A multi-degree-of-freedom impedance fixture for automated frequency response function measurements.

Abstract

A system and method are provided for characterizing the response of a structure under test to excitation forces applied using a test fixture. The fixture is selectively coupleable to the structure under test and configured to hold the structure under test in a known position and orientation relative to the fixture. A plurality of excitation devices and response sensors are coupled to the fixture. Excitation forces applied to the fixture by the excitation devices are transmitted by the fixture to the structure under test, and each response sensor measures a dynamic response indicative of the response of the structure under test and the fixture to the applied excitation forces. A controller receives the response sensor data and applies a mathematical coordinate transformation to project forces and moments corresponding to the applied excitation and measured dynamic responses onto target points on the structure under test and calculates a system response function based at least in part on the projections.

Description

[Technical field]

[0001] SYSTEMS AND METHODS FOR MEASURING A SYSTEM RESPONSE FUNCTION OF A SYSTEM OR STRUCTURE FIELD OF THE DISCLOSURE The present invention relates to systems and methods for applying an excitation force to a system or structure and measuring the response of the system or structure to the applied excitation force.

[0002] Summary of the Invention In some implementations, the system response function (SRF) is characterized by applying a known excitation force to the structure under test and then measuring the resulting response (e.g., acceleration response). To obtain meaningful results, one or more exciter devices and one or more response sensors are coupled to the structure under test in different directions (e.g., x, y, and z directions of a Cartesian coordinate system). The exciter device may include, for example, a shaker device configured to apply a vibration or impact force to the structure under test, and the response sensor may include, for example, an accelerometer. In some implementations, the exciter device and the response sensor may be permanently installed on the structure under test. However, permanent installation requires the use of new equipment to measure the SRF for each different structure. When measuring the SRF of multiple different structures (e.g., assembled on a production line), using new equipment for each structure increases manufacturing costs and can introduce experimental uncertainties and errors between measurements due to inaccuracies and variations in the equipment). Conversely, when the same set of instruments is used for SRF measurements on several different structures by temporarily installing the instruments on each structure, experimental uncertainties and measurement errors can still occur due to variations in the placement of the instruments, as well as possible changes in the instruments due to repeated installation, removal, and associated handling.

[0003] Thus, in various embodiments, the systems and methods described in this disclosure provide a fixture for permanently installing measurement hardware at a predefined location for fast and reliable automated SRF measurements. In some embodiments, the fixture is coupled to a test bench and configured to hold a structure under test during the SRF measurement process. After the SRF measurement process is completed, the structure under test is removed (e.g., disconnected from the fixture) and another structure under test can be selectively coupled to the fixture for SRF measurement. In this manner, the equipment (e.g., excitation devices and response sensors) remain in place while a different structure is coupled to the fixture for SRF measurement, and the positioning of each exciter device and response sensor relative to the other excitation devices and response sensors, as well as relative to the structure under test, remains constant for SRF measurements for different structures to, among other things, enable consistent data acquisition.

[0004] When measuring the SRF of multiple different structures (e.g., different structures of the same design assembled on a production line), installing the equipment for each test on the structure under test increases test time and effort. Also, experimental uncertainties and errors can occur between measurements due to inaccuracies and variations in the equipment. Conversely, when the same set of equipment is used for SRF measurements on multiple different structures by permanently installing the equipment in an impedance fixture and connecting the impedance fixture to each structure under test, experimental uncertainties and measurement errors can be minimized because there is no possibility of equipment changes due to variations in equipment placement and repeated installation, removal, and associated handling. In some implementations, the impedance fixture acts as an "instrumentation washer" to connect the structure under test to the test bench. This "instrumentation washer" holds all the exciters and sensors (otherwise "glued") to the structure under test. Therefore, test results and measurements can be more accurate (no operator uncertainty) and faster, and the Cartesian coordinate system remains the same during all measurements (the coordinate system is defined by the permanently installed equipment).

[0005] In some implementations, the impedance fixture (including permanently mounted equipment) acts as a passive structural component mounted between the structure under test and the test bench (similar to a complex engineered washer). The impedance fixture does not change the intended motion of the structure under test (e.g., steering from left to right in a test procedure to characterize the acoustic performance of a steering system on a bench). In some implementations, when the SUT is turned off (no steering), the exciter devices attached to the impedance fixture are operated one at a time to characterize the SRF of the system. In some implementations, the measurement location of interest (e.g., the center of the steering mount) is not accessible for direct measurements (i.e., measuring force and moment excitations and translational and rotational responses at the center of the mount). In this scenario, a coordinate transformation may be used to project the force excitation and response measurements on the impedance fixture to the point of interest (e.g., the center of the steering mount). In other words, the force excitation and response measurements of the impedance fixture (near the point of interest) are used to determine a "virtual excitation and response". In some implementations, the impedance fixture is rigid in the area close to the point of interest so that an accurate coordinate transformation can be performed. In other words, the impedance fixture behaves like a rigid body in the frequency range of interest (where the SRF is analyzed; e.g., 10 Hz to 3 kHz) without local flexibility (the impedance fixture's own natural frequency of 10 Hz to 3 kHz). Otherwise, local flexibility could introduce errors in the coordinate transformation (which is a linear projection).

[0006] In one embodiment, the invention provides a system for characterizing a response of a structure under test (and / or a combined response of the structure under test and a fixture coupled thereto) to an applied excitation force. The system includes a fixture, a plurality of excitation devices, and a plurality of response sensors. The fixture is selectively coupleable to the structure under test and configured to hold the structure under test in a known position and a known orientation relative to the fixture. Each excitation device of the plurality of excitation devices is coupled to the fixture at a different known position and a different known orientation relative to the fixture and configured to controllably apply an excitation force to the fixture. Each response sensor of the plurality of response sensors is coupled to the fixture and configured to sense a dynamic response. The excitation forces applied to the fixture by each excitation device are transmitted by the fixture to the structure under test, and the dynamic response measured by each response sensor is indicative of a response of the structure under test to the applied excitation force. In some implementations, the system includes a controller configured to receive the response sensor data, apply a mathematical coordinate transformation to project the forces and moments to a target point on the structure under test, and calculate a system response function based at least in part on the projection. In some embodiments, the excitation device is arranged to apply linear excitation forces in directions parallel to at least three different axes to a target point on the structure under test and to apply rotational excitation forces about each of the at least three different axes to the target point on the structure under test.

[0007] In some embodiments, the present invention provides a method of operating a system by selectively coupling a first structure under test to a fixture, selectively and controllably operating a plurality of excitation devices to apply a plurality of excitation forces to the first structure under test, receiving force response data, and then applying a mathematical coordinate transformation to project the forces and moments to a target point before calculating a system response function. The first structure under test is then decoupled from the fixture, and a second structure under test is coupled to the fixture without changing the relative positions and orientations of the excitation devices or response sensors. The excitation devices are then selectively and controllably operated to apply a plurality of excitation forces to the second structure under test, receiving new force response data for the second structure under test, and again applying the mathematical coordinate transformation to project the forces and moments of the second structure under test to a target point before calculating a system response function for the second structure under test.

[0008] Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a perspective view of a schematic diagram of the excitation force applied to the structure under test and the response acceleration measured during the SRF measurement process. [Diagram 2] FIG. 1 is a block diagram of a control system for the automated SRF measurement process. [Diagram 3] 3 is a flow chart of a method for performing an automated SRF measurement process using the system of FIG. 2. [Figure 4] 3 is a flow chart illustrating another example of a method for performing an automated SRF measurement process using the system of FIG. 2. [Figure 5A] FIG. 1 is a perspective view of a test bench including a pair of C-shaped fixtures for selectively holding a steering gear assembly during the SRF measurement process according to one embodiment. [Figure 5B] FIG. 5B is a perspective view of the C-shaped fastener of FIG. 5A. [Figure 5C]FIG. 5B is another perspective view of the C-shaped fastener of FIG. 5A. [Figure 5D] FIG. 5B is yet another perspective view of the C-shaped fastener of FIG. 5A. [Figure 5E] FIG. 5B is yet another perspective view of the C-shaped fastener of FIG. 5A. [Figure 5F] FIG. 5B is a perspective view of the C-fixture of FIG. 5A without the exciter device to show other details of the C-fixture construction. [Figure 6A] FIG. 13 is a perspective view of a test bench with three L-shaped fixtures for selectively holding a steering gear assembly during the SRF measurement process according to another embodiment. [Figure 6B] FIG. 6B is a perspective view of the L-shaped fixture of FIG. 6A showing the location of the exciter device. [Figure 6C] FIG. 6C is a perspective view of an example of the L-shaped fixture of FIG. 6B with three tri-axis accelerometers. [Figure 6D] FIG. 7C is a perspective view of another example of the L-shaped fixture of FIG. 7B with up to eight tri-axis accelerometers. [Figure 6E] FIG. 7C is another perspective view of another example of the L-shaped fixture of FIG. 7B with up to eight tri-axis accelerometers. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Before describing any embodiments of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or carried out in various ways.

[0011] FIG. 1 illustrates an example of a steering system 101 coupled to a test bench 102. While coupled to the test bench 102, the steering system undergoes a process to characterize a system response function (SRF) at a center point 103 of the steering mount of the steering system 101. More specifically, in some implementations, the process measures a composite system response of the steering system 101 and the test bench 102 to which the steering system 101 is coupled in the x, y, and z directions of a Cartesian coordinate system, as well as the corresponding rotational α, β, and γ, as shown by the reference numbers in FIG. 1. In some implementations, this type of SRF characterization may be performed by applying force and moment excitations in each Cartesian and rotational direction and measuring the resulting linear and angular acceleration responses. To reduce system, measurement, and computational complexity, in some other implementations, a mathematical coordinate transformation is used to project the forces and responses to a point of interest (i.e., the center point 103 of the steering mount). In the example of Figure 1, the arrows pointing towards the steering system 101 represent the projected forces, and the arrows extending from the cube-shaped three-axis accelerometer 105 represent the projected responses. Thus, measurements of rigid regions close to the target location (e.g., the centre point 103 of the steering mount) can be used to obtain translational and rotational information. However, this requires relatively high-precision knowledge of the location and orientation of each force / response measurement relative to the point of interest (e.g., the centre point 103 of the steering mount).

[0012] In some implementations, a plurality of exciter devices (e.g., "shakers" configured to apply vibration forces by alternating linear motion of a weighted body of the shaker) and a plurality of response sensors (e.g., accelerometers) are configured on a rigid fixture that is selectively coupleable to a structure under test (e.g., steering system 101 of FIG. 1) at known fixed locations. FIG. 2 illustrates an example of a control system for performing a series of multi-degree-of-freedom excitation / response measurements of a structure under test. The controller 201 includes an electronic processor 203 and a non-transitory computer-readable memory 205. The memory 205 stores data and / or computer-executable instructions. The electronic processor 203 is communicatively coupled to the memory 205 and executes instructions stored in the memory 205 to provide the functionality of the controller 201 (e.g., including the functionality described herein).

[0013] The controller 201 is communicatively coupled to the plurality of exciter devices 207.1, 207.2, 207.n and configured to selectively apply an excitation signal to one or more of the exciter devices 207.1, 207.2, 207.n. In response to receiving an excitation signal, each exciter device 207.1, 207.2, 207.n is configured to induce an excitation force (e.g., a vibration force and / or an impact force) in accordance with the excitation signal. In some implementations, the exciter devices 207.1, 207.2, 207.n are magnetic actuation devices, and the control signal is provided in the form of an alternating current applied to an electromagnetic coil of the exciter device 207.1, 207.2, 207.n to drive movement of the weighted body of the exciter device 207.1, 207.2, 207.n. In other embodiments, the exciter device may be pneumatically, hydraulically, or mechanically actuated (eg, a device having a pretensioned spring that is released to apply the impact), for example.

