Integer ratiometric analysis of rotating assets

Abstract

A computer-executable ratiometric analysis method determines integer components of a rational number ratio or a close approximation of an irrational number ratio. In one embodiment the method uses a ratio of rotational speeds of two rotating assets in a machine or process, generates a new rational number based on the ratio of speeds, and calculates the integer components of the new rational number. The result is the integer ratio relationship between the initial two rational numbers. The method may be used in machinery analysis applications to determine whether a low-order integer ratio relationship exists between two machinery rotating components. Low-order integer ratio relationships in machinery are generally harmful in related machinery rotating components, and detection of such relationships is an important tool in preventing damage to machinery components. In a more general embodiment the algorithm can be used to determine the closest integer roots of any fractional number where this information would be of interest to an analyst in understanding the fractional number.

Claims

1. A computer-implemented method for calculating an integer ratio that expresses a relationship between rotational speeds of two rotating assets in a machine or process, the method comprising: (a) acquiring a value S.sub.1 indicating a rotational speed of a first asset of the two rotating assets; (b) acquiring a value S.sub.2 indicating a rotational speed of a second asset of the two rotating assets; (c) determining a speed ratio R according to $R=\frac{S_1}{S_2};$ (d) creating in computer memory a first array having X.sub.1 number of array positions; (e) creating in computer memory a second array having X.sub.2 number of array positions; (f) generating a first scalar value Y.sub.1 according to
Y.sub.1=RX.sub.1; (g) generating a second scalar value Y.sub.2 according to $Y_2=\frac{X_2}{R};$ (h) averaging the first scalar value Y.sub.1 into the first array N.sub.1 number of times, each time adding a value of one to any array position in the first array at which the first scalar value Y.sub.1 terminates, according to
new value of V.sub.1=old value of V.sub.1+1; (i) averaging the second scalar value Y.sub.2 into the second array N.sub.2 number of times, each time adding a value of one to any array position in the second array at which the second scalar value Y.sub.2 terminates, according to
new value of V.sub.2=old value of V.sub.2+1; (j) determining an integer value A as being a number of array positions in the first array having a value of V.sub.1 for which $\frac{V_1}{N_1}$ is greater than $\frac{1}{N_1};$ (k) determining an integer value B as being a number of array positions in the second array having a value of V.sub.2 for which $\frac{V_2}{N_2}$ is greater than $\frac{1}{N_2};$ and (l) adjusting one or more of the rotational speed of the first asset and the rotational speed of the second asset to relieve a potentially harmful ratiometric condition if a ratio of A and B indicates that such a condition exists in the machine or process.

2. The method of claim 1 wherein an intensity of A is defined as $I_1=\frac{V_1}{N_1}$ and an intensity of B is defined as $I_2=\frac{V_2}{N_2}.$

3. The method of claim 2 further comprising generating an alert message if A and B are non-zero and the intensity I.sub.1 or the intensity I.sub.2 is more than a predetermined threshold value.

4. The method of claim 3 wherein the alert message comprises one or more of a message or indicator displayed on a display device, an email message, a text message, and a warning light.

5. The method of claim 1 wherein at least steps (a) through (k) of the method are repeated continuously to detect rotational speed relationships that are potentially detrimental to the machine or process.

6. The method of claim 1 further comprising displaying the ratio R of A and B on a display device.

7. The method of claim 1, wherein if A or B are zero, the method further comprises increasing one or more of X.sub.1 and X.sub.2 and repeating steps (d) through (k).

8. The method of claim 1, wherein if A or B are zero, the method further comprises increasing one or more of N.sub.1 and N.sub.2 and repeating steps (h) through (k).

9. The method of claim 1 further comprising: (m) displaying on a display device a list of rotating assets in the machine or process; and (n) input from an input device to select the two rotating assets from the list of rotating assets, wherein steps (a) through (l) are performed for the two rotating assets selected in step (m).

10. The method of claim 1 wherein step (h) comprises wrapping the first scalar value Y.sub.1 around the first array N.sub.1 number of times; and step (i) comprises wrapping the second scalar value Y.sub.2 around the second array N.sub.2 number of times.

11. The method of claim 1 wherein N.sub.1=N.sub.2.

12. The method of claim 1 wherein X.sub.1=X.sub.2.

13. The method of claim 1 further comprising repeating at least steps (b) through (l) multiple times, wherein each time the steps are repeated the second asset is one of the rotating assets having a rotational speed that has not previously been compared to the rotational speed of the first asset.

14. The method of claim 13 further comprising repeating at least steps (b) through (l) until the rotational speed of the first asset has been compared to the rotational speeds of all the other rotating assets.

15. A computer-implemented method for calculating a ratio of integer numbers that expresses a relationship between rotational speeds of rotating assets in a machine or process, the method comprising: (a) displaying on a display device a list of rotating assets in the machine or process; (b) receiving input from an input device to select two of the rotating assets from the list of rotating assets; acquiring a value S.sub.1 indicating a rotational speed of a first asset of the two rotating assets selected in step (b); (d) acquiring a value S.sub.2 indicating a rotational speed of a second asset of the two rotating assets selected in step (b); (e) determining a speed ratio R according to: $R=\frac{S_1}{S_2};$ (f) creating in computer memory a first array having X.sub.1 number of array positions; (g) creating in computer memory a second array having X.sub.2 number of array positions; (h) generating a first scalar value Y.sub.1 according to
Y.sub.1=RX.sub.1; (i) generating a second scalar value Y.sub.2 according to $Y_2=\frac{X_2}{R};$ (j) averaging the first scalar value Y.sub.1 into the first array N.sub.1 number of times, each time adding a value of one to any array position in the first array at which the first scalar value Y.sub.1 terminates, according to
new value of V.sub.1=old value of V.sub.1+1; (k) averaging the second scalar value Y.sub.2 into the second array N.sub.2 number of times, each time adding a value of one to any array position in the second array at which the second scalar value Y.sub.2 terminates, according to
new value of V.sub.2=old value of V.sub.2+1; (l) determining an integer value A as being a number of array positions in the first array having a value of V.sub.1 for which $\frac{V_1}{N_1}$ is greater than $\frac{1}{N_1};$ (m) determining an integer value B as being a number of array positions in the second array having a value of V.sub.2 for which $\frac{V_2}{N_2}$ is greater than $\frac{1}{N_2};$ and (n) repeating at least steps (c) through (m) continuously to detect rotational speed relationships that are potentially detrimental to the machine or process.

16. The method of claim 15 further comprising automatically generating a control system output to adjust one or more of the rotational speed of the faster asset and the rotational speed of the slower asset to relieve a potentially harmful ratiometric condition if A and B are non-zero and $\frac{V_1}{N_1}\mathrm{or}\frac{V_2}{N_2}$ is more than the predetermined threshold value.

17. An apparatus for calculating a ratio of integer numbers that expresses a relationship between rotational speeds of two rotating assets in a machine or process, the apparatus comprising: means for acquiring a value S.sub.F indicating a rotational speed of a faster asset of the two rotating assets; means for acquiring a value S.sub.S indicating a rotational speed of a slower asset of the two rotating assets; means for determining a speed ratio R according to: $R=\frac{S_S}{S_F};$ means for creating in computer memory a first array having X.sub.1 number of array positions; means for creating in computer memory a second array having X.sub.2 number of array positions; means for generating a first scalar value Y.sub.1 according to
Y.sub.1=RX.sub.1; means for generating a second scalar value Y.sub.2 according to $Y_2=\frac{X_2}{R};$ means for averaging the first scalar value Y.sub.1 into the first array N.sub.1 number of times, each time adding a value of one to any array position in the first array at which the first scalar value Y.sub.1 terminates, according to
new value of V.sub.1=old value of V.sub.1+1; means for averaging the second scalar value Y.sub.2 into the second array N.sub.2 number of times, each time adding a value of one to any array position in the second array at which the second scalar value Y.sub.2 terminates, according to
new value of V.sub.2=old value of V.sub.2+1; means for determining a number A which is a number of array positions in the first array having a value of V.sub.1 for which $\frac{V_1}{N_1}$ is greater than $\frac{1}{N_1};$ means for determining a number B which is a number of array positions in the second array having a value of V.sub.2 for which $\frac{V_2}{N_2}$ is greater than $\frac{1}{N_2};$ and means for generating a control system output to adjust one or more of the rotational speed of the faster asset and the rotational speed of the slower asset to relieve a potentially harmful ratiometric condition if one or more of A, B and R indicate that such a condition exists in the machine or process.

18. A computer-implemented method for controlling a machine or process based at least in part on an integer relationship between two numbers S.sub.1 and S.sub.2 that indicate an operational relationship between at least two components of the machine or process, the method comprising: (a) determining a ratio R according to: $R=\frac{S_1}{S_2};$ (b) creating in computer memory a first array having X.sub.1 number of array positions; (e) creating in computer memory a second array having X.sub.2 number of array positions; (d) generating a first scalar value Y.sub.1 according to
Y.sub.1=RX.sub.1; (e) generating a second scalar value Y.sub.2 according to $Y_2=\frac{X_2}{R};$ (f) averaging the first scalar value Y.sub.1 into the first array N.sub.1 number of times, each time adding a value of one to any array position in the first array at which the first scalar value Y.sub.1 terminates, according to
new value of V.sub.1=old value of V.sub.1+1; (g) averaging the second scalar value Y.sub.2 into the second array N.sub.2 number of times, each time adding a value of one to any array position in the second array at which the second scalar value Y.sub.2 terminates, according to
new value of V.sub.2=old value of V.sub.2+1; (h) determining an integer value A as being a number of array positions in the first array having a value of V.sub.1 for which $\frac{V_1}{N_1}$ is greater than $\frac{1}{N_1};$ (i) determining an integer value B as being a number of array positions in the second array having a value of V.sub.2 for which $\frac{V_2}{N_2}$ is greater than $\frac{1}{N_2};$ and (j) generating a control system output to adjust the operational relationship between the at least two components of the machine or process to relieve a potentially harmful ratiometric condition if one or more of A, B and R indicate that such a condition exists, where $R\frac{A}{B}.$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other embodiments of the invention will become apparent by reference to the detailed description in conjunction with the figures, wherein elements are not to scale so as to more clearly show the details, wherein like reference numbers indicate like elements throughout the several views, and wherein:

(2) FIG. 1 depicts components of a paper processing machine;

(3) FIG. 2 depicts steps of a method for calculating integer ratiometric speeds of two rotating assets in a machine or production process according to a preferred embodiment;

(4) FIG. 3 is a graphic depiction of an exemplary application of the method of FIG. 2 according to a preferred embodiment;

(5) FIG. 4 is another graphic depiction of an exemplary application of the method of FIG. 2 according to a preferred embodiment; and

(6) FIGS. 5 and 6 depict a possible user interface screen of a display device according to a preferred embodiment.

DETAILED DESCRIPTION

(7) An example of the operation of a preferred embodiment of the invention will be described as applied to the monitoring of rotating components in a paper processing machine as depicted in FIG. 1. In this example, a lumpbreaker roll having a diameter of 34.063 inches and rotating at 3.78 Hz (referred to herein as the faster asset) is nipped to a couch roll having a diameter of 54.030 inches and rotating at 2.52 Hz (referred to herein as the slower asset). Although the diameter ratio for these components (0.63045) does not result in a ratiometric problem, the simple speed ratio is 0.6666, which is about 2:3. As depicted in the zoomed view of the couch roll and the lumpbreaker roll in FIG. 1, this speed relationship results in two locations on the lumpbreaker roll repeatedly contacting three locations on the couch roll. This situation can result in serious barring vibration problems as discussed at length in the Background section.

(8) Although the example of the lumpbreaker roll and couch roll applies to two components that are in contact with each other, it should be appreciated that the methods described herein could be applied to components that are widely separated in a process or machine. In this case, despite a process time delay between their positions, their ratio relationship can be accurately calculated in a steady speed process.

(9) FIG. 2 depicts an embodiment of a computer-executable method for calculating an integer ratio of speeds of two rotating assets in a production process or machine. First, the rotational speeds of the two rotating assets are acquired simultaneously, such as using magnetic or optical tachometers or speeds provided by a control system (step 10). These can be instantaneous values rather than a stream of tachometer pulses. In some embodiments, this may involve monitoring speeds of every relevant rotating asset within a process or machine, and selecting speeds of two of the assets to be compared. In the present example, the speed of the faster asset, S.sub.F, is 3.78 Hz and the speed of the slower asset, S.sub.S, is 2.52 Hz. The speed values are provided to a microprocessor of a process monitoring computer. The microprocessor calculates the simple speed ratio R as:

(10) $\begin{array}{cc}R=\frac{S_S}{S_F}=\frac{2.52}{3.78}=0.6666\mathrm{.Math.}.& \left(\mathrm{step}12\right)\end{array}$
This and other steps in the process are preferably performed by the microprocessor based on computer executable instructions loaded into the memory of the computer.

(11) Two arrays are created in memory accessible to the microprocessor. A first array is created having X.sub.1 number of array positions, such as X.sub.1=1024 (step 14). This first array represents the virtual circumference of the slower asset, A first scalar value Y.sub.1 is created (step 15) where
Y.sub.1=X.sub.1R=10240.6666 . . . =682.6666 . . .
This first scalar value Y.sub.1 represents the virtual circumference (682.666 . . . ) of the faster asset. Next, the second array is created having X.sub.2 number of array positions (step 16), such as X.sub.2=1024, and a second scalar value Y.sub.2 is created (step 17) where

(12) $Y_2=\frac{X_2}{R}=\frac{1024}{0.6666\mathrm{.Math.}}=1536.$
This second scalar value Y.sub.2 represents the virtual circumference (1536) of the slower asset.

(13) The first scalar value Y.sub.1 is synchronously averaged into the first array over N.sub.1 number of rotations of the faster asset (step 18). Essentially, the first scalar value (682.66) is wrapped around the first array (1024), as if the first array was a closed loop of samples. At each array position in the first array at which the first scalar value terminates, a value of one is added (new value V.sub.1=old value V.sub.1+1). For values of N.sub.1 greater than one, the subsequent wrappings of the first scalar value begin again at the fractional position where the previous wrap terminated. This process is performed N.sub.1 times. At the completion of this step, there may be several positions in the first array having values greater than one, meaning that the wrapping of the first scalar value ended at those positions more than one time. A count is then made of the number (A) of array positions in which the intensity I.sub.1 of A is greater than

(14) $\frac{1}{N_1},$
where

(15) 0$I_1=\frac{V_1}{N_1}$
(step 20).

(16) The second scalar value Y.sub.2 is synchronously averaged into the second array over N.sub.2 number of rotations of the slower asset (step 22). This involves wrapping the second scalar value (1536) around the second array (1024), as if the second array was a closed loop of samples. At each array position in the second array at which the second scalar value terminates, a value of one is added (new value V.sub.2=old value V.sub.2+1). For values of N.sub.2 greater than one, the subsequent wrappings of the second scalar value begin again at the fractional position where the previous wrap terminated. This process is performed N.sub.2 times. At the completion of this step, there may be several positions in the second array having values greater than one, meaning that the wrapping of the second scalar value ended at those positions more than one time. A count is then made of the number (B) of array positions in which the intensity I.sub.2 of B is greater than

(17) $\frac{1}{N_2},$
where

(18) $I_2=\frac{V_2}{N_2}$
(step 24).

(19) In preferred embodiments, N.sub.1=N.sub.2. However, it is not necessary that N.sub.1=N.sub.2, and the invention is not limited to any particular relationship between N.sub.1 and N.sub.2.

(20) If both A and B are both non-zero (step 26), the speed ratio of the faster asset to the slower asset is expressed as A to B (step 28). If A and B are both non-zero and the intensity I.sub.1 of A or the intensity I.sub.2 of B or both are more than some predetermined threshold, for example larger than 1% (step 30), then a significant ratio match has been detected. In this situation, an alert message may be generated (step 32). In various embodiments, the alert message may comprise a warning indicator or message displayed on an operator's computer display, an email or text message sent to appropriate personnel, a warning light on a control panel, or all of the above. The predetermined intensity threshold of step 30 is preferably programmable, and its value is determined based on the particular process/machine being monitored and the particular components within the process/machine that are being compared. In preferred embodiments, the threshold is based on the intensity of A and/or B, where the intensity is the value of each position divided by the number of averages. Intensity is a value from 0 to 1 and is preferably expressed as a percentage.

(21) In preferred embodiments, when a ratio match is detected, actions are suggested from which an operator may choose to address the situation. These optional actions may be listed on a computer display device as discussed in more detail hereinafter. Preferably, each action introduces some incremental change in the operation of the machine or process that will break up the detrimental ratiometric relationship. For example, (1) in systems that provide for speed adjustment, the rotational speed of one or both of the assets in the ratio may be slightly increased or decreased, (2) in a roll press, nip pressures may be changed slightly, (3) felt stretch may be changed slightly, (4) valve openings may be adjusted (since a change in load can slightly change speed), and (5) the physical diameter of components may be slightly changed, such as by grinding.

(22) With continued reference to FIG. 2, if A or B or both are zero (step 26), then either there is no integer ratiometric relationship between the speeds of the two assets, or a very high integer relationship exists and more averages or a larger array will be needed to calculate it. Preferred embodiments of the method provide for automatic adjustments of the calculation such as resampling using a larger value of X (more samples in the two arrayssteps 34 and 36) or increasing the number of averages (larger values of N.sub.1 or N.sub.2steps 40 and 42) or both.

(23) FIG. 3 depicts a graphical representation of the wrapping of the two scalar values Y.sub.1 and Y.sub.2 around the two arrays over six sampling periods (N.sub.1=N.sub.2=6). This depiction corresponds to the example described above with reference to FIG. 2 (R=0.666 . . . , X.sub.1=X.sub.2=1024, Y.sub.1=682.666 . . . , Y.sub.2=1536). As shown in the upper right portion of FIG. 3, after the sixth sampling period, there are three positions in the first array having values of two (positions 342, 683 and 1024). Thus, there are three positions in the first array having values of greater than 1/N.sub.1 (1/6), indicating that A=3. As shown in the lower right portion of FIG. 3, after the sixth sampling period, there are two positions in the second array having values of three (positions 512 and 1024). Thus, there are two positions in the second array having values of greater than 1/N.sub.2 (1/6), indicating that B=3.

(24) FIG. 4 depicts another way to visualize the sampling process for the example described above.

(25) Preferred embodiments of a ratiometric analyzer application may generate a user interface screen 100 such as shown in FIG. 5. The interface screen preferably includes an Asset column 102 that lists the rotating assets in a machine or process and a Speed column 104 listing the rotational speeds of the assets. If the rotational speed of any asset is related to the rotational speed of another asset by an integer ratio, and the intensity of the integer ratio is more than the predetermined threshold, then the speeds of those two assets are deemed to match each other. In this situation, the matching assets are listed in the Match column 106 and their speed ratio is listed in the ratio column 108. An intensity column 110 indicates how significant the ratio matching is based on the repeat rate of the impact per rotation. For example an intensity of 0.5 or 50% means that the same spots match together every 2 rotations. A Delay S column 112 indicates the last time a speed measurement was updated. If a speed is not updating then the calculations based on that speed would be unreliable.

(26) As shown in FIG. 6, if a user clicks on any of the assets in the Asset column 102, a dialog box 114 appears showing the asset speed and a divisor. A devisor would be needed for speed encoder output, for example if an encoder generated 100 pulses per rotation then a devisor of 100 would have to be used to get to its basic rotational speed. If the user clicks on the Actions button 116 in the dialog box 114. an Actions dialog box 118 is displayed. This box lists one or more actions 120 that could affect the rotational speed of the selected asset, thereby affecting the ratio of the selected asset speed to the speed of other assets in the system. For example, for the Filler Fan Pump asset, the user has the options of directly adjusting the speed of the pump motor by0.01 Hz, adjusting the setting of the discharge valve of the pump, and adjusting the setting of the inlet valve of the pump. In embodiments wherein this application resides within a DCS or other control system or device, the adjustments to relieve a harmful ratiometric condition could be done automatically within defined criteria.

(27) The foregoing description of preferred embodiments for this invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise form disclosed. Obvious modifications or variations are possible in light of the above teachings. The embodiments are chosen and described in an effort to provide the best illustrations of the principles of the invention and its practical application, and to thereby enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the invention as determined by the appended claims when interpreted in accordance with the breadth to which they are fairly, legally, and equitably entitled.