A method for detecting and locating insulation failures in aircraft motors
By wrapping a semiconductor layer around the copper conductor in the stator slot of an aircraft motor and setting up an insulation failure detection circuit with a resistive-inductive branch network, the problem of not being able to accurately locate the location of winding insulation failure in the prior art is solved, achieving the effects of accurate location and cost saving.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-20
- Publication Date
- 2026-04-03
AI Technical Summary
Existing technology cannot accurately locate the specific location of insulation failure in aircraft motor windings, which necessitates replacing the entire insulation layer and increases maintenance costs.
A semiconductor layer is wrapped around the copper conductor in each stator slot of the aircraft motor, and a resistive-inductive branch network is set up in the semiconductor layer to form an insulation failure detection circuit. The circuit is powered by an external power supply and the non-ground voltage of the insulation failure detection circuit is judged to accurately locate the insulation failure location.
It enables precise location of windings with insulation failure, reducing maintenance costs by requiring only partial insulation replacement, thus saving on repair expenses.
Smart Images

Figure CN116593833B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of motor failure detection and location, and more specifically, to a method for detecting and locating insulation failures in aircraft motors. Background Technology
[0002] The stator of an aircraft motor typically contains multiple windings. Insulation failure of the windings is one of the main causes of stator failure. After insulation failure in each winding, the winding is very prone to inter-turn short circuits, which can lead to various faults.
[0003] One approach to detect insulation failure in windings is to wrap a semiconductor layer around the cable's insulation layer. When the motor is operating normally, there is no potential difference in the semiconductor layer, and no voltage is generated. However, when an insulation failure occurs in a winding, the insulation layer is broken down, and the conductor inside the cable connects with the semiconductor layer, thereby generating a potential difference and voltage in the semiconductor layer. By detecting whether there is voltage or potential difference, it is possible to detect whether the winding has experienced insulation failure.
[0004] However, the above-mentioned methods for detecting winding insulation failure can only detect whether there is a winding insulation failure. Since there are multiple windings in the stator, it is impossible to determine the winding with insulation failure and the specific location of the insulation failure in the insulation layer by simply detecting voltage or potential difference. This leads to the need to replace the entire insulation layer, which greatly increases maintenance costs. Summary of the Invention
[0005] The problem this invention aims to solve is to provide a method for detecting and locating insulation failures in aircraft motors, which can accurately determine the specific location of the insulation failure in the winding and insulation layer without replacing the entire insulation layer, thus greatly reducing maintenance costs.
[0006] To address the above problems, this invention provides a method for detecting and locating insulation failures in aircraft motors, comprising:
[0007] Step S1: For each stator slot in the aircraft motor, a semiconductor layer is wrapped around the insulating layer surface outside each copper conductor in the stator slot.
[0008] Step S2: For each semiconductor layer, multiple regions are divided on the semiconductor layer, and a resistive inductive branch network is set in each region. The resistive inductive branch networks are connected to form an insulation failure detection circuit.
[0009] Step S3: Power the three-phase windings of the aircraft motor with an external power source;
[0010] Step S4: Determine whether there is a non-ground voltage at the four terminal corners of the insulation failure detection circuit.
[0011] If not, return to step S3 to continue supplying power to the three-phase winding;
[0012] If so, the output indicates the presence of insulation failure, and the location and potential difference of the insulation failure where the potential changes in the insulation failure detection circuit are collected as the location result and output.
[0013] In this solution, after the semiconductor layer is wrapped, the insulation failure detection circuit is deployed on the semiconductor layer. When the aircraft motor is working normally, the insulation layer does not fail, and the insulation failure detection circuit has no input voltage. When the insulation layer of any of the windings fails, the input voltage of the power supply circuit surges into the insulation failure detection circuit. The insulation failure detection circuit obtains the precise location of the insulation failure based on the input voltage, providing location guidance for subsequent maintenance. This allows maintenance to be performed by replacing only a portion of the insulation layer, rather than replacing the entire insulation layer, greatly reducing maintenance costs.
[0014] Preferably, in step S1, the semiconductor layer, which unfolds into a square shape, is wrapped around the surface of the insulating layer, and a notch is left on the semiconductor layer as a voltage monitoring point for monitoring the voltage.
[0015] In this solution, the detection of whether an insulation failure has occurred can also be achieved through the voltage monitoring point set on the semiconductor layer. If the voltage monitoring point has a voltage to ground, it means that an insulation failure has occurred; otherwise, no insulation failure has occurred, which can further verify the accuracy of the insulation failure.
[0016] Preferably, the procedure further includes the following steps before performing step S4:
[0017] Determine whether there is voltage at the voltage monitoring point:
[0018] If so, the detection result indicating the presence of insulation failure is output, and the process proceeds to step S4;
[0019] If not, return to step S3 to continue supplying power to the three-phase winding.
[0020] In this scheme, the voltage monitoring point's judgment of voltage is used as a prerequisite judgment for step S4. Only when there is voltage at the voltage monitoring point will the process lead to step S4 to locate the insulation failure location. When there is no voltage at the voltage monitoring point, it means that there is no input voltage in the insulation failure detection circuit. Therefore, the process returns directly to continue power supply, thereby saving steps and improving the analysis speed.
[0021] Preferably, in step S2, the semiconductor layer is divided into multiple regions, and the semiconductor electrical parameters of each region are equivalently set as inductance and resistance. The equivalent inductors and resistors are connected end to end according to the position of each region to form the inductor-resistance branch network corresponding to the semiconductor layer.
[0022] Preferably, the insulation failure detection circuit includes:
[0023] A first resistor, one end of which is grounded;
[0024] A first inductor, one end of which is connected to the other end of the first resistor;
[0025] A second resistor, one end of which is connected to the other end of the first inductor;
[0026] A second inductor, one end of which is connected to the other end of the second resistor;
[0027] A third inductor, one end of which is connected to one end of the first resistor;
[0028] A third resistor, one end of which is connected to the other end of the third inductor;
[0029] A fourth inductor, one end of which is connected to the other end of the first inductor and one end of the second resistor;
[0030] A fourth resistor, one end of which is connected to the other end of the fourth inductor;
[0031] A fifth inductor, one end of which is connected to the other end of the second inductor;
[0032] A fifth resistor, one end of which is connected to the other end of the fifth inductor;
[0033] A sixth resistor, one end of which is connected to the other end of the third resistor;
[0034] A sixth inductor, one end of which is connected to the other end of the sixth resistor, and the other end of which is connected to the other end of the fourth resistor;
[0035] A seventh resistor, one end of which is connected to the other end of the sixth inductor and the other end of the fourth resistor;
[0036] A seventh inductor, one end of which is connected to the other end of the seventh resistor, and the other end of which is connected to the other end of the fifth resistor;
[0037] An eighth inductor, one end of which is connected to the other end of the third resistor and one end of the sixth resistor;
[0038] An eighth resistor, one end of which is connected to the other end of the eighth inductor, and the other end of which is grounded;
[0039] A ninth inductor, one end of which is connected to the other end of the sixth inductor and one end of the seventh resistor;
[0040] A ninth resistor, one end of which is connected to the other end of the ninth inductor;
[0041] A tenth inductor, one end of which is connected to the other end of the seventh inductor and the other end of the fifth resistor;
[0042] A tenth resistor, one end of which is connected to the other end of the tenth inductor;
[0043] An eleventh resistor, one end of which is connected to the other end of the eighth resistor;
[0044] An eleventh inductor, one end of which is connected to the other end of the eleventh resistor, and the other end of which is connected to the other end of the ninth resistor;
[0045] A twelfth resistor, one end of which is connected to the other end of the eleventh inductor and the other end of the ninth resistor;
[0046] A twelfth inductor, one end of which is connected to the other end of the twelfth resistor, and the other end of which is connected to the other end of the tenth resistor.
[0047] Preferably, the power supply circuit includes:
[0048] An H-bridge control unit, wherein the input terminal of the H-bridge control unit is connected to an external power supply;
[0049] A thirteenth resistor, one end of which is connected to the output terminal of the H-bridge control unit;
[0050] A thirteenth inductor, one end of which is connected to the other end of the thirteenth resistor, and the other end of which is connected to the first winding of the aircraft motor;
[0051] A fourteenth resistor, one end of which is connected to the output terminal of the H-bridge control unit;
[0052] A fourteenth inductor, one end of which is connected to the other end of the fourteenth resistor, and the other end of which is connected to the second winding of the aircraft motor;
[0053] A fifteenth resistor, one end of which is connected to the output terminal of the H-bridge control unit;
[0054] A fifteenth inductor, one end of which is connected to the other end of the fifteenth resistor, and the other end of which is connected to the third winding of the aircraft motor.
[0055] Preferably, in step S4, the point voltages at the four opposite corners of the fault point equipotential line are detected respectively, and the corresponding voltage drop ratios are obtained by processing the four point voltages in pairs. The corresponding insulation failure location is obtained by comparing each voltage drop ratio with a pre-configured fault point ratio table.
[0056] In this scheme, considering that the three voltage drop ratios calculated from the four diagonal points of the fault point equipotential line at each insulation failure location are unique and different, the specific location of the insulation failure location can be accurately obtained simply by comparing the voltage drop ratio with the fault point ratio. Attached Figure Description
[0057] Figure 1 This is a flowchart of the steps of the present invention;
[0058] Figure 2 This is a schematic diagram of the stator slot of the aircraft motor of the present invention;
[0059] Figure 3 This is an axial unfolded view of the semiconductor layer of the present invention;
[0060] Figure 4 This is a schematic diagram showing the location of the insulation failure detection circuit of the present invention;
[0061] Figure 5 This is a circuit structure diagram of the insulation failure detection circuit of the present invention;
[0062] Figure 6 This is a circuit diagram of the power supply circuit for the aircraft motor of the present invention;
[0063] Explanation of reference numerals in the attached diagram: 1. Stator slot; 2. Copper conductor; 3. Insulating layer; 4. Semiconductor layer; 5. H-bridge control unit. Detailed Implementation
[0064] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0065] In a preferred embodiment of the present invention, based on the above-mentioned problems existing in the prior art, a method for detecting and locating insulation failures in aircraft motors is provided, such as... Figure 1-4 As shown, it includes:
[0066] Step S1: For each stator slot 1 in the aircraft motor, a semiconductor layer 4 is wrapped around the surface of the insulating layer 3 outside each copper conductor 2 in the stator slot 1.
[0067] Step S2: For each semiconductor layer 4, multiple regions are divided on the semiconductor layer 4, and a resistive inductive branch network is set in each region. The resistive inductive branch networks are connected to form an insulation failure detection circuit.
[0068] Step S3: Power the three-phase windings of the aircraft motor with an external power source;
[0069] Step S4: Determine whether there is a non-ground voltage at the four terminals of the insulation failure detection circuit.
[0070] If not, return to step S3 to continue supplying power to the three-phase windings;
[0071] If so, the output will indicate the presence of insulation failure, and the location and potential difference of the insulation failure where the potential changes in the insulation failure detection circuit will be collected as the location result and output.
[0072] Specifically, in this embodiment, after the semiconductor layer 4 is wrapped, an insulation failure detection circuit is deployed on the semiconductor layer 4. When the aircraft motor is working normally, the insulation layer 3 does not experience insulation failure, and the insulation failure detection circuit has no input voltage. When the insulation layer 3 of any winding experiences insulation failure, the input voltage of the power supply circuit surges into the insulation failure detection circuit. The insulation failure detection circuit obtains the precise location of the insulation failure based on the input voltage, providing location guidance for subsequent maintenance. This allows for the replacement of only a portion of the insulation layer 3 during maintenance, rather than replacing the entire insulation layer 3, greatly reducing maintenance costs.
[0073] Preferably, the insulation failure detection circuit covers the entire semiconductor layer 4, and the semiconductor layer 4 covers the entire insulation layer 3, so that if an insulation failure occurs at any point on the insulation layer 3, the input voltage of the power supply circuit can be used for the semiconductor layer 4, thereby achieving full coverage detection of the insulation failure location on the insulation layer 3.
[0074] Preferably, the semiconductor layer 4 can be a thin foil rolled around the insulating layer 3.
[0075] In a preferred embodiment of the present invention, in step S1, a square semiconductor layer 4 is wrapped around the surface of the insulating layer 3, and a notch is left on the semiconductor layer 4 as a voltage monitoring point for monitoring voltage.
[0076] Specifically, in this embodiment, the detection of whether an insulation failure has occurred can also be achieved through a voltage monitoring point set on the semiconductor layer 4. If there is a voltage to ground at the voltage monitoring point, it means that an insulation failure has occurred; otherwise, no insulation failure has occurred, which can further verify the accuracy of the insulation failure.
[0077] Preferably, the voltage monitoring point is attached. Figure 2 and attached Figure 3 The circled area in the diagram.
[0078] In a preferred embodiment of the present invention, the method further includes the following steps before performing step S4:
[0079] Determine if there is voltage at the voltage monitoring point:
[0080] If so, output the detection result indicating the presence of insulation failure and proceed to step S4;
[0081] If not, return to step S3 to continue supplying power to the three-phase windings.
[0082] Specifically, in this embodiment, the judgment of voltage at the voltage monitoring point is used as a prerequisite judgment for step S4. Only when there is voltage at the voltage monitoring point will it lead to step S4 to locate the insulation failure location. When there is no voltage at the voltage monitoring point, it means that there is no input voltage in the insulation failure detection circuit. Therefore, it directly returns to continue the power supply operation to save steps and improve the analysis speed.
[0083] Preferably, taking the A-phase winding as an example, the insulation failure location is at A', causing the conductor at A' to short-circuit with the corresponding semiconductor layer 4, resulting in the potential at the fault location in the semiconductor layer 4 becoming UA'. At this time, the potential at the insulation failure location is UA', while the potential at the voltage monitoring point is 0, generating a potential difference in the semiconductor layer 4, thereby generating a voltage at the voltage monitoring point.
[0084] Preferably, when the location of insulation failure is different, the location and amplitude of the potential generated in the semiconductor layer 4 are different, which makes the voltage at the voltage monitoring point different. Therefore, by identifying the voltage signal, the location of insulation failure can be accurately located.
[0085] In a preferred embodiment of the present invention, in step S2, the semiconductor layer 4 is divided into multiple regions, and the semiconductor electrical parameters of each region are equivalently set as inductance and resistance. According to the position of each region, the equivalently set inductance and resistance are connected end to end in sequence to form the inductance-resistance branch network corresponding to the semiconductor layer 4.
[0086] In a preferred embodiment of the present invention, such as Figure 5 As shown, the insulation failure detection circuit includes:
[0087] A first resistor R1 is connected to ground at one end.
[0088] A first inductor L1 is connected at one end to the other end of a first resistor R1.
[0089] A second resistor R2 is connected at one end to the other end of the first inductor L1;
[0090] A second inductor L2 is connected at one end to the other end of a second resistor R2.
[0091] A third inductor L3 is connected to one end of the first resistor R1;
[0092] A third resistor R3 is connected at one end to the other end of a third inductor L3.
[0093] A fourth inductor L4 is connected at one end to the other end of the first inductor L1 and one end of the second resistor R2.
[0094] A fourth resistor R4, one end of which is connected to the other end of a fourth inductor L4;
[0095] A fifth inductor L5, one end of which is connected to the other end of the second inductor L2;
[0096] A fifth resistor R5, one end of which is connected to the other end of a fifth inductor L5;
[0097] A sixth resistor R6 is connected at one end to the other end of the third resistor R3.
[0098] A sixth inductor L6 is connected to the other end of a sixth resistor R6, and the other end of a sixth inductor L6 is connected to the other end of a fourth resistor R4.
[0099] A seventh resistor R7 is connected at one end to the other end of the sixth inductor L6 and the other end of the fourth resistor R4.
[0100] A seventh inductor L7 is connected to the other end of a seventh resistor R7, and the other end of a seventh inductor L7 is connected to the other end of a fifth resistor R5.
[0101] The eighth inductor L8 is connected at one end to the other end of the third resistor R3 and one end of the sixth resistor R6.
[0102] The eighth resistor R8 is connected to the other end of the eighth inductor L8, and the other end of the eighth resistor R8 is grounded.
[0103] A ninth inductor L9, one end of which is connected to the other end of the sixth inductor L6 and one end of the seventh resistor R7;
[0104] A ninth resistor R9, one end of which is connected to the other end of a ninth inductor L9;
[0105] The tenth inductor L10 is connected at one end to the other end of the seventh inductor L7 and the other end of the fifth resistor R5.