[0014] The controller 201 is also communicatively coupled to a number of response sensors 209.1, 209.2, 209.m. In some implementations, the response sensors 209.1, 209.2, 209.m each include one or more accelerometers (or, for example, a three-axis accelerometer). When an excitation force is applied to the structure under test (e.g., the steering system 101) by the exciter devices 207.1, 207.2, 207.n, the response sensors 209.1, 209.2, 209.m measure how the structure under test (and fixtures attached thereto) responds to the applied excitation force (i.e., how the applied force moves through the structure under test to another location) and each transmits a signal to the controller 201 indicative of the measured response (e.g., a measured acceleration, velocity, and / or displacement). In some implementations where testing is performed using an impedance fixture, the dynamic response of the connected parts (e.g., the structure under test, the fixture, and any other components that may be coupled to them) are measured by the response sensors 209.1, 209.2, 209.m to perform in situ block force measurements. In some implementations, the response sensors 209.1, 209.2, 209.m (or another load sensor / accelerometer) may be positioned proximate the exciter devices 207.1, 207.2, 207.n and configured to transmit a signal to the controller 201 indicative of the actual excitation force applied by the exciter devices to the structure under test.

[0015] 3 illustrates a first example of a method executed by the controller 201 to collect measurement data when a structure under test is coupled to a fixture equipped with equipment described herein. The controller 201 selects a particular exciter device among the plurality of exciter devices 207.1, 207.2, 207.n (step 301) and selects a particular response sensor among the plurality of response sensors 209.1, 209.2, 209.m (step 303). The controller 201 then induces an excitation force in the structure under test by applying an excitation signal to the selected exciter device (step 305) and measures the response based on the output signal from the selected response sensor (step 307). In some implementations, if the SRF measurement is determined as a measured response relative to an applied force, the induced force must also be known. Thus, in some implementations, a load cell is also included (e.g., installed between the exciter device and the fixture) and used to measure the actual force applied by the exciter. In some embodiments, the controller 201 may be configured to repeat the process of FIG. 3 for multiple different exciter device / response sensor combinations to collect sufficient data to fully characterize the SRF of the structure under test.

[0016] In some implementations, the controller 201 is further configured to apply a mathematical coordinate transformation to determine the excitation force and corresponding response at a target point of the structure under test (e.g., the center point 103 of the steering mount in the example of FIG. 1). In some implementations, the controller 201 may be configured to perform this mathematical coordinate transformation using one or more of a virtual point transformation, a finite difference approximation, and a multi-point connection. Also, in some implementations, the computational functions described herein may be distributed across multiple different controllers / computers. For example, a first controller may be used to operate the exciter device, and a second different computer system is configured to receive sensed data from the response sensor and / or load cell and perform the coordinate transformation as a post-processing step (e.g., using MATLAB or software).

[0017] FIG. 4 shows an example of a method executed by the controller 201 to use a mathematical transformation to determine the SRF at a target point of a structure under test (e.g., the center point 103 of the steering mount in the example of FIG. 1). The controller 201 selects a first exciter device (step 401) and applies an excitation signal to the selected exciter device (step 403) (while in some implementations also measuring the actual applied excitation force using a load cell coupled to the exciter device). The controller 201 then selects a first response sensor (step 405) and captures the output of the selected response sensor (step 407). The controller 201 then selects a next response sensor (step 411) and captures the output of the next selected response sensor (step 407) while continuing to apply the excitation signal to the selected exciter device. This is repeated until the controller 201 receives a response signal from each of the multiple response sensors (step 409). In the example of FIG. 4, only one exciter device is actuated at each time and the output of the response sensor is read sequentially. However, in other embodiments, the system may be configured to simultaneously read the outputs of all of the response sensors using a multi-channel data acquisition system. Furthermore, in some embodiments, the system may be designed to operate the exciter device to simultaneously apply excitation power from multiple different excitation devices in addition to, or instead of, operating the excitation devices one at a time.

[0018] After collecting response signal measurements from each response sensor while applying the excitation signal to the first exciter device, the controller 201 selects a next exciter device (step 415) and repeats the process of collecting response signal outputs from each response sensor while the excitation signal is applied to the second exciter device. This process is also repeated until response signal data has been collected by the controller 201 from each of the plurality of response sensors 209.1, 209.2, 209.m while the excitation signal is applied to each of the plurality of exciter devices 207.1, 207.2, 207.n, i.e., until response signal data has been collected by the controller 201 for each of the plurality of exciter device / response sensor combinations. Once an excitation signal has been applied to all of the exciter devices (step 413) and response signal data has been collected from each response sensor (step 409), the controller 201 applies a mathematical transformation to the collected data to determine a system response function at a target point on the structure under test (e.g., the center point 103 of the steering mount in the example of FIG. 1) (step 417).

[0019] Using one or more fixture mounts that can be selectively coupled to multiple different structures under test (e.g., multiple different steering systems 101 produced by a manufacturing / assembly line) (e.g., as further described in the examples below), and using instruments (e.g., exciter devices 207.1, 207.2, 207.n and response sensors 209.1, 209.2, 209.m) coupled to (or fixedly integrated into) the fixture mounts, consistent excitation / response measurements can be collected for SRF characterization of multiple different structures under test. This reduces measurement time and effort, and also ensures that sources of measurement error are eliminated. Also, because the position and orientation of the instrumentation on each fixture is known, and the fixtures are configured to selectively couple to each structure under test at the same known point (e.g., the steering mount of the steering system 101 in the example of FIG. 1), the controller 201 can be pre-programmed and / or pre-calibrated to know the position of the instruments relative to a known point on the structure under test (e.g., the center point 103 of the steering mount in the example of FIG. 1). Using mathematical coordinate transformations, the forces and moments can then be accurately projected to the center point 103. The use of the fixture thus facilitates a complete description (e.g., 3 translations and 3 rotations) of the structure under test at the point of interest.

[0020] In some embodiments, as described in some of the examples below, the fixture design is configured to protect equipment from damage when different structures under test (e.g., the next steering system 101) are coupled to the fixture for SRF measurements. Additionally, in some embodiments, the fixture is configured with application specific geometric designs to apply excitation forces and measure system responses at locations that provide more accurate and easily achievable transformations.

[0021] FIG. 5A illustrates an example of a test system for collecting SRF measurements of a steering system 507. The test system includes a test bench platform 501 having two arms 503a, 503b extending therefrom. A C-fixture 505 is coupled to the top of each arm 503a, 503b and configured to selectively couple to a steering mount of the steering system 507. Each C-fixture 505 includes a plurality of exciter devices 509 mounted thereon. In some implementations, an accelerometer for measuring the applied excitation force and / or the system response to the applied excitation force is also positioned downstream of the steering system 507 (e.g., a three-axis accelerometer 511) and / or the C-fixture 505. For example, as shown in the example of FIG. 5A, an additional three-axis accelerometer 513 is positioned on the arm 503a, 503b supporting the C-fixture. Additionally, in some embodiments (as also shown in the example of FIG. 5A), one or more tri-axis accelerometers 515 may be coupled to an acoustic receiver (e.g., a plate connecting the fixture to a test bench). The example of FIG. 5A also shows other tri-axis accelerometers positioned at other locations that may be used in addition to or instead of the locations of tri-axis accelerometers 511, 513, 515. Alternatively or additionally, in some embodiments, multiple accelerometers are coupled to or incorporated within the C-shaped fixture 505.

[0022] 5B-5E show different perspectives of the C-fixture 505 when it is not coupled to the arms 503a, 503b or steering system 507. FIG. 5F shows the C-fixture 505 with the exciter devices removed to provide an unobstructed view of the geometry of the C-fixture 505 and the placement of the acceleration sensors. The C-fixture 505 is referred to herein as "c-shaped" because the multiple exciter devices are positioned to apply excitation forces to the C-fixture 505 at positions that generally form a "c" shape around a target point 525 to which the excitation forces and responses are projected by mathematical transformation.

[0023] This illustrated arrangement of the exciter devices is only one example of a potential configuration, and other positions and orientations may be used in other implementations. In some implementations, the exciter devices are configured such that all directions and moments at the target point 525 are fully excited by the exciter devices. In the example of Figures 5B-5E, the multiple exciter devices include four exciter devices 509x1, 509x2, 509x3, and 509x4 positioned and oriented to apply excitation forces in a linear x-direction relative to the C-shaped fixture 505. In particular, two x-direction exciter devices 509x1 and 509x2 are positioned to apply excitation forces above and below the target point 525 (e.g., positioned in the same vertical plane as the center point 525), and the other two x-direction exciter devices 509x3 and 509x4 are positioned to apply excitation forces on either side of the target point 525 (e.g., positioned in the same horizontal plane as the center point 525).

[0024] The multiple exciter devices also include two exciter devices 509y1, 509y2 positioned and oriented to apply an excitation force in a linear y-direction relative to the C-fixture, with one y-direction exciter device 509y1 positioned to apply an excitation force in the y-direction above the target point 525 and the other y-direction exciter device 509y2 positioned to apply an excitation force in the y-direction below the target point 525. Both y-direction exciter devices 509y1, 509y2 are positioned in the same vertical plane as the target point 525.

[0025] Finally, the plurality of exciter devices includes two exciter devices 509z1, 509z3 positioned and oriented to apply an excitation force in a linear z-direction relative to the C-fixture, with one z-direction exciter device 509z1 positioned to apply an excitation force in the z-direction on a first side of the target point 525 and the other z-direction exciter device 509z2 positioned to apply an excitation force in the z-direction on the other side of the target point. Both z-direction exciter devices 509z1, 509z2 are positioned in the same vertical plane as the target point 525.

[0026] This arrangement of exciter devices shown in the examples of Figures 5B-5E allows forces indicative of both translational and rotational forces at target point 525 to be applied near target point 525. For example, x-direction exciter devices 509x1 and 509x2 apply forces indicative of a translational force in the x-direction and also indicative of a rotational force about the y-axis. Similarly, other x-direction exciter devices 509x3 and 509x4 apply forces indicative of a translational force in the x-direction and also indicative of a rotational force about the z-axis. The y-direction exciter device applies forces indicative of a translational force in the y-direction and also indicative of a rotational force about the x-axis. The z-direction exciter device applies forces indicative of a translational force in the z-direction and also indicative of a rotational force about the x-axis.

[0027] The C-fixture 505 includes four three-axis accelerometer locations around a target point 525 and are positioned in the same yz-plane as the target point 525. A first three-axis accelerometer 521a is positioned above the target point 525 at a location where an excitation force is applied to the C-fixture by an x-direction exciter device 509x1 and a y-direction exciter device 509y1. A second three-axis accelerometer 521b is positioned on a first side of the target point 525 in the same horizontal plane as the target point 525 at a location where an excitation force is applied to the C-fixture by an x-direction exciter device 509x3 and a z-direction exciter device 509z1. A third three-axis accelerometer 521c is positioned on a second side of the target point 525 opposite the second three-axis accelerometer 521, in the same horizontal plane as the target point 525, at a location where an excitation force is applied to the C-shaped fixture by the x-direction exciter device 509x4 and the z-direction exciter device 509z2. Finally, a fourth three-axis accelerometer 521d is positioned below the target point 525 at a location where an excitation force is applied to the C-shaped fixture by the x-direction exciter device 509x2 and the y-direction exciter device 509y2.

[0028] In the example of Figures 5A-5F, the first triaxial accelerometer 521a and the fourth triaxial accelerometer 521d are aligned with the target point 525 along the z-axis. Similarly, in the example of Figures 5A-5F, the second triaxial accelerometer 521b and the third triaxial accelerometer 521c are aligned with the target point 525 along the y-axis. The triaxial sensors are used to measure the combined dynamic response of the structure under test and the fixture coupled to it. The four triaxial sensors shown in the example of Figures 5A-5F are arranged in a "cross pattern" and perform coordinate transformations on the acceleration response data. In this way, a "virtual" response (i.e., three translations and three rotations) can be calculated at the target point 525 using the four adjacent sensors. In other implementations, other sensor positions and orientations may be utilized.

[0029] Although not shown in the examples of Figures 5A-5F, in some embodiments, the C-fixture 505 also includes a number of load cells integrated into each exciter device or positioned between each exciter device and the C-fixture. These load cells measure the actual excitation forces applied to the C-fixture by each corresponding exciter device. Thus, in some embodiments, the system is configured to perform two coordinate transformations. First, the eight applied forces (i.e., as measured by the load cells) are projected to the center of the steering mount to obtain a "virtual excitation" due to three forces and three moments. Then, the responses from the four response sensors are projected to the same point to obtain a "virtual response" at the target point 525. These are the structural acceleration responses (three translations and three rotations) due to the "virtual applied forces".

