Microsoft Word C046423e doc Reference number ISO 10846 5 2008(E) © ISO 2008 INTERNATIONAL STANDARD ISO 10846 5 First edition 2008 08 15 Acoustics and vibration — Laboratory measurement of vibro acoust[.]
Normal translations
Figure 2 illustrates a schematic test setup for evaluating resilient supports subjected to normal translational vibrations To ensure compliance with ISO 10846 standards, the test arrangement must incorporate the essential components outlined in sections 5.1.2 to 5.1.6, facilitating accurate and standardized vibration measurements.
5.1.2 The resilient support under test
The test element is positioned on a heavy and rigid foundation table
Measurements must be conducted with the test element under a representative and specified preload to ensure accurate results Static preload can be applied using methods such as a hydraulic actuator that also functions as a vibration exciter mounted within a load frame, or by utilizing a dedicated frame designed solely for static preload When employing a static preload frame, auxiliary vibration isolators should be installed on the input side of the test element to effectively decouple it from the frame, ensuring precise measurement conditions.
A force distribution plate is often required between the force transducer(s) and the actuator to ensure effective load distribution In addition to evenly spreading the applied force, this plate also provides a uniform vibration input to the resilient element, enhancing measurement accuracy and system performance Implementing a force distribution plate is essential for achieving precise force measurement and consistent vibration input in testing setups.
The force measurement system on the input side of the resilient support consists of one or more dynamic force transducers (load cells)
To ensure accurate force measurement during testing, it may be necessary to use a force distribution plate positioned between the input flange of the test element and the dynamic force transducer(s) This force distribution plate not only helps distribute the applied load evenly but also enhances contact stiffness between the transducer(s) and the input flange Additionally, it promotes uniform vibration of the input flange, contributing to more reliable and precise test results.
Minimizing the mass of the distribution plate between the force transducer(s) and the test element is essential, as it directly influences the discrepancy between the measured driving point stiffness and the dynamic transfer stiffness of the component A smaller distribution plate mass leads to more accurate measurements and enhances measurement fidelity Maintaining a minimal mass allows for a higher upper limiting frequency (f_UL), improving the dynamic testing range and overall test precision Therefore, reducing the distribution plate mass is crucial for achieving reliable stiffness measurements and extending the effective frequency response of the testing setup.
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Acceleration measurements should be taken on both the input and output sides of the test element to ensure accurate assessment When mid-point positions are inaccessible, indirect measurement techniques, such as signal summation or averaging the signals from two symmetrically placed accelerometers, can be used to estimate mid-point accelerations effectively.
As an option, instead of accelerometers, displacement or velocity transducers may be used, provided that their frequency range is appropriate
The dynamic excitation system must be appropriate for the specified excitation level and frequency range of interest to ensure accurate testing conditions Any type of exciter is permitted, including hydraulic actuators capable of providing static preload, electrodynamic vibration exciters (shakers) with connection rods, or piezoelectric exciters, offering flexibility in selecting the most suitable excitation method for the application.
Vibration isolators are effective for dynamically decoupling exciters and reducing flanking transmission through the frame during static preload application However, in test rigs utilizing hydraulic actuators for both static and dynamic loading, implementing such decoupling is often impractical due to its negative impact on low-frequency measurement accuracy.
Transverse translations
Schematic examples of test setups for resilient supports subjected to translational vibrations perpendicular to the normal load are illustrated in Figures 3 and 4 The test arrangement must include all components specified in sections 5.2.2 to 5.2.6.
The test element is positioned on a heavy, rigid foundation table (see Figure 3) or between stiff columns on a rigid foundation (see Figure 4)
Measurements should be conducted with the test element under a representative and specified normal preload to ensure accurate results Static preload can be applied using various methods, such as a hydraulic actuator mounted in a load frame with the test element, or a dedicated frame designed solely to provide static preload These approaches help maintain consistent testing conditions and enhance the reliability of measurement outcomes.
A force distribution plate is often essential between force transducers and the actuator to ensure optimal performance It serves a dual purpose: distributing the load evenly across the transducer and providing a uniform vibration input to the resilient element Incorporating a force distribution plate enhances measurement accuracy and improves the overall reliability of the testing setup Proper application of this component is crucial for consistent force transmission and precise testing outcomes.
The dynamic force measurement system can include either multiple force transducers designed to measure dynamic shear forces or multiple transducers for assessing normal dynamic forces This flexibility allows accurate detection of shear or normal forces during dynamic testing, ensuring precise data collection for various engineering applications.
A force distribution plate may be required between the test element's input flange and the dynamic force transducer(s) to ensure proper load distribution This plate not only helps distribute the applied force evenly but also enhances contact stiffness between the transducer(s) and the input flange Additionally, using a force distribution plate promotes uniform vibration of the input flange, which is essential for accurate dynamic testing results.
Reducing the mass of the distribution plate between the force transducer(s) and the test element is crucial for accurate measurements, as it directly influences the discrepancy between the measured driving point stiffness and the dynamic transfer stiffness of the test element Minimizing this mass enhances measurement precision and is essential for achieving a higher upper limiting frequency (f UL), thereby improving the overall dynamic testing performance.
Acceleration measurements shall be made on the input and output sides of the test element
Accelerometers should be positioned on the horizontal symmetry axes of the test element flanges or force distribution plates for accurate measurement If these direct locations are inaccessible, indirect acceleration measurement can be achieved by combining signals from symmetrically placed accelerometers, such as averaging their outputs to ensure precise data collection.
Provided that displacement or velocity transducers have the appropriate frequency response, they may be used instead of accelerometers
The dynamic excitation system must be suitable for the appropriate excitation level and the frequency range of interest Any type of exciter is permitted, including hydraulic actuators, electrodynamic exciters with connection rods, and piezoelectric exciters Proper selection of the excitation system ensures reliable performance across the specified frequency range.
Suppression of unwanted vibrations
The test procedures according to this part of ISO 10846 cover measurements of transfer stiffness for unidirectional excitations one by one in normal and in transverse directions
Unequal excitation, boundary condition variations, and differing test element properties can cause unintended strong responses at specific frequencies, despite the intended input vibration To address this, qualitative measures for suppressing unwanted input vibrations are discussed, including the use of symmetrical test arrangements with two identical resilient elements, which can effectively reduce these unwanted responses In section 6.1.3, precise quantitative requirements for vibration suppression are outlined, ensuring accurate control of input vibrations during testing.
For effective excitation in the normal direction, using symmetrical positioning of a single exciter or a pair of exciters is the most favorable method This approach helps suppress transverse and rotational vibrations on the input side, ensuring smoother operation and improved system stability Proper exciter alignment is essential for minimizing vibrations and enhancing overall performance.
To minimize coupling between the normal and other vibration directions caused by the test object's properties, using a symmetrical arrangement with two or four identical test objects is effective Additionally, implementing a guiding system, such as roller bearings on the sides of the excitation mass, helps suppress unwanted input vibrations, ensuring more accurate testing conditions.
NOTE When low-friction bearings are used as a guiding system, the force transducers for measuring the input force
F 1 are to be placed between this guiding system and the test element to avoid errors due to uncertain transmission properties of these guiding components
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For excitation in the transverse direction, coupling between the transverse and rotational input vibrations will always occur
Figures 3 and 4 illustrate measures that can enhance unidirectional vibrations on the input side, with Figure 3 demonstrating how a guiding system effectively suppresses input rotations The symmetrical setup shown in Figure 4 features two nominally equal test objects, highlighting the use of guiding low-friction bearings and a balanced arrangement of test elements to optimize vibration control and measurement accuracy.
4 dynamic decoupling spring, static preload
Figure 2 — Example of laboratory test rig for measuring the dynamic driving point stiffness for normal translations
10 © ISO 2008 – All rights reserved a) Overview b) Input side (details)
4 dynamic decoupling spring, static preload
Figure 3 — Example of laboratory test rig for measuring the dynamic driving point stiffness for transverse translations
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Figure 4 — Example of symmetrical test arrangement for measuring the dynamic driving point stiffness for transverse translations
6 Criteria for adequacy of the test arrangement
General requirements
Each test facility has a limited frequency range in which valid tests can be performed One limitation is given by the usable bandwidth of the vibration actuator
Other limitations follow from the requirements for measuring the acceleration and the input force, and from the unwanted vibration
6.1.2 Limitation due to the acceleration of the output flange
In Figures 2 to 4, the following dynamic measurement quantities are indicated:
⎯ a 1 acceleration of the input flange and the Input-force distribution plate, which is on the test element;
⎯ a 2 acceleration of the output flange
The stiffness measurements according to this part of ISO 10846 are valid only for those frequencies where
A too-small level difference (∆L 1,2) may result from insufficient stiffness mismatch between the test element and the foundation or from flanking transmission To mitigate this, employing vibration isolators to decouple the test element's top from the load frame and the vibration exciter from the frame can significantly reduce flanking transmission, enhancing the accuracy of the measurements.
6.1.3 Limitation due to unwanted input vibrations
Input accelerations in directions other than those of the excitation shall be suppressed according to 5.3
Measurements based on this section of ISO 10846 are only valid at frequencies where the input acceleration in the excitation direction exceeds the acceleration in the perpendicular directions by at least 15 dB.
In normal excitation conditions, the input acceleration along the excitation direction (a₁z) occurs along the line of excitation at the interface between the force distribution plate and the input flange of the resilient element Unwanted transverse inputs (a₁x and a₁y) should be measured at the edge of the force distribution plate, specifically between the force transducers and the input flange.
For transverse excitation in the x- or y-direction, it is essential to measure the unwanted inputs, such as a 1z, a 1y, or a 1x, at the edge of the force distribution plate located between the force transducers and the input flange This measurement ensures accurate assessment of the force distribution and helps identify any extraneous forces that could affect system performance Proper placement and measurement of these inputs are crucial for reliable test results, as illustrated in Figure 3b Understanding how to measure these unwanted inputs enhances the precision and integrity of force testing procedures in transverse directions.
Determination of upper limiting frequency
The upper limiting frequency (f UL) is the frequency above which the dynamic driving point stiffness should not be used to represent the dynamic transfer stiffness It is determined by comparing the measured driving point stiffness at a given frequency with the constant low-frequency value, which is defined as the average stiffness from 1 Hz to 20 Hz The upper limiting frequency (f UL) is identified as the lowest frequency at which the driving point stiffness level decreases by 2 dB compared to the low-frequency stiffness.
Force transducers
Force transducers must be calibrated at laboratory temperature within the specified frequency range, ensuring a frequency-independent sensitivity level within 0.5 dB Calibration should be performed using the mass-loading methodology outlined in ISO 7626-1 to ensure accuracy and compliance with international standards.
If there is an appropriate compensation routine (i.e digital application of an appropriate transfer function), the resultant sensitivity-level function shall meet the 0,5 dB requirement
Force transducers must be designed to minimize sensitivity to environmental factors like humidity, magnetic and electrical fields, acoustical influences, and strain, ensuring accurate measurements Additionally, their sensitivity to cross-axis forces should be limited to less than 5% of the main axis sensitivity, enhancing precision and reliability in various operating conditions.
Accelerometers
Accelerometers must be calibrated at laboratory temperature within the relevant frequency range, ensuring a sensitivity level that remains frequency independent within 0.5 dB The calibration process should adhere to ISO 16063-21 standards to guarantee accuracy and consistency.
Accelerometers must be designed to be sufficiently insensitive to external environmental factors, including humidity, magnetic and electrical fields, acoustical disturbances, and strain Additionally, their sensitivity to cross-axis accelerations should be limited to less than 5% of the primary sensitivity axis, ensuring accurate and reliable measurement performance.
If displacement or velocity transducers are used, the same requirements as for accelerometers apply
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Summation of signals
To ensure accurate signal addition from force transducers or accelerometers, the maximum permissible tolerance is 5% This can be achieved by using identical transducers with sensitivities within 5% of each other or by employing a multi-channel analyzer for summation When using a multi-channel analyzer, it is essential to apply corrections for transducer sensitivity differences exceeding 5% and for variations in channel gain factors, as outlined in section 6.6.
Analysers
Narrow-band analysers must meet specific criteria to ensure accurate measurements, including a spectral resolution that provides at least five distinct frequencies within each one-third-octave band Additionally, the frequency response between channels used for acceleration measurements on both input and output sides should differ by less than 0.5 dB at the same frequency resolution If the response difference exceeds this limit, corrective adjustments are necessary to account for variations in channel gain factors, ensuring precise and reliable data collection.
To compare channel gains effectively, a broadband signal such as white noise should be applied to both channels The narrow-band spectrum of the output ratio's magnitude level should be less than 0.5 dB; if it exceeds this threshold, a correction factor based on the measured gain ratio must be applied This approach ensures accurate assessment of the channels' dynamic stiffness, adhering to best practices in signal analysis.
7.1 Installation of the test elements
The test element is securely attached to the force distribution plate and foundation to ensure optimal contact across the entire flange surface Non-essential devices that are not part of the resilient element should be deactivated and removed to guarantee accurate testing conditions Proper attachment and removal procedures are crucial for reliable test results and effective force distribution.
To ensure optimal contact between the resilient support and the test rig, it is recommended to use grease or double-sided tape; however, using tape may introduce issues at high frequencies For test elements with large flanges, flattening may be necessary to achieve clear and accurate test results.
Rubber-type test elements are prone to creep, which causes changes in load or deflection over time To ensure accurate measurements, these elements must be preloaded with 100% of their permissible static load Additionally, the change in load or deflection due to creep should be less than 10% per day before valid testing can be conducted, ensuring reliable and consistent test results.
Transducers designed for measuring static loads or displacements are widely available, along with comprehensive documentation to support their application Selecting the appropriate transducer depends on the specific load or deflection range of the resilient test element, ensuring accurate and reliable measurement Proper selection and documentation are essential for effective testing and data collection in static load applications.
No particular preloading procedure is required for steel springs, but the appropriate preload shall be applied
7.2 Selection of force measurement system and force distribution plates
Depending upon the size and symmetry of the test isolator and on the maximum permissible load, one or more (up to 4) force transducers shall be applied
The force distribution plates should be designed to be as small and lightweight as possible, ensuring minimal impact on the system It is essential that the system's resonances do not occur within the frequency range of interest to maintain measurement accuracy The minimum lateral dimensions of the plates are determined based on the size of the test object, ensuring proper support and reliable results.
To evaluate the rigid body behavior of the force measurement system, apply a point force at the center of the system The frequency response function, obtained by measuring the applied force with a calibrated force transducer, should be examined for flatness across the desired frequency range A consistent, flat frequency response indicates proper system behavior and reliable measurement performance.
7.3 Mounting and connection of accelerometers
Accelerometers must be mounted on both the input and output sides of the test element to accurately measure parameters 1 and 2, as illustrated in Figures 2 to 4 Ensure the sensors are securely attached with a rigid connection to prevent measurement errors Mounting procedures should strictly follow ISO 5348 standards to ensure consistency and reliability in test results.
Selecting appropriate positions on the force distribution plates or test object flanges is crucial for accurate transducer placement For predominantly vertical or transverse vibrations, a single accelerometer positioned outside the axis of symmetry can be sufficient It is important to verify that rotational vibrations do not cause measurement errors exceeding 0.5 dB, ensuring precise and reliable vibration analysis.
NOTE Measuring the accelerations at different distances from the symmetry axis can perform the check on rotational vibration
To prevent errors due to flange rotations, the signals from two accelerometers that are positioned symmetrically with respect to the vertical symmetry axis may be averaged
7.4 Mounting and connections of the vibration exciter
A connection rod may be required between the vibration exciter and the test element's input side to ensure effective transmission of vibrations It must be designed to prevent resonance, which could cause strong transverse vibrations and excessive sound radiation Proper design of the connection rod is essential to maintain vibration integrity and minimize noise during testing.
One of the following source signals shall be used:
⎯ a bandwidth-limited white noise signal
Ensure that the source signal is applied for a sufficient duration to enable averaging, so that measured results vary by no more than 0.1 dB when the averaging time is doubled When using discretely stepped sinusoidal or periodically swept sine signals, maintain a frequency spacing of 0.2 Hz for frequencies up to 20 Hz For frequencies above 20 Hz, each one-third-octave band should include at least five source signal frequencies to ensure accurate measurement and analysis.
The measurements shall be carried out under one or more specified load conditions, representing the range of loads in practice
The measurements shall be carried out under one or more specified environmental temperatures, representing the range of the environmental temperatures in practice The environmental temperature shall be
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Resilient elements under test must be conditioned at the appropriate environmental temperature within a ±3 °C tolerance for at least 24 hours prior to testing, ensuring consistent and reliable measurement results.
When testing elements with dynamic stiffness highly sensitive to temperature or humidity variations, it is essential to define specific tolerances for these environmental conditions Establishing acceptable temperature and humidity ranges ensures that measurement results are accurate and considered valid Controlling these parameters minimizes variability, leading to reliable and repeatable testing outcomes in accordance with best practices.
During a pre-run, determine the force level (L F1) and acceleration level (L a1) both with and without the vibration source active If feasible, adjust the source output so that there is at least a 15 dB difference across all relevant frequency bands between measurements with the source on and off.
Mounting and connection of accelerometers
Accelerometers should be securely mounted on both the input and output sides of the test element to accurately measure parameters 1 and 2, respectively, as illustrated in Figures 2 to 4 The connection must be rigid to ensure precise measurements Mounting procedures must conform to ISO 5348 standards to maintain consistency and reliability in testing.
Careful selection of positions on the force distribution plates or flanges of the test object is essential for optimal transducer placement For vibrations primarily in the vertical or transverse directions, a single accelerometer placed outside the axis of symmetry may suffice It is important to verify that rotational vibrations do not introduce measurement errors exceeding 0.5 dB, ensuring accurate and reliable vibration analysis.
NOTE Measuring the accelerations at different distances from the symmetry axis can perform the check on rotational vibration
To prevent errors due to flange rotations, the signals from two accelerometers that are positioned symmetrically with respect to the vertical symmetry axis may be averaged.
Mounting and connections of the vibration exciter
A connection rod is often used between the vibration exciter and the test element's input side to ensure effective transmission of vibrations It must be carefully designed to prevent resonance, which can cause strong transverse vibrations and unwanted sound radiation, thereby maintaining test accuracy and equipment integrity Proper design of the connection rod is essential to avoid resonance-related issues during vibration testing.
Source signal
One of the following source signals shall be used:
⎯ a bandwidth-limited white noise signal
When applying the source signal, it must be sustained long enough to enable averaging, ensuring that the measured results do not vary by more than 0.1 dB when the averaging time is doubled For discretely stepped or periodically swept sine signals, the frequency spacing of the source signal should be 0.2 Hz for frequencies up to 20 Hz For frequencies above 20 Hz, each one-third-octave band should include at least five source signal frequencies to ensure accurate measurements.
Measurements
The measurements shall be carried out under one or more specified load conditions, representing the range of loads in practice
The measurements shall be carried out under one or more specified environmental temperatures, representing the range of the environmental temperatures in practice The environmental temperature shall be
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Ensure that resilient elements under test are exposed to the appropriate environmental temperature within a ±3°C tolerance for at least 24 hours prior to testing, to guarantee accurate measurement conditions in accordance with ISO 2008 standards.
To ensure accurate measurement results, it is essential to define specific tolerances for temperature and humidity when the dynamic stiffness of the test element is highly sensitive to environmental conditions If the dynamic stiffness is significantly affected by changes in temperature or humidity, measurements should only be considered valid within these established environmental tolerances This approach maintains the reliability and consistency of test outcomes under varying conditions.
During the pre-run, determine the force level (LF1) and acceleration level (La1) both with and without the vibration source operating If feasible, adjust the source output to ensure at least a 15 dB level difference across all relevant frequency bands when comparing measurements with the source on and off.
A pre-run should be conducted to verify that the acceleration in the excitation direction exceeds that in other directions Measurement data that do not satisfy the condition specified in Inequality (2) must be excluded from the dynamic stiffness analysis Ensuring accurate directional acceleration measurements is crucial for reliable evaluation of the dynamic stiffness function.
Another pre-run shall be performed to check the appropriate accelerometer positions, when single accelerometers are used for measuring a 1 and a 2
Key measurements should include accelerations a 1x, a 1y, a 1z on the input side, force F 1 on the input side, and accelerations a 2x, a 2y, a 2z on the output side The z-direction aligns with the normal axis, while x- and y-directions correspond to the perpendicular transverse axes Measurement data not meeting the criteria specified in sections 6.1 and 6.2 must be excluded from the dynamic stiffness function analysis.
For a measurement method to be valid, it is essential that the vibration behavior of the isolator exhibits approximate linearity, ensuring accurate and consistent results (see 7.7) Additionally, the contact interfaces between the vibration isolator and the adjacent source and receiver structures should be considered point contacts, which is crucial for reliable measurements.
It is the responsibility of the user to demonstrate the frequency range of validity
Measurement results should include an evaluation of their uncertainty, preferably following ISO/IEC Guide 98-3 guidelines If reported, the expanded uncertainty must be provided along with the corresponding coverage factor to achieve a 95% coverage probability, as defined in ISO/IEC Guide 98-3.
Guidance on the evaluation of uncertainty and on the determination of the expanded uncertainty is given in Annex B
Full application of ISO/IEC Guide 98-3 for determining expanded uncertainty is currently limited to specialized laboratories due to insufficient knowledge of major uncertainty sources and reproducibility data Improving this situation requires systematic investigations into various uncertainty contributions as outlined in Annex B However, progress remains slow because of the diversity of test elements and equipment, along with limited funding for comprehensive studies.
Test for linearity
The ISO 10846 series focuses on dynamic transfer stiffness and its measurement methods, which are based on linear models of resilient element vibration behavior However, real vibration isolators often exhibit only approximate linearity, making precise definitions challenging Consequently, this part of the standard addresses the limitations of linear assumptions and highlights the need for practical measurement approaches that account for non-linear characteristics in vibration isolation systems.
ISO 10846 as approximately linear, the validity of dynamic transfer stiffness data in relation to input vibration levels will be considered
Because conducting a full linearity test is impractical, data measured according to ISO 10846 should be evaluated for proportionality Specifically, the assessment involves analyzing the ratio of input force to input acceleration, velocity, or displacement This approach ensures compliance with the standards outlined in section 3.12, Notes 1 and 2, and provides a practical method for verifying the linear behavior of the system.
The validity of dynamic driving point stiffness data, measured according to ISO 10846, is only applicable for input amplitudes that are equal to or lower than those used during testing It is essential that an approximate proportionality between input force and displacement is demonstrated within these specified levels The maximum input level for which the data remain valid must be clearly indicated in the test report to ensure accurate interpretation and application.
The proportionality test involves evaluating input spectra, starting with a one-third-octave-band spectrum A, and comparing it to a second spectrum B, which has levels at least 10 dB lower than A If the driving point stiffness levels for both spectra do not differ by more than 1.5 dB, the data are considered valid for input levels up to those of spectrum A When maximum input levels achievable in the test rig are lower than typical levels in practical applications, the rig must be modified or replaced to ensure valid data If initial tests produce unacceptable results, the process should be repeated at lower input levels until a valid proportionality between input force and displacement or acceleration is established, ensuring reliable measurements for real-world scenarios.
The valid input levels are defined by one-third-octave-band levels of input displacements or accelerations, depending on the measurement These levels must be equal to or lower than those used in tests with higher input levels that produce valid results.
Based on the maximum input levels, simplified testing data can be generated and presented optionally For instance, the test information may specify a maximum root mean square (r.m.s.) input displacement, providing a clear and concise measure for evaluating system performance.
If a test element does not meet the proportionality criteria between input force and displacement, it is classified as non-linear The ISO 10846 standard does not specify measurement procedures for non-linear cases but provides a framework to develop application-specific test procedures For example, it allows for the use of sinusoidal excitations with defined amplitudes to assess non-linear behavior effectively.
Calculation of dynamic driving-point stiffness
When input forces F 1 and accelerations a 1 have been measured, the calculation of dynamic driving-point stiffness requires conversion of accelerations to displacements u 1
For simple harmonic vibration and using phasor notation:
The dynamic driving-point stiffness is a complex quantity with magnitude k 1,1 ( ) f and phase angle ϕ1,1 ( ) f
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Determination of the loss factor η(f), as defined in 3.7, is optional It may be estimated from
This loss factor is also the tangent of the phase angle
One-third-octave-band values of the frequency-averaged dynamic driving-point stiffness
One-third-octave-band averages of k 1,1 shall be obtained as follows:
⎩ ∑ ⎭ (6) where the summation is performed over a minimum of n = 5 frequencies
NOTE 1 Averaging over the squared magnitude is chosen to emphasize the maxima in the stiffness values, which are usually the most important ones
Note 2 indicates that the outcome of Equation (6) is obtained directly from measurements using a real-time, one-third-octave-band analyzer, assuming a flat power spectral density function of the input displacement u₁.
NOTE 3 It is evident that the presentation in terms of one-third-octave-band stiffness forms a practical reduction of the produced data However, phase information is lost.
One-third-octave-band values of the frequency-averaged transfer stiffness
One-third-octave-band averages of k 2,1 shall be obtained by using the results of Equation (6) as follows: av av(2,1) av(1,1) k =k ≈k (7)
If f u f UL , then the accuracy of the approximation in Equation (7) is equal to or within 2 dB
The results are presented in terms of the “level of frequency-band-averaged dynamic transfer stiffness” in accordance with 3.17
Geometric centre frequencies f m for one-third-octave pass bands shall be used in accordance with ISO 266.
Presentation of one-third-octave-band results
The presentation of dynamic transfer stiffness levels for one-third-octave bands shall be in tables and/or in graphical form A table shall contain centre frequencies of one-third-octave bands, levels of dynamic stiffness in decibels and a specification of the reference value (i.e 1 N/m)
The format of the graphs shall be as follows:
⎯ vertical scale: 20 mm for 10 dB or equivalently for a factor 10 1/2 in magnitude;
⎯ horizontal scale: 5 mm per one-third-octave band
These dimensions may be enlarged or reduced in print, as long as the proper ratio is maintained Grids may be used for sake of clarity
An example of the graph format is illustrated in Figure 5, featuring both a decibel scale on the left (vertical axis) and a logarithmic vertical scale in newtons per metre on the right This dual-scale design enhances clarity by providing comprehensive measurement context, making it easier to interpret the data accurately Incorporating both decibel and logarithmic units ensures improved readability and detailed analysis for users.
The presentation should clearly specify the transfer stiffness involved, indicating whether it pertains to the normal or transverse direction Additionally, it must include details about the test conditions, such as temperature, static preload, and any other relevant parameters This information is essential for a comprehensive understanding of the test setup and results.
Figure 5 — Example of the graph for presenting one-third-octave-band levels of the dynamic transfer stiffness at specified test conditions with an example of scale values
Presentation of narrow-band data
For a comprehensive analysis, it is recommended to present the magnitude and phase spectra of the dynamic transfer stiffness, along with the spectra of the loss factor Employing the frequency resolution of the narrow-band analysis ensures accurate and detailed spectral representation, facilitating better understanding of the dynamic behavior of the system.
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It is the user's responsibility to provide adequate supplementary information regarding the accuracy of narrow-band phase or loss factor data when using this section of ISO 10846 Ensuring precise and comprehensive data enhances the reliability of measurements and compliance with standards Proper contextual information allows for better interpretation and application of the phase and loss factor data in relevant assessments.
The dynamic stiffness magnitude should be presented in a clear graphical format, clearly indicating the reference value of 1 N/m It is recommended that the graphs are designed to effectively illustrate the variations in dynamic stiffness levels, ensuring easy interpretation and comparison.
⎯ vertical scale: 20 mm for 10 dB or equivalently for a factor of magnitude 10 1/2 ;
⎯ horizontal scale: 15 mm per octave band
The presentation of the phase data shall be in graphical form
The format of the graphs should preferably be as follows:
⎯ vertical scale: 40 mm for the range −180° to +180°;
⎯ horizontal scale: 15 mm per octave band
The presentation of the loss factor shall be in graphical form The format of the graphs should preferably be as follows:
⎯ vertical scale: 20 mm for a factor 10 in loss factor η;
⎯ horizontal scale: 15 mm per octave band
Linear scales for frequency and stiffness are allowed for narrow-band data in the frequency range 0 Hz up to
NOTE 2 Concerning the above-mentioned graphical formats, also see the remarks in 8.4 on printing
All relevant information shall be recorded, such as: a) the name of the organization that performed the test; b) information on the test element, including
The element's description should clearly define the test element and non-test elements (auxiliary parts not involved in testing), especially when this is not immediately obvious Clear differentiation ensures proper identification and accurate testing procedures, supporting effective testing practices and compliance with relevant standards.
This article emphasizes the importance of comprehensive documentation for vibration attenuators, including manufacturer data related to their application and test arrangements It highlights the necessity of providing photographs or diagrams of the resilient elements and test setup, along with descriptions of auxiliaries used for static preloads Additionally, detailed specifications of force distribution plates—covering dimensions, material, and mass—as well as foundation descriptions and attachment methods, are crucial Measurement spectrum data should be included to verify that acceleration levels meet specified inequalities, ensuring proper performance Furthermore, validation data demonstrating the suitability of measurement positions outside the axis of symmetry are essential, along with precise static preload values expressed in newtons.
20 © ISO 2008 – All rights reserved h) environmental temperature(s) and its variation during the tests, in degrees Celsius; i) other test conditions, such as:
⎯ pre-conditioning of the test element,
The article highlights the importance of documenting any relevant special conditions, such as static deflection and low-frequency superimposed vibrations, including their amplitude and frequency It emphasizes the need to provide a detailed description of the test signals used during testing The spectrum of the acceleration level (La 1) at the input side of the test element, or displacement levels when measured, should be clearly specified Additionally, it is crucial to list the measurement and analysis equipment employed, including details like type, location, serial number, calibration status, and manufacturer Finally, presenting frequency-averaged dynamic transfer stiffness in one-third-octave-band levels offers comprehensive insights into the test results.
For testing at 20 Hz, it is acceptable to present narrow-band data on dynamic driving point stiffness levels The test report should include a description of the linearity test (refer to section 7.7), specifying the amplitude range of acceleration (a₁) or displacement (u₁) within which the data are considered valid Additionally, it should detail tests on the influence of background noise and specify tolerances for environmental temperature and humidity, particularly for resilient elements where dynamic stiffness is highly sensitive to these conditions.
Optional data includes narrow-band magnitude and phase spectra of dynamic driving-point stiffness, as well as narrow-band spectra of the loss factor, providing detailed insights into the system's vibrational characteristics Additionally, simplified information on the upper input level limits—such as maximum RMS displacements—ensures the validity of the test data Furthermore, a static load-deflection curve (refer to Annex A) offers essential baseline information for understanding the structural response under static loading conditions.
The test report shall make reference to this part of ISO 10846 and shall include at least the items mentioned in Clause 9 under a), b), g), h), l) and m)
The test report shall include an evaluation of uncertainty; see 7.6.3.
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Including the static load-deflection curve, within the range of 0% to 100% of the maximum permissible load, in the test report can provide valuable insights into material or structural performance It is recommended to include a description or reference to the measurement procedure used, such as in References [4] and [5], ensuring clarity and traceability This addition enhances the comprehensiveness of the report and supports accurate assessment of load-bearing behavior.
The uncertainty in measuring dynamic transfer stiffness according to ISO 10846 arises from multiple sources, each contributing to overall measurement variability Some of these factors are predictable, allowing for better control and accuracy, while others are less predictable, especially for occasional users Understanding these diverse partial contributions is essential for improving measurement reliability and minimizing uncertainty in dynamic transfer stiffness assessments.
Dynamic transfer stiffness is calculated by the ratio of input acceleration, velocity, or displacement to the input force, serving as a frequency response function Its uncertainty can vary depending on the frequency, highlighting the importance of accurately analyzing this parameter across different frequencies for reliable measurements.
Uncertainty contributions in measuring a frequency response function primarily stem from measurement instrumentation such as accelerometers, force transducers, signal analyzers, and signal processing parameters These sources of uncertainty can be effectively managed due to the availability of high-quality, well-understood transducers and analyzers suitable for the targeted frequency range Furthermore, comprehensive literature exists on transducer and analyzer calibration methods, as well as best practices in signal processing, ensuring reliable and accurate measurement outcomes.
Uncertainty contributions related to laboratory test rigs and resilient elements are often difficult to quantify and control due to the wide variety of test setups allowed under ISO 10846 The scarcity of systematic studies and interlaboratory comparisons on these sources of uncertainty makes it challenging to accurately assess their impact These uncertainties can vary significantly depending on the specific combination of test elements and test rigs, especially for large or very stiff test specimens where these contributions may surpass the uncertainties from transducers, analyzers, and signal processing As a result, many users may find it difficult to determine precise uncertainty values related to these factors, impacting the overall accuracy of test results.
The use of ISO 10846's dynamic driving point stiffness to determine dynamic transfer stiffness introduces additional uncertainty in the analysis This discrepancy between the two stiffness measures is expected to grow with increasing frequency, impacting the accuracy of vibrational assessments (see Clauses 4 and 6.2).
This section of ISO 10846 establishes specific requirements to limit uncertainty contributions, making it possible to accurately estimate various sources of measurement uncertainty The subsequent clauses detail the individual sources of uncertainty and provide a structured approach for evaluating partial uncertainty contributions, which ultimately determine the overall measurement uncertainty.
B.2 Level of frequency-averaged dynamic transfer stiffness
The general expression for the calculation of the level of frequency-averaged dynamic transfer stiffness for one-third-octave bands, k av
L , is given by the following equation: av= av ins rep rig dps lin k k
Copyright International Organization for Standardization
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