A method for calculating the uncertainty of a balance calibration

Abstract

The application provides a balance calibration uncertainty calculation method, considers the contribution degrees of a balance calibration system, systematic errors and random errors to the uncertainty, and comprehensively calculates the uncertainty of the balance static calibration according to the influences of the three parts on the uncertainty. The application intuitively gives the contribution of each factor in the balance calibration system to the calibration uncertainty, and facilitates researchers to measure the quality of each part of the calibration system. Meanwhile, the overall structure of the calibration system and the calibration method mentioned in the application is the same as the mainstream calibration system and calibration method, so that the calculation method can be partially referenced by other calibration systems, and has certain universality.

Description

Technical Field

[0001] This invention belongs to the field of sensor testing technology, specifically relating to a method for calculating the uncertainty of static calibration of a wind tunnel balance. Background Technology

[0002] Before being used in wind tunnel testing, a wind tunnel balance must undergo ground static calibration to obtain the correspondence between load input and signal output. The quality of static calibration directly determines the quality of wind tunnel test data. To effectively characterize and measure the quality of balance static calibration, researchers have proposed indicators such as calibration accuracy and precision. However, most existing indicators only provide the impact of a single calibration on the balance's static calibration and do not measure the impact of the entire calibration system on the balance's static calibration. Therefore, this invention proposes an uncertainty method for balance static calibration, comprehensively considering factors such as manufacturing errors, installation errors, and stress deformation of the balance and calibration system, and providing the balance calibration uncertainty including three parts: the balance calibration system, systematic errors, and random errors. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a method for calculating the uncertainty of balance calibration, which includes three parts: balance calibration system, systematic error, and random error, and has a certain degree of universality.

[0004] The technical solution of this invention is: a method for calculating the uncertainty of balance calibration, comprising:

[0005] A balance calibration system is established, and the earth axis system and body axis system are defined; the balance calibration system includes a loading stage, a balance, a loading head, a force generator, and a laser displacement sensor, wherein the force generator includes a pull wire, a pulley, and weights;

[0006] The installation error of the balance, the machining error of the loading head, the installation error of the pulley, the length of the pull wire, and the relative distance between the laser displacement sensors were measured respectively.

[0007] Before applying the load, the distance between the laser displacement sensor and the loading head is measured and recorded;

[0008] The installation error of the loading head is calculated based on the measured relative distance between the laser displacement sensors and the distance between the laser displacement sensors and the loading head.

[0009] After the load is applied, the distance between the laser displacement sensor and the loading head is measured and recorded;

[0010] Based on the relative distance between the laser displacement sensors, and the distance between the laser displacement sensors and the loading head before and after the load is applied, the linear and angular displacements of the loading head in the ground axis system after the load is applied are calculated.

[0011] Based on the obtained balance installation error, loading head machining error, pulley installation error, draw line length, loading head installation error, and loading head linear and angular displacement, determine the expressions for the six components of the balance.

[0012] Calculate the combined standard uncertainty of each component of the balance under a single loading condition based on the expressions for the six components of the balance.

[0013] Based on the combined standard uncertainty of the six components of the balance under a single loading condition, the effects of the calibration system, systematic error, and random error on the uncertainty of the six components of the balance are calculated. Based on the above three effects, the uncertainty of the static calibration of the balance is calculated.

[0014] The origin O of the ground axis system is located at the balance calibration center; the X-axis is parallel to the ground and points from the balance calibration center to the front end of the balance; the Y-axis is vertically downward; the Z-axis is determined by the X and Y axes using the right-hand rule; the origin O1 of the body axis system is located at the balance calibration center; the X1 axis points from the balance calibration center to the front end of the balance; the Y1 axis is vertically downward; the Z1 axis is determined by the X1 and Y1 axes using the right-hand rule.

[0015] The balance calibration system includes a loading platform, a loading head, a force generator, and a laser displacement sensor. The force generator includes a pull wire, a pulley, and weights. The loading platform is fixed to the ground. The balance is connected to the loading platform, and the loading head is connected to the balance. Multiple force generators are connected to the loading head, and multiple laser displacement sensors are installed on the outside of the loading head. One end of the pull wire of the force generator is connected to the bearing point on the loading head, passes through the pulley, and the other end is connected to the weights. The downward gravity of the weights can be converted by the pulley to apply forces in different directions to the loading head.

[0016] There are a total of 10 force generators, including: force generator G22 located in the positive X-axis direction of the loading head, force generator G21 located in the negative X-axis direction of the loading head, force generators G32 and G34 located in the positive Z-axis direction of the loading head, force generator G31 located in the negative Z-axis direction of the loading head, force generator G0 located in the negative Y-axis direction of the loading head, and force generators G11, G12, G13, and G14 located in the positive Y-axis direction of the loading head.

[0017] A total of 7 laser displacement sensors are used to measure the distance between the loading head and the sensors, including: laser displacement sensor 1 measures the displacement of the front end of the loading head in the Y-axis direction, laser displacement sensor 2 measures the displacement of the rear end of the loading head in the Y-axis direction, laser displacement sensor 3 measures the displacement of the front end of the loading head in the Z-axis direction, laser displacement sensor 4 measures the displacement of the rear end of the loading head in the Z-axis direction, laser displacement sensor 5 measures the displacement of the right end of the loading head in the Y-axis direction, laser displacement sensor 6 measures the displacement of the left end of the loading head in the Y-axis direction, and laser displacement sensor 7 measures the displacement of the front end of the loading head in the X-axis direction.

[0018] The installation error γ of the balance tp It refers to the angle between the Y1 axis of the body axis system and the Y axis of the ground axis system;

[0019] The loading head machining error refers to the machining position error δP of the loading head bearing point. mn It is obtained by subtracting the measured value and the theoretical value of the distance between the bearing point and the center position of the loading head. The subscript m is the direction of the coordinate axis of the earth axis system, and the subscript n is the number of the force generator connected to the bearing point.

[0020] The pulley installation error refers to the positional installation error δW of the pulley in the ground axis system. mn It is obtained by subtracting the actual installation position and the theoretical installation position of the pulley in the ground axis system;

[0021] The length of the weight pull line refers to the distance from the point where the pull line is tangent to the pulley to the bearing point of the loading head, including: the length of the pull line H0 of the force generator; G 21 G 22 Force generator pull wire length H 21 H 22 G 31 G 32 G 34 Force generator pull wire length H 31 H 32 H 34 ;

[0022] The relative distance between the laser displacement sensors refers to the relative distance between the laser points they each hit on the loading head, including the distance D between laser displacement sensors 1 and 2. 12 The distance D between laser displacement sensors 3 and 4 34 The distance D between laser displacement sensors 5 and 6 56 .

[0023] The loading head installation error refers to the angle between the three axes of the body axis system and the three axes of the ground axis system before the load is applied, including:

[0024] Loading head angle of attack installation error δαjzt The calculation formula is:

[0025]

[0026] Loading head deflection angle installation error δβ jzt The calculation formula is:

[0027]

[0028] Loading head roll angle installation error δγ jzt The calculation formula is:

[0029]

[0030] In the above formula, l 0i The distance between the laser displacement sensor and the loading head before the load is applied is given by the subscript i, which indicates the i-th laser displacement sensor.

[0031] The calculations yield the linear and angular displacements of the loading head in the ground axis system after the load is applied, including:

[0032] Linear displacement X of the loading head in the earth axis system f The calculation formula is:

[0033] X f =l7-l 07

[0034] Linear displacement Y of the loading head in the Earth axis system f The calculation formula is:

[0035]

[0036] Linear displacement Z of the loading head in the earth axis system f The calculation formula is:

[0037]

[0038] Angular displacement α of the loading head in the Earth axis system f The calculation formula is:

[0039]

[0040] Angular displacement β of the loading head in the Earth axis system f The calculation formula is:

[0041]

[0042] Angular displacement γ of the loading head in the Earth axis system f The calculation formula is:

[0043]

[0044] In the above formula, l i The distance between the laser displacement sensor and the loading head after the load is applied is given, with the subscript i indicating the i-th laser displacement sensor.

[0045] The six components of the balance refer to the yaw moment of the balance about the Y1 axis. Lateral force along the Z1 axis Pitching moment about the Z1 axis Normal force along the Y1 axis Rolling torque about the X1 axis Axial force along the X1 axis in,

[0046] Yaw moment The expression is:

[0047]

[0048] Lateral force The expression is:

[0049]

[0050] Pitch moment The expression is:

[0051] Normal force The expression is:

[0052] Rolling torque The expression is:

[0053] Axial force The expression is:

[0054]

[0055] In the formula, G i Number G i The force and torque applied by the force generator to the loading head; δP mn For the machining error of the loading head; δα jzt ,δβ jzt δγ jzt For loading head installation error; X f Y f Z f α f β f γ f γ represents the linear and angular displacements of the loading head in the ground axis system after the load is applied.tp For balance installation error; δW mn For pulley installation error; H0, H 21 H 22 H 31 H 32 H 34 This refers to the length of the pull line.

[0056] The combined standard uncertainty of each component of the balance under a single loading condition is denoted as u. cj The subscript 'c' represents the six components of the balance. The subscript j indicates the load applied in the j-th group; the formula for calculating the combined standard uncertainty of the balance component c in the j-th load group is:

[0057]

[0058] In the formula, f is the expression for each component of the balance; Input quantity x a The first derivative, x a The parameters in the expressions for each component of the balance include the force G applied by the force generator to the loading head. i Loading head machining error δP mn Loading head installation error δα jzt ,δβ jzt δγ jzt After the load is applied, the linear displacement and angular displacement X of the loading head in the ground axis system f Y f Z f α f β f γ f Balance installation error γ tp Pulley installation error δW mn The lengths of the weight pull wires H0 and H 21 H 22 H 31 H 32 H 34 n is the input quantity x a The number of; u(x) a ) represents the input quantity x a Uncertainty value; u(x) a ,x b ) represents the input quantity x a With input quantity x b The covariance.

[0059] The effect of the balance calibration system on the uncertainty of the six components u c The calculation formula is:

[0060]

[0061] In the above formula, u cj is the combined standard uncertainty of the six components of the balance under a single load, and represents the combined standard uncertainty of the balance component c under the j-th load; m is the number of applied load groups.

[0062] The effect of the systematic error on the uncertainty of the six components of the balance is denoted as the deviation limit B. c The subscript 'c' represents the six components of the balance. The calculation process is as follows:

[0063] The residual between the calculated load value and the actual load value is denoted as ε. cji The subscript 'c' represents the six components of the balance; the subscript 'j' indicates that this is the j-th load group; the subscript 'i' indicates the i-th repetition of the current load group. The formula for calculating the residual is:

[0064]

[0065] In the formula F cji This represents the inverse value of the balance component c when the j-th load is repeatedly applied for the i-th time. This represents the actual loading value of the balance component c in the j-th load group;

[0066] The deviation limit estimate of the balance component c in the j-th load group is denoted as B. cj The calculation formula is:

[0067]

[0068] In the formula, h represents the number of times the j-th load group is repeatedly applied;

[0069] The deviation limit B of the balance component c c The calculation formula is:

[0070]

[0071] In the formula, n is the number of loading groups for the balance component c, where repeated loading is only counted as one group.

[0072] The uncertainty effect of the random error on the balance component c is denoted as the accuracy limit P. c The subscript 'c' represents the six components of the balance. The calculation process is as follows:

[0073] The standard deviation of the residual of the balance component c under the j-th load group is denoted as S(ε). cj The calculation formula is:

[0074]

[0075] In the formula Let c be the deviation limit estimate of the balance component c in the j-th load group; h is the number of repeated loading groups of the j-th load group.

[0076] The accuracy limit estimate P of the balance component c under the j-th load group. cj The calculation formula is:

[0077]

[0078] In the formula, k is the safety factor, and we take k = 2;

[0079] The accuracy limit P of the balance component c c The calculation formula is:

[0080]

[0081] In the formula, n is the number of loading groups for component c, where repeated loading is counted as only one group.

[0082] Based on the above three influencing factors, the uncertainty A of the static calibration of the balance is calculated comprehensively. c The subscript 'c' represents the six components of the balance, including:

[0083]

[0084] In the above formula, u c The effect of the balance calibration system on the uncertainty of the balance component c;

[0085] In the above formula, B c The effect of systematic error on the uncertainty of the balance component c;

[0086] In the above formula, P c This represents the effect of random error on the uncertainty of the balance component c.

[0087] The advantages of this invention compared to the prior art are:

[0088] 1. Existing calibration techniques typically do not consider the manufacturing errors of the various components of the calibration system, while this invention fully considers the manufacturing error of the loading head bearing point, that is, the difference between the measured value and the theoretical value of the distance between the bearing point and the center position of the loading head, which can more accurately calculate the load of the calibration system on the balance.

[0089] 2. Existing calibration techniques typically assume that the pulley position, wire length, and balance installation state are all in their theoretical positions. Therefore, these factors are not individually listed when calculating calibration accuracy and precision, resulting in a calculation that reflects the combined effects of the calibration system and a single calibration, making the results unclear and unintuitive. This invention divides the balance calibration uncertainty into three parts: the balance calibration system, systematic error, and random error. This allows researchers to more intuitively determine the contribution of each part to the balance uncertainty.

[0090] 3. The balance calibration system mentioned in this invention includes a loading stage, a loading head, a force generator, a laser displacement sensor, etc., and its structure is the same as most existing calibration systems. Therefore, the algorithm proposed in this invention can be partially applied to other calibration systems and has a certain degree of universality. Attached Figure Description

[0091] Figure 1 This is a flowchart of the method of the present invention.

[0092] Figure 2 This is a schematic diagram of a balance static calibration system. In the diagram, 1 represents force generator G22, 2 represents force generator G32, 3 represents force generator G34, 4 represents force generator G0, 5 represents force generator G21, 6 represents force generator G31, 7 represents force generator G11, 8 represents force generator G12, 9 represents force generator G13, 10 represents force generator G14, 11 represents the loading head, 12 represents the pull wire, and 14 represents the loading platform.

[0093] Figure 3 This is a schematic diagram of a laser displacement sensor installed outside the loading head. Detailed Implementation

[0094] The uncertainty calculation method proposed in this invention will be described in detail below, and its features and advantages will become clearer with the explanation.

[0095] like Figure 1 As shown, the technical solution of the present invention includes the following steps:

[0096] (1) Define the Earth axis system and the body axis system coordinate system;

[0097] (2) Assemble the loading stage, balance, loading head, force generator and laser displacement sensor to form a balance calibration system;

[0098] (3) Installation error of the measuring balance;

[0099] (4) Measure the machining error of the loading head;

[0100] (5) Measure the installation error of the pulley;

[0101] (6) Measure the length of the pull wire;

[0102] (7) Measure the relative distance between laser displacement sensors;

[0103] (8) Before applying the load, measure and record the distance between the laser displacement sensor and the loading head;

[0104] (9) The loading head installation error is calculated based on the relative distance between the laser displacement sensors in step (7) and the distance between the laser displacement sensor and the loading head in step (8).

[0105] (10) After applying the load, measure and record the distance between the laser displacement sensor and the loading head;

[0106] (11) Based on the relative distance between the laser displacement sensors in step (7), and the distance between the laser displacement sensors and the loading head before and after applying the load in steps (8) and (10), the linear displacement and angular displacement of the loading head in the ground axis system after applying the load are calculated.

[0107] (12) Based on the balance installation error in step (3), the loading head machining error in step (4), the pulley installation error in step (5), the pull line length in step (6), the loading head installation error in step (9), and the loading head linear displacement and angular displacement in step (11), determine the expressions for the six components of the balance.

[0108] (13) Calculate the combined standard uncertainty of each component of the balance in a single loading based on the expressions of the six components of the balance in step (12).

[0109] (14) Based on the combined standard uncertainty of the six components of the balance in a single loading in step (13), the influence of the calibration system on the uncertainty of the six components of the balance is calculated.

[0110] (15) The effect of systematic error on the uncertainty of the six components of the balance was calculated;

[0111] (16) The effect of random error on the uncertainty of the six components of the balance was calculated;

[0112] (17) Based on the effects of the calibration system on the uncertainty of the six components of the balance in step (14), the effects of the systematic error on the uncertainty of the six components of the balance in step (15), and the effects of the random error on the uncertainty of the six components of the balance in step (16), the uncertainty of the static calibration of the balance is calculated.

[0113] In step (1), the origin O of the earth axis system is located at the balance calibration center; the X-axis is parallel to the ground and points from the balance calibration center to the front end of the balance; the Y-axis is vertically downward; the Z-axis is determined by the X and Y axes using the right-hand rule. The origin O1 of the body axis system is located at the balance calibration center; the X1 axis points from the balance calibration center to the front end of the balance; the Y1 axis is vertically downward; the Z1 axis is determined by the X1 and Y1 axes using the right-hand rule.

[0114] In step (2), the balance calibration system includes a loading platform, a loading head, a force generator (including a pull wire, pulley, and weights), and a laser displacement sensor. In use, first fix the loading platform to the ground, then connect the balance to the loading platform, then connect the loading head to the balance, and finally connect the 10 force generators to the loading head, as shown below. Figure 2 As shown. Finally, seven laser displacement sensors are installed outside the loading head, as follows. Figure 3 As shown. One end of the pull wire of each of the 10 force generators is connected to the bearing point on the loading head, passes through a pulley in the middle, and the other end is connected to a weight. The downward force of the weight, through the pulley, can be applied to the loading head in different directions. The 10 force generators are as follows: force generator G22 is located in the positive X-axis direction of the loading head; force generator G21 is located in the negative X-axis direction; force generators G32 and G34 are located in the positive Z-axis direction; force generator G31 is located in the negative Z-axis direction; force generator G0 is located in the negative Y-axis direction; and force generators G11, G12, G13, and G14 are located in the positive Y-axis direction. Seven laser displacement sensors can measure the distance between the loading head and the sensors. Sensor 1 measures the displacement of the front end of the loading head in the Y-axis direction, sensor 2 measures the displacement of the rear end of the loading head in the Y-axis direction, sensor 3 measures the displacement of the front end of the loading head in the Z-axis direction, sensor 4 measures the displacement of the rear end of the loading head in the Z-axis direction, sensor 5 measures the displacement of the right end of the loading head in the Y-axis direction, sensor 6 measures the displacement of the left end of the loading head in the Y-axis direction, and sensor 7 measures the displacement of the front end of the loading head in the X-axis direction.

[0115] In step (3), the installation error γ of the balance tp It refers to the angle between the Y1 axis of the body axis system and the Y axis of the ground axis system.

[0116] In step (4), the loading head machining error refers to the machining position error δP of the loading head bearing point. mn It is obtained by subtracting the measured value and the theoretical value of the distance between the bearing point and the center position of the loading head. The subscript m is the direction of the coordinate axis of the earth axis system, and the subscript n is the number of the force generator connected to the bearing point.

[0117] In step (5), the pulley installation error refers to the positional installation error δW of the pulley in the ground axis system. mn The error is obtained by subtracting the actual installation position and the theoretical installation position of the pulley in the ground axis system. The subscript m represents the direction of the coordinate axis of the ground axis system, and the subscript n represents the pulley (force generator) number. In step (2), there are a total of 6 pulleys in the balance calibration system. Each pulley has 3 coordinates in the ground axis system. Except for the direction coordinate of the force they apply, which has no theoretical installation position, each pulley has installation errors in 2 coordinate directions. The specific installation errors to be measured are shown in Table 1. The G0 pulley has installation errors in 2 directions, namely the X-axis and Z-axis. The G21 and G22 pulleys have installation errors in 2 directions, namely the Y-axis and Z-axis. The G31, G32, and G34 pulleys have installation errors in 2 directions, namely the X-axis and Y-axis.

[0118] Table 1 shows the installation errors of the six pulleys that need to be measured.

[0119]

[0120]

[0121] In step (6), the length of the weight pull line refers to the distance from the point where the pull line is tangent to the pulley to the bearing point of the loading head, including: the length of the pull line of the G0 force generator, H0; G 21 G 22 Force generator pull wire length H 21 H 22 G 31 G 32 G 34 Force generator pull wire length H 31 H 32 H 34 .

[0122] In step (7), the relative distance between the laser displacement sensors refers to the relative distance between the laser points they each hit on the loading head, including: the distance D between laser displacement sensors 1 and 2. 12 ;D, the distance between laser displacement sensors 3 and 4 34 ;D, the distance between laser displacement sensors 5 and 6 56 .

[0123] In step (8), before applying the load, the distance l between the laser displacement sensor and the loading head is... 0i The subscript i represents the i-th laser displacement sensor. In the balance calibration system in step (2), i = 1 to 7.

[0124] In step (9), the loading head installation error refers to the angle between the three axes of the body axis system and the three axes of the ground axis system before the load is applied, including:

[0125] Loading head angle of attack installation error δα jzt The calculation formula is:

[0126]

[0127] Loading head deflection angle installation error δβ jzt The calculation formula is:

[0128]

[0129] Loading head roll angle installation error δγ jzt The calculation formula is:

[0130]

[0131] In the above formula, l 0i In step (8), the distance between the laser displacement sensor and the loading head before the load is applied is given, and the subscript i indicates the i-th laser displacement sensor.

[0132] In the above formula, D 12 D 34 D 56 The relative distance between the laser displacement sensors in step (7) is given.

[0133] In step (10), after the load is applied, the distance l between the laser displacement sensor and the loading head is... i The subscript i represents the i-th laser displacement sensor. In the balance calibration system in step (2), i = 1 to 7.

[0134] In step (11), the linear and angular displacements of the loading head in the ground axis system after the load is applied are calculated, including:

[0135] Linear displacement X of the loading head in the earth axis system f The calculation formula is:

[0136] X f =l7-l 07

[0137] Linear displacement Y of the loading head in the Earth axis system f The calculation formula is:

[0138]

[0139] Linear displacement Z of the loading head in the earth axis system f The calculation formula is:

[0140]

[0141] Angular displacement α of the loading head in the Earth axis system f The calculation formula is:

[0142]

[0143] Angular displacement β of the loading head in the Earth axis system f The calculation formula is:

[0144]

[0145] Angular displacement γ of the loading head in the Earth axis system f The calculation formula is:

[0146]

[0147] In the above formula, l i In step (10), after the load is applied, the distance between the laser displacement sensor and the loading head is given, and the subscript i indicates the i-th laser displacement sensor.

[0148] In the above formula, l 0iIn step (8), the distance between the laser displacement sensor and the loading head before the load is applied is given, and the subscript i indicates the i-th laser displacement sensor.

[0149] In the above formula, D 12 D 34 D 56 The relative distance between the laser displacement sensors in step (7) is given.

[0150] In step (12), the six components of the balance refer to the yaw moment of the balance about the Y1 axis. Lateral force along the Z1 axis Pitching moment about the Z1 axis Normal force along the Y1 axis Rolling torque about the X1 axis Axial force along the X1 axis Yaw moment The expression is:

[0151] Lateral force The expression is:

[0152] Pitch moment The expression is:

[0153] Normal force The expression is:

[0154] Rolling torque The expression is:

[0155]

[0156] Axial force The expression is:

[0157]

[0158] In the above formula, G i In step (2), number G i The force and torque applied by the force generator to the loading head, in units of kg or kg·m;

[0159] In the above formula, δP mn The loading head machining error in step (4) is represented by the subscript m, which is the direction of the earth axis coordinate system, and the subscript n is the number of the force generator connected to the bearing point.

[0160] In the above formula, δα jzt ,δβjzt δγ jzt This refers to the loading head installation error in step (9);

[0161] In the above formula, X f Y f Z f α f β f γ f In step (11), after the load is applied, the linear and angular displacements of the loading head in the ground axis system are defined.

[0162] In the above formula, γ tp The installation error of the balance in step (3);

[0163] In the above formula, δW mn The installation error of the pulley in step (5) is indicated by the subscript m, which represents the direction of the coordinate axis of the ground axis system, and the subscript n, which represents the pulley (force generator) number.

[0164] In the above formula, H0 and H 21 H 22 H 31 H 32 H 34 The length of the pull wire in step (6) is given.

[0165] In step (13), the combined standard uncertainty of each component of the balance under a single loading condition is denoted as u. cj The subscript 'c' represents the six components of the balance scale. The subscript j indicates the j-th load group. The formula for calculating the combined standard uncertainty of the balance component c in the j-th load group is:

[0166]

[0167] In the above formula, f is the expression for each component of the balance in step (12);

[0168] In the above formula Input quantity x a The first derivative, x a The parameters in the expressions for each component of the balance in step (12) include the force G applied by the force generator to the loading head. i Loading head machining error δP mn Loading head installation error δα jzt ,δβ jzt δγ jzt After the load is applied, the linear displacement and angular displacement X of the loading head in the ground axis system f Y f Z f α f β fγ f Balance installation error γ tp Pulley installation error δW mn The lengths of the weight pull wires H0 and H 21 H 22 H 31 H 32 H 34 ;

[0169] In the above formula, n is the input quantity x a The number of;

[0170] In the above formula, u(x) a ) represents the input quantity x a Uncertainty value; u(x) a ,x b ) represents the input quantity x a With input quantity x b The covariance.

[0171] In step (14), the uncertainty of the balance calibration system affects the six components. c The calculation formula is:

[0172]

[0173] In the above formula, u cj The combined standard uncertainty of each component of the balance in step (13) under a single loading condition is represented by the combined standard uncertainty of the balance component c under the j-th loading condition.

[0174] In the above formula, m is the number of applied load groups.

[0175] In step (15), the influence of the systematic error on the uncertainty of the six components of the balance is denoted as the deviation limit B. c The subscript 'c' represents the six components of the balance. The calculation process is as follows:

[0176] The residual between the calculated load value and the actual load value is denoted as ε. cji The subscript 'c' represents the six components of the balance; the subscript 'j' indicates that this is the j-th load group; the subscript 'i' indicates the i-th repetition of the current load group. The formula for calculating the residual is:

[0177]

[0178] In the above formula, F cji This represents the inverse value of the balance component c when the j-th load is repeatedly applied for the i-th time.

[0179] In the above formula This represents the actual loading value of the balance component c in the j-th load group.

[0180] The deviation limit estimate of the balance component c in the j-th load group is denoted as B. cj The calculation formula is:

[0181]

[0182] In the above formula, h represents the number of times the j-th load group is repeatedly applied.

[0183] The deviation limit B of the balance component c c The calculation formula is:

[0184]

[0185] In the above formula, n is the number of loading groups for component c (repeated loading is only counted as 1 group).

[0186] In step (16), the uncertainty effect of random error on the balance component c is denoted as the accuracy limit P. c The subscript 'c' represents the six components of the balance. The calculation process is as follows:

[0187] The standard deviation of the residual of the balance component c under the j-th load group is denoted as S(ε). cj The calculation formula is:

[0188]

[0189] In the above formula The deviation limit estimate of the balance component c in step (15) in the j-th group of loads;

[0190] In the above formula, h is the number of repeated loading groups of the j-th load group.

[0191] The accuracy limit estimate P of the balance component c under the j-th load group. cj The calculation formula is:

[0192]

[0193] In the above formula, k is the safety factor, and we take k = 2;

[0194] The accuracy limit P of the balance component c c The calculation formula is:

[0195]

[0196] In the above formula, n is the number of loading groups for component c (repeated loading is only counted as 1 group).

[0197] In step (17), the uncertainty A of the static calibration of the balance is calculated. c The subscript 'c' represents the six components of the balance scale:

[0198]

[0199] In the above formula, u c The effect of the balance calibration system on the uncertainty of the balance component c in step (14);

[0200] In the above formula, B c The effect of the systematic error in step (15) on the uncertainty of the balance component c;

[0201] In the above formula, P c The effect of random error on the uncertainty of balance component c in step (16).

[0202] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention based on the above-disclosed technical content without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for calculating the uncertainty of balance calibration, characterized in that, include: A balance calibration system is established, and the earth axis system and body axis system are defined; the balance calibration system includes a loading stage, a balance, a loading head, a force generator, and a laser displacement sensor, wherein the force generator includes a pull wire, a pulley, and weights; The installation error of the balance, the machining error of the loading head, the installation error of the pulley, the length of the pull wire, and the relative distance between the laser displacement sensors were measured respectively. Before applying the load, the distance between the laser displacement sensor and the loading head is measured and recorded; The installation error of the loading head is calculated based on the measured relative distance between the laser displacement sensors and the distance between the laser displacement sensors and the loading head. After the load is applied, the distance between the laser displacement sensor and the loading head is measured and recorded; Based on the relative distance between the laser displacement sensors, and the distance between the laser displacement sensors and the loading head before and after the load is applied, the linear and angular displacements of the loading head in the ground axis system after the load is applied are calculated. Based on the obtained balance installation error, loading head machining error, pulley installation error, draw line length, loading head installation error, and loading head linear and angular displacement, determine the expressions for the six components of the balance. Calculate the combined standard uncertainty of each component of the balance under a single loading condition based on the expressions for the six components of the balance. Based on the combined standard uncertainty of the six components of the balance under a single loading condition, the effects of the calibration system, systematic error, and random error on the uncertainty of the six components of the balance are calculated. Based on the above three effects, the uncertainty of the static calibration of the balance is calculated.

2. The method for calculating the uncertainty of balance calibration according to claim 1, characterized in that, The origin O of the ground axis system is located at the balance calibration center; the X-axis is parallel to the ground and points from the balance calibration center to the front end of the balance; the Y-axis is vertically downward; the Z-axis is determined by the X and Y axes using the right-hand rule; the origin O1 of the body axis system is located at the balance calibration center; the X1 axis points from the balance calibration center to the front end of the balance; the Y1 axis is vertically downward; the Z1 axis is determined by the X1 and Y1 axes using the right-hand rule.

3. The method for calculating the uncertainty of balance calibration according to claim 2, characterized in that, The balance calibration system includes a loading platform, a loading head, a force generator, and a laser displacement sensor. The force generator includes a pull wire, a pulley, and weights. The loading platform is fixed on the ground, the balance is connected to the loading platform, the loading head is connected to the balance, multiple force generators are connected to the loading head, and multiple laser displacement sensors are installed on the outside of the loading head. One end of the pull wire of the force generator is connected to the bearing point on the loading head, passes through the pulley, and the other end is connected to the weights. The downward gravity of the weights can be converted by the pulley to apply forces in different directions to the loading head.

4. The method for calculating the uncertainty of balance calibration according to claim 3, characterized in that, There are a total of 10 force generators, including: force generator G22 located in the positive X-axis direction of the loading head, force generator G21 located in the negative X-axis direction of the loading head, force generators G32 and G34 located in the positive Z-axis direction of the loading head, force generator G31 located in the negative Z-axis direction of the loading head, force generator G0 located in the negative Y-axis direction of the loading head, and force generators G11, G12, G13, and G14 located in the positive Y-axis direction of the loading head. A total of 7 laser displacement sensors are used to measure the distance between the loading head and the sensors, including: laser displacement sensor 1 measures the displacement of the front end of the loading head in the Y-axis direction, laser displacement sensor 2 measures the displacement of the rear end of the loading head in the Y-axis direction, laser displacement sensor 3 measures the displacement of the front end of the loading head in the Z-axis direction, laser displacement sensor 4 measures the displacement of the rear end of the loading head in the Z-axis direction, laser displacement sensor 5 measures the displacement of the right end of the loading head in the Y-axis direction, laser displacement sensor 6 measures the displacement of the left end of the loading head in the Y-axis direction, and laser displacement sensor 7 measures the displacement of the front end of the loading head in the X-axis direction.

5. The method for calculating the uncertainty of balance calibration according to claim 4, characterized in that, The installation error γ of the balance tp It refers to the angle between the Y1 axis of the body axis system and the Y axis of the ground axis system; The loading head machining error refers to the machining position error δP of the loading head bearing point. mn It is obtained by subtracting the measured value and the theoretical value of the distance between the bearing point and the center position of the loading head. The subscript m is the direction of the coordinate axis of the earth axis system, and the subscript n is the number of the force generator connected to the bearing point. The pulley installation error refers to the positional installation error δW of the pulley in the ground axis system. mn It is obtained by subtracting the actual installation position and the theoretical installation position of the pulley in the ground axis system; The cable length refers to the distance from the point where the cable is tangent to the pulley to the bearing point of the loading head, including: the cable length H0 of the G0 force generator; G 21 G 22 Force generator pull wire length H 21 H 22 G 31 G 32 G 34 Force generator pull wire length H 31 H 32 H 34 ; The relative distance between the laser displacement sensors refers to the relative distance between the laser points they each hit on the loading head, including the distance D between laser displacement sensors 1 and 2. 12 The distance D between laser displacement sensors 3 and 4 34 The distance D between laser displacement sensors 5 and 6 56 .

6. The method for calculating the uncertainty of balance calibration according to claim 5, characterized in that, The loading head installation error refers to the angle between the three axes of the body axis system and the three axes of the ground axis system before the load is applied, including: Loading head angle of attack installation error δα jzt The calculation formula is: Loading head deflection angle installation error δβ jzt The calculation formula is: Loading head roll angle installation error δγ jzt The calculation formula is: In the above formula, l 0i The distance between the laser displacement sensor and the loading head before the load is applied is given by the subscript i, which indicates the i-th laser displacement sensor.

7. The method for calculating the uncertainty of balance calibration according to claim 6, characterized in that, The calculations yield the linear and angular displacements of the loading head in the ground axis system after the load is applied, including: Linear displacement X of the loading head in the earth axis system f The calculation formula is: X f ＝l7-l 07 Linear displacement Y of the loading head in the Earth axis system f The calculation formula is: Linear displacement Z of the loading head in the earth axis system f The calculation formula is: Angular displacement α of the loading head in the Earth axis system f The calculation formula is: Angular displacement β of the loading head in the Earth axis system f The calculation formula is: Angular displacement γ of the loading head in the Earth axis system f The calculation formula is: In the above formula, l i The distance between the laser displacement sensor and the loading head after the load is applied is given, with the subscript i indicating the i-th laser displacement sensor.

8. The method for calculating the uncertainty of balance calibration according to claim 7, characterized in that, The six components of the balance refer to the yaw moment of the balance about the Y1 axis. Lateral force along the Z1 axis Pitching moment about the Z1 axis Normal force along the Y1 axis Rolling torque about the X1 axis Axial force along the X1 axis in, Yaw moment The expression is: Lateral force The expression is: Pitch moment The expression is: Normal force The expression is: Rolling torque The expression is: Axial force The expression is: In the formula, G i Number G i The force and torque applied by the force generator to the loading head; δP mn For the machining error of the loading head; δα jzt ,δβ jzt δγ jzt For loading head installation error; X f Y f Z f α f β f γ f γ represents the linear and angular displacements of the loading head in the ground axis system after the load is applied. tp For balance installation error; δW mn For pulley installation error; H0, H 21 H 22 H 31 H 32 H 34 This refers to the length of the pull line.

9. The method for calculating the uncertainty of balance calibration according to claim 8, characterized in that, The combined standard uncertainty of each component of the balance under a single loading condition is denoted as u. cj The subscript 'c' represents the six components of the balance. The subscript j indicates the load applied in the j-th group; the formula for calculating the combined standard uncertainty of the balance component c in the j-th load group is: In the formula, f is the expression for each component of the balance; Input quantity x a The first derivative, x a The parameters in the expressions for each component of the balance include the force G applied by the force generator to the loading head. i Loading head machining error δP mn Loading head installation error δα jzt ,δβ jzt δγ jzt After the load is applied, the linear displacement and angular displacement X of the loading head in the ground axis system f Y f Z f α f β f γ f Balance installation error γ tp Pulley installation error δW mn Wire lengths H0 and H 21 H 22 H 31 H 32 H 34 n is the input quantity x a The number of; u(x) a ) represents the input quantity x a Uncertainty value; u(x) a ,x b ) represents the input quantity x a With input quantity x b The covariance.

10. The method for calculating the uncertainty of balance calibration according to claim 9, characterized in that, The effect of the balance calibration system on the uncertainty of the six components u c The calculation formula is: In the above formula, u cj is the combined standard uncertainty of the six components of the balance under a single load, and represents the combined standard uncertainty of the balance component c under the j-th load; m is the number of applied load groups.

11. The method for calculating the uncertainty of balance calibration according to claim 9, characterized in that, The effect of the systematic error on the uncertainty of the six components of the balance is denoted as the deviation limit B. c The subscript 'c' represents the six components of the balance. The calculation process is as follows: The residual between the calculated load value and the actual load value is denoted as ε. cji The subscript c represents the six components of the balance; the subscript j indicates that this is the j-th load group. The subscript i represents the i-th repeated loading of the current load group, and the formula for calculating the residual is: In the formula F cji This represents the inverse value of the balance component c when the j-th load is repeatedly applied for the i-th time. This represents the actual loading value of the balance component c in the j-th load group; The deviation limit estimate of the balance component c in the j-th load group is denoted as B. cj The calculation formula is: In the formula, h represents the number of times the j-th load group is repeatedly applied; The deviation limit B of the balance component c c The calculation formula is: In the formula, Let n be the deviation limit estimate of the balance component c in the j-th load group; n is the number of load groups for the balance component c, where repeated loading is only counted as one group.

12. The method for calculating the uncertainty of balance calibration according to claim 11, characterized in that, The uncertainty effect of the random error on the balance component c is denoted as the accuracy limit P. c The subscript 'c' represents the six components of the balance. The calculation process is as follows: The standard deviation of the residual of the balance component c under the j-th load group is denoted as S(ε). cj The calculation formula is: In the formula, h is the number of repeated loading groups of the j-th load group; The accuracy limit estimate P of the balance component c under the j-th load group. cj The calculation formula is: In the formula, k is the safety factor, and we take k = 2; The accuracy limit P of the balance component c c The calculation formula is: In the formula, n is the number of loading groups for component c, where repeated loading is counted as only one group.

13. The method for calculating the uncertainty of balance calibration according to claim 9, characterized in that, Based on the above three influencing factors, the uncertainty A of the static calibration of the balance is calculated comprehensively. c The subscript 'c' represents the six components of the balance, including: In the above formula, u c The effect of the balance calibration system on the uncertainty of the balance component c; In the above formula, B c The effect of systematic error on the uncertainty of the balance component c; In the above formula, P c This represents the effect of random error on the uncertainty of the balance component c.

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