Mounting of accelerometers with structural adhesives: Experimental characterization of the dynamic response

ABSTRACT The use of accelerometers to monitor the vibrations of either complex machinery or simple components involves some considerations about the mounting of the sensor to the structure. Different types of mounting solutions are commonly used, but in all cases they can be classified in one of these categories: stud mounting, screw mounting, adhesive mounting, magnetic mounting, and probe sensing. Indeed, each of them has a specific field of application depending on e.g. the mounting surface conditions, the temperature, the accessibility to the specific mounting point, etc. The choice of the mounting solution has an important effect on the accuracy of the usable frequency response of the accelerometer, since the higher the stiffness of the fixing, the higher the low-pass frequency limit of the mounting. This article specifically focuses on adhesive mounting of accelerometers, which includes a great number of different products from the temporary adhesives like the beeswax to the permanent ones like cyanoacrylate polymers. Among the variety of commercial adhesives, three specific products have been experimentally compared to assess their transmissivity and the results are reported in this article. A two-component methylmethacrylate (HBM X60), a modified silane (Terostat 737), and a cyanoacrylate (Loctite 454) adhesive have been used to join two aluminum bases, one connected to an accelerometer and the other to the head of electromagnetic shaker. A design of experiment (DOE) approach was used to test the system at several levels of amplitude and frequency of the external sinusoidal excitation supplied by the shaker.


INTRODUCTION
The vibration monitoring activity is the most used technique to assess the working condition of a machinery. The aims of this activity are: monitoring the noise level of a component, monitoring the vibration transmitted to close system components, increasing the precision of an end-effector, A c c e p t e d M a n u s c r i p t 3 a wide frequency response. Since the introduction of the first piezoelectric accelerometer was in the '50s (MEMS come lately), a relevant amount of papers on signal processing can be traced in literature, defining the know-how on vibration analysis so far. It is interesting to observe that despite the thousands of papers describing how to treat the vibration signal, only few papers focuses on a correct setup of the vibration sensors [1]. This practical aspect is demanded to the university courses on vibrations analysis, personal experience or to information given by the accelerometer suppliers [2][3][4]. This paper focuses on a specific aspects of the accelerometer setup, the mounting between the sensor and the surface of the component. The most frequent solutions adopted can be classified in few categories: stud mounting, screw mounting, adhesive mounting, magnetic mounting and probe mounting. Each of them has a specific field of application depending on e.g. the mounting surface conditions, the temperature, the accessibility to the specific mounting point, etc. A detailed description of all the mounting techniques is not the purpose of the paper, but in the classic handbook on shock and vibration [5] all details are provided. Among the several techniques, the stud/screw and adhesive mounting are the most used. These types of mounting results in a rigid connection with high stiffness and wide frequency range response. The higher the stiffness of the fixture, the higher the low-pass frequency limit of the mounting. While an high stiffness is always provided through the screw coupling, the stiffness of the adhesive bond depends on the physical characteristics of the adhesive, which are not always supplied by the vendor. The aim of this paper is to assess experimentally the dynamic response of three different adhesives which cover the different type of structural adhesive used in on-field applications. Structural adhesives are a standard in the A c c e p t e d M a n u s c r i p t 4 fastening of sensors and accelerometers, since they provide a fast and simple mounting without the need of drilling permanent threaded holes on the chassis of the machine [5].
The aim of the paper is to assess which is the effect of the adhesive film used to bond the stud in terms of vibration monitoring and signal transmission. Despite the wealth of information about static mechanical properties of adhesive, like elastic modulus and strength, often supplied directly from the manufacturer, technical literature reports less information about the dynamic of adhesives and mainly in case of high strain rate loading [6] and viscoelastic properties [7]. This work investigates the effects of different adhesives on the vibration monitoring commonly used in industry. The adhesives are used to join two aluminium bases, the first one connected with a threaded coupling to an accelerometer and the second one coupled with the head of electromagnetic shaker. The description of the experimental procedure and the detailed experimental set up are shown in Section 2.3. The decision to use an aluminium substrate is one of the most demanding condition for the adhesive, since aluminium surface properties are not ideal for the adhesive bonding due to oxide formation. According to technical literature the more reactive the surface is (such as mild steel or brass) the stronger the bonding will be. The Materials and Method section describes as well the design of experiment approach used. It consist of three variables in the experimental plan: adhesive type, frequency and amplitude of the signal. The adhesive choice is led by a practical consideration: typically the adhesive mounting of an accelerometer is performed with a commercial, general purpose adhesive which can be found in every industrial site. Thus a superglue, a modified silane adhesive and a strain gauge

Design of Experimental plan
The concept of Design of Experiments (DoE) was developed to optimize the experimental effort for multiple variables involved in a problem [8]. The same principles can be also applied to numerical studies, treating each numerical analysis with a different set of problem parameters as a 'virtual experiment' [9]. In this work the DoE technique was used to estimate the factors with the strongest influence on the dynamic mechanical response of adhesive for mounting accelerometers. Three factors were considered in the analysis namely: G4 is a reference configuration in which there is no adhesive but continuum material. We did not added the beeswax as another level, even though it is one of the most typical way to connect an accelerometer for two main reasons. First the beeswax is stiff in axial direction, but compliant along the plane, therefore it is not recommended for triaxial accelerometers. Second, we wanted to test a general connection, able to mount an accelerometer also upside-down, so the beeswax is not applicable.
We decided to pick three very different adhesives also in term of viscoelastic behaviour. A DMA on the selected adhesives would have been useful, but in literature we could not trace precise information about the viscoelastic behaviour of the adhesives chosen. We can only qualitatively assess that the adhesives have very different viscoelastic behaviour based on the chemistry of the polymers involved [10,11]. in particular the stiffer adhesives (G1 and G3) have limited viscous effect, while the softer one (G2) is quite viscoelastic. According to our intent the viscoelasticity could play a potential beneficial role since it stiffen the adhesive layer improving the signal  Table 1 with a schematic of the mounting configuration. The two aluminium blocks (white squares in the schematics of Table 1) are connected with a thin layer of adhesive (in black), the lower one is connected to the shaker, the upper one has a threaded connection for the accelerometer (grey semicircles). The only difference for the reference configuration with respect to the other cases, is the mass of the single block which is double weighted in order to keep the same nominal natural frequency. We decided not to consider the adhesive layer thickness in the experimental plan even though it is important in the adhesive stiffness and strength [12][13][14][15][16][17], since it is a typical uncontrolled parameter in a practical application of a bonded accelerometer. The description of the deposition of the adhesive layer and the curing process is reported in Section 2.3.
Among the several DoE techniques available, a full factorial plan is adopted, with three replicates for each experimental plan. This approach is combined with a blocking procedure to take into account the different bonding of the adherents. The blocking procedure is a useful tool, typical of the DoE approach, used to avoid any influence of the experimental set up or the operator, as described in [8,18,19]. A c c e p t e d M a n u s c r i p t 8 The statistical software Design Expert was used to build the set of experimental test to be run and to randomize the order of the experiment. The software was also used to post process the results of the analysis by means of the analysis of variance analyses (ANOVA).

System response
The statistical influence of the variables is evaluated in terms of two system responses. Since the shaker excitation is a sine wave at given frequency, the amplitude of the corresponding spectral component is the main output choice. In particular the outputs of the experiments are: i. Spectral amplitude at excitation frequency (SA for brevity) ii.
Percentage of signal energy stored at excitation frequency (SE for brevity) The SA is obtained after the FFT of the measured signal, considering the amplitude of the vibratory signal at the excitation frequency, the SE is the energy of the signal at the excitation frequency over the total energy of the system.

Experimental set-up
The experimental set-up consists in a small electrodynamic shaker, a monoaxial accelerometer, an input and an output board of National Instruments. Table 2   In each test the head of shaker moves harmonically with characteristics listed in Table 1. The amplitude is not measured in absolute "g" value, but as percentage of the maximum control voltage. The sampling frequency is 50 kHz and the acquisition time is 2 seconds. The acquisition system waits a couple of seconds before starting to avoid acquisition of transient effects of the shaker. In order to obtain the system response, the power spectrum of the vibration data is computed as reported in (1)

ANOVA analyses
Multivariable problems can be approached following a statistical method. The Design of Experiment procedure, a powerful statistical technique based on the analysis of variance analyses can be conveniently applied to these classes of problems. ANOVA calculates the variance (standard deviation) of a response considering a specific variable and the global variance of the responses. The ratio between these two variances is called the F-Test value.
In a stochastic (random) process F-value equals one, which means that the considered variable has no effect on the response, because it cannot be distinguished from experimental noise (or numerical error). Conversely the larger the F-Test value the more the variable influences the process. There are a number of approaches to represent the results graphically to demonstrate the effects of the variables on the system outputs. One of the most popular is the normal plot, used to estimate whether a certain set of data follows a Gaussian distribution or not. If the data approximates a straight line the phenomenon is statistically "normal" i.e. follows a stochastic  Figure 2 shows the half-normal probability plots from an ANOVA according to [18] . The analysis was performed on two outputs of the problem (system response) described in Section 3.1. Figure  In Figure 2 the X-axis represents the standardized effect associated with each factor considered.

Half Normal plot of the responses
The greater the standardized effect, the higher the influence of the variable on the response. The Y-axis represents the half-normal probability associated with each effect. The half normal plot is simply obtained by the normal plot with absolute values of the response (no effect of the sign).
Additional statistical information on the half normal plot construction can be found in [18].

Variables interactions and relevance
The effect of the variables in case of interaction is reported in Figure 4a for SA and in Figure 4b for SE. The same graphs are reported in Figure 5 for  Figure 4 and Figure 5 are due to the standard deviation of the experiments in the three replicates for each configuration tested. Figure 4a shows that the amplitude of signal produce an increase in the SA, which is more pronounced at some specific frequencies (2500 Hz and 7500 Hz), while is not evident at the lowest frequency. This behaviour is probably due to the dynamics (e.g. resonance) of the shaker foundation. This is consistent with the subsequent Figure   5a (despite the different ordinate), showing that a normalization with respect to the reference condition removes the variability highlighted in Figure 4a. The adhesive influence is quite evident in Figure 5a, in which it is shown that there is an influence of the adhesive in terms of amplitude of the signal, but the shape of three curves is the same, both for very stiff adhesive like the HBM X60 and very flexible polymers like the silano-modified Terostat 937.
From the point of view of an accelerometer user this behaviour is positive, because the adhesive do not disturb the signal but it only scale the amplitude. The absence of the adhesive influence in Figure 3b confirms that there is no effect of the adhesive in the shape of the measured signal.
Moreover Figure 5b shows that only the frequency slightly affects SER.

conclusion
In this paper three structural adhesives have been experimentally compared to assess their transmissivity in terms of dynamic response. The chosen adhesives are comprehends the most used in accelerometers setup for diagnostics purposes in both laboratory and on-field The effect of the amplitude, relevant for the absolute measurement SA and SE, obviously vanish in both SAR and SER, because the signal is normalized over the reference.

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The adhesive influence is quite evident in SAR, in which it is shown that there is an influence of the adhesive in terms of amplitude of the signal

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The variable interaction for SAR and SER parameters is the same, both for very stiff adhesive like the HBM X60 and very flexible polymers like the silano-modified Terostat 937.
Above them two results are worth mentioning as design guidelines: the response amplitude depends on the structural characteristics of the adhesive and the transfer function of the adhesive layer doesn't distort the signal regardless of the type of adhesive. Therefore, as long as the adhesive layer is thin enough the adhesive type does not influence the transmissivity of the signal and therefore it possible to use the most convenient one according to cost related evaluations or availability. A c c e p t e d M a n u s c r i p t 26