[0106] A tenth resistor R10 is connected at one end to the other end of a tenth inductor L10.
[0107] An eleventh resistor R11 is connected at one end to the other end of the eighth resistor R8.
[0108] The eleventh inductor L11 is connected to the other end of the eleventh resistor R11, and the other end of the eleventh inductor L11 is connected to the other end of the ninth resistor R9.
[0109] The twelfth resistor R12 is connected at one end to the other end of the eleventh inductor L11 and the other end of the ninth resistor R9.
[0110] The twelfth inductor L12 is connected at one end to the other end of the twelfth resistor R12, and at the other end of the twelfth inductor L12 is connected to the other end of the tenth resistor R10.
[0111] Specifically, in this embodiment, the inductors and resistors on the insulation failure detection circuit are arranged in a rotationally symmetrical manner on the semiconductor layer 4, so as to divide the semiconductor layer 4 into regions of equal size for arranging the inductor-resistor branch network.
[0112] Preferably, the specifications of each inductor and resistor are not limited.
[0113] In a preferred embodiment of the present invention, such as Figure 6 As shown, the power supply circuit includes:
[0114] H-bridge control unit 5, the input terminal of H-bridge control unit 5 is connected to external power supply VDD;
[0115] The thirteenth resistor R13 is connected at one end to the output terminal of the H-bridge control unit 5.
[0116] The thirteenth inductor L13 is connected to the other end of the thirteenth resistor R13, and the other end of the thirteenth inductor L13 is connected to the first winding E1 of the aircraft motor.
[0117] The fourteenth resistor R14 is connected at one end to the output terminal of the H-bridge control unit 5.
[0118] The fourteenth inductor L14 is connected at one end to the other end of the fourteenth resistor R14, and at the other end of the fourteenth inductor L14 is connected to the second winding R2 of the aircraft motor.
[0119] The fifteenth resistor R15 is connected at one end to the output terminal of the H-bridge control unit 5.
[0120] The fifteenth inductor L15 is connected at one end to the other end of the fifteenth resistor R15, and at the other end of the fifteenth inductor L15 is connected to the third winding E3 of the aircraft motor.
[0121] Specifically, in this embodiment, when the aircraft motor is working normally, the insulation failure detection circuit and the power supply circuit are not connected. However, when an insulation failure occurs, the input voltage of the power supply circuit flows from the insulating layer 3 into the insulation failure detection circuit on the semiconductor layer 4 to form an electrical connection.
[0122] In a preferred embodiment of the present invention, in step S4, the point voltages at the four opposite corners of the fault point equipotential line are detected respectively, and the corresponding voltage drop ratios are obtained by processing the four point voltages in pairs. The corresponding insulation failure location is obtained by comparing each voltage drop ratio with a pre-configured fault point ratio table.
[0123] Specifically, in this embodiment, considering that the three voltage drop ratios calculated from the four diagonal points of the fault point equipotential line at each insulation failure location are unique and different, the specific location of the insulation failure location can be accurately obtained simply by comparing the voltage drop ratio with the fault point ratio.
[0124] While the disclosure is as stated above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of this disclosure, and all such changes and modifications will fall within the protection scope of this invention.
Claims
1. A method for detecting and locating insulation failures in aircraft motors, characterized in that, Includes the following steps: Step S1: For each stator slot (1) in the aircraft motor, a semiconductor layer (4) is wrapped around the surface of the insulating layer (3) on the outside of each copper conductor (2) in the stator slot (1); Step S2: For each of the semiconductor layers (4), multiple regions are divided on the semiconductor layer (4), and a resistive inductive branch network is set in each of the regions, and the resistive inductive branch networks are connected to form an insulation failure detection circuit. Step S3: Power the three-phase windings of the aircraft motor with an external power source; Step S4: Determine whether there is a non-ground voltage at the four terminal corners of the insulation failure detection circuit. If not, return to step S3 to continue supplying power to the three-phase winding; If so, the output indicates the presence of insulation failure, and the location and potential difference of the insulation failure where the potential changes in the insulation failure detection circuit are collected as the location result and output.