[0030] As seen in Figures 5E and 5F, the C-fixture 505 includes an installation aid 519 for properly aligning the steering system 507 with the C-fixture 505 and coupling the steering gear 507 to the C-fixture 505. The installation aid 519 also facilitates consistent coordinate compatibility between SRF measurements of different steering systems 507. In this example, the installation aid 519 includes an upwardly facing cylindrical protrusion positioned and dimensioned to engage an opening in a steering mount of the steering system 507. Additionally, as seen in Figures 5B, 5C, and 5D, the C-fixture 505 includes an integrally formed mounting bracket 527 configured to couple the C-fixture 505 to the arms 503a, 503b of the test system. As shown in Figure 5A, each C-fixture 505 is coupled to the arms 503a, 503b by extending a bolt from an opening in the mounting bracket 527 to engage the arms 503a, 503b.

[0031] The C-fixture 505 provides spaced force application and response measurement to facilitate finite difference approximations for projecting the excitation forces and response measurements to a target point 525 (i.e., the center point of the steering mount). The C-fixture 505 includes eight exciter devices and four accelerometers mounted (e.g., fixedly coupled) to the C-fixture 505 so that the same equipment can be used for automated SRF measurements of multiple different steering systems 507. The known positions of the exciter devices, and in some embodiments, the output signals from the load cells, allow the controller 201 to determine the known input forces (i.e., actual excitation forces) applied to the C-fixture 505.

[0032] As mentioned above, in various embodiments, the geometry of the fixture can be designed for a particular application. Thus, the C-shaped fixture 505 of Figures 5A-5F is designed to collect SRF measurements of a steering system 507 including two steering mounts, and the controller 201 is configured to project the excitation force and response measurements to a target point 525 (i.e., the center point of each steering mount) using a finite difference approximation. In contrast, Figures 6A-6E show an example using an L-shaped fixture 607 designed to collect SRF measurements of a steering system 609 including three steering mounts, and the controller 201 is configured to use a virtual point transformation to project the excitation force and response measurements to the center point of each steering mount.

[0033] FIG. 6A illustrates an example of a test setup including a test bench platform 601 including a plurality of slots 603 sized and positioned to selectively connect the test bench platform 601 to a T-slot table. A mounting adapter 605 is also coupled to the test bench platform 601. In the example of FIG. 6A, the mounting adapter is a hollow linear structure having a rectangular cross section that is welded to the test bench platform 601. In some implementations, the mounting adapter 605 is a rectangular tube of carbon steel configured with one or more internal sensors and configured for shock mount cable management. In this example, three L-shaped fixtures 607a, 607b, 607c are installed on the mounting adapter 605 positioned at positions that each correspond to a different one of the three steering mounts of the steering system 609. To collect SRF measurements of the steering system 609, the steering system 609 is selectively coupled to the test system by selectively engaging each steering mount 611 with a different one of the L-shaped fixtures 607a, 607b, 607c.

[0034] 6B-6E show detailed views of one of the L-shaped fixtures 607a from the example of FIG. 6A. FIG. 6B shows an example of an L-shaped fixture 607a with the response sensors omitted to more clearly show the geometry of the L-shaped fixture 607a and the placement and orientation of the exciter device. FIG. 6C shows an L-shaped fixture 607 with a first exemplary configuration of response sensors, and FIGS. 6D and 6E show an L-shaped fixture 607 with further examples of response sensor arrangements that may be used in some embodiments in addition to or instead of the response sensor configuration of FIG. 6C. In some embodiments, additional response sensors may be added to the mounting adapter 605 and test bench platform 601 to characterize the SRF between the L-shaped fixture (coordinate transformation of excitations applied to obtain forces and moments at the center of the L-shaped fixture 607) and other "remote" sensors (e.g., additional sensors mounted to the mounting adapter 605 and / or test bench platform 601).

[0035] As shown in Figure 6B, the steering system 609 is coupled to the L-shaped fixture 607a by passing the steering mount bolt 621a through the steering mount opening of the steering system 609. As shown in Figure 6E, the L-shaped fixture 607a includes a helically threaded opening 621b positioned to receive and engage the steering mount bolt 621a. Thus, after positioning the steering mount near the L-shaped fixture 607a and passing the steering mount bolt 621a through the steering mount opening of the steering system 609, the steering mount bolt 621a is rotated by a threading action to engage the threaded opening 621b and tightened to securely fasten the steering system 609 to the L-shaped fixture 607a.

[0036] The L-shaped fixture 607a in this example includes eight exciter devices 623x1, 623y1, 623z1, 623z2, 623z3, 623z4, 623_1, 623_2. The body of the L-shaped fixture 607a includes four mounting protrusions 625a, 625b, 625c, 625d. In some implementations, each mounting protrusion 625a, 625b, 625c, 625d is integrally formed as part of the body of the L-shaped fixture 607a (e.g., part of a single molded piece), and in some other implementations, the mounting protrusions 625a, 625b, 625c, 625d are coupled to the body of the L-shaped fixture by, for example, one or more mounting bolts. Each mounting projection 625a, 625b, 625c, 625d is approximately cube-shaped and therefore presents five distinct exposed flat surfaces. In some implementations, the exciter devices 623x1, 623y1, 623z1, 623z2, 623z3, 623z4, 623_1, 623_2 are coupled to some of the exposed flat surfaces of the mounting projections 625a, 625b, 625c, 625d. The L-shaped fixture 607a also includes a protective plate 627 positioned to shield the equipment (e.g., the exciter devices and / or the response sensors) from physical damage (e.g., accidental impact from other objects).

[0037] As shown in FIG. 6B, in this example, two exciter devices are attached to each mounting projection 625a, 625b, 625c, 625d, and in this example, the outer surface of the body of the L-shaped fixture 607a has a curved shape (e.g., in the xy plane cross section). The arrangement of the mounting projections along this curved surface affects the relative orientation of the exposed flat surfaces of the mounting projections, which in turn affects the relative orientation of the attached exciter devices. In the example of FIG. 6A-6E, each mounting projection 625a, 625b, 625c, 625d includes an exposed upper flat surface and an exposed lower flat surface (e.g., a horizontal flat surface) that are all parallel to each other. The remaining exposed flat surfaces (e.g., vertical flat surfaces) of each mounting projection 625a, 625b, 625c, 625d are all perpendicular to a plane (e.g., an xy plane) that is parallel to the horizontal flat surface. However, due to the curvilinear shape of the body of the L-shaped fastener 607a, the vertical planar surface of each mounting protrusion 625a, 625b, 625c, 625d is not necessarily parallel to the vertical planar surfaces of the other mounting protrusions.

[0038] As shown in FIG. 6B, in this example, mounting projection 625b and mounting projection 625c are positioned at opposite ends of the curved shape of the body, such that each exposed flat surface of mounting projection 625b is perpendicular to the corresponding exposed flat surface of mounting projection 625c (i.e., the outwardly facing flat surface of mounting projection 625b is in a plane perpendicular to the plane occupied by the outwardly facing flat surface of mounting projection 625c). However, the arrangement of mounting projection 625a and mounting projection 625d is in other positions between the ends of the curved shape of the body, and thus is arranged at other relative angles. Thus, in this example, the outwardly facing flat surface of mounting projection 625a is in a plane that is angularly offset by 30° from the plane occupied by the outwardly facing flat surface of mounting projection 625b and angularly offset by 60° from the plane occupied by the outwardly facing flat surface of mounting projection 625c. Similarly, in this example, the outwardly facing flat surface of mounting protrusion 625d lies in a plane that is angularly offset by 30° from the plane occupied by the outwardly facing flat surface of mounting protrusion 625c and angularly offset by 60° from the plane occupied by the outwardly facing flat surface of mounting protrusion 625b.

[0039] In this example, each exciter device is configured to apply an excitation force in a direction perpendicular to the surface to which it is attached. Thus, in this example, all of the exciter devices attached to the vertical flat surfaces of the mounting projections 625a, 625b, 625c, 625d are configured to apply excitation forces in a direction parallel to the xy plane, but the directions of the applied excitation forces are not parallel to any single common axis. Conversely, in this example, all of the exciter devices attached to the horizontal flat surfaces of the mounting projections 625a, 625b, 625c, 625d are configured to apply excitation forces in a direction parallel to a single common axis (e.g., parallel to the z axis), but the directions of the applied excitation forces are not all parallel to a common location.

[0040] As shown in FIG. 6B, exciter devices 623z1, 623z2, 623z3, and 623z4 are coupled to horizontal planar surfaces of mounting projections 625b, 625a, 625d, and 625c, respectively. Thus, exciter devices 623z1, 623z2, 623z3, and 623z4 are each configured to apply excitation forces in a direction parallel to the same axis (i.e., the z-axis of L-shaped fixture 607a). However, due to the curved shape of the body of L-shaped fixture 607a, the excitation forces applied by exciter devices 623z1, 623z2, 623z3, and 623z4 are not parallel to a single shared plane.

[0041] The other exciter devices 623_1, 623x1, 623y1, and 623_2 are coupled to the vertical planar surfaces of the mounting projections 625a, 625b, 625c, and 625d, respectively. Thus, the exciter devices 623_1, 623x1, 623y1, and 623_2 are configured to apply excitation forces in a direction parallel to the same plane (i.e., the xy plane of the L-shaped fixture 607a). Due to the curved shape of the body of the L-shaped fixture 607a, the excitation forces applied by the exciter devices 623_1, 623x1, 623y1, and 623_2 are not parallel to the same axis. However, due to the placement of mounting protrusions 625b and 625c at either end of the curved shape, the directions of the excitation forces imparted by exciter device 623x1 and exciter device 623y1 are perpendicular to each other in the xy plane (i.e., the excitation force imparted by exciter device 623x1 is parallel to the x-axis and the excitation force imparted by exciter device 623y1 is parallel to the y-axis). Furthermore, the direction of the force imparted by exciter device 623_1 is parallel to the xy plane but is angularly offset from the x-axis by 30°, and the direction of the excitation force imparted by exciter device 623_2 is parallel to the xy plane but is angularly offset from the y-axis by 30°.

[0042] The arrangement of the mounting protrusions and exciter devices shown in FIG. 6B is merely an example, and in other embodiments, the L-shaped fixture may include more or fewer mounting protrusions. Furthermore, in some embodiments, the relative angle of the mounting protrusions (and therefore the direction of the excitation force imparted by the exciter device) can be changed by changing the shape of the outer surface of the body of the L-shaped fixture and / or by adjusting the position of the mounting protrusions along the outer surface. Furthermore, in some embodiments, the outer surface of the body of the L-shaped fixture may have a shape that is not curved. For example, in some embodiments, the curved outer surface of the body of the L-shaped fixture may be replaced with two or more flat surfaces, and the relative positioning of the exciter devices and / or mounting protrusions on the different flat surfaces of the body of the L-shaped fixture can change the relative angle of the direction of the excitation force imparted by the exciter device.

[0043] Returning now to the example of FIG. 6B, the L-shaped fixture 607a includes a total of eight exciter devices, namely, four exciter devices 623z1, 623z2, 623z3, 623z4, each configured to impart an excitation force in a direction parallel to the same common axis (e.g., z-axis) but not parallel to any single plane, and four exciter devices 623x1, 623y1, 623_1, 623_2, each configured to impart an excitation force in a direction parallel to the same common plane (e.g., xy-plane) but not parallel to any single axis. Furthermore, the common axis of the excitation forces imparted by the first four exciter devices 623z1, 623z2, 623z3, 623z4 (e.g., z-axis) is perpendicular to the common plane of the excitation forces imparted by the other four exciter devices 623x1, 623y1, 623_1, 623_2 (e.g., xy-plane).

[0044] Similar to the example of Figures 5A-5F, the arrangement of excitation devices on the L-shaped fixture in the example of Figures 6A-6E allows the test system to apply excitation forces in six degrees of freedom per mount (e.g., linear x-direction, linear y-direction, linear z-direction, rotation about the x-axis (α), rotation about the y-axis (β), and rotation about the z-axis (γ)). The response of the steering system 609 to these controllably applied excitation forces is measured by multiple response sensors mounted or integrated on the L-shaped fixture 607a and, in some embodiments, on a further downstream connecting structure (e.g., on the mounting adapter 605 and / or the test bench platform 601). Figure 6C shows a first example in which the L-shaped fixture 607a includes three triaxial accelerometers 631a, 631b, 631c. The first triaxial accelerometer 631a is coupled to the outwardly facing flat surface of the mounting protrusion 625a. The second tri-axis accelerometer 631b is positioned in a notch formed in the body of the L-shaped fixture 607a beyond the end of the curved outer surface of the body of the L-shaped fixture 607a, and the third tri-axis accelerometer 631c is similarly positioned beyond the other end of the curved outer surface of the body of the L-shaped fixture 607a. As shown in FIG. 6E, the second tri-axis accelerometer 631b is positioned adjacent to the threaded opening 621b where the steering mount is coupled to the L-shaped fixture 607a, and the third tri-axis accelerometer 631c is positioned further radially from the threaded opening 621b and at a slightly lower height along the z-axis than the second tri-axis accelerometer 631b. Thus, all three tri-axis accelerometers 631a, 631b, 631c are positioned to sense acceleration in a direction parallel to the z-axis, but the x- and y-direction measurements of each tri-axis accelerometer 631a, 631b, 631c are at a different angular offset relative to the x- and y-direction measurements of the other tri-axis accelerometers.

[0045] In some implementations, a minimum of three triaxial accelerometers are used to measure the response to the applied excitation force and gather enough data to use a virtual point transformation technique on the measured response to the projected excitation force and the target position (e.g., the center point of the steering mount). FIG. 6C shows an example of a three-sensor implementation. However, in other implementations, the triaxial accelerometers used to measure the response of the steering system 609 to the applied excitation force can be positioned at other locations on the L-shaped fixture 607a. Additionally, in some other implementations, the L-shaped fixture 607a may be configured to include more than two triaxial accelerometers to "over-determine" the set of equations for the transformation operation.

[0046] 6D and 6E show further examples of triaxial accelerometer arrangements on the L-shaped fixture 607a that may be used in some embodiments instead of or in addition to the arrangement of three triaxial accelerometers 631a, 631b, 631c as shown in FIG. 6C. For example, the triaxial accelerometers may be positioned on the outwardly facing flat surfaces of the other mounting prongs (i.e., triaxial accelerometer 631d positioned on mounting prong 625c, triaxial accelerometer 631f positioned on mounting prong 625b, and triaxial accelerometer 631e positioned on mounting prong 625d). Additionally or alternatively, in some embodiments, a response sensor may be positioned on the L-shaped fixture 607a at a location radially away from the threaded opening (i.e., the point where the steering system 609 is coupled to the L-shaped fixture 607a) that faces the curved outer surface of the L-shaped fixture 607a (e.g., between the L-shaped fixture 607a and the steering system 609). FIG. 6E shows the placement of two three-axis accelerometers 631g, 631h positioned in notches formed in the mounting platform on which the steering system 609 rests when coupled to the L-shaped fixture 607a.

[0047] 6B-6E show a detailed example of only one L-shaped fixture 607a of the three L-shaped fixtures shown in the test system of FIG. 6A. In some embodiments, the other two L-shaped fixtures 607b, 607c include the same number, type, and arrangement of components as L-shaped fixture 607a (e.g., as shown in FIGS. 6B-6E). However, in some other embodiments, the quantity, type, and / or arrangement of one or both of the other L-shaped fixtures 607b, 607c may be different. For example, the L-shaped fixtures may include different quantities or arrangements / orientations of exciter devices and / or response sensors.

[0048] Also, the above examples refer to a Cartesian coordinate system having x, y, and z axes. However, in some implementations, the fixtures may be positioned at different orientations relative to each other (e.g., L-shaped fixtures 607a, 607b, 607c shown in the example of FIG. 6A). In some implementations, the x, y, and z axes for each individual fixture are defined relative to the fixture itself and not relative to a global coordinate system. Thus, in some such implementations, the z-axis used for one fixture may be angularly offset from the z-axis used for another fixture. In other implementations, the system is configured to use a single global coordinate system for all fixtures. In some implementations, the controller (e.g., controller 201 of FIG. 2) is programmed and / or calibrated to know the relative positions and orientations of each exciter device and each response sensor of each fixture used to measure the SRF data of the structure under test.

[0049] The present invention therefore provides, inter alia, a system and method for characterizing a system response (e.g., a system response function) of a structure under test using a fixture having an exciter device and a response sensor attached thereto, and determining the system response at a target location for a structure under test by projecting an applied excitation force and the measured response of the fixture and the structure under test coupled thereto to the target location. Other features and advantages are set forth in the following claims.

Claims

1. 1. A system for characterizing a response of a structure under test, the system comprising: a fixture selectively coupleable to the structure under test, the fixture configured to hold the structure under test in a known position and orientation relative to the fixture; a plurality of excitation devices, each excitation device of the plurality of excitation devices coupled to the fixture at a different known position and a different known orientation relative to the fixture and configured to controllably apply an excitation force to the fixture; a plurality of response sensors, each response sensor of the plurality of response sensors coupled to the fixture and configured to sense a dynamic response, the excitation force applied to the fixture by each of the excitation devices being transmitted by the fixture to the structure under test, and the dynamic response measured by each of the response sensors being indicative of a response of the structure under test to the applied excitation force transmitted by the fixture from the structure under test to the response sensor; A system comprising:

2. receiving dynamic response data from the plurality of response sensors indicative of the response of the structure under test to the applied excitation force; applying a mathematical transformation to the received dynamic response data to calculate a dynamic response of the structure under test at a target point on the structure under test; calculating a system response function of the structure under test based at least in part on the calculated dynamic response at the target points; The system of claim 1 , further comprising a controller configured to:

3. The controller is further configured to selectively apply excitation signals to the plurality of excitation devices, the excitation signals being applied to the excitation devices causing the excitation devices to apply excitation forces corresponding to the excitation signals; applying the mathematical transform includes applying the mathematical transform to excitation force data indicative of the excitation forces applied by the plurality of excitation devices to calculate corresponding excitation forces at the target points of the structure under test; calculating the system response function of the structure under test includes calculating the system response function based at least in part on the calculated corresponding excitation forces at the target points and the calculated dynamic responses at the target points. The system of claim 2.

4. The plurality of excitation devices includes a plurality of vibration shaker devices, each configured to apply a vibration force along a motion axis of the vibration shaker device, the plurality of excitation devices: applying linear vibration forces to a target point on the structure under test in directions parallel to at least three different axes; applying a rotational vibration force about each of the at least three different axes to the target point of the structure under test; a plurality of excitation devices coupled to said fixture in positions and orientations configured to The system of claim 1 , comprising:

5. The fixture is configured to be selectively coupled to the structure under test at coupling points, and the plurality of excitation devices include a first x-axis excitation device coupled to the fixture at a first location and configured to apply a first linear excitation force to the fixture; a second x-axis excitation device coupled to the fixture at a second location and configured to apply a second linear excitation force to the fixture; Including, an excitation axis of the first linear excitation force is parallel to an excitation axis of the second linear excitation force, and the first location and the second location are aligned with a coupling point of the fastener along the second axis; The system of claim 1 .

6. The plurality of excitation devices include a third x-axis excitation device coupled to the fixture at a third location and configured to apply a third linear excitation force to the fixture; a fourth x-axis excitation device coupled to the fixture at a fourth location and configured to apply a fourth linear excitation force to the fixture; Further includes an excitation axis of the third linear excitation force and an excitation axis of the fourth linear excitation force are parallel to the excitation axis of the first linear excitation force, and the third location and the fourth location are aligned with the coupling point of the fastener along a third axis. The system of claim 5.

7. 7. The system of claim 6, wherein the second axis is perpendicular to the third axis, and the second axis and the third axis lie in a plane perpendicular to the excitation axis of the first linear excitation force.

8. The plurality of excitation devices include a first y-axis excitation device coupled to the fixture and configured to apply a fifth linear excitation force to the fixture, an excitation axis of the fifth linear excitation force being parallel to the second axis; a second y-axis excitation device coupled to the fixture and configured to apply a sixth linear excitation force to the fixture, the excitation axis of the sixth linear excitation force being parallel to the second axis on an opposite side of the coupling point from the excitation axis of the fifth linear excitation force; a first z-axis excitation device coupled to the fixture and configured to apply a seventh linear excitation force to the fixture, an excitation axis of the seventh linear excitation force being parallel to the third axis; a second z-axis excitation device coupled to the fixture and configured to apply an eighth linear excitation force to the fixture, the excitation axis of the eighth linear excitation force being parallel to the third axis on an opposite side of the coupling point from the excitation axis of the seventh linear excitation force; The system of claim 7 further comprising:

9. The plurality of response sensors include a first tri-axis accelerometer coupled to the fixture at an intersection of an excitation axis of the first linear excitation force applied by the first x-axis excitation device and an excitation axis of the fifth linear excitation force applied by the first y-axis excitation device; a second tri-axis accelerometer coupled to the fixture at an intersection of the excitation axis of the second linear excitation force applied by the second x-axis excitation device and the excitation axis of the sixth linear excitation force applied by the second y-axis excitation device; a third tri-axis accelerometer coupled to the fixture at an intersection of an excitation axis of the third linear excitation force applied by the third x-axis excitation device and an excitation axis of the seventh linear excitation force applied by the first z-axis excitation device; a fourth triaxial accelerometer coupled to the fixture at an intersection of the excitation axis of the fourth linear excitation force applied by the fourth x-axis excitation device and the excitation axis of the eighth linear excitation force applied by the second z-axis excitation device; The system of claim 8 further comprising:

10. 7. The system of claim 6, wherein positioning of the first x-axis excitation device and the second x-axis excitation device causes the first x-axis excitation device and the second x-axis excitation device to apply a rotational excitation force, respectively, about the third axis, and positioning of the third x-axis excitation device and the fourth x-axis excitation device causes the third x-axis excitation device and the fourth x-axis excitation device to apply a rotational excitation force, respectively, about the second axis.

11. The plurality of response sensors include sensing linear dynamic responses of the structure under test relative to a target point in directions parallel to at least three different axes; Sensing a rotational dynamic response about each of the at least three different axes relative to the target point of the structure under test. a plurality of excitation devices coupled to said fixture in positions and orientations configured to The system of claim 1 , comprising:

12. 10. The system of claim 1, wherein the fixture includes a C-shaped fixture including a structure that extends across two opposing sides of a coupling point where the C-shaped fixture is coupled to the structure under test.

13. 10. The system of claim 1, wherein the fixture includes an L-shaped fixture including a structure that extends across two adjacent sides of a coupling point where the L-shaped fixture is coupled to the structure under test.

14. 2. The system of claim 1, further comprising a controller configured to apply a mathematical coordinate transformation to project the force and moment of the excitation force applied by the excitation device and the dynamic response sensed by the response sensor onto the target point of the structure under test based at least in part on a known position and a known orientation of the excitation device and the response sensor relative to the target point of the structure under test.

15. 15. The system of claim 14, wherein the position and orientation of the excitation device and the response sensor relative to the target point of the structure under test are known due to a known placement of the excitation device and the response sensor on the fixture and a known geometry of the structure under test relative to the fixture.

16. The system of claim 14 , wherein applying the mathematical coordinate transformation comprises applying at least one selected from the group consisting of a virtual point transformation, a finite difference approximation, and a multi-point connection.

17. 13. A method for characterizing a system response function using the system of claim 1, the method comprising: coupling a first structure under test to the fixture; Selectively and controllably operating the plurality of excitation devices to apply a plurality of excitation forces to the first structure under test; receiving force response data from the plurality of response sensors indicative of the response of the first structure under test to each of the applied excitation forces; applying a mathematical coordinate transformation to project the force and moment of the excitation force applied by the excitation device and the dynamic response sensed by the response sensor onto a target point of the first structure under test; calculating a system response function of the first structure under test based at least in part on the projected forces and moments; A method comprising:

18. separating the first structure under test from the fixture; coupling a second structure under test to the fixture; selectively and controllably operating the plurality of excitation devices to apply the plurality of excitation forces to the second structure under test, wherein the known position and the known orientation of the excitation devices relative to the fixture are not altered; receiving force response data from the plurality of response sensors indicative of the response of the second structure under test to each of the applied excitation forces; applying the mathematical coordinate transformation to project forces and moments of the excitation force applied by the excitation device and the dynamic response sensed by the response sensor onto a target point of the second structure under test; calculating a system response function of the second structure under test based at least in part on the projected forces and moments; 20. The method of claim 17, further comprising:

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