Iso 868 Pdf Free Download

Shore hardness measurements subject rubber bodies to standardized indentations. While easily performed, the measurements are subject to uncertainties. Although typical variances for Shore hardness are found in standards, operator and instrument effects are not well described, requiring statistically designed experiments to estimate effects and variance components. This paper focuses on uncertainty in Shore A hardness measurements of tyre tread elements and quantifies operator and instrument effects. Evaluation of uncertainty of Shore A measurements were performed on tyres under controlled conditions using three instruments, two tyres and five operators. Results show that the operator variance component and instrument effects are larger than the reference variance contribution in ISO 11819-3:2017. The interaction between operator and instrument is estimated to be the largest source of variation, while operator and instrument main effects are of similar size as the error component. Recommendations to reduce uncertainties include ignoring instantaneous values and requiring an instrument stand.

Content may be subject to copyright.

Discover the world's research

• 20+ million members
• 135+ million publications
• 700k+ research projects

Join for free

Journal Pre-proofs

Evaluation of uncertainty on Shore hardness measurements of tyre treads and

implications to tyre/road noise measurements with the Close Proximity meth-

od

Tiago Vieira, Joacim Lundberg, Olle Eriksson

PII: S0263-2241(20)30420-6

DOI: https://doi.org/10.1016/j.measurement.2020.107882

Reference: MEASUR 107882

To appear in: Measurement

Received Date: 11 February 2020

Revised Date: 24 March 2020

Accepted Date: 21 April 2020

Please cite this article as: T. Vieira, J. Lundberg, O. Eriksson, Evaluation of uncertainty on Shore hardness

measurements of tyre treads and implications to tyre/road noise measurements with the Close Proximity method,

Measurement (2020), doi: https://doi.org/10.1016/j.measurement.2020.107882

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover

page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version

will undergo additional copyediting, typesetting and review before it is published in its final form, but we are

providing this version to give early visibility of the article. Please note that, during the production process, errors

may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2020 The Author(s). Published by Elsevier Ltd.

Evaluation of uncertainty on Shore hardness measurements of tyre treads and implications to

tyre/road noise measurements with the Close Proximity method

Tiago Vieira a,b, *, Joacim Lundberg a,b, Olle Eriksson a

a: Swedish National Road and Transport Research Institute (VTI), Olaus Magnus vaeg 35, SE 58195, Linkoeping, Sweden

b: Department of Building Materials, Brinellvaegen 23, KTH Royal Institute of Technology, SE 10044, Stockholm, Sweden

Abstract

Shore hardness measurements subject rubber bodies to standardized indentations. While easily

performed, the measurements are subject to uncertainties. Although typical variances for Shore

hardness are found in standards, operator and instrument effects are not well described, requiring

statistically designed experiments to estimate effects and variance components. This paper focuses

on uncertainty in Shore A hardness measurements of tyre tread elements and quantifies operator and

instrument effects.

Evaluation of uncertainty of Shore A measurements were performed on tyres under controlled

conditions using three instruments, two tyres and five operators. Results show that the operator

variance component and instrument effects are larger than the reference variance contribution in ISO

11819-3:2017. The interaction between operator and instrument is estimated to be the largest source

of variation, while operator and instrument main effects are of similar size as the error component.

Recommendations to reduce uncertainties include ignoring instantaneous values and requiring an

instrument stand.

Keywords: hardness, tyre, Shore A, uncertainty, variation, CPX hardness correction

1 Introduction

Tyres are a complex construction with several different materials that are designed to work together

in order to fulfil different performance demands, including friction, noise, rolling resistance and wear,

among others. It is usually time consuming and more expensive to rely on laboratory measurements

only when evaluating mechanical properties of tyres. An alternative to a viscoelastic characterization

of the rubber material found in the tyre tread is the Shore hardness measurement. Shore hardness is

an easily measurable variable that describes how a rubber body reacts when a standardized indenter

is pressed against it.

The hardness values are relevant technological properties, however, and as highlighted by Petik (1983)

they are not a physical quantity and cannot be expressed in terms of SI units. This means that the

hardness values are not additive and are not multiples of a unit of measurement. They should rather

be interpreted by relative distances between points on the same scale, i.e. 80 Shore A should not be

interpreted as twice as hard as 40 Shore A. Additionally, hardness measurements are not repeatable

at the exact same place in the sense that the test itself causes local changes in the material at the

tested point (Petik, 1990), which would therefore lead to a different hardness value if this exact point

were to be tested again. This is further emphasised in ISO 868:2003 (International Organization for

* e-mail addresses: Tiago Vieira (corresponding author): tiago.vieira@vti.se, Joacim Lundberg:

joacim.lundberg@vti.se, Olle Eriksson: olle.eriksson@vti.se

Standardization, 2003b), which states that there is no simple relationship between indentation

hardness and any fundamental properties of the material tested. Even though some relationships

between hardness values and material properties can be found in the literature, e.g. Mix and Giacomin

(2011), it is clearly stated by the authors that such relationships are only valid under given conditions

and should be used with care. Mix and Giacomin (2011) suggest inspecting the indented surface and

only used the proposed relationships if no severe imprint from the test indenter is found. Qi et al.

(2003) modelled the Shore hardness indentation with a nonlinear finite element model and the results

matched the measured Shore values. They point out that the effect of a limited elastomeric chain

extensibility can be relevant and that this effect removes the possibility of a one-to-one mapping

between elastic modulus and Shore hardness.

The Shore hardness measurement is a traditional method used in the rubber industry in order to

characterize rubber materials. As indicated by Brown (2006), the test results are affected by the

operator, the time of application and deviations from a perfectly elastic behaviour (e.g. filled rubbers

such as tyre treads) despite correct calibration and measurements according to the standard testing

procedure. Spetz (1993) examined the repeatability of hardness measurements on rubber materials

and concluded that the operator was the main source of variability. Brown and Soekarnein (1991)

investigated the different sources of variability in rubber hardness measurements and concluded that

the operator substantially accounts for the observed variations. Mohamed and Aggag (2003)

examined the uncertainty of Shore hardness testers and reported standard uncertainty values for

different sources, including the instrument inclination, the instrument resolution, temperature

variation effect on the force transducer, and repeatability effect, among others. The authors show

that an instrument misalignment of 0.1° leads to an error of 0.628 Shore A.

Measuring hardness of tyres poses additional difficulties when compared to the tests commonly used

in the rubber industry, as the operator must press the instrument on a tyre tread element and not on

a rubber sample. It is often the case that the instrument's foot covers a larger area than the tread

element on the tyre. When the instrument is handheld the measurement uncertainty is even more

affected by the operator, as the result depends on how the instrument is pressed against the tread

element. This difficulty is increased further for studded winter tyres as it is difficult to find a large

enough area on the tyre tread to perform the measurement given the increased siping and presence

of the protruding studs.

Shore A hardness is used, for instance, when the acoustical performance of a tyre/pavement system

is characterized with the Close Proximity (CPX) method, as standardized by ISO 11819-2 (International

Organization for Standardization, 2017a). This standard utilises two reference tyres, the SRTT tyre

(named P1) and the Avon AV4 tyre (named H1). As the tyre ages, its mechanical properties change,

mostly due to exposure to ozone and oxygen and due to mechanical wear (Gent and Walter, 2005).

The Shore A hardness was selected as the method to take tyre ageing and wear into account when

measuring tyre/pavement noise with the CPX method. Therefore, the uncertainty in the rubber

hardness measurements on tyres directly affects the uncertainty of noise levels obtained by the CPX

method. Despite the involved uncertainties, this method is nevertheless relatively easy to measure on

tyres and has a correlation with the ageing process, as indicated by Sandberg and Ejsmont (2007).

Sandberg and Glaeser (2008) evaluated the Shore hardness change in a period of 30 weeks during

which six different tyre models were tested. Each tyre model was represented by a total of five

nominally identical tyres, four being in new condition and one being worn down to a remaining tread

depth of 2 mm. The tyres were exposed to controlled temperature conditions of 55 °C in a climate

chamber and it was concluded that the hardness increases more during the first 17 weeks, after which

it continues to increase, though at a lower rate. Bühlmann et al. (2013) evaluated the Shore hardness

of two P1 and two H1 reference tyres used in CPX measurements. The tyres were new yet subjected

to run-in according to ISO 11819-3:2017 (International Organization for Standardization, 2017b). The

authors observed a hardness increase of up to 6.3 Shore A in a period of approximately 7 months

during which each tyre ran a distance of approximately 3 000 km under air temperatures between

5 °C and 32 °C. (Ho et al., 2013) reported a Shore hardness increase of 8.3 Shore A in the period of 12

months using a tyre exposed to environmental conditions in Hong Kong, with an average temperature

of 23 °C and average humidity of 79 %. Oddershede and Kragh (2014) analysed the relation between

the tyre/road noise as measured by the CPX method (International Organization for Standardization,

2017a) and the Shore hardness concluding that the measured noise level is affected by the tyre's

hardness at an average rate of 0.09 dB/Shore A. (Bühlmann et al., 2018a) used a dataset of 172

tyre/road noise measurements and concluded that the relationship between noise increase and

hardness increase is tyre specific, meaning that different tyres will have different noise level increases

as the Shore hardness increases. The tyre rubber hardness is also included when modelling tyre/road

noise (Li et al., 2018, , Forssén et al., 2018).

A comparison of Shore hardness results was carried out by Kragh et al. (2010) using 3 different

instruments and 10 different tyres. The reported results imply a difference between operators and

instruments, even though the statistical significance was unclear. The tyres were conditioned to a

temperature between 20 and 21 °C. Not all operators used all instruments and it should be

emphasized that the measurements were carried out before the CPX standard was published. The

Dutch CPX Round Robin test performed in 2017 also indicated the importance of correcting the

tyre/pavement noise values by the tyres' Shore hardness values (Peeters et al., 2018). The use of a

Shore hardness correction for the CPX method was also evaluated by Wehr et al. (2018) by analysing

46 CPX measurements with 4 reference tyres having the same model (SRTT reference tyre) and

performing a combined Shore hardness-temperature correction. The authors concluded that the

combined hardness-temperature correction could lead to a higher precision when evaluating the

acoustical properties of road surfaces. They also commented on the importance of the already

expected uncertainty in the measurements of the tyre hardness parameter. In Bühlmann et al. (2018b)

the authors compiled data from several tyre/pavement noise results to analyse the effect of rubber

hardness. The results from a total of 172 data points indicated a median effect of 0.13 dB/Shore A for

the SRTT tyre, however with a rather large spread. In a later work, Bühlmann (2019) analysed a dataset

of tyre hardness results for CPX measurements between 2013 and 2016. The results indicated that the

Shore hardness values were not normally distributed and had a standard deviation of 1.6 Shore A for

both reference tyres, i.e. tyre SRTT and tyre Avon AV4. Moreover, the author concluded that this

variation in rubber hardness is the factor that contributes the most to the uncertainty in the CPX

measurements, up to 0.7 dB.

The Shore hardness measurement is a relevant method, both in the rubber industry and when

evaluating tyre properties, when a simple and easily available method is desirable. As a pneumatic

tyre has non-linear viscoelastic behaviour (Gent and Walter, 2005), it is not expected that Shore

hardness can fully capture all properties of the filled rubber in the tyre tread. Some small modifications

in the Shore hardness measurements have proven to give more comprehensive results. An example is

shown by Kucherskii and Kaporovskii (1997) who proposed a method of hardness measurement under

constant deformation, which means that the indenter penetrates the specimen at a fixed depth. These

authors obtained a linear relationship between the modified hardness values and the rubber elastic

modulus. Austrell and Aylin (2012) used a modified Shore hardness measurement, a number of

different indentation depths and a finite element simulation, and successfully obtained the rubbers´

hyperelastic constants from the Shore hardness tests.

Instead of using a handheld instrument, another approach to evaluate Shore hardness and even the

magnitude of the complex modulus of elasticity for rubber materials has been shown by Sherif and

Almufadi (2018). The method proposed by these authors consists of subjecting the rubber specimen

to an impact by a steel sphere and measuring the time of contact and maximum force due to contact.

The results indicated good agreement with the specimen's Shore A values obtained by a conventional

hardness instrument mounted on a test stand.

1.1 Objectives

This paper examines the variation associated with the operator and instrument effects of the Shore A

hardness measurement on pneumatic tyres, as well as the implication of uncertainties in the resulting

tyre/pavement noise levels as measured by the CPX method. Interactions between operator and

instruments and between operator and tyres were also considered in this research. The instruments

used here are commonly used to measure tyre hardness and the operators had different levels of

experience in measuring Shore hardness of tyres. An additional study was performed using only one

instrument and two operators in order to evaluate if the so-called hardness drift is in a linear

relationship to the logarithm of time when measuring hardness of tyre treads. Finally, the possibility

of using this hardness drift effect to reduce uncertainties associated with the Shore hardness

measurement of tyres is considered.

1.2 Limitations

It should be stressed that the validity of the function that relates Shore hardness to a noise correction

factor in the CPX method is not evaluated here. The temperature-hardness dependency is not

examined in this paper, and neither is the relationship between Shore hardness and rubber's

rheological properties. The authors did not expect that Shore measurements can substitute for the

much more comprehensive master curves. It is nevertheless a relevant and easily performed

measurement that directly impacts, for instance, tyre/pavement noise measurements.

2 Hardness measurement and uncertainties

2.1 The Shore A hardness indenter

To characterize rubber hardness an indentation is commonly performed with a rigid indenter having

a prescribed shape and loading (Gent, 2013). Among the different hardness scales available, the Shore

A hardness is measured with a steel indenter having a truncated cone shape with a diameter of 0.79

mm and an angle of 35° (International Organization for Standardization, 2003b) , see Figure 1. A lower

hardness leads to higher penetration depth of the rubber surface, from Shore A hardness of 0, leading

to a maximum indentation depth of 2.5 mm up to a hardness of 100, leading to an indentation of 0

mm (International Organization for Standardization, 2003b).

Figure 1. The steel indenter of a Shore A hardness measurement device. The full protrusion height h, the circumference ø, and

the angle α with measurements accord with the standard ISO 868:2003 (International Organization for Standardization,

2003b).

2.2 The Shore A hardness measurement and the CPX method

The Shore hardness measurement is delineated by several different standards depending on the

desired application and materials being measured. Even though the same measurement principle is

used, slight differences can be found, for instance, the different test time spans required when

performing measurements. According to ISO 11819-3:2017, related to the CPX method, the test

consists in rapidly, yet without shock, pressing the indenter against a tyre tread block and reading the

resulting Shore A value within 2 s (International Organization for Standardization, 2017b). In ISO

868:2003, used for control of material hardness, it is stated that for an instantaneous reading the

hardness value should be read within 1 s after the indenter establishes firm contact with the tested

surface. For ISO 48-4:2018 (International Organization for Standardization, 2018), used for

specification of material properties, the standard test time is 3 s for vulcanized rubber, which is a

compromise between an instantaneous value and a long enough time to establish equilibrium (Brown,

2006). The test times are arbitrary and other values could be used (Brown, 2006); however it is

important to report the test time used during measurements as this will affect the measured values.

The original idea for Shore hardness measurement was that it would be carried out with a portable

instrument. It is possible, however, to perform it using a stand, losing portability yet achieving better

precision (International Organization for Standardization, 2018). When it comes to hardness

measurement of tyres for the CPX method, it is more common that the instruments are handheld

rather than operated on a stand.

