. 5A-5C, operations, according to the present invention, for determining a shape (i.e., the crown) of a longitudinally extending cylindrical body are illustrated. Using the laser system described above, a set of measurements of relative displacement distance (also referred to as "measurements" or "readings") are obtained for each of a plurality of surface locations along the longitudinal direction of an elongated cylindrical body, such as an industrial roll (Block 100). Each set of measurements of relative displacement distance are then stored for subsequent processing (Block 110). Storing may include storing in computer memory, such as random access memory (RAM) or read-only memory (ROM). Storing may also include storing on computer usable media including, but not limited to, floppy disks, hard disks, CD-ROMs, optical storage devices, and magnetic storage devices.

Referring to FIG. 5B, operations for obtaining measurements for a plurality of surface locations along the longitudinal direction of an elongated cylindrical body (Block 100) include illuminating a surface portion of the cylindrical body at each location with a laser beam such that the laser beam reflects from the cylindrical body surface and contacts a spot position on a sensor adjacent to the cylindrical body (Block 102). The spot position on a sensor contacted by a reflected laser beam relates to the distance from the laser to the cylindrical body. The distance between the zero position and spot position on a sensor at each location is measured (Block 104). The distance between the zero position and the spot position on the sensor is related to a relative displacement distance. Relative displacement distance is defined as the distance from the laser to a surface location (e.g., a or c in FIG. 3) on the cylindrical body 11 relative to the distance from the laser to a reference position (e.g., b in FIG. 3) on the body surface. Relative displacement distance may range from about 0.000001 inches to about 1000 inches. An electrical signal corresponding to each measurement of distance between a zero position and a spot position on a sensor is generated (Block 106). This electrical signal is then stored (Block 110, FIG. 5A).

The number of surface locations along the longitudinal direction of a cylindrical body is user defined, and may depend on the length of a cylindrical body. Typically, the number of surface locations selected is between about 1 and about 10,000, with a preferred number being about 400, most preferably 401. The distance between surface locations may also be user defined, and may range between about 0.001 inches to about 100 inches. In addition, a pair of diametrically opposed laser beams may be utilized to obtain one or more sets of measurements, as described above. After measurements have been obtained at the various surface locations of the elongated cylindrical body, measurements stored within each set that are not within a predetermined tolerance range for a respective surface location are removed (Block 120, FIG. 5A). Referring now to FIG. 5C, a mean value of relative displacement distance is determined for each set of stored measurements (Block 122). For example, the values of each measurement in a set are summed and the sum is divided by the number of measurements in the set. Measurements in each set that exceed a mean value of all measurements in a respective set by a predetermined amount are then discarded (Block 124). In addition, measurements determined to have been taken over inconsistencies in the surface of the cylindrical body are also discarded (Block 126).

Referring back to FIG. 5A, the remaining measurements within each respective set, are then used to obtain an average value of relative displacement distance for each set (Block 130). The relative dimension of the cylindrical body (defined herein) is then determined at each of the designated locations using the average value of relative displacement distance for each respective stored set (Block 140). Preferably, diametrically opposed (i.e., 180°) laser beams are utilized to measure relative displacement distances and relative dimensions. The results from Block 140 for each laser are added. The shape or crown value at any longitudinal distance as computed from Block 140 can be compared with a theoretical crown (Block 150).

III. Operations for Measuring Roundness of a Cylindrical Body Referring now to FIGS. 6A-6B, operations, according to the present invention, for determining roundness of a longitudinally extending cylindrical body are illustrated. Using the laser system described above, a set of measurements of relative displacement distance as defined above (i.e., measurements) are obtained for each of a plurality of surface locations along a circumference of an elongated cylindrical body, such as an industrial roll (Block 200). Each set of measurements of relative displacement distance are then stored for subsequent processing (Block 210). Storing may include storing in computer memory, such as random access memory (RAM) or readonly memory (ROM). Storing may also include storing on computer usable media including, but not limited to, floppy disks, hard disks, CD-ROMs, optical storage devices, and magnetic storage devices.

Referring to FIG. 6B, operations for obtaining measurements for a plurality of surface locations along the circumference of an elongated cylindrical body (Block 200) include illuminating a surface portion of the cylindrical body at each location with a laser beam such that the laser beam reflects from the body surface and contacts a spot position on a sensor adjacent the body (Block 202). The spot position on a sensor contacted by a reflected laser beam relates to the distance from the laser to the cylindrical body. The distance between the zero position and spot position on a sensor at each location is measured (Block 204). The distance between the zero position and the spot position on the sensor is related to a relative displacement distance. Relative displacement distance is defined as the distance from the laser to a surface location (e.g., a or c in FIG. 3) on the cylindrical body 11 relative to the distance from the laser to a reference position (e.g., b in FIG. 3) on the body surface. Relative displacement distance may range from about 0.000001 inches to about 1000 inches. An electrical signal corresponding to each measurement of distance between a zero position and a spot position on a sensor is generated (Block 206). This electrical signal is then stored (Block 210, FIG. 6A).

The number of surface locations along the longitudinal direction around the circumference of a cylindrical body is user defined, and may depend on the diameter of a cylindrical body. Typically, the number of surface locations selected is between about 100 and about 5,000, which may be selectively reduced to between about 180 and about 360 with the most preferred number being about 360. In addition, a pair of diametrically opposed laser beams may be utilized to obtain one or more sets of measurements, as described above.

After measurements have been obtained at the various circumferential surface locations of the cylindrical body, measurements stored within each set that exceed a predetermined value are identified (Block 220, FIG. 5A). Each measurement identified as exceeding a predetermined value is then replaced by a respective linearly interpolated value obtained using measurements within a respective set that do not exceed the predetermined value (Block 230). Preferably, a linear interpolation is made between measurements on opposite, adjacent circumferential sides of a measurement identified as exceeding a predetermined value so as to obtain a replacement measurement value therefor. The measurements within each respective set are then used to obtain an average value of relative displacement distance for each set (Block 240).

To determine roundness, the relative dimension (defined herein) of the cylindrical body is then determined at each of the designated circumferential locations using the average value of relative displacement distance for each respective stored set (Block 250). Preferably, multiple (e.g., two) laser beams are utilized to measure relative displacement distances and thus relative dimensions. Most preferably, the laser beams are diametrically (i.e., 180°) opposed. The results from Block 250 from each laser are added. The roundness of the cylindrical body at any circumferential location can then be compared with a theoretical roundness (Block 260).

The present invention has been described hereinabove with reference to flowchart illustrations of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations of FIGS. 5A-5C and FIGS. 6A-6B and combinations of blocks in the flowchart illustrations of FIGS. 5A-5C and FIGS. 6A-6B, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart block or blocks.

The computer program instructions may be executed by a processor to cause a series of operational steps to be performed by the processor to produce a computer implemented process such that the instructions which execute on the processor provide steps for implementing the functions specified in the flowchart block or blocks. The computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart block or blocks. As will be appreciated by one of skill in the art, aspects of the present invention may be embodied as a method, system, or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the aspects of the present invention may take the form of a computer program product on a computer-usable storage medium having computer-usable program code means embodied in the medium. Any suitable computer readable medium may be utilized including hard disks, CD-ROMs, optical storage devices, or magnetic storage devices.

IV. Hardware and Software Requirements Hardware for implementing the present invention is generally consistent with typical personal computing equipment. Preferably, the present invention is implemented on an International Business Machines® (IBM) or IBM®-compatible personal computer. Even more preferable is hardware based on an Intel Pentium® processor, or equivalent. Also preferred is a printer suitable for text and graphical report printing. However, the present invention may be implemented via other computing devices, including, but not limited to, mainframe computing systems and mini-computers. The present invention may run on standard desktop computer platforms such as, but not limited to, Windows 95®, Windows 98®, Windows NT®, and UNIX®.

Computer program code for carrying out operations of the present invention is preferably written in an object oriented programming language such as Java®, Smalltalk, Visual Basic, or C++. However, the computer program code for carrying out operations of the present invention may also be written in conventional procedural programming languages, such as the "C" programming language. The program code may execute entirely on the user's computer, as a stand-alone software package, or it may execute partly on the user's computer and partly on a remote computer. In the latter scenario, the remote computer may be connected to the user's computer through a LAN or a WAN, or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). The following examples are set forth to illustrate the invention, and are not meant as a limitation thereon.

Example 1

The laser system of the invention was used to determine a crown profile for a roll used in a papermaking facility. The scan direction for the lasers was from the front to the drive along the roll length. The roll had a diameter of 42.055 inches, a measured length of 378 inches, and a face length of 378 inches.

The actual crown and the theoretical crown were determined at various stations along the length of the roll. These values (expressed in inches) along with the crown deviation with respect to the theoretical crown are set forth in the table below:

The theoretical crown, actual crown, and crown deviation were determined to be 0.02 inches, 0.0204 inches, and 0.0004 inches respectively at station 10. The theoretical crown angle was set at 70°. FIG. 7 is an illustration of actual crown and theoretical crown as a function of roll length.

Example 2 The laser system of the invention was used to determine a crown profile for a roll used in a papermaking facility. The scan direction for the lasers was from the front to the drive along the roll length. The roll had a diameter of 60.5 inches, a measured length of 244 inches, and a face length of 244 inches.

The theoretical crown, actual crown, and crown deviation were determined to be 0.052 inches, 0.0522 inches, and 0.0002 inches respectively at Station 10. The theoretical crown angle was set at 70°. FIG. 8 is an illustration of actual crown and theoretical crown as a function of roll length.

Example 3

An example of an algorithm for determining the shape (i.e., crown) of an industrial roll is set forth below. At various surface locations along the longitudinal axis of the industrial roll, each of two diametrically opposed lasers reads a number of measurements (also referred to as "readings"). An average measurement is computed for each laser as follows:

laser 'n' average =

Σ laser'n'jreading (1)

wherein: laser 'n_average is the average laser reading at a given location for each of the lasers, with 'n' being equal to 1 or 2, depending on the laser; laser 'n'_reading are the readings taken at a given location for each laser; and laseraverage is the number of readings collected from each laser to form one laser reading per surface location.

The laser readings are then sorted in decreasing order of their deviation from the mean value of the set of laseraverage computed as:

absolute value of [laser 'n average-laser 'n_reading] (2) which serves as a basis for discarding the unacceptable values.

The number of readings remaining for each surface location per laser are determined as follows:

laseraverage-laserdiscard (3)

wherein laseraverage is defined above and laserdiscard represents the number of readings taken from each laser that represent extreme values. A new average reading (defined below as "laser 'n'_new_average") is then computed for each laser based on the number of readings remaining after the discard operation according to equation (4):

laser 'n'jiewjaverage = { [laseraverage-laserdiscard]} x

Σ laser'n'jreading (4)

The newly-computed average readings (defined as the number of readings remaining after discard) are then tested to determine if they were taken over a drilled hole according to the following:

if (laser 'n'_new_average) < badjreading then good eading 'ri = laser 'n'_reading (5)

wherein: bad_reading represents the magnitude of the reading that is greater than a predetermined upper limit; and goodjreading 'n' is equal to an acceptable laser reading with 'n' corresponding to the first or second laser. Upon obtaining readings that meet the above criteria, the relative dimension (i.e., crown amount) of the roll is then computed as the sum of the two laser readings at each surface location:

Laser_reading = {goodjreading 1 + good eading 2} (6) Over the complete length of the roll, 401 laser readings are typically computed to obtain the crown profile of the roll.

Example 4

An example of an algorithm for determining the roundness of an industrial roll is set forth below. At various locations along the circumference of the industrial roll, each of two diametrically opposed lasers reads a number of measurements along the circumference of the roll for one complete roll revolution.

Readings are taken for the lasers along the roll circumference and constitute a set. Each of the laser readings in the set is evaluated against a predetermined upper limit. If a reading exceeds the predetermined upper limit, then it is set equal to a large value such as, for the sake of illustration, 100.

The resulting sets of data for each of the lasers is further processed to determine deviation. The deviation check is carried out with the first (i.e., reference) reading being designated as the laser 'n'_reading, and consecutive readings along the circumference being designated as laser 'n'_reading'i' with i being equal to 1 , 2, 3, etc. approaching an upper limit of 1500.

The check operation set forth in (1) described below is carried out to find out if the T th reading is satisfactory. If the T reading satisfies the condition, then this reading becomes the reference reading and the next adjacent reading is evaluated. If the check operation in (1) fails, then the reading in which T equals 2 is evaluated against the reference reading.

f (abso\ te[laser'n_' reading-laser'n' eading?] > {\ x unit deviation}) then laser'n' eading'ϊ = maximize (1)

wherein: unitjdeviation is representative deviation between circumferentially adjacent laser readings; and maximize is equal to a user-defined predetermined constant. Laser readings that have a value of maximize are then replaced with linearly interpolated values of circumferentially adjacent values which satisfy the condition set forth in (1). The linear interpolation is as follows:

data point - previous salidj oint +

[next alidj oint +

+ pri) x pi (2)

wherein: data point represents the linear interpolated value; previous alidjjoint represents a reading taken prior to the ϊ th reading along the roll circumference that satisfies condition (1); next jalid point represents a reading taken subsequent to the ϊ th reading along the roll circumference that satisfies condition (1); pi represents the number of indices to the previous_valid_point from the ϊ th reading; and pn represents the number of indices to the next_valid_point from the T th reading.

The above calculations result in a new set of readings, designated as laser 'n_new_reading

If the number of laser readings per surface location along the roll longitudinal axis (laser'n'jiumber) exceeds 360, then only 180 to 360 of these are selected as follows:

k = (laser'n'jiumber + 359)/360 (3)

One reading for every 'k'th reading is retained as the rest are discarded, resulting in a new number of laser readings (laser'n'jiewjnumber) where 'n' represents the first or second laser.

The values for Iaser1_new_number and Iaser2_new_number are then compared. If the difference between laserl iewjnumber and Iaser2_new_number\s greater than a predetermined deviation (e.g., 5 percent based on laserl _new_number which is typically an upper limit), an error is generated to repeat the scan cycle for the roundness of the roll.

If the difference is within the predetermined deviation, the readings from the two lasers are coordinated such that they correspond to the same circumferential location on the roll. For example, the ϊ th measurement from the second laser will be shifted 180° to correspond to the measurement taken from the first laser. Thereafter, the laser readings are then added together to yield a roundness value expressed in diameter format.

The foregoing is illustrative of the present invention and is not to be construed as limiting thereof. Although a few exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures. Therefore, it is to be understood that the foregoing is illustrative of the present invention and is not to be construed as limited to the specific embodiments disclosed, and that modifications to the disclosed embodiments, as well as other embodiments, are intended to be included within the scope of the appended claims. The invention is defined by the following claims, with equivalents of the claims to be included therein.

Claims

What is Claimed is:

1. A method of determining a shape of a longitudinally extending, cylindrical body, the method comprising the steps of: obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the body, wherein each measurement of relative displacement distance represents surface height of the body relative to a reference; storing each set of measurements; removing measurements from each stored set that are not within a predetermined tolerance range for a respective surface location; obtaining an average value of relative displacement distance for each stored set of measurements using measurements remaining within each respective stored set; and determining a reference dimension at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

2. A method according to Claim 1 wherein the step of obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the body comprises: illuminating a surface portion of the body at each surface location with a laser beam so that the laser beam reflects from the body surface and contacts a spot position on a sensor positioned adjacent the body; measuring a distance between a zero position and a spot position on the sensor at each surface location; and generating an electrical signal corresponding to each measurement of distance between a zero position and a spot position on the sensor.

3. A method according to Claim 1 wherein the step of removing measurements from each stored set that are not within a predetermined tolerance range for each respective surface location comprises: determining a mean value of relative displacement distance for each stored set of measurements; discarding measurements in each stored set that exceed the mean value for the respective stored set by a predetermined amount; discarding measurements in each stored set that were taken over an inconsistency in the body surface; and determining an average value of relative displacement distance for each stored set using measurements remaining within each respective stored set.

4. A method according to Claim 3, wherein the inconsistency in the body surface is a drilled hole.

5. A method according to Claim 1 further comprising the step of comparing the reference dimension from the reference to the body at each of the plurality of surface locations with a theoretical reference dimension.

6. A method according to Claim 1 wherein the step of obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body comprises: illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the cylindrical body surface and contact respective spot positions on respective first and second sensors positioned adjacent the cylindrical body; measuring a distance between a zero position and a spot position on each respective first and second sensor; and generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor.

7. A method according to Claim 6 wherein the step of determining a reference dimension from the reference to the cylindrical body at each of the plurality of surface locations comprises combining the average value of relative displacement distance for each respective set obtained by the first and second sensors.

8. A method according to Claim 1 wherein the cylindrical body is a cylindrical industrial roll.

9. A method according to Claim 1 wherein the surface of the cylindrical body is deformable.

10. A method of determining a shape of a longitudinally extending, cylindrical body, the method comprising the steps of: a. obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body, wherein each measurement of relative displacement distance represents surface height of the body relative to a reference, comprising: illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the body surface and contact respective spot positions on respective first and second sensors positioned adjacent the cylindrical body; measuring a distance between a zero position and a spot position on each respective first and second sensor; generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor; and storing each set of measurements; b. removing measurements from each stored set that are not within a predetermined tolerance range for a respective surface location comprising: determining a mean value of relative displacement distance for each stored set of measurements; discarding measurements in each stored set that exceed the mean value for the respective stored set by a predetermined amount; discarding measurements in each stored set that were taken over an inconsistency in the body surface; and determining an average value of relative displacement distance for each stored set using measurements remaining within each respective stored set; c. obtaining an average value of relative displacement distance for each set of measurements using remaining measurements within each respective set; and d. determining a reference dimension of the body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

11. A method according to Claim 10 further comprising the step of comparing the reference dimension of the cylindrical body at each of the plurality of surface locations with a theoretical reference dimension.

12. A method according to Claim 10 wherein the step of determining a reference dimension of the cylindrical body at each of the plurality of surface locations comprises combining the average value of relative displacement distance for each respective stored set obtained by the first and second sensors.

13. A method according to Claim 10 wherein the cylindrical body is a cylindrical industrial roll.

14. A method according to Claim 10 wherein the surface of the cylindrical body is deformable.

15. A method according to Claim 10 wherein the inconsistency in the body surface is a drilled hole.

16. A system for determining a shape of a longitudinally extending, cylindrical body, comprising: a. means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body, wherein each measurement of relative displacement distance represents surface height of the cylindrical body relative to a reference; and b. a data processing system in communication with the measurement obtaining means, comprising: means for storing each set of measurements; means for removing measurements from each stored set that are not within a predetermined tolerance range for a respective surface location; means for obtaining an average value of relative displacement distance for each stored set of measurements using measurements remaining within each respective stored set; and means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

17. A system according to Claim 16 wherein the means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body comprises: means for illuminating a surface portion of the cylindrical body at each location with a laser beam so that the laser beam reflects from the cylindrical body surface and contacts a spot position on a sensor positioned adjacent the body; means for measuring a distance between a zero position and a spot position on the sensor at each location; and means for generating an electrical signal corresponding to each measurement of distance between a zero position and a spot position on the sensor.

18. A system according to Claim 16 wherein the means for removing measurements from each stored set that are not within a predetermined tolerance range for each respective surface location comprises: means for determining a mean value of relative displacement distance for each stored set of measurements; means for discarding measurements in each stored set that exceed the mean value for the respective stored set by a predetermined amount; means for discarding measurements in each stored set that were taken over an inconsistency in the body surface; and means for determining an average value of relative displacement distance for each stored set using measurements remaining within each respective stored set.

19. A system according to Claim 18 wherein the inconsistency is a drilled hole.

20. A system according to Claim 16 wherein the data processing system further comprises means for comparing the reference dimension of the cylindrical body at each of the plurality of surface locations with a theoretical reference dimension.

21. A system according to Claim 16 wherein the means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body comprises: means for illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the cylindrical body surface and contact respective spot positions on respective first and second sensors positioned adjacent the cylindrical body; means for measuring a distance between a zero position and a spot position on each respective first and second sensor; and means for generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor.

22. A system according to Claim 17 wherein the means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations comprises means for combining the average value of relative displacement distance for each respective set obtained by the first and second sensors.

23. A system according to Claim 16 wherein the cylindrical body is a cylindrical industrial roll.

24. A system according to Claim 16 wherein the surface of the cylindrical body is deformable.

25. A system for determining a shape of a longitudinally extending, cylindrical body, comprising: a. means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body, wherein each measurement of relative displacement distance represents surface height of the cylindrical body relative to a reference, the measurement obtaining means comprising: means for illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the body surface and contact respective spot positions on respective first and second sensors positioned adjacent to the cylindrical body; means for measuring a distance between a zero position and a spot position on each respective first and second sensor; and means for generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor; and b. a data processing system in communication with the measurement obtaining means, comprising: means for storing each set of measurements; means for determining a mean value of relative displacement distance for each stored set of measurements; means for discarding measurements in each stored set that exceed the mean value for the respective stored set by a predetermined amount; means for discarding measurements in each stored set that were taken over an inconsistency in the body surface; means for determining an average value of relative displacement distance for each stored set using measurements remaining within each respective stored set; means for obtaining an average value of relative displacement distance for each set of measurements using remaining measurements within each respective set; and means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

26. A system according to Claim 25 wherein the inconsistency is a drilled hole.

27. A system according to Claim 25 wherein the data processing system further comprises means for comparing the reference dimension of the cylindrical body at each of the plurality of surface locations with a theoretical reference dimension.

28. A system according to Claim 25 wherein the means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations comprises means for combining the average value of relative displacement distance for each respective stored set obtained by the first and second sensors.

29. A system according to Claim 25 wherein the cylindrical body is a cylindrical industrial roll.

30. A system according to Claim 25 wherein the surface of the cylindrical body is deformable.

31. A computer program product for determining a shape of a longitudinally extending, cylindrical body, the computer program product comprising a computer usable storage medium having computer readable program code means embodied in the medium, the computer readable program code means comprising: computer readable program code means for storing a plurality of sets of measurements of relative displacement distance for each of a plurality of surface locations along the longitudinal direction of the cylindrical body, wherein each measurement of relative displacement distance represents surface height of the body relative to a reference; computer readable program code means for removing measurements from each stored set that are not within a predetermined tolerance range for a respective surface location; computer readable program code means for obtaining an average value of relative displacement distance for each stored set of measurements using measurements remaining within each respective stored set; and computer readable program code means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

32. A computer program product according to Claim 31 wherein the computer readable program code means for removing measurements from each stored set that are not within a predetermined tolerance range for each respective surface location comprises: computer readable program code means for determining a mean value of relative displacement distance for each stored set of measurements; computer readable program code means for discarding measurements in each stored set that exceed the mean value for the respective stored set by a predetermined amount; computer readable program code means for discarding measurements in each stored set that were taken over an inconsistency in the cylindrical body surface; and computer readable program code means for determining an average value of relative displacement distance for each stored set using measurements remaining within each respective stored set.

33. A computer program product according to Claim 32 wherein the inconsistency is a drilled hole.

34. A computer program product according to Claim 31 further comprising computer readable program code means for comparing the reference dimension of the cylindrical body at each of the plurality of surface locations with a theoretical reference dimension.

35. A computer program product according to Claim 31 wherein the cylindrical body is a cylindrical industrial roll.

36. A computer program product according to Claim 31 wherein the surface of the cylindrical body is deformable.

37. A method for determining roundness of a longitudinally extending, cylindrical body, the method comprising the steps of: obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body, wherein each measurement of relative displacement distance represents a surface height of the body relative to a reference; storing each set of measurements; identifying measurements in each stored set that exceed a predetermined value; replacing the identified measurements in each respective stored set with a linearly interpolated value obtained using measurements within each respective set that do not exceed the predetermined value; obtaining an average value of relative displacement distance for each stored set of measurements using measurements within each respective stored set that do not exceed the predetermined value; and determining a reference dimension of the body at each of the plurality of surface locations along the circumference of the cylindrical body using the average value of relative displacement distance for each respective stored set.

