Application of in-situ blocked forces for characterising structure borne vibration of heavy industrial machinery Florian Cabaret 1 , Jacob McCormick 2 , Kian Samami 3 , Oliver Farrell 4 Farrat Isolevel Ltd Altrincham WA15 8HJ, United Kingdom Andrew Elliott 5 , Joshua Meggitt 6 University of Salford, Acoustics Research Centre Salford M5 4WT, United Kingdom

ABSTRACT Industrial machinery can generate excessive vibration, potentially reducing their productivity and disturbing their surroundings. Thus, it is essential to control vibration in industrial envi- ronments and accurate predictions are required to adopt mitigation measures in the initial de- sign stages. It is first necessary to perform measurements on the vibration source to character- ise its operational behaviour, and the obtained properties can be expressed in terms of its blocked forces according to ISO 20270:2019. The data can be obtained from the source mounted on a specific receiver, but still deliver intrinsic quantities that remain valid for any different receiver structures. Although good agreements have already been achieved between predictions and on-board validations from light weight structures, proving the theory is well understood, it has not yet been tested extensively on heavier assemblies which will be the focus of this work. A source characterisation case study is presented in this paper for a typical heavy industrial installation, known as a press, softly mounted on an inertia block isolated from the surrounding factory floor. A description of how the passive properties of the press were ob- tained and vibration predictions at different positions of the coupled assembly will also be given.

1. INTRODUCTION

The vast majority of companies offering insulation solutions for industrial machines rely on de- signs that are several decades old and fairly similar for all types of machines, rarely taking into ac- count their specificities in terms of dynamic behaviours. Therefore, solutions simply based on expe- rience, most likely uneconomical and unoptimized, are offered to an industry in constant search of

1 fc@farrat.com

2 jm@farrat.com

3 km@farrat.com

4 of@farrat.com

5 a.s.elliott@salford.ac.uk

6 j.w.r.meggitt@salford.ac.uk

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performance, quality and sustainability. This situation offers real prospects for development and state of the art vibro-acoustics approaches can be used to address the above-described problems.

To predict the vibro-acoustic response of any industrial system, the source of vibration must firstly be characterised. While an acoustic source can easily be described independently from its environ- ment using its sound power, a vibration source presents a structural power that depends on the type of structure it is attached to. This has caused a certain number of limitations that have been addressed with the popularisation of the blocked force method for source characterisation [1]. The blocked force is an intrinsic source property and can be obtained by means of in-situ measurements taken on the structure attached as in real operation, where no unpractical conditions such as free-free or fixed boundaries need to be established. This method is now commonly used and has been successfully applied to relatively small scale assemblies such as a spindle from a tire-suspension assembly [2], an air generation and treatment unit (AGTU) to be installed on a train [3], or a small air compressor attached to an inertia block [4]. The responses on the receiving structure can then be evaluated by combining the blocked force with the frequency response functions of the combined system; itself obtained from the individual assembly sub-systems through a process known as dynamic sub-struc- turing [5][6]. Dynamic sub-structuring has proven to be extremely powerful thanks to its capability to associate measured and simulated FRFs of individual elements which would be part of the same assembly to predict its overall behaviour once coupled. In the context of heavy industrial machinery design, dynamic sub-structuring offers design engineers the ability to lower the design iterations and optimise the isolation solutions before its physical installation.

This paper presents a case study where the in-situ blocked force together with the sub-structuring method (so-called component-TPA) are applied on a heavy industrial machine resiliently mounted to an isolated foundation. The blocked forces are firstly calculated at the feet of the press and used to derive the level of vibration on and off the foundation, and compared to those directly measured when the source is operating. Finally, various sub-structuring approaches, considering three sub-elements of the assembly (vibration source, resilient mounts and receiver) are applied to predict the level of vibration experienced at two locations of the structure and are compared with actual operational measurements.

2. THEORY

The assembly used as part of the experiment is composed of five elements (see Figure 1), namely: the vibration source (S), isolation mounts (I 1 ), inertia block (IB), isolation pads (I 2 ) and receiver (R). An industrial press was used as a vibration source. It was softly mounted on a concrete foundation (inertial block) providing mass, damping and increasing the system stability as a result of increased stiffness and lower centre of gravity. This inertia block is decoupled from the surrounding factory floor with isolators, which provide a soft connection reducing structure-borne vibration transmitted to the environment.

Figure 1 describes the elements of the assembly and their interfaces, presenting the excitation and response positions used for the experimental measurements. (a) is the location of the internal forces within the source, (b) represents the source-isolation mounts interface, (c) is the isolation mounts- inertia block interface, (d) is the inertia block-isolators interface, (e) is the isolators-receiver interface and (f) is the location of a point on the receiver away from the interface.

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Figure 1: Assembly diagram showing the five elements (S, I 1 , IB, I 2 , R) with their interfaces (a, b, c, d, e, f)

Assembly A describes the source together with its resilient mounts. Assembly B represents the isolated foundation and surrounding factory floor decoupled by a set of isolators. In the context of this paper, the latter is considered as a single element forming the receiver. Finally, Assembly C is used to describe the entire coupled assembly. Two subscripts detail the interfaces where response and excitation measurements are captured respectively. For instance, 𝐘 𝐶,𝑓𝑏 refers to the mobility matrix of the assembly C where the response is observed at (f) when exciting (b).

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2.1. In-situ blocked force

Since contact forces transmitted from a source to a receiver are dependent on the mounting condi- tion as well as the receiver, they cannot be transferred from one assembly to another [7]. These quan- tities are therefore limited and cannot be used for predictive engineering analysis. However, an inde- pendent characterisation of the source can be achieved using the blocked force. Blocked forces have the advantage that they can be used to predict vibrational behaviour when coupled to any receiving structure [8].

In order to characterise the source S, the free velocity 𝐯෤ 𝑆,𝑏 can be measured at the contact points (b) while the source is installed in free-free boundary condition and running at constant operation conditions. The blocked forces can be determined in-situ according to:

−1 𝐯෤ 𝑆,𝑏 (1)

𝐟 ҧ 𝑆,𝑏 = 𝐘 𝑆,𝑏𝑏

−1 is the free source mobility, and 𝐯෤ 𝑆,𝑏 is the oper- ational free velocity.

where 𝐟 ҧ 𝑆,𝑏 is the blocked force at interface (b), 𝐘 𝑆,𝑏𝑏

In practice, operating heavy industrial vibration sources in free conditions is not feasible. Fortu- nately, the blocked forces can also be obtained with the source connected to an arbitrary receiving structure, independently from its boundary conditions. This is achieved using the so-called in-situ blocked force relation,

Assembly oy Assembly BR

−1 𝐯 𝐶,𝑏 (2)

𝐟 ҧ 𝑆,𝑏 = 𝐘 𝐶,𝑏𝑏

where 𝐟 ҧ 𝑆,𝑏 is the blocked force at interface (b), 𝐘 𝐶,𝑏𝑏 is the mobility at the source-isolation mounts interface of the coupled assembly C and 𝐯 𝐶,𝑏 is the operational velocity of the coupled source at (b). Once the blocked force has been characterised, it can be used to predict the vibration response at any point on the receiver according to the equation,

𝐯 𝐶,𝑓 = 𝐘 𝐶,𝑓𝑏 𝐟 ҧ 𝑆,𝑏 (3)

where 𝐘 𝐶,𝑓𝑏 is the forward transfer mobility from the defined blocked force positions (b) to the remote receiver position (f).

2.2. Dynamic sub-structuring

Sub-structuring methodologies are a powerful tool to predict the passive properties of a coupled structure before its construction. To the authors knowledge, no previous works have considered the application of sub-structuring methods on such a heavy industrial machinery. For this reason, various sub-structuring formulations will be used and compared to identify the most suitable for this type of application.

Structure-borne vibration has an influence on the precision of a machine, and can potentially dam- age its inner tooling, ultimately affecting its overall productivity by increasing the maintenance needed. Therefore the internal level of vibration is a valuable quantity for OEMs and industrial plants, and having access to a vibration prediction at the machine feet is considered as an appropriate indi- cator for it. Additionally, the level of vibration transmitted to the surroundings is another crucial quantity to be predicted to design optimised isolation systems, thus transfer mobilities from a source to a receiver should also be estimated before realisation of the anti-vibration structure.

As formulated in [6], two of the most common sub-structuring methods are the primal and dual formulations. They can deliver the mobility matrix of a coupled assembly in its entirety. The primal formulation, expressed in Equation 4, is easily implemented and is often used to assemble finite ele- ment models,

𝐘 𝐶 = ሺ𝐋 T 𝐘 −1 𝐋ሻ −1 (4)

where 𝐋 is a Boolean localisation matrix describing the force equilibrium and the compatibility of the coupling DOFs, and 𝐘 is a block diagonal matrix containing the independent assembly element mo- bility matrices.

However, it has the downside of requiring several matrix inversions (each block matrix of 𝐘 must be inverted), and is therefore suspectable to error amplifications [5]. For this reason, the dual formu- lation is often preferred dual, requiring a single matrix inversion,

𝐘 𝐶 = 𝐘−𝐘 𝐁 T ሺ𝐁 𝐘 𝐁 T + 𝚪ሻ −1 𝐁 𝐘 (5)

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where 𝐘 is a block diagonal matrix containing the independent assembly element impedance matrices, 𝐁 is a signed Boolean matrix describing the coupling DOFs, and 𝚪 describes the inverse point imped- ances of any coupling isolators present. Since the size of the required inversion is reduced to those of the interface DOFs alone after pre- and post-multiplication by 𝐁 and 𝐁 T , this formulation should be computationally more efficient and not as sensitive to errors.

More direct formulations can also be used to calculate the point and transfer mobilities of a coupled assembly from its individual sub-elements properties, without having to extract particular sections of the mobility matrices, as it is the case with Equations 4 and 5. In particular, the point and transfer functions at (b) and (f) interfaces respectively can be obtained conveniently with the following equa- tions [9]:

−1

−1 𝐘 𝐼 + 𝐘 𝐼 + 𝐘 𝑆,𝑏𝑏 ቃ

𝐘 𝐶,𝑏𝑏 = 𝐘 𝑆,𝑏𝑏 ቂ− 𝐘 𝐼 ൫𝐘 𝐼 + 𝐘 𝐵,𝑐𝑐 ൯

𝐘 𝑆,𝑏𝑏 (6)

−1

−1 𝐘 𝐼 ቂ− 𝐘 𝐼 ൫𝐘 𝐼 + 𝐘 𝐵,𝑐𝑐 ൯

−1 𝐘 𝐼 + 𝐘 𝐼 + 𝐘 𝑆,𝑏𝑏 ቃ

𝐘 𝐶,𝑓𝑐 = 𝐘 𝐵,𝑓𝑐 ൣ𝐘 𝐼 + 𝐘 𝐵,𝑐𝑐 ൧

𝐘 𝑆,𝑏𝑏 (7)

In the present paper we will combine the blocked force method, and each of the sub-structuring for- mulations presented above. This is achieved by replacing the forward transfer mobility in equation 3 with a sub-structured prediction obtained by equations 4-7. This combination of blocked force and dynamic sub-structuring is known widely as Component-TPA [2], though was previous referred to as Virtual Acoustic Prototyping [10]. 3. EXPERIMENTAL TEST SET-UP

Three components of the assembly were individually characterised with FRFs obtained from im- pact excitations and acceleration responses at the interface locations of each element. The equipment used for these experiments consisted of 4533-B001 B&K single axis accelerometers as response sen- sors, and a 087B50 ICP instrumentation hammer for performing the structure excitations. The force and acceleration quantities as well as the FRFs were collected with a Sirius Dewesoft data acquisition system at a sampling rate of 5000 Hz with a frequency resolution of 0.153 Hz.

3.1. Source

The vibration source used for the case study is a 40-tonne industrial press manufacturing alumin- ium items. It performs cutting operations obtained from up and down movements of its dies and can work at operational speeds ranging between 100 and 300 revolutions per minute.

The machine is installed on resilient rubber mounts, which is viewed as the most practical option to get as close as possible to free-free conditions. Twelve sensors were used to measure operational accelerations and collect FRFs on the four feet in the three directions X, Y and Z; quantities required to obtain its blocked forces and for sub-structuring analysis.

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Figure 2: Vibration source on isolation mounts, with (b) interface positions

3.2. Isolation mounts

Bespoke isolation mounts manufactured by Farrat Isolevel were used in this experiment. Four 600 x 400 x 50 mm Isomat Squaregrip SG9050II pads inserted in a steel frame were used as resilient interfaces between the press and the foundation. They were characterised vertically with a dynamic hydraulic testing press (MTS, USA). This testing machine uses the ISO 6721 Part 12 test standards for conducting DMA (determination of dynamic properties) of materials in compression, at frequen- cies up to 200 Hz. Out of all the information potentially extracted from the test, only the complex dynamic stiffness (K*) was required to obtain the isolator mobility 𝑌 𝐼 used in all sub-structuring for- mulations.

Figure 3: Dynamic compression for isolation mounts characterisation

3.3. Receiver

The receiver is a 4.9 x 3.7 x 1.5 m concrete foundation, weighing 66.6 tonnes and supported by 42 Isomat BR4050II pads [11] presenting the following dimensions: 330 x 245 x 50 mm. This isolated foundation [12] was engineered to prevent vibration generated by the press to be transmitted to the surrounding environment without compromising the internal stability of the system which could af- fect the quality of the process.

The system, corresponding to Assembly B in Figure 1, was excited in the vertical direction at the four connection points with the isolation mounts (c) and responses were collected at the (c), (d) and (f) interfaces to obtain the point and transfer FRFs characterising the passive properties of the system.

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Figure 4: Receiver structure with (c), (d) and (f) interfaces

3.4. Coupled assembly

Figure 5 presents the coupled structure (Assembly C) composed of the press softly mounted on its inertia block, decoupled from the factory floor by isolation pads.

The assembly was excited to obtain the mobility matrices at (b) and (c) interfaces, used in the blocked force calculations presented in section 4.1. Operational measurements were also performed at a constant operating speed of 300 revolutions per minute (5 Hz) to collect structure accelerations at all positions. Comparisons between the latter and the predictions will be presented in the following section.

Figure 5: Coupled assembly with interface positions

4. RESULTS

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In the following sub-sections, in-situ blocked force method will be applied and validated, by com- bining the blocked forces of the press and measured transfer FRFs to obtain vibration predictions at remote positions of the receiver. Additionally, transfer mobilities of the coupled assembly will also be obtained from the individual properties of the sub-elements and different sub-structuring ap- proaches (component-TPA) providing acceleration predictions at various positions of the system will be compared.

4.1. Blocked forces predictions

The in-situ blocked forces at the press feet have been identified by inverting the coupled FRFs matrix that can be multiplied by the operational velocities measured at the (b) interfaces as shown in Equation 2. Knowing these loads, a predicted velocity can be obtained at the (f) positions located on the factory floor surrounding the isolated foundation, using the measured transfer FRFs between (b) and (f), as presented in Equation 3.

The predicted vertical acceleration at a remote position of the receiver provides a satisfactory fit with the in-situ direct operational measurement of the coupled assembly as shown in Figure 6, vali- dating the in-situ TPA approach. Some disparities are observed below 4 Hz and between the peaks, as they are located at frequencies not excited by the vibration source. The slight deviations at the operating speed of the press (5 Hz) and at frequencies above 50 Hz could be explained by the diffi- culty to get suitable signal-to-noise ratio at remote positions of the receiver (f) when exciting the machine feet (b), due to the large dimensions of the structure and the two stages of isolation to get across i.e. isolation mounts and isolation pads supporting the foundation.

Figure 6: Logarithmic representation of the average vertical acceleration at (f) measured (blue) and predicted using Equation 3 (red-dashed) in narrow band frequency (top) and in third octave bands (bottom) between 1 and 100 Hz.

4.2. Sub-structuring predictions

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As well as being measured, the mobility matrix 𝐘 𝐶,𝑏𝑏 can be calculated from the mobilities of each element of the assembly, using different formulations, as described in Equations 4 to 6. They can then be inserted in Equation 8 with the afore-validated blocked forces at (b) to predict the operational velocity experienced at the feet of the machine:

𝐯 𝐶,𝑏 = 𝐘 𝐶,𝑏𝑏 𝐟 ҧ 𝑆,𝑏 (8)

These calculated vertical accelerations are compared with the operational one measured at the (b) positions as part of the coupled assembly C. Apart from some slight differences observed at frequen- cies above 25 Hz from the direct formulation, all approaches are found to be in excellent agreement with the measured acceleration throughout the entire range of frequency between 1 and 100 Hz.

Figure 7: Logarithmic representation of the average vertical acceleration at (b) measured (blue) and predicted using Equation 6 (red-dashed), Equation 4 (green-dashed) and Equation 5 (violet-dashed) in narrow band frequency (top) and in third octave bands (bottom) between 1 and 100 Hz.

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Since industrial machinery is often manufactured with integrated resilient mounts, it is also inter- esting to consider both elements (S and I 1 ) as constituting the vibration source. In this case, the source is considered to be Assembly A (see Figure 1) and the blocked forces can be obtained at the (c) interfaces. The passive properties of the receiver between (c) and (f) can be obtained from the indi- vidual characterisation of the different sub-structures using Equations 4, 5 and 7, and estimations of the level of vibration on the factory floor can be obtained from:

𝐯 𝐶,𝑓 = 𝐘 𝐶,𝑓𝑐 𝐟 ҧ 𝐴,𝑐 (9)

The direct formulation offers a satisfactory agreement with the in-situ operational measurement of the coupled assembly at the peak defining the source operational cadence, before slightly overesti- mating the subsequent harmonics. The primal and dual formulations present similar results across the frequency range of interest, showing higher acceleration amplitudes at the operating speed and har- monics up to 40 Hz, before getting closer to the in-situ measurement. The discrepancies observed are possibly coming from the difficulty of exciting such a large and heavy structure, probably resulting in consequential errors in the FRFs collected in-situ.

ae —— ae Se

Figure 8: Logarithmic representation of the average vertical acceleration at (f) measured (blue) and predicted using Equation 7 (red-dashed), Equation 4 (green-dashed) and Equation 5 (violet-dashed) in narrow band frequency (top) and in third octave bands (bottom) between 1 and 100 Hz. 5. CONCLUSIONS

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This paper has investigated the in-situ blocked force together with sub-structuring approaches in the context of heavy industrial machinery vibration source. The assembly consisted in a 40-tonne press softly mounted on a receiver, made of a 66-tonne inertia block decoupled from the rest of the factory floor by means of bespoke rubber pads.

The vibration source was characterised in terms of its blocked forces at each of its connection point with the rest of the assembly. These quantities, obtained by inverting the coupled FRF matrix, proved to be able to correctly predict the response at remote locations of the receiver, using measured transfer mobilities of the coupled assembly.

Moreover, different sub-structuring approaches using individual characterisation of all sub-assem- blies have been combined with the blocked force method to predict the level of vibration obtained at different positions of the assembly, in particular at the feet of the press and on the plant floor sur- rounding the isolated foundation. The different formulations resulted in excellent predictions at the machine feet, while the acceleration levels were moderately overpredicted on the factory floor. It is thought that the observed variations are most likely resulting from the difficulty to excite this type of large and heavy structures to obtain accurate FRF measurements. This tends to prove that all com- pared approaches are intrinsically appropriate but highly dependent on the quality of the measured data.

Although the results presented in the paper are promising, future work should be undertaken with the implementation of analytical or numerical data within the models. Using simulation techniques to characterise certain sub-systems would eliminate potential errors due to the complexity of meas- uring heavy-weight assemblies combined with the difficulty of accessing/including the correct num- ber of interface degrees of freedom. Most importantly, the results presented suggest that this type of engineering study could be undertaken before physical realisation of the assembly, allowing for op- timised isolation systems to be designed early in a project.

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