Introduction to Multi-Axis Testing
March 29, 2018
When a vehicle moves down the road it experiences vibrations not along one axis, but along many. Therefore, it makes sense that automotive engineers test products along more than one axis. In the past, engineers implemented the tests along one axis at a time. They would mount the product to a single-axis shaker, test, then take the product off, re-orient, remount and retest on a second and finally the third axis. This is sequential, single-axis method for testing along more than one axis.
Now engineers can test products along multiple axes at once. In addition to being more realistic and time-efficient, this multi-axis method causes products to fatigue faster. A product, while not failing in sequential, single-axis testing, may fail in a more realistic, multi-axis test of the same time duration. For this reason, and others, multi-axis vibration testing is becoming increasingly popular; we present this article to discuss multi-axis test configurations, concerns, and control methods.
Types of multi-axis tests
There are many different ways to configure a multi-axis vibration test. The two key characteristics of any configuration, however, are 1) the number of shakers involved, and 2) the number of axes/degrees of freedom involved. Let us consider some examples.
A MESA (multi-exciter/single-axis) configuration involves two or more shakers (exciters) that shake in the same direction along one axis. Such a setup is used to test over-sized products that require a shaker on each end, in which case the shakers are often synchronized and use the same test profile. See Figure 1.
A four-post configuration has four shakers moving along the same axis (See Figure 2) and is often used for full vehicle testing with a shaker underneath each wheel. Testing involves playing back four recorded field data files, one from each wheel to a corresponding shaker. The recorded vibrations are played back simultaneously, as if the vehicle were actually moving.
In recent years the automotive world has seen a rising interest in another types of multi-axis shaker configurations. The three-axis configuration belongs to the MEMA class (multi-exciter/multi-axis), and involves at least three shakers and motion along the X, Y, and Z axes simultaneously (See Figure 3).
Three-axis testing is primarily used for component or sub-system testing and is accomplished by random vibration testing along each axis using either identical or individualized test profiles. The primary advantage of this configuration is that it provides more realistic testing as compared to traditional single axis testing. We know a vehicle experiences vibration from many directions simultaneously during use, and the three-axis configuration accommodates the three major directions.
Although a three-axis configuration incorporates the three linear directions of motion, it does not accommodate the three rotational directions of motion—roll, pitch, and yaw. A six degrees of freedom (6-DOF) system handles all six: X, Y, Z, roll, pitch, and yaw. There are numerous ways to configure a 6-DOF system but they won’t be discussed in this article.
Four-post testing is just one of the multi-axis modes used in the automotive industry. Another common application is squeak and rattle testing. No automobile driver likes a squeaky seat, but sometimes a seat needs to experience a very particular set of vibrations along more than one axis before the seat emits noise, a scenario that can only be simulated with multi-axis testing. We have also already talked about how multi-axis testing brings products to fatigue failure faster, performing a more realistic test because fatigue damage is applied more realistically than during sequential, single-axis testing. The advantages of multi-axis testing are clear.
With multi-axis configurations come a number of concerns; one is the coupling multiple shakers to the table. Ideally, a shaker along one axis would be able to successfully transfer its motion to the table without affecting the other axes of motion and, when coupling is done properly, a shaker is able to move the table along one axis without causing significant motion in the other two axes.
When excitation along one axis excites another axis, or axes, cross-axis motion has occurred—physical cross-talk. An example is a slip table moving side to side when it should only be moving forward and backward. While it is impossible to completely eliminate cross-axis motion, proper coupling methods can minimize the effect. A common coupling method employs hydrostatic bearings, which allow connections to pivot freely while still allowing transmission of motion from shaker to table. Another method involves sliding bearings. Whatever the coupling method, the goal is the same: to transmit motion without exciting the other axes, and to let the table move as freely as possible (without being impeded by the coupling) when any excitation is applied.
Resonances are a significant concern in multi-axis testing. Cross-axis motion makes resonances are more difficult to control because excitation along any several axes can potentially excite a resonance along another axis or axes. See ‘Defining the Global Error of a Multi-Axis Vibration Test‘ which describes the potentially elevated noise floor and non-linear concerns involved in multi-axis testing. The head expander (or table), too, demands concern, since it must be designed so that resonances are minimized not just along one axis, but along several.
Accelerometer concerns are also amplified in multi-axis testing. Transverse sensitivities produce larger effects since the system is intentionally moving in all directions. In addition, accelerometer placement deserves weighty consideration, with respect to both the number of accelerometers and their locations. Most tables or fixtures aren’t perfectly rigid, and as such, location matters (see Figure 4). Since multiple accelerometers are often used in conjunction with each other to determine motion in a particular degree of freedom, placement effects become magnified.
Even the design of the head expander, i.e. table, is affected by multi-axis configurations, as resonances must be minimized not just along one axis, but along several.
Controlling multi-axis vibration
There are several ways to control simultaneous, multi-axis vibration; perhaps the most popular is matrix control. Matrix control applies to a MIMO (multiple input, multiple output) system that is typically over-determined (more accelerometers than mechanical degrees of freedom). The key in matrix control is the transfer function matrix containing the terms that define how each direction of motion affects the other directions of motion. This matrix defines, for example, how excitation in the Y-axis affects the X-axis, the Y-axis (i.e., the gain along the Y-axis), and the Z-axis.
Matrix control receives information from the accelerometers, determines the vibration along each mechanical degree of freedom involved, and, with knowledge of the transfer function matrix and the system response, is able to compute the drives necessary for control. Although natural dangers with control involving matrices are events when a matrix is not able to be inverted or when the matrix inverse is very large), a method exists to accommodate these events; see MIL-STD-810G. Matrix control theory is comprehensive, taking into account the relationship of each axis with every other axis, and it is able to define simultaneous control all of the shakers involved as an inter-related set instead of each shaker being controlled independently.
Another, simpler, control method is extremal control. Extremal control in multi-axis testing is like extremal control in single-axis testing—the controller controls off of the accelerometer with the maximum (or minimum) value. Unlike matrix control, with extremal control one control loop cannot account for all of the axes simultaneously. Rather, a three-axis system requires one independent control loop per axis of motion, and each separate control loop is controlled using the extremal method.
In either control strategy scenario, there is an understanding that reasonable control tolerances for multi-exciter testing need to be addressed, a point also referenced to in MIL-STD-810G.
This article only briefly addresses multi-axis configurations, concerns, and available control methods—it is not an exhaustive account but rather a brief overview of multi-axis vibration testing. Test engineers can use this overview to identify topics of interest for specific testing situations.