2. The insulation failure detection and location method according to claim 1, characterized in that, In step S1, the semiconductor layer (4), which is square after unfolding, is wrapped around the surface of the insulating layer (3), and a notch is left on the semiconductor layer (4) as a voltage monitoring point for monitoring voltage.
3. The insulation failure detection and location method according to claim 2, characterized in that, Before performing step S4, the following is also included: Determine whether there is voltage at the voltage monitoring point: If so, the detection result indicating the presence of insulation failure is output, and the process proceeds to step S4; If not, return to step S3 to continue supplying power to the three-phase winding.
4. The insulation failure detection and location method according to claim 1, characterized in that, In step S2, the semiconductor layer (4) is divided into multiple regions, and the semiconductor electrical parameters of each region are equivalently set as inductance and resistance. According to the position of each region, the equivalent inductors and resistors are connected end to end in sequence to form the inductor-resistance branch network corresponding to the semiconductor layer (4).
5. The insulation failure detection and location method according to claim 1, characterized in that, The insulation failure detection circuit includes: A first resistor, one end of which is grounded; A first inductor, one end of which is connected to the other end of the first resistor; A second resistor, one end of which is connected to the other end of the first inductor; A second inductor, one end of which is connected to the other end of the second resistor; A third inductor, one end of which is connected to one end of the first resistor; A third resistor, one end of which is connected to the other end of the third inductor; A fourth inductor, one end of which is connected to the other end of the first inductor and one end of the second resistor; A fourth resistor, one end of which is connected to the other end of the fourth inductor; A fifth inductor, one end of which is connected to the other end of the second inductor; A fifth resistor, one end of which is connected to the other end of the fifth inductor; A sixth resistor, one end of which is connected to the other end of the third resistor; A sixth inductor, one end of which is connected to the other end of the sixth resistor, and the other end of which is connected to the other end of the fourth resistor; A seventh resistor, one end of which is connected to the other end of the sixth inductor and the other end of the fourth resistor; A seventh inductor, one end of which is connected to the other end of the seventh resistor, and the other end of which is connected to the other end of the fifth resistor; An eighth inductor, one end of which is connected to the other end of the third resistor and one end of the sixth resistor; An eighth resistor, one end of which is connected to the other end of the eighth inductor, and the other end of which is grounded; A ninth inductor, one end of which is connected to the other end of the sixth inductor and one end of the seventh resistor; A ninth resistor, one end of which is connected to the other end of the ninth inductor; A tenth inductor, one end of which is connected to the other end of the seventh inductor and the other end of the fifth resistor; A tenth resistor, one end of which is connected to the other end of the tenth inductor; An eleventh resistor, one end of which is connected to the other end of the eighth resistor; An eleventh inductor, one end of which is connected to the other end of the eleventh resistor, and the other end of which is connected to the other end of the ninth resistor; A twelfth resistor, one end of which is connected to the other end of the eleventh inductor and the other end of the ninth resistor; A twelfth inductor, one end of which is connected to the other end of the twelfth resistor, and the other end of which is connected to the other end of the tenth resistor.
6. The insulation failure detection and location method according to claim 1, characterized in that, The power supply circuit includes: An H-bridge control unit (5) is provided, the input of which is connected to the external power supply. A thirteenth resistor, one end of which is connected to the output terminal of the H-bridge control unit (5); A thirteenth inductor, one end of which is connected to the other end of the thirteenth resistor, and the other end of which is connected to the first winding of the aircraft motor; A fourteenth resistor, one end of which is connected to the output terminal of the H-bridge control unit (5); A fourteenth inductor, one end of which is connected to the other end of the fourteenth resistor, and the other end of which is connected to the second winding of the aircraft motor; A fifteenth resistor, one end of which is connected to the output terminal of the H-bridge control unit (5); A fifteenth inductor, one end of which is connected to the other end of the fifteenth resistor, and the other end of which is connected to the third winding of the aircraft motor.
7. The insulation failure detection and location method according to claim 1, characterized in that, In step S4, the point voltages at the four opposite corners of the fault point equipotential line are detected respectively. The corresponding voltage drop ratios are obtained by processing the four point voltages in pairs. The corresponding insulation failure location is obtained by comparing each voltage drop ratio with a pre-configured fault point ratio table.
Citation Information
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