WO2001038885A1

WO2001038885A1 - Angular velocity monitor

Info

Publication number: WO2001038885A1
Application number: PCT/US2000/032173
Authority: WO
Inventors: Martin J. Dowling
Original assignee: Crane Nuclear, Inc.
Priority date: 1999-11-24
Filing date: 2000-11-22
Publication date: 2001-05-31
Also published as: AU1794301A

Abstract

The invention generally pertains to monitoring of machinery, and, more particularly, measuring instantaneous angular velocity of a shaft. The invention provides a simple, easy to install, inexpensive apparatus and method of using the apparatus to monitor instantaneous (true multiple-per-rev) angular velocity or rotational speed of rotational equipment. The invention accomplishes this by using a tape having alternating reflective and non-reflective areas, the tape bonded to, for instance, a shaft. Markings on the tape define the alternating reflective and non-reflective areas. When a light source is directed at the tape, a reflected beam is created, which is detected by a light sensor. The light sensor thus generates a signal, which is used by a processor to perform calculations including instantaneous angular velocity. As described herein, formulas are presented and designed to avoid the phase shifting properties resulting from the discontinuity at the tape seam (where the ends of the tape meet). The processor further records a time of arrival of the reflected beam such that the time of arrival is combined with the signal to perform the calculations.

Description

ANGULAR VELOCITY MONITOR

Cross Reference to Related Application

This application claims the benefit of U. S. Provisional Application No. 60/167,275, filed

November 24, 1999.

Field of the Invention

The invention generally pertains to monitoring of machinery and, more particularly,

measuring instantaneous shaft speed, otherwise known as the instantaneous angular velocity.

Background of the Invention The instantaneous angular velocity of a rotating shaft is a key parameter for evaluating

motor torque and efficiency, as well as monitoring rubs in journal bearings, oscillation in shafts and couplings, and the integrity of teeth in gearboxes. As used herein, the term "instantaneous"

refers to the ability to actually measure angular velocity in 'real-time', not just a once-per-rev

(i.e., one pulse per shaft revolution) system or even a multiple times per revolution system,

which averages the velocity as a function of measurements per distance (i.e., the circumference

of the shaft). Also, as used herein, the terms "instantaneous angular velocity", "angular velocity"

and "speed" are used interchangeably as these terms relate to the present invention. The angular velocity can be an effective measure of the balance of driving equipment, the health of drive train

transmissions, and variation in loading in driven equipment. Some examples will be given to

show the value of this measurement. In journal bearings a film of oil separates the rotating shaft from the bearing. Side loads occur on the shaft due to such causes as coupling misalignment, shaft bending, and unbalance on

pump vanes or turbine blades caused by debris buildup or corrosion pitting. When side loads

become great enough, the shaft rubs against the bearing. This causes wear in the bearing and

shaft. Contact occurs rarely at first, but after considerable degradation it occurs almost every revolution. The earlier and least expensive it can be detected, the better. Since a rub

momentarily slows down the rotational speed of the shaft, an instantaneous angular velocity

monitor can detect a contact in the early stages.

A second illustration is oscillation that may occur when an engine drives a load through a transmission linkage, e.g. a coupling. When the shaft or coupling oscillates in a flexible manner, torsional oscillation results. If the oscillation is severe enough, the coupling may become

damaged, creating a hazard both for the machine and for personnel working nearby. The instantaneous angular velocity can be measured on both sides of a coupling to determine which

side is originating the oscillation, how severe it is, and how much is being absorbed and

transmitted through the coupling.

For reciprocating machines, such as in diesel engines and reciprocating pumps, angular

velocity measurements can help determine the amount of unbalance in the reciprocating

component. In the case of an engine, if some cylinders are firing better than others, the latter will

give a momentary greater angular acceleration to the shaft. When a shaft undergoes acceleration and deceleration during its rotation, an average velocity can be considerably misleading, potentially sufficient to invalidate the data and or ability to troubleshoot the mechanical problem. Likewise, if the friction is greater in one cylinder than another in a multiple-cylinder reciprocating pump, this will show up as a drag on the angular velocity at certain times of the cycle.

Perhaps the best means for monitoring weak teeth in a gearbox is by observing the

angular velocities of the input and output shafts. When a weak tooth enters a mesh, the output shaft momentarily slows down because it has lost its driver, and the input shaft momentarily

accelerates because it has lost its load. An analysis of the repetition frequency at which this anomaly occurs reveals which gear has the weak tooth. The optimum way of measuring this shaft acceleration and deceleration is by monitoring the instantaneous angular velocity, which is

a more direct measure than, for instance, placing vibration probes on the housing. A weak tooth shows up as a strong transmission error, and this signal serves as early warning of a problem on

the weak tooth. Each transmission error has associated with it a change in the force between the driving and driven gear. This dynamic increment reflects the momentary change in useful tangential tooth load. In spur gears, this force, which is tangential to the gear disk, can be

resolved into a lateral force and an incremented torque in the shaft of the gear. The lateral force

in the shaft produces a reaction at the supporting bearings and results in gear case vibration.

Transmission error is often the primary cause of vibration in spur gearboxes.