As all the tests performed here were performed by handheld instruments, the operator effect is

expected to be substantial and typical for Shore hardness measurements for pneumatic tyres,

especially used for CPX measurements. The experiments were planned to detect any remaining

differences between both instruments and operators, with all the instruments calibrated in

accordance with the standard and checked with a standard control block.

2.3 Uncertainty components and their relation to uncertainty in the CPX method

This paper describes the sources of variation and estimates their sizes. A measure has high accuracy if

the expectation of the measurements is close to the true value. ISO 5725-1:2003 (International

Organization for Standardization, 2003a) defines accuracy as "the closeness of agreement between a

test result and the accepted reference value" (page 7). The standard also adds that the term accuracy

"involves a combination of random components and a common systematic error or bias component"

(page 7). According to ISO 5725-1:2003 (International Organization for Standardization, 2003a)

precision is the general term for variability between repeated measurements and the "closeness of

agreement between independent test results obtained under stipulated conditions" (page 7). Still,

according to ISO-5725:2003, operator and equipment are included among the several other factors

that may contribute to variability (page 3). The variation can be separated into variance components

such as variation between operators and residual (error) variation. In this text, a measure is said to

have high uncertainty if it varies widely from one measurement to another on the same subject. This

uncertainty is a result of low accuracy and/or low precision.

Four different uncertainty components are listed in the uncertainty assessment of ISO 11819-3:2017

(International Organization for Standardization, 2017b) that contribute to the overall uncertainty of

the reference tyres, δt , according to Eq. 1:

where δ 1 is the uncertainty related to variation in noise levels between different tyre samples for tyres

of the same type, δ 2 is the uncertainty related to the change in tyre properties due to age and wear

which are not corrected by the hardness correction, δ 3 is the uncertainty related to the correction of

rubber hardness, and δ 4 is the uncertainty related to the correction for air temperature. The variation

component δ3 , as specified in ISO 11819-3:2017 (International Organization for Standardization,

2017b), is not separated into operator and instrument components, possibly describing only variation

when one operator or one type of instrument repeatedly tests the same object with the same

instrument.

This paper focuses on the uncertainty component δ 3 . It should be highlighted that, according to ISO

11819-3:2017, this uncertainty component is affected by both the hardness and the uncertainty

related to the rubber hardness coefficient, , in accordance with Eq. 3, see section 4.6. However,

this paper is limited to uncertainties related to hardness measurements only. Thus, uncertainties in

the hardness coefficient are outside the scope of this investigation. Therefore, this paper does not

intend to provide an overall estimation of δ 3, but instead only to evaluate the variance related to

operator and instruments on the hardness measurement and how it affects the resulting noise levels.

The investigation presented in this paper can indicate whether the use of different instruments and

operators has a substantial effect on the hardness results. This, in turn, will indicate whether it would

be interesting to have a variance component exclusively for the hardness measurement or,

alternatively, if the method should be reformulated to remove such effects altogether. The Shore

hardness measurement for tyre tread elements should not be substantially affected by the instrument

nor by the operator. Such effects are undesirable as this would mean that the same tyre would be

estimated to have a different hardness and, consequently, different noise values depending on both

the operator that measured it and the instrument used.

2.4 The measurement time and hardness drift

Due to the viscoelastic behaviour of the rubber material in the tyre tread, the measurement time will

affect the resulting Shore value. The so-called hardness drift, which is the decrease in the measured

Shore hardness over time, was previously studied by Casa et al. (1995). The authors used a modified

instrument with a microcontroller to perform the tests and evaluate the hardness drift. They

concluded that this phenomenon could be modelled by a linear regression of hardness and the

logarithm of time (see Eq. 2). The slope of this regression, m, is always negative and reflects the

material relaxation over time. The intercept, H1 is the hardness value observed after 1 second.

3 Measurement method

To evaluate the Shore hardness of pneumatic tyres the procedure described in ISO 11819-3:2017

(International Organization for Standardization, 2017b, Annex A) was applied. Three different Shore

hardness instruments were used in this work, all complying with the requirements of ISO 868:2003

(International Organization for Standardization, 2003b). One of the instruments was digital and could

be programmed to make readings at a specified time, counted from the instant the instrument's

indenter was pressed against the rubber. The other two instruments were analogue and had two

moving hands that rotate on a fixed dial indicating the instantaneous hardness value and the

maximum hardness value.

Note that, according to the measurement procedure found in ISO 11819-3:2017, the Shore hardness

value "shall be read within 2 s after the presser foot has made contact with the tread" (International

Organization for Standardization, 2017b, p. 11). This means that both reading the value directly after

the instrument is pressed against the tyre tread and waiting two seconds before reading it are valid

procedures and in accordance with the standard. The digital instrument was adjusted to wait two

seconds after its needle has been pressed against the tyre tread before evaluating the Shore hardness.

This time delay was introduced to investigate if a systematic difference could be found. The other two

instruments that were analogue provided the readings directly, i.e. no waiting time between pressing

the indenter against the rubber surface and reading the hardness values.