38. A method according to Claim 37, wherein the step of obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the circumference of the cylindrical body comprises: illuminating a surface portion of the cylindrical body at each location with a laser beam so that the laser beam reflects from the cylindrical body and contacts a spot position on a sensor positioned adjacent the body; measuring a distance between a zero position and a spot position on the sensor at each location; and generating an electrical signal corresponding to each measurement of distance between a zero position and a spot position on the sensor.

39. A method according to Claim 37, wherein the step of replacing the identified measurements in each stored set that exceed a predetermined value with a linearly interpolated value comprises: equating each measurement that exceeds the predetermined value with a linearly interpolated value calculated from measurements on opposite circumferential adjacent sides of the respective measurement that exceeds the predetermined value.

40. A method according to Claim 37 wherein the step of obtaining a set of measurements of relative displacement distances for each of a plurality of surface locations along the longitudinal direction of the cylindrical body comprises: illuminating surface portions of the body at each location with first and second laser beams so that the first and second laser beams reflect from the cylindrical body surface and contact respective spot positions on respective first and second sensors positioned adjacent the cylindrical body; measuring a distance between a zero position and a spot position on each respective first and second sensor; and generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor.

41. A method according to Claim 37 wherein the step of determining a reference dimension of the cylindrical body at each of the plurality of surface locations further comprises combining the average value of measurements for each respective set obtained by the first and second sensors.

42. A method according to Claim 37 wherein the cylindrical body is a cylindrical industrial roll.

43. A method according to Claim 37 wherein the surface of the cylindrical body is deformable.

44. A method for determining roundness of a longitudinally extending, cylindrical body, the method comprising the steps of: a. obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body, wherein each measurement of relative displacement distance represents a surface height of the cylindrical body relative to a reference, comprising: illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the cylindrical body surface and contact respective spot positions on respective first and second sensors positioned adjacent the cylindrical body; measuring a distance between a zero position and a spot position on each respective first and second sensor; and generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor; and storing each set of measurements; b. identifying measurements in each stored set that exceed a predetermined value; c. replacing the identified measurements in each respective stored set with a linearly interpolated value obtained using measurements within each respective set that do not exceed the predetermined value; d. obtaining an average value of relative displacement distance for each stored set of measurements using measurements within each respective stored set that do not exceed the predetermined value; and e. determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

45. A method according to Claim 44, wherein the step of replacing the identified measurements in each stored set that exceed a predetermined value with a linearly interpolated value comprises: equating each measurement that exceeds the predetermined value with a linearly interpolated value calculated from measurements on opposite adjacent circumferential sides of the respective measurement that exceeds the predetermined value.

46. A method according to Claim 44 wherein the step of determining a reference dimension of the body at each of the plurality of surface locations further comprises combining the average value of measurements for each respective set obtained by the first and second sensors.

47. A method according to Claim 44 wherein the cylindrical body is a cylindrical industrial roll.

48. A method according to Claim 44 wherein the surface of the cylindrical body is deformable.

49. A system for determining roundness of a longitudinally extending, cylindrical body, comprising: means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body, wherein each measurement of relative displacement distance represents a surface height of the cylindrical body relative to a reference; and a data processing system in communication with the measurement obtaining means, comprising: means for storing each set of measurements; means for identifying measurements in each stored set that exceed a predetermined value; means for replacing the identified measurements in each respective stored set with a linearly interpolated value obtained using measurements within each respective set that do not exceed the predetermined value; means for obtaining an average value of relative displacement distance for each stored set of measurements using measurements within each respective stored set that do not exceed the predetermined value; and means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

50. A system according to Claim 49, wherein the means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along the circumference of the cylindrical body comprises: means for illuminating a surface portion of the cylindrical body at each location with a laser beam so that the laser beam reflects from the cylindrical body and contacts a spot position on a sensor positioned adjacent the cylindrical body; means for measuring a distance between a zero position and a spot position on the sensor at each location; and means for generating an electrical signal corresponding to each measurement of distance between a zero position and a spot position on the sensor.

51. A system according to Claim 49, wherein the means for replacing the identified measurements in each stored set that exceed a predetermined value with a lineariy interpolated value comprises: means for equating each measurement that exceeds the predetermined value with a linearly interpolated value calculated from measurements on opposite adjacent circumferential sides of the respective measurement that exceeds the predetermined value.

52. A system according to Claim 49 wherein the means for obtaining a set of measurements of relative displacement distances for each of a plurality of surface locations along the longitudinal direction of the cylindrical body comprises: means for illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the cylindrical body surface and contact respective spot positions on respective first and second sensors positioned adjacent the cylindrical body; means for measuring a distance between a zero position and a spot position on each respective first and second sensor; and means for generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor.

53. A system according to Claim 52 wherein the means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations further comprises means for combining the average value of measurements for each respective set obtained by the first and second sensors.

54. A system according to Claim 49 wherein the cylindrical body is a cylindrical industrial roll.

55. A system according to Claim 49 wherein the surface of the cylindrical body is deformable.

56. A system for determining roundness of a longitudinally extending, cylindrical body, comprising: a. means for obtaining a set of measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body, wherein each measurement of relative displacement distance represents a surface height of the cylindrical body relative to a reference, comprising: means for illuminating surface portions of the cylindrical body at each location with first and second laser beams so that the first and second laser beams reflect from the body surface and contact respective spot positions on respective first and second sensors positioned adjacent the body; means for measuring a distance between a zero position and a spot position on each respective first and second sensor; and means for generating respective first and second electrical signals corresponding to each measurement of distance between a zero position and a spot position on each respective first and second sensor; and b. a data processing system in communication with the measurement obtaining means, comprising: means for storing each set of measurements; means for identifying measurements in each stored set that exceed a predetermined value; means for replacing the identified measurements in each respective stored set with a linearly interpolated value obtained using measurements within each respective set that do not exceed the predetermined value; means for obtaining an average value of relative displacement distance for each stored set of measurements using measurements within each respective stored set that do not exceed the predetermined value; and means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

57. A system according to Claim 56, wherein the means for replacing the identified measurements in each stored set that exceed a predetermined value with a linearly interpolated value comprises: means for equating each measurement that exceeds the predetermined value with a linearly interpolated value calculated from measurements on opposite circumferential adjacent sides of the respective measurement that do not exceed the predetermined value.

58. A system according to Claim 56 wherein the means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations further comprises means for combining the average value of measurements for each respective set obtained by the first and second sensors.

59. A system according to Claim 56 wherein the cylindrical body is a cylindrical industrial roll.

60. A system according to Claim 56 wherein the surface of the cylindrical body is deformable.

61. A computer program product for determining roundness of a longitudinally extending, cylindrical body, the computer program product comprising a computer usable storage medium having computer readable program code means embodied in the medium, the computer readable program code means comprising: computer readable program code means for storing a set of measurements of relative displacement distance for each of a plurality of surface locations along a circumference of the cylindrical body, wherein each measurement of relative displacement distance represents a surface height of the cylindrical body relative to a reference; computer readable program code means for identifying measurements in each stored set that exceed a predetermined value; computer readable program code means for replacing the identified measurements in each respective stored set with a linearly interpolated value obtained using measurements within each respective set that do not exceed the predetermined value; computer readable program code means for obtaining an average value of relative displacement distance for each stored set of measurements using measurements within each respective stored set that do not exceed the predetermined value; and computer readable program code means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations using the average value of relative displacement distance for each respective stored set.

62. A computer program product according to Claim 61 , wherein the computer readable program code means for replacing the identified measurements in each stored set that exceed a predetermined value with a linearly interpolated value comprises computer readable program code means for equating each measurement that exceeds the predetermined value with a linearly interpolated value calculated from measurements on opposite adjacent sides of the respective measurement that exceeds the predetermined value.

63. A computer program product according to Claim 61 wherein the computer readable program code means for determining a reference dimension of the cylindrical body at each of the plurality of surface locations further comprises computer readable program code means for combining the average value of measurements for each respective set obtained by the first and second sensors.

64. A computer program product according to Claim 61 wherein the cylindrical body is a cylindrical industrial roll.

65. A computer program product according to Claim 61 wherein the surface of the cylindrical body is deformable.