Another example of the importance of angular velocity is the determination of instantaneous speed on a motor shaft. On induction motors, speed is essential in order to

evaluate rotor power (I²R) losses, which in turn are used to calculate torque and efficiency. Instantaneous speed is a key parameter in monitoring induction motors.

In summary, monitoring instantaneous angular velocity or frequency allows for the early detection of unbalanced loads, rubbing shafts, weak gears and a myriad of other mechanical problems. Further, angular velocity or frequency is a very important parameter for calculating the performance and output of induction motors.

It should be noted that none of these scenarios of rotational mechanical problems is adequately addressed by a once-per-rev system such as a tachometer. A once-per-rev system

yields an average speed, which is adequate for a system having a constant velocity. One measurement per revolution is far too infrequent to detect any of these problems. This type of

system is, in fact, inadequate when the speed changes during a revolution. For example, it is

highly unlikely that a once-per-rev system will capture a momentary rub, which only occupies a small fraction of one shaft revolution. Similarly, the chances of detecting a weak tooth on a

sixty-tooth gear are poor when the measurement window is less than one tooth. Thus, measurement at one or two points of rotational speed alone does not permit complete analysis of

system operation. For example, the once-per-rev tachometer undersamples the angular velocity

signal, which is why sampling multiple times per revolution is important.

There are several known methods and devices used to monitor changes in angular velocity of a rotating shaft. One such apparatus is the torsiograph, which is an inertial device,

attached to the end of a shaft, that senses changes in angular velocity by sensing differences

between the shaft and a freely rotating mass moving at the average velocity of the shaft. The

mass is coupled sufficiently to attain the same average velocity, but loosely enough to maintain its own inertia despite temporary changes in velocity of the shaft. The torsiograph is primarily a

temporary device since its attachment usually requires removing a portion of the machine's housing. This disrupts the internal environment of the machine and potentially poses a safety hazard during the test. Because of its complexity and bulk it is also a fairly expensive means for monitoring changes in the angular velocity. Another approach uses torque sensors such as strain gages. For example, a Wheatstone

Bridge may be installed on either side of a flexible coupling to measure oscillation. This enables

the determination of where the torsion is originating, how much is transmitted through the

coupling, and if the coupling is dampening or amplifying the oscillation. This approach requires

skilled personnel to precision bond the torque gages on a cylindrical shaft while maintaining

correct orientation of the torque gages. In other words, the torque gages must be bonded to the circumference of the shaft correctly, usually at an angle of 45 degrees from the central axis of the

shaft. Furthermore, there is a major problem in communicating the signal from the rotating shaft

to stationary instrumentation. The two most common methods for measuring angular velocity are close-coupled

telemetry and slip rings. Telemetry requires installation of a transmitter, battery and antenna on the shaft while maintaining rotor balance. It also requires a corresponding antenna, receiver and demodulator for connection to the instrumentation. The system must be tuned in terms of

frequency and must be set up to insure that the range of strain will be within the modulating

signal parameters.

The other method, slip rings, requires mounting the slip rings to the diameter of the shaft, which is a complex machining job. Further, the contacts on the slip rings degrade over time and the signal becomes noisy. Both slip rings and telemetry are considered short-term solutions and are generally used on a temporary basis. They are both expensive and labor intensive to install.

The use of torque gages allows shaft stress and torque to be measured. On the other hand, torque gages do not sense the relative velocity or displacement of the coupling because the coupling's material properties are not considered. A more permanent solution is to use a toothed wheel (a 60-tooth gear is often used) mounted on a shaft. The toothed wheel serves as a target for a metal detector such as a magnetic pickup or an eddy current proximity probe. As each tooth passes the sensor, a pulse is produced. Time is measured between pulses and, since the teeth are evenly spaced, the signal is easily demodulated, for instance by performing a frequency spectrum

analysis, resulting in a measure of the angular velocity. However, the toothed wheel is intrusive and it is usually necessary to install the toothed wheel prior to installation of the machine.

Another solution along the same line is an optical encoder. The optical encoder can be

installed at the end of a shaft or mounted on the circumference of the shaft, in which case it must be made to fit the particular diameter of the shaft. In the simplest implementation, the optical

encoder includes a pattern of radial lines, (for example, 360 lines), on an otherwise transparent disk so that each line represents a circular degree. A light source and a detector are mounted on

opposite sides of the disk so that each line breaks the beam, thereby creating a pulse. The optical encoder is infrequently used on large machines because of the difficulty in finding room on the

shaft to mount the optical encoder.

Devices intended for a once-per-rev system of monitoring are usually simpler and easier to install. For grooved shafts, a proximity detector such as an eddy current or magnetic pickup

can be used to detect the groove at each revolution, thus requiring no adapter for the shaft.

Another once-per-rev system is an optical one in which a small piece of reflective tape is

bonded to the shaft. A light beam and detector are aimed at the same spot or position on the

shaft. At each revolution, the tape mirrors the light back to the detector and produces a once-per- rev pulse or signal. (As used herein, the terms "pulse" and "signal" are used interchangeably.)

There is typically a considerable amount of noise in the signal because the remainder of the shaft passing, for instance, under the light has uncontrolled reflectivity. A once-per-rev signal can sometimes be acquired by means of an accelerometer mounted on, for instance, a bearing cap. This is especially true for roughly running shafts. However, smoothly running machines often do not provide a once-per-rev signal sufficiently above the

noise, thereby resulting in a generally unreliable technique.

In summary, the problem with multiple-per-rev systems such as the torsiograph and torque meter is that these systems are cumbersome to install on already existing equipment.

Gears and optical encoders further require machined adapters for each shaft. On the other hand,

once-per-rev systems are unable to accurately detect speed changes that occur during the

revolution. Such systems lack the precision required for monitoring and diagnostic purposes, and typically do not adequately monitor once-per-rev phenomena such as a weak gear tooth or

bearing rub.

U.S. Patent No. 5,438,882 to Karim-Panahi, et al. (1995) teaches a method for measuring torque on a rotating shaft using two axially separated markings on a shaft in conjunction with

corresponding photodetectors to ascertain twist of the shaft and thereby infer torque. In addition

to the fact that the Karim-Panahi, et al. device was designed to measure torque, it fails to address

the special situation of monitoring the transmission link between two shafts. JP Patent Application No. 61/205830 to Saito (1986) uses a similar apparatus of two axially separated

markings on a shaft and two corresponding detectors.

U.S. Patent No. 5,214,278 to Banda (1993) measures speed on a rotating shaft by using a plurality of axially extending non-reflective stripes alternating with reflected surfaces defined by the surface of a polished shaft itself. Additionally, as described above, a pair of reflected beams and detectors are utilized to detect wobble or lateral position of the shaft as a function of the time-dependent measurements of the pair of reflected light beams. This system is unnecessarily complex and it requires precision in applying the non-reflective stripes with even spacing between the stripes. Further, the device ascertains shaft position using intensity of light. When such a system is used, for instance, using the shaft as the reflector, there is a greater signal-to-

noise ratio than when a clear or crisp signal is received by a digital system, which tends to be

more of a black/white signal. Such amplitude modulation reduces the signal-to-noise ratio

compared to off-on digital detection methodology.

U.S. Patent No. 5,118,932 to Brownrigg, et al. (1992), which is incorporated herein by reference in its entirety, employs a complex system using a light source, a beamsplitter and gradient index lenses to collimate the light beam into two light beams which project onto a

reflective grating at different angles and turbine engine shaft speed is measured by

interferometric means. Because of the high temperature environment, the reflective grating is formed in the surface of the shaft.

U.S. Patent No. 4,580,871 to Matsunaga, et al. (1986) presents an enclosed optical encoder having a precisely prefabricated grating on a cylindrical rotor wherein the grating has

alternating reflective and nonreflective areas formed on the fringe of the rotor. U.S. Patents Nos.

5,045,691 to Steward, et al. (1991) and 4,866,269 to Wlodarczyk, et al. (1989) utilize disk-type

optical encoders mounted on a shaft wherein the disk incorporates reflective segments or protrusions within the surface of the disk. Systems incorporating such disks are fairly expensive and also have the additional disadvantage of placing another component on the shaft that may contribute adversely to the balance of the shaft.

Since the once-per-rev systems are typically so easy to install, it would be desirable to somehow extend these systems to multiple-per-rev use. The shaft groove monitors obviously are not capable of being extended because there is only one groove on the shaft. Further, in previously known systems which use tape wrapped around the circumference of a shaft, when the

two ends of the tape are joined together there is an (unpredictable) anomaly or discontinuity in the spacing that makes the resulting pulses suddenly jump when the light beam crosses the

spacing anomaly. In addition, the discontinuity causes the next series of evenly spaced pulses to be totally out of phase with the first set thus obliterating any correlation between revolutions.

For example, a Fast Fourier Transform (FFT) calculated using pulse time intervals over several

rotations will give nonsensical results. Some commercial systems attempt to overcome this

problem by artificially dividing the time between pulses into, say, 60 equally spaced units and

thereby offer tachometers with a "60 per rev" pulse rate. These tachometers do not, however, track the actual changes in angular velocity throughout a cycle and thus are actually no better than once-per-rev units.

In High Frequency Spectral Analysis Study for Helicopter Bearing and Gear Failure

Detection, January 22, 1990, a report for the Naval Air Development Center by the present

inventor, discloses using a strip of tape with regular markings to monitor transmission error in

helicopter gearboxes was presented, but no method was provided to overcome the discontinuity where the ends of the tape join.

In view of the disadvantages associated with currently available monitoring systems,

there is a need for a simple, easy to install, inexpensive apparatus to monitor instantaneous (true

multiple-per-rev) angular velocity of rotational equipment.

Summary of the Invention

It is an object of this invention to provide a simple, easy to install, inexpensive apparatus and method of using the apparatus to monitor instantaneous (true multiple-per-rev) angular velocity or rotational speed of rotational equipment. It is another object of this invention to determine instantaneous angular velocity and oscillation for the purpose of detecting, identifying and diagnosing gear tooth weakness, journal

bearing rub, anti-friction bearing race and rolling element problems, excessive flex in couplings, engine and pump unbalance, as well as providing an accurate measurement of instantaneous

angular velocity or speed. Ultimately, motor torque and efficiency may be determined, thereby indicating the need to repair or replace the equipment.

It is a further object of this invention to provide an apparatus to monitor instantaneous angular velocity that is readily applied without using complex procedures such as etching a shaft. It is a further object of this invention to supplement, and in some cases, replace vibration

monitoring on bearings, gears, and machinery with the apparatus of the present invention since

this can be done more effectively and economically. It is a further object to supplement, and in some cases, replace current and power signature analysis on electric motors when the purpose is

to ascertain instantaneous angular velocity or speed.

The invention accomplishes this by using a tape having alternating reflective and non-

reflective areas, the tape bonded to, for instance, a shaft. Markings on the tape define the

alternating reflective and non-reflective areas. When a light source is directed at the tape, a

reflected beam is created, which is detected by a light sensor. The light sensor thus generates a signal, which is used by a processor to perform calculations including instantaneous angular velocity. As described herein, formulas are presented and designed to avoid the phase shifting

properties resulting from the discontinuity at the tape seam (where the ends of the tape meet). The processor further records a time of arrival of the reflected beam such that the time of arrival

is combined with the signal to perform the calculations. Depending on the line density of the markings on the tape and the accuracy of a processor in recording the time of arrival of the signal, accurate determinations of instantaneous angular velocity can be made.

The apparatus of the present invention is non-intrusive, accommodates uneven sampling,

and requires only a very small section of exposed shaft for attachment of the tape. Further, the tape of the present invention has a negligible mass and therefore, does not contribute adversely to

the balance of the shaft. In another embodiment of the present invention, the tape is easily

applied to a shaft and thus easily removed. In this way, the tape is replaceable with minimal

effort and expense. Because of the relative low cost of the tape, the tape can be considered disposable. Brief Description of the Drawings

A full and enabling disclosure of the present invention, including the best mode thereof,

to one of ordinary skill in the art, is set forth more particularly in the remainder of the

specification, including reference to the accompanying figures wherein:

Fig. 1 shows a basic configuration of a machine monitoring system according to the

present invention.

Fig. 2 shows a tape mounted on the rotating shaft. Fig. 3 is a detail view of a pattern on the tape.

Fig. 4 shows a simplified configuration for monitoring the transmission link between two

shafts. Fig. 5 shows a reconstruction of the instantaneous velocity using a simple two-point approach.

Fig. 6 compares a simulated shaft velocity trace and a calculated trace using the

techniques of the invention for a ramp function. Fig. 7 compares a simulated shaft velocity trace and a calculated trace using the techniques of the invention for a sinusoidal function.

Fig. 8 compares a simulated shaft velocity trace and a calculated trace using the

techniques of the invention for an exponential function.

Fig. 9 shows a calculated velocity trace versus shaft angle using the techniques of the invention for a ramp function.

Fig. 10 shows a calculated velocity trace versus shaft angle using the techniques of the invention for a sinusoidal function.

Fig. 11 shows a calculated trace versus shaft angle using the techniques of the invention for an exponential function.

Detailed Description of the Preferred Embodiments

Reference will now be made in detail to the presently preferred embodiments of the

invention, one or more examples of which are illustrated in the drawings. Each example is

provided by way of explanation of the invention, and is not meant as a limitation of the

invention. For example, features illustrated or described as part of one embodiment can be used on or in conjunction with other embodiments to yield yet a further embodiment. It is intended

that the present invention includes such modifications and variations.

The present invention provides an apparatus to overcome the deficiencies of prior

systems utilized to measure characteristics of rotating machinery. In such prior systems, a tape is placed upon, for instance, a shaft to measure characteristics of the rotation. Discontinuity occurs when ends of a tape are joined together, typically forming a gap, which is easily detected by monitoring equipment. The apparatus of the present invention utilizes a gapless tape, (as used herein, the term "gapless" means that the tape will not have the gap or discontinuity formed when ends of the prior known tapes are joined together), as well as provides specific formulas and/or software algorithms to correctly extract timing and velocity information. The apparatus of

the present invention is applicable to a broad range of machinery problems ranging from unbalance in reciprocating pumps, to torsional oscillation in flexible couplings, to detection of

rubs in journal bearings (a type of bearing not considered in the previously cited report High

Frequency Spectral Analysis Study for Helicopter Bearing and Gear Failure Detection).

The present invention is directed to an apparatus and method for evaluating the

instantaneous angular velocity and variations thereof for rotating machinery. Referring to the drawings, wherein the same reference numerals indicate like elements throughout the several

figures, there is shown in Fig. 1 the basic configuration of the system. A tape 10 (see, for

instance, Fig. 2) with an imprinted or inscribed pattern 38 thereon (as seen in Fig. 3), is disposed on, for instance, encircles or girdles the circumference of the shaft 12. (The imprinted or

inscribed pattern 38 is also referred to as the velocity measurement column of the tape 10.) A power supply 14 provides energy for a light source 16, which may be a continuous beam or

otherwise, aimed at the shaft 12. Preferably the light source 16 is generated by a laser, but any

beam of steady, focused light will do. When the light source 16 is directed at the tape 10 and shines on the reflective/non-reflective pattern of the tape 10, a series of reflected light beams or

pulses strike a photo-detector, light detector or light sensor 18, positioned to detect the reflected beam, which generates an electrical output (e.g. a signal or pulse) during each period of reflected beam. Exemplary of such light sensors 18 include fiberoptic monitors, and may include more

than one light sensor per apparatus. Preferably, the electrical signal or pulse is passed through a pulse shaping circuit to sharpen the signal to provide more precise timing information. Such a circuit includes, for

instance, a pulse shaper 20 such as a Schmidt Trigger Oscillator. The pulse can be formed to any

convenient shape, level and sharpness by the pulse shaper 20. Fig. 2 represents a perspective

view of the reflective tape 10 on a shaft 12 according to the present invention. The tape 10,

according to the present invention, will have alternating reflective and non-reflective areas. With

reference to Fig. 3, for instance, substantially regularly spaced markings 22 form the pattern 38 on the tape 10. The distance between each of the regularly spaced markings 22 defines a

periodic interval 28. In one embodiment, the tape 10, is formed of a reflective material, such that the periodic intervals 28 are reflective. In such an embodiment, a non-reflective substance would form the markings 22, (i.e. lines). As would be understood by those skilled in the art, the pattern

can just as easily be reversed (reflective replacing non-reflective) and be equally effective. As shown in Fig. 3, the tape 10 may include a long strip of reflective material, or even a sleeve sized

to form a shrink-wrap fit to the circumference of the shaft.

A leading or first end 24 of the tape 10, has a section 36 that is free of markings and has a length at least about 2 times the periodic interval 28. In the embodiment where the tape 10 is

formed of a reflective material, the section 36 will be a solid reflective section. Typically the section 36 is between 2 and 3 times the length of the periodic intervals 28. It is desirable that this

section 36 have a dimension somewhat greater than two times the periodic interval 28 in order to distinguish it from the periodic intervals, such as those formed by gaps in the ends of a tape that do not overlap, and which cause a high signal-to-noise ratio. It is also desirable that the section 36 be less than 3 times the periodic interval 28 so as not to miss any more samples than necessary. A preferred value for the section 36 generally is about 2.5 times the length of the periodic intervals 28.

The tape 10 should be applied in accordance with the following procedure. Before bonding, the tape 10 is temporarily placed around the shaft 12. The tape 10 is cut in such a

manner that there is a small amount (a few millimeters) of overlap when the tape is disposed on and encircles the shaft 12. Turning to Fig. 3, the leading or first end 24 of the tape 10 is not cut.

To install the tape 10, the cut or second end 26 is bonded first, the tape is wrapped around the shaft 12, and the leading or first end 24 is placed on top of, thereby overlapping, the cut end. This insures that the section 36 of the leading end 24 will be present and detectable by the light

sensor 18. Additionally, it will be understood that the tape 10 may be applied to the shaft while

the shaft is rotating.

In the rare case in which the leading or first end 24 of the tape 10, after overlapping the cut or second end 26, partly conceals a line or marking 22 making it uncertain how that line will

show up or be detected by the light sensor, then an extra piece of tape with no lines or markings

22 can be placed on top of or positioned over the overlap joint to make it unambiguous (so the joint will not show up as a line or produce an ambiguous signal at the last marking).

The periodic interval 28 of the tape 10 does not have to be, and rarely will be, an integer

divisor of the circumference of the shaft 12. The line spacing determines the sampling rate of the

angular velocity. This rate is approximately the rotation rate in Hz times the number of lines exposed around the shaft. The long (leading end) section serves as a once-per-rev phase reference.

The markings 22 on the tape 10 are chosen with a line density that is greater than or equal to the desired sampling rate divided by the shaft rotational speed in Hertz. If, for example, a sampling rate of 3000 samples per second (sps) is desired and the shaft speed is 30 Hz, then there should be at least 100 markings on the tape. If the diameter is 6 inches and the circumference is

18.85 inches, then the required line density is at least 5.3 lines per inch. With this sample rate,

up to the first 50 orders of running speed can be monitored. Often, however, higher line densities are used in order to detect faster variations in angular velocity.

A time of arrival of the light beam reflected off of the tape created by the light sensor is

detected and recorded. In order to determine the time, the signal can either be sampled at a very

high rate or, preferably, is acquired by a priority interrupt on a clock mechanism or timer such as

a processor clock, which typically operates at hundreds of megahertz. In the latter case, the signal may enter a timing circuit or processor loop that is driven by the high speed clock. Each signal causes a momentary interrupt at which point the time is recorded.

Calculating the velocity has traditionally been accomplished by dividing the known

distance interval between markings (which can be in units of actual distance or expressed as

fractions of a circumference or in degrees) by the known time between the present and previous

pulses. There is a small problem with this approach, namely, the resulting velocity is the value somewhere between the pulses, not at the pulses. Thus, there is a phase shift (delay) in the correspondence between time and velocity. In other words, when the velocity is calculated from

a generated pulse, it should correspond directly to the time of each pulse. The delay is even more

significant at the discontinuity, as described above, at the tape's gap when no overlap is present, and is different from the delay for the regular periodic intervals.

The angular velocity can be plotted against time or phase angle. Fig. 5 represents a graph of velocity versus time reflecting this phase shift. Note the calculated or reconstructed values of velocity is the average velocity measured between two pulses, "o", are between the actual or original values of velocity, "x".

The preferred embodiment of the present invention uses an odd number finite difference

calculus, typically a 3 point finite difference calculus to calculate the angular velocity at the same

point in time as the light pulses occur, and thus avoids all phase shifts as described above. For

regular intervals, the angular velocity is calculated as follows:

* regular intervals V*^* ££

where v is angular velocity, t is time, k is an integer index for the present value, k+1 is the index for the next value, k-1 is the index for the previous value, and H is 2 times the periodic

interval divided by the dimension of the circumference of the shaft. For the time values

described in the formula above, pulses generated by three consecutive markings would be monitored and a time of arrival of each pulse measured. The time value for the first and third

markings would be used to calculate the velocity for the intermediate or second marking. The

circumference is measured by the ruler-like scale 34, (as seen, for instance in Fig. 3), which is a

column present adjacent the regularly spaced markings on the tape, indicating the dimension of

the circumference of the shaft. The above formula is considered a three point formula because it covers a range of three points (k-1, k, and k+1) even though the coefficient on the k term is zero.

To calculate the velocity at the end point of the tape: For the point or marking immediately before the section free of markings at the leading edge of the tape:

before rø = H

For the point immediately after the section free of markings: V after 00 = H

"-' ••(k) ^"*^" 4t(_k + i ) — t_{(k + 2})

Using these formulas, which only requires storing three consecutive time values in RAM or a register at a time, the improvement in correlation between values can be seen in Figs. 6, 7,

and 8. These graphs represent velocity versus time of both "o" and "x", wherein these values are

now aligned at the actual time of arrival of the received pulse by using the above-mentioned

formulas. Fig. 6 represents the calculated and actual values of velocity as a function of ramp,

(i.e., velocity is proportional to the time), v = kt, where k as used here is an arbitrary constant and

t is time. Fig. 7 represents velocity v = Asin(k)t, where A is the amplitude of the sine wave, k is the radian frequency, and t is time. Fig. 8 represents velocity v = e^kl, where k is constant and t is time. The formulas as described above further can be used for any type of angular parameter that

may be monitored.

An average instantaneous angular velocity may also be calculated, where, for instance, a pair of light sources and sensors are positioned opposite each other relative to the tape and

circumference of the shaft. For instance, each pair of a light source and a light sensor would be positioned 180 degrees around the circumference of the shaft from each other. When the

instantaneous angular velocity is calculated as described above, the mean of the angular

velocities from each of the pair of light source/sensor is combined to calculate the average instantaneous angular velocity. The average instantaneous angular velocity will be more

accurate in the presence of transverse shaft vibration because this vibration will make the instantaneous angular velocity at each of the light sensors appear greater on one side and smaller

on the other. There are other finite difference formulas that can be used, but those with an odd number of terms generally have an advantage because these formulas help to establish and maintain the phase relationship between receipt of the reflected beam by the light sensor in view of a time of

arrival. A formula having three terms is preferred because it preserves the instantaneous nature

of the velocity measurement while providing second order accuracy. In other words, the errors are proportional to the square of the independent variable, (in this case, time or degrees).

It is often desirable to convert the velocity data to displacement for direct comparison with slow speed runout and transmission error data. The preferred method to do this is to first interpolate the velocity data to a constant interval basis with respect to the shaft. This can be

done using any standard interpolation technique for unequal interval data such as moving a low order polynomial fit along the data or using a spline function (a smooth piecewise polynomial

function). The polynomial fit is the easiest to implement but the spline gives the best results and

is preferred, although either is acceptable. When the data has been reconstructed in an equal interval format, eliminating the discontinuity formed by the gap where the ends of the tape join,

then the data can be numerically integrated to obtain displacement. Likewise, the equal interval data can be differentiated to give a representation that can be compared to accelerometer data.

The equal interval representation can also be used to calculate the Fast Fourier Transform for

spectral analysis.

The section free of markings 36 at the leading edge 24 on the tape 10 serves as a phase

reference and a once-per-rev indicator. Note that the tape can also be modified to show directionality of the shaft rotation by using a short section between the section free of markings

36 and the periodic interval 28. The preferred phase reference is the beginning of the first periodic interval 28 after the section free of markings 36. In an alternative embodiment, the end of the tape is not overlapped, but a gap is left at the

end between 2 and 3 times the periodic interval. In this case the tape has standard spacing only.

The section free of markings is then a section of the shaft where the two ends of the tape do not

join. This is not a preferred embodiment because the reflectivity of the exposed shaft is uncontrolled and can introduce noise.

The velocity data can easily be represented on an order-related basis by plotting the

velocity data versus a fraction of a revolution, in other words, angular fractions in radians or

degrees. This produces traces or graphs that look somewhat different than their time-related counterparts as can be seen in Figs. 9, 10, and 11. Compare Figs. 6 and 9, 7 and 10, and 8 and 11.

The instantaneous angular velocity, as determined by the apparatus of the present

invention, after representation on an order-related basis as discussed above, may be interpolated

to provide a simulated periodic order-related basis, which may then be integrated to determine the instantaneous angular displacement for direct comparison with slow speed runout measurements. Additionally, the instantaneous angular velocity may be differentiated to

determine the instantaneous angular acceleration for direct comparison with accelerometric data.

Another use of the velocity data created by the apparatus of the present invention includes analyzing the data in the frequency domain in order to better observe oscillatory frequencies.

Applications for the apparatus of the present invention are numerous. When instantaneous angular velocity can be ascertained with certainty, motor torque and efficiency can be calculated using rotor power (I²R) losses based on slip calculated from measured shaft speed, thus aiding in detection of problems within the rotating machinery. Shaft rub in journal bearings is monitored by detecting a momentary slow-down and speed-up of the shaft. In incipient stages the contact occurs sporadically and thus appears as a

subharmonic of running speed. Later, as the rub worsens, impact occurs every revolution and appears as a once-per-rev discrete component.

The present invention is also a valuable tool for analyzing balance in reciprocating

machines. Unbalance in reciprocating engines may be monitored by detecting a different

oscillatory pattern for particular cylinders during the period of their greatest power output. Likewise, unbalance in reciprocating pumps is detected by observing a different oscillatory

pattern for particular cylinders during the period of their greatest load. In yet another alternative embodiment, two diametrically opposed beams and sensors directed at the same strip of tape may be used, and the average of their velocities at interpolated

corresponding times may be ascertained, thereby detecting and countermanding the effect of transverse shaft radial vibration.

Turning to Fig. 4, yet another embodiment of the present invention is illustrated. For

transmission linkages 40, for instance, a gearbox or coupling, between two different shafts 12,

e.g. an input and an output shaft, one or more light sensors 18 may be arranged per shaft to receive a reflected light beam. In the case where more than one light sensor is utilized, the signals may be interpolated to have a common equal interval time base and the instantaneous

angular velocity or a derived function such as displacement is subtracted to detect momentary variations. In other words, the processor 32 may further perform the function of interpolating the instantaneous angular velocity calculations from one of the shafts to create a common time scale; and comparing the signals, e.g. by subtracting, to obtain a measure of transmission error through the linkage between the shafts, whereby anomalous behavior of the transmission linkage may be analyzed..

Weak, cracked, and missing teeth in gear meshes are detected by observing significant

momentary changes in relative velocity between input and output shafts. In the case of flexible

couplings, oscillation is detected by observing variation in the relative velocity between input and output shafts.

From the foregoing description, it can be seen that the present invention comprises an improved method and apparatus for on-line analysis of rotating machines. It will be appreciated

by those skilled in the art that changes could be made to the embodiment described above without departing from the broad inventive concept thereof. It is understood, therefore, that this invention is not limited to the particular embodiment disclosed, but is intended to cover

modification within the spirit and scope of the present invention as defined by the following claims.

Claims

I Claim:

1. An apparatus to measure instantaneous angular velocity of a rotating shaft,

comprising:

(a) a gapless tape disposed around the circumference of the shaft, said tape comprising:

(1) substantially regularly spaced markings defining alternating

reflective and non-reflective areas, wherein the distance between each of said regularly spaced

markings defines a periodic interval;

(2) a section of said tape being free of markings and having a length of at least about two times the periodic interval; and

(3) ruler-type markings adjacent said regularly spaced markings for indicating the circumference of the shaft;

(b) a light source directed at said tape to create a reflected beam from a

reflection of said light source from said tape;

(c) a light sensor positioned to detect the reflected beam from said tape and generate a signal upon detection of said reflected beam; and

(d) a processor for calculating the instantaneous angular velocity of the shaft

from each signal generated by said light sensor in view of a time of arrival of each signal, and for

determining variations in instantaneous angular velocity of the shaft.

2. The apparatus of claim 1, further comprising a timer operably connected to said light sensor and said processor for recording said time of arrival of each signal from said light sensor.

3. The apparatus of claim 1, wherein said processor calculates the instantaneous angular velocity using odd number of point finite difference calculus to calculate the instantaneous angular velocity in alignment in time with said signal from said light sensor.

4. The apparatus of claim 1, wherein said processor calculates the instantaneous angular velocity according to the following equations:

V ^ ^v periodic intervals v^/ ^

(2) v _before (k) =

(3) v _after (k) = H

^"-^( ) 4 (k + 1 ) ^~~ k + 2) where v _before is the angular velocity measured at said marking before said section free of markings, v _after is the angular velocity measured at said marking after said section free of

markings, v _{regular ιnterva}|_S is the angular velocity measured at the periodic interval, t is the time of arrival of each signal generated by said light sensor by said marking, k is an integer index for the

present value, k+1 is the index for the next value, k-1 is the index for the previous value, and H is 2 times the periodic interval divided by the circumference of the shaft.

5. The apparatus of claim 1, wherein said processor further calculates motor torque and efficiency from said variations in shaft speed.

6. The apparatus of claim 1, wherein shaft rub in journal bearings is detected by

momentary slow-down and speed-up of the shaft at a subharmonic and a first harmonic repetition rate of speed.

7. The apparatus of claim 1, wherein unbalance in a reciprocating engine is detected by a different oscillatory pattern for particular cylinders during a period of greatest power output

of the engine.

8. The apparatus of claim 1, wherein unbalance in a reciprocating pump is detected by a different oscillatory pattern for particular cylinders during a period of greatest load on the pump.

9. The apparatus of claim 1, wherein said gapless taped includes a first end and a

second end that is overlapped with said first end to form a gapless joint, and further comprising

an additional piece of tape positioned over the joint formed by the overlap of said ends of said gapless tape to prevent said joint from producing an ambiguous signal at a last marking.

10. An apparatus to measure instantaneous angular velocity and detect transverse

shaft vibration of a rotating shaft, the apparatus comprising:

(a) a tape disposed around the circumference of the shaft, said tape

comprising: (1) a first end and a second end overlapped with said first end to form

a gapless joint;

(2) substantially regularly spaced markings defining alternating

markings defines a periodic interval; (3) a section at said second end of said tape being free of markings and

having a length of at least about two times the periodic interval; and

(4) ruler-type markings adjacent said regularly spaced markings for

indicating the circumference of the shaft; (b) at least two light sources positioned on opposite sides of the shaft, said light sources directed at said tape to create a reflected beam from a reflection of each of said light

sources from said tape;

(c) at least two light sensors positioned to detect each of said reflected beams

from said tape and generate a signal upon detection of said reflected beams; and

(d) a processor for calculating the instantaneous angular velocity of the shaft from each signal generated by said light sensors in view of a detected time of arrival of each signal, and determining variations in the instantaneous angular velocity, said processor further

calculating an average instantaneous angular velocity from a mean value of said instantaneous angular velocities from each of said light sensors.

11. An apparatus to measure the instantaneous angular velocity difference between two rotating shafts connected by a transmission linkage, comprising:

(a) a reflective tape disposed around the circumference of each of the shafts,

said tape comprising:

(1) substantially regularly spaced markings defining alternating

reflective and non-reflective areas, wherein the distance between each of said regularly spaced markings defines a periodic interval;

(2) a section along said tape being free of markings and having a length of at least about two times the periodic interval; and

(b) a light source directed at each of said tapes to create a reflected beam from a reflection of light from each tape applied to each shaft; (c) a light sensor positioned to detect the reflected beam from each of said tapes and generate a signal upon detection of said reflected beam; and

(d) a processor for calculating the instantaneous angular velocity of each of the shafts from each signal generated by said light sensor in view of a time of arrival of each

signal, and determining variations in shaft speed from the instantaneous angular velocity

calculations.

12. The apparatus of claim 11, further comprising at least one timer operably connected to said light sensors and said processor for recording the time of arrival of each signal from said light sensors.

13. The apparatus of claim 11, wherein said processor calculates the instantaneous

angular velocity using odd number of point finite difference calculus to calculate the

instantaneous angular velocity in alignment in time with said signals from said light sensors.

14. The apparatus of claim 13, wherein said processor further performs the functions of:

(a) interpolating the instantaneous angular velocity calculations from one of

the shafts to create a common time scale; and

(b) comparing each of said signals to obtain a measure of transmission error

through the transmission linkage between the shafts.

15. The apparatus of claim 11, and wherein weak, cracked, and missing teeth in gear meshes are detected by significant momentary changes in relative instantaneous angular velocity between the shafts.

16. The apparatus of claim 11, and wherein coupling oscillation is detected by oscillation in the relative instantaneous angular velocity between the shafts.

17. A method to measure instantaneous angular velocity of a rotating shaft, including

variations in the instantaneous angular velocity, comprising the steps of:

(a) disposing a tape around the circumference of the shaft, said tape

comprising:

(1) substantially regularly spaced markings defining alternating reflective and non-reflective areas, wherein the distance between each of said regularly spaced

markings defines a periodic interval; (2) a section of said tape being free of markings and having a length of

at least about two times the periodic interval; and

(3) ruler-type markings adjacent said regularly spaced markings for indicating the circumference of said shaft;

(b) directing light at said tape to create a discontinuous reflected beam from a

reflection from said tape;

(c) detecting and recording discontinuities of said reflected beam;

(d) detecting and recording a time of arrival of each of said discontinuities of said reflected beam; and

(e) calculating the instantaneous angular velocity of the shaft from each of said discontinuities in view of the time of arrival of each discontinuity and determining

variations in instantaneous angular velocity .

18. The method of claim 17, and further comprising the steps of: (a) positioning a light sensor to detect the reflected beam from said tape and generating a signal; and wherein the steps of detecting and recording the time of arrival of each of said discontinuities and calculating instantaneous angular velocity are performed by a

processor.

19. The method of claim 18, and further wherein the step of detecting and recording the time of arrival of each of said discontinuous reflected beam is performed by a timer.

20. The method of claim 18, further comprising the step of applying said tape while

the shaft is rotating.

21. A method to measure instantaneous angular velocity of a rotating shaft, including

variations in the instantaneous angular velocity, comprising the steps of:

(a) disposing a tape at least partially around a shaft; and

(b) directing light at said tape.