Two different tyres were included in the experimental programme, the first being the Avon AV4 tyre

used as a reference tyre for the evaluation of tyre/pavement noise with the Close Proximity (CPX)

method. The measurement method was standardized according to ISO 11819-2:2017 (International

Organization for Standardization, 2017a) and the reference tyre according to ISO 11819-3:2017

(International Organization for Standardization, 2017b). The second tyre included was the non-

profiled PIARC test tyre (PIARC, 2009). This smooth tyre with no tread blocks was selected as it

eliminates the effect of the operators' task in positioning the hardness instrument foot over a large

enough area in order to perform the measurement. The Avon AV4 tyre used for CPX noise

measurements was selected since, in contrast to the PIARC tyre, it has thread blocks and is commonly

measured using the investigated methods. The two tyres together allow an evaluation of how the

tread blocks affect the measurements. The two tyres and their differences are shown in Figure 2.

Five different operators were selected to perform the measurements and evaluate how different

operators can affect the test result. The operators were selected at VTI, some of them having had

previous experience and familiarity with both the measurement instrument(s) and with the Shore

measurement method, while others performed the measurement for the first time. All operators also

performed measurements on a reference hardness plate to account for any potential difference in

instrument behaviour. The instruments used are shown in Figure 3 and the reference hardness plate

used for calibration of the instruments is shown in Figure 4.

The tests were performed under controlled temperature conditions and normalized to the reference

temperature of 20 °C in accordance with ISO 11819-3:2017 (International Organization for

Standardization, 2017b). The temperature was measured with an infrared thermometer before each

hardness measurement and at the same location where the operator would then position the

instrument to evaluate hardness. All the hardness instruments, the thermometer and the tyres were

conditioned in a tyre storage room with controlled temperature conditions. The nominal temperature

was 16 °C, which is within the acceptable temperature range of 20 °C ± 5 °C required by ISO 11819-

3:2017 (International Organization for Standardization, 2017b) and the observed temperature values

during the measurements were also within this temperature range. The results were then corrected

to a reference temperature of 20 °C by applying the temperature correction procedure found in ISO

11819-3:2017 (International Organization for Standardization, 2017b).

Figure 2. The two tyres used, the non-profiled PIARC reference tyre (left) and the H1 (Avon AV4) reference tyre for the CPX

method (right).

Figure 3. The three Shore hardness measurement instruments. Left from Bareiss, model HPE II, middle from Zwick Roell, model

3115, and right from Bareiss, model HP.

Figure 4. The hardness control test ring which has an outer diameter of approximately 18 mm and a nominal hardness of 60

Shore A.

For the hardness drift measurements, the procedure was identical, and in addition the test was filmed

allowing an evaluation of how the hardness values decrease over time. The Shore hardness values

were then sampled from the films every 0.3 seconds using a video editing software over a period of

10 s. For such tests only the digital instrument was used and only two operators performed the tests

on the same tyre. These tests were performed with a handheld instrument, in contrast to Casa et al.

(1995) who used a modified instrument. Due to this difference, the results here are not directly

comparable but the concept of hardness drift is the same.

4 Results

4.1 Standard Shore hardness measurements

Even though the tyres were under controlled temperature conditions, the effect of an operator

measuring and touching the tyre surface was enough to increase the surface temperature. This was

detectable by the temperature measurements, and it was observed that the tyres heated up to 3.2 °C

during measurements.

An Analysis of Variance (ANOVA) was used to analyse temperature corrected hardness. Tyre and

Instrument were used as fixed factors while Operator was used as a random factor because the

operators included in the study can be seen as a sample from a distribution of possible operators.

Checking for interactions, it was found that instrument*operator and tyre*operator were significant

while other interactions were excluded from the model. The resulting R2 for this model was 0.966. The

analysis is summarised in Table 1.

Table 1.Temperature corrected hardness analysed with ANOVA

The mean values for instrument and operator are shown in Table 2, while the means for tyre and

operator are shown in Table 3.

Table 2. Mean values and margin means of hardness for combinations of instrument and operator

Table 3. Mean values and margin means of hardness for combinations of tyre and operator

Operators 2 to 5 had similar averages, while operator 1 had lower readings on average. The variance

component for operator was estimated to be 0.45 (Shore A)2 and was significantly greater than 0 (P <

0.001). Instruments 2 to 3 gave similar values, while instrument 1 gave about 4 units lower values on

average. The difference was significant (p< 0.001). There was also a significant difference between

tyres, but the presence in tyre main effects is regarded more as an adjustment in the analysis rather

than a result of this study.

The interaction pattern can also be seen in Table 2 and Table 3. The difference between instruments

was not the same for each operator which is shown as a significant interaction (p < 0.001). This was

the largest estimated effect with a variance component of 1.13 (Shore A)2. There was also a significant

operator*tyre interaction with an estimated variance component of 0.45 (Shore A)2 (p<0.001).

4.2 Difference in hardness between inner and outer rib

Hardness was measured on an inner and an outer position on each tyre at four equispaced points

around the tread, as specified in ISO 11819-3:2017 (International Organization for Standardization,

2017b). An analysis was carried out to compare these two positions. The response variable in this

analysis was the difference between the inner rib and the outer rib. The analysis was otherwise similar

to the one in section 4.1. There is a difference in 0.56 Shore A in average (p<0.001), where the inner

rib showed the highest values. The analysis showed no significant main effects, i.e. no effect from only

operator, instrument or tyre. There was however a complicated pattern of significant interactions,

where each two-factor interaction was significant. As an example, Table 4 shows how the mean

difference between inner and outer ribs varied for combinations of operator and tyre. The numbers

indicate that there was a difference in measured hardness between the inner and outer positions and

that the size of that difference varied between combinations of tyre and operator. The values also

averaged out to only a small variation in margin means.

Table 4. Mean values and margin means of difference between ribs for combinations of instrument and operator.

Another example is given in Table 5, showing the mean difference between inner and outer ribs for

combinations of tyre and instrument. There was variation in the combinations that averaged out to a

small difference between the margin means.

Table 5. Mean values and margin means of difference between inner and outer rib for tyres and instruments.

4.3 Number of measurements

The operators were allowed to repeat the measuring procedure until the acceptance criterion in ISO

11819-3:2017 was met, which means that four consecutive Shore hardness values did not differ more

than 2 Shore A units (International Organization for Standardization, 2017b). The number of

observations for combinations of operator*tyre*instrument varied from 32 to 146. An ANOVA with

number of measurements as response variable, but otherwise similar to the previous analysis, showed

a significant main effect of operator and significant operator*tyre interaction. The residuals in this

analysis were not close to having constant variance and normal distribution, which means that this

analysis was only approximate. The mean values for operator*tyre and the margin means are shown

in Table 6. The number of measurements were roughly the same for each cell except for tyre Avon

AV4 * operator 5, which was higher.

Table 6. Mean values and margin means of number of measurements.

4.4 Operator experience

The operators can be divided into three groups based on experience level: "beginners",

"intermediate" and "experienced". An analysis of hardness similar to the one above but with operator

replaced by group as a fixed factor and operator as random factor nested within group was used to

study if variation in operators could be partly explained by their experience level. This analysis did not

show a significant group effect and not any significant interaction involving group. The main effect for

operator was not significant but the main effect for instrument, the interaction

instrument*operator(group) and the interaction tyre*operator(group) remained significant.

4.5 Hardness drift measurements

The measurement results using the hardness drift method are presented in Figure 5. The two different

operators are identified as Op. 1 and Op. 2, and the following number identifies the measurement

number, e.g. Op. 2-3 is the third measurement carried out by operator 2. A base-2 logarithm was used

in the time axis, which translates 2 seconds into a value of 1 on the horizontal axis. Any values obtained

before 0.1 second after the instrument contacted the tread element were excluded from this analysis

as such values did not follow the same linear logarithm of time - hardness relationship used for all

other values.

Figure 5. Hardness drift results.

The resulting regression parameter estimates, including confidence intervals for each regression

coefficient, are presented in Table 7. All the regression coefficients were significant according to the

results.

Table 7. Hardness drift statistical parameters from the regression analysis presented in Figure 5.

4.6 Implications to tyre/road noise measurement

The tyre/road noise levels measured by the CPX method have a correction term for the tyre hardness

(International Organization for Standardization, 2017b). The correction term, in dB, is a function

of the Shore A hardness value measured on the reference tyres as shown in Eq. 3:

where HA is the measured Shore A hardness, Href is the reference value of 66 Shore A and is the

rubber hardness coefficient, in dB/Shore A, which is 0.20 dB/Shore A for the tyre H1. The estimated

variance components for HA measurements are shown in Table 8.

Table 8. The variance components in terms of Shore A hardness

Estimated Variance Component for HA [(Shore A)2]

When measuring the hardness of a tyre, the measurement is carried out by a randomly sampled

operator, meaning that the measurement will include a sampled value from the distribution of

operator effects and from the interactions involving operator. The variation in hardness results

between operators led to an uncertainty in the correction coefficient . Given that a unit in

hardness corresponds to 0.2 units in noise correction, all variance components that included the

operator gave a combined uncertainty in noise level of 0.24 dB, while the residual variation was 0.14

dB, both expressed as standard deviations.

Instrument was a fixed factor in this analysis. Fixed factor effects are not usually called variance

components and Instrument is therefore not summarised with an estimated variance component in

Table 8. The sum of squared effects can be solved out in a similar way as the variance between random

factor effects and can thus be used to estimate the variance between the fixed factor levels. As a

comparison with the variance components, the estimated variation between instruments expressed

as standard deviation was 0.40 dB.

Because the operators in this study were sampled while tyre and instrument were not, it is not obvious

how one should answer a question like "What is the uncertainty if we sample a new observation with

an unknown operator and an unknown instrument?". One would need to carefully define which

source of variation to be included in the answer. The analysis can take into account observations made

by operators other than the five in this study but not for another instrument. Interactions with

operator and instrument act as sampled in one dimension but not the other. Instead of trying to show

uncertainty based on the estimated effects and components, the variation is shown in another way.

The sample standard deviation between all measurements of the Avon AV4 tyre and the PIARC was

2.55 and 2.30, respectively. These numbers, however, should be interpreted with care. They treat

both data sets as independent random samples while the data in fact do have dependencies and are

not random samples. Choosing another summary measure, like interquartile range, would give some

other numbers but would also be difficult to interpret because of the structures and dependencies in

the data even if the measures themselves are easy to calculate.

5 Discussion

5.1 Standard Shore Hardness measurements

The ANOVA indicated that the variables that significantly affected the hardness results were not only

the operator, but also the instrument and the tyre. Moreover, the analysis indicated a significant

interaction between instrument and operator as well as between operator and tyre. No other

interactions were found significant. For operator, the estimated variance component was 0.45 (Shore

A)2 . The operator effect can be explained by the difficulties in positioning the instrument and indenting

the tyre in a repeatable way. The handheld instruments are difficult to be steadily holden and can

easily be tilted during the measurement. The operator can also affect the speed and force with which

the instrument is pressed against the tyre, thus further influencing the result.

As to the number of measurements that each operator performed before meeting the acceptance

criterium according to ISO 11819-3:2017 (International Organization for Standardization, 2017b), the

results show significant operator main effects. A significant interaction between operator and tyre

was also found. The combination of operator 5 and tyre Avon AV4 had a greater number of

measurements than the rest. This is not surprising as the AV4 tyre has a more complicated tread

pattern compared to the PIARC tyre, which has no tread pattern. This leads to a difficulty in positioning

the indenter and performing repeatable tests. This is, of course, the commonest case, as most

commercial tyres used for regular road traffic have a tread pattern.

There were significant operator effects on the measured hardness. When adding experience group,

there were significant operator effects within groups but no significant group effects. Similar results

were found for interaction between operator and instrument. This interaction was significant, but if

experience group was added to the model, the interaction between operator within group and

instrument was significant while the interaction between group and instrument was not. The same

result was also seen for interaction between operator and tyre. These results indicate that there is a

variation between operators and interactions with operators but none of these appears to be

explained by variation in experience.

Regarding the instrument variation, one instrument was digital while the other two were analogue.

The digital instrument gave lower results compared to the other two instruments, and also

significantly different. As the digital instrument evaluated the hardness value at exactly 2 seconds

after contacting the tyre surface, it is likely that the measuring time was more accurately followed.

The other instruments, however, can measure only the instant and maximum value, which were more

easily influenced by how the operator pressed it against the tyre.

Concerning the two significant two-factor interactions, the largest one was between instrument and

operator, with an estimated variance component of 1.13 (Shore A)2. The other significant interaction

was between operator and tyre, having an estimated variance component of 0.45 (Shore A)2, which

was comparable to the operator effect.

5.2 Difference in hardness between inner and outer ribs

The differences between measurements on inner and outer ribs had only two-factor interactions as

significant explanatory variables. As interactions but no main effect was detected here, it means that

certain combinations of tyre, operator and instrument led to an increase in variance that can't be

explained by the sum of tyre effects, operator nor instrument effects. The reason for these differences

requires further studies.

5.3 Hardness drift

The hardness drift analysis indicated that the Shore hardness measured on tyres follows a linear

relationship with log-transformed time. To obtain this linear relationship all the datapoints recorded

within the first 0.1 seconds were excluded from the analysis, which is not an important information

loss because the focus was to look at the measured result in the proximity of 2 seconds. This was

necessary as the initial values did not follow the linear relationship and were not representative of the

hardness drift. The hardness data obtained by the regressions did not result, however, in much more

stable results. There was a substantial variation between the regression lines and a smaller variation

of values around these lines. If the hardness were to be measured at a given time, one observation

can be made at that time. Otherwise many observations can be taken in the proximity of that time

and all data in that proximity can be used in an estimate of the value for that specified time. For a

given time (for example 2 seconds, shown with a vertical line in Figure 5), the variation in the vertical

direction becomes an indication of uncertainty in the measured values. If the lines were similar and

the observations were more varying, it would be beneficial to use the values of the lines at 2 seconds.

With the results obtained here, the variation between the regression lines was much larger than the

variation around these lines. Therefore, it is not a large gain in precision to use data in a proximity of

2 seconds rather than to use only the observation at exactly 2 seconds. However, it is known that tyre

ageing affects rubber hardness (International Organization for Standardization, 2017b). Hence, a more

comprehensive characterization of the rubber material, by means of the drift slopes, could be useful

to better describe this change in hardness.

5.4 Effect on CPX measurements

The analysis of the uncertainty of the hardness correction factor, (Error! Reference source not

found.), gave uncertainty components for operator influence, instrument influence and a residual.

The typical value for the uncertainty in the correction for tyre hardness for the H1 tyre (Avon AV4) is

0.2 dB according to ISO 11819-3:2017 (International Organization for Standardization, 2017b).

Comparing this value to the uncertainties obtained in this investigation, it can be seen that the typical

values in the standard are somewhat lower. When instead comparing either the operator uncertainty

(0.24 dB) or the instrument uncertainty (0.40 dB) components, there was a substantial difference from

the typical value in the standard. As to the residual component (0.14 dB), this was lower than the

uncertainty given in the standard. Overall, the results here indicate that the typical values in the

standard underestimates the variability related to Shore A hardness measurements when also taking

the variation between instruments and between operators into consideration. This can be partially

explained as the tests were made both with a digital and two analogue instruments. With analogue

instruments, the maximum value is usually taken during measurements. Those maximum values had

to be excluded from the hardness drift analysis as they were shown to be different from the

subsequent values.

6 Conclusions

This paper investigated both operator and instrument influences on Shore A hardness measurements

of pneumatic tyres, as well as the implications to tyre/pavement noise measurements with the CPX

method. Additionally, the concept of hardness drift was explored, even though with a reduced number

of experiments, to check if it is also observable when measuring pneumatic tyres and if it could be

used to reduce the uncertainty. This is a limited study in the sense that instrument was a fixed factor

in the analysis and that the number of operators and tyres are limited. Still, relevant conclusions

regarding the influence of the operator and the instrument on the Shore hardness measurement are

shown, leading to implications in the CPX method for measuring tyre/road noise.

The results showed significant main effects for the operator, the instrument and the tyres. Two

significant two-factor interactions between instrument*operator and operator*tyre were also found.

The variance components observed here were greater than the typical total variance related to the

Shore A hardness measurement reported in ISO 11819-3:2017 (International Organization for

Standardization, 2017b). This suggests a re-examination of such values in the standard.

The operators had different levels of experience, and the effect of grouping operators by experience

levels was attempted to explain the number of measurements required to reach the acceptance

criterium (4 measurements within +/- 2 Shore A). No significant effect was found, meaning that a

higher experience level did not contribute to reaching this acceptance criterion with fewer

measurements.

A hardness drift was detectable for the hardness measurement of tyres. The slope of this drift was not

always the same and varied both between individual measurements taken by the same operator, as

well as between operators. This can be further studied and possibly useful to characterize tyre ageing.

The initial (and thus maximum) values of hardness measurements are different from the subsequent

values and should therefore not be used. Therefore, it is not recommended to use instantaneous nor

maximum readings. A suggestion regarding the procedure described in ISO 11819-3:2017 is to specify

the measuring time more strictly. Instead of accepting a reading "within 2 s after the presser foot has

made contact with the tread" (International Organization for Standardization, 2017b, p. 11), the

reading should be taken at a specific time, e.g. 2 s.

The authors find it challenging to suggest how to lower the variation components connected to the

operator without changing the current standardized procedure. This may include extended

learning/exercises for the operators; however as pointed out here, it is hard to judge the experience

level. It is likely that using an instrument stand is the most efficient way to reduce these components.

Therefore, it is also suggested that this be implemented in setting the standard. There was also a large

variation between instruments, but that is more easily reduced by specifying the measuring time and

not taking maximum or instantaneous values.

Acknowledgements

The first and second author's work was part of their PhD programme, which was sponsored by the

Swedish Transport Administration and by VTI. The authors would like to thank Dr Piotr Mioduszewski

from the Gdańsk University of Technology (TUG) and Lykke Iversen from the Danish Road Directorate

(DRD) for lending their hardness measurement instruments to be used in the tests presented here.

The authors would also like to thank Maria Polukarova, Lisa Ydrefors and Mikael Bladlund (all VTI),

who helped with the measurements.

References

AUSTRELL, P.-E. & AYLIN, A. 2012. Hyperelastic constants from a modified hardness test using energy

balance obtained from FE-analysis. Plastics, Rubber and Composites: Macromolecular

Engineering.

BROWN, R. 2006. Physical Testing of Rubber, United States, Springer.

BROWN, R. P. & SOEKARNEIN, A. 1991. An investigation of the reproducibility of rubber hardness tests.

Polymer Testing, 10, 117-137.

BÜHLMANN, E. 2019. Improvements in the CPX method and its ability to predict traffic noise

emissions. Inter-Noise. Madrid, Spain.

BÜHLMANN, E., EGGER, S., MIODUSZEWSKI, P. & SANDBERG, U. 2018a. An in-depth look at the tire

rubber hardness influence on tire/road noise measurements. In: HERRIN, D., CUSCHIERI, J. &

EBBITT, G. (eds.) Inter-Noise. Chicago, USA: Institute of Noise Control Engineering of the

United States of America.

BÜHLMANN, E., MIODUSZEWSKI, P. & SANDBERG, U. 2018b. An in depth look at the tire rubber

hardness influence on tire/road noise measurements. Inter-Noise. Chicago, USA.

BÜHLMANN, E., SCHULZE, S. & ZIEGLER, T. 2013. Ageing of the new CPX reference tyres during a

measurement season. Inter-Noise. Innsbruck, Austria.

CASA, F., FENZI, M. & TONTODONATI, L. 1995. Study of hardness drift: A method for investigating the

viscous behaviour of cured rubber. Polymer Testing, 14, 355-367.

FORSSÉN, J., HOFFMANN, A. & KROPP, W. 2018. Auralization model for the perceptual evaluation of

tyre–road noise. Applied Acoustics, 132, 232-240.

GENT, A. N. 2013. Chapter 1 - Rubber Elasticity: Basic Concepts and Behavior. In: MARK, J. E., ERMAN,

B. & ROLAND, C. M. (eds.) The Science and Technology of Rubber (Fourth Edition). Boston:

Academic Press.

GENT, A. N. & WALTER, J. D. 2005. The pneumatic tire. Washington DC, United States: NHTSA.

HO, K.-Y., HUNG, W.-T., NG, C.-F., LAM, Y.-K., LEUNG, R. & KAM, E. 2013. The effects of road surface

and tyre deterioration on tyre/road noise emission. Applied Acoustics, 74, 921-925.

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 2003a. Accuracy (trueness and precision) of

measurement methods and results - Part 1: General principles and definitions. International

Organization for Standardization.

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 2003b. Plastics and ebonite - Determination

of indentation hardness by means of a durