To achieve accuracy in all measurements, the physical mounting of accelerometers on a test structure is the first, and often most problematic link in the measurement chain. Problems here will corrupt the measurement and cannot be corrected later.
The Accelerometer Mounting Check (AMC) – based on Brüel & Kjær’s patented technology – provides an easier and faster way of testing accelerometer mounting and verifying, that your transducers mounted correctly, replacing lengthy visual and manual inspection.
Let’s dive into the details.
The Theory Behind The Technology
We model an accelerometer mounted on a structure as a mass-spring-damper system where ms, mb and mt are the seismic mass of the accelerometer, the mass of its base and the mass associated with the test object, respectively (Figure 1). The two first masses are connected by a spring with stiffness kPZ that represents the piezoelectric element.
ACCELEROMETER TYPE 4533-B
Figure 1: Type 4533-S and mass-spring-damper system
A spring/damper element kM is added to model the influence of the test object. The masses can move along the vertical axis, and their coordinates are xs, xband xt, respectively. The easiest way to derive the equations of motion is to use Lagrange’s equations.
First we construct the Lagrangian L=T-V, where T and V are kinetic and potential energy of the system:
With no external forces acting on the system and omitting dissipation.
The Lagrange equation is:
Where xj is one of the coordinates xs, xb and xt. Differentiation yields three equations of motions.
In matrix notation these are:
Or in a more compact format:
The system has three degrees of freedom (DOF), one of them being the rigid-body motion of the assembly. Following the AMC approach, a periodic electrical charge is applied to the piezoelectric element, making it contract and expand. This applies forces (denoted by the grey arrows in Figure 1) acting on the seismic mass and base.
Simultaneously, AMC measures the response of the accelerometer, which is proportional to the deformation of the piezoelectric element (xs - xb) and calculates the AMC FRF between the response and applied charge.
It is possible to obtain the AMC FRF analytically. As the elements of the matrix [α(ω)]=([K]-ω2 [M])-1 are the FRFs between the corresponding DOFs, the AMC FRFs can be combined from the elements of [α(ω)] = ([K] - ω2 [M])-1 are the FRFs between the corresponding DOFs, the AMC FRFs can be combined from the elements of [α(ω)].
Figure 2 illustrates AMC FRFs computed for three important scenarios: A properly mounted accelerometer, a free hanging accelerometer and the accelerometer properly mounted on a structure made of a light material (like wood) or on thin metal or plastic plate. Comparing the measured curves, AMC is able to detect the mounting quality.
Figure 2: AMC frequency response functions
If during the test, an accelerometer falls off the structure, its AMC FRF will rather look like the grey curve that corresponds to the free hanging accelerometer; the algorithm detects if the two curves significantly differ in the white region and asks the user to check the accelerometer mounting.
If the accelerometer is mounted on a structure made of light material, the reference AMC FRF may look like the blue curve (kM → ∞, mt small). In the white region, it is almost impossible to distinguish it from the free hanging AMC FRF, and thus the AMC can fail.
To prevent this, the BK Connect™ software introduces a pre-test wizard to recognize such situations.
In addition, Accelerometer Mounting Check automatically verifies that accelerometers are working and whether the mounting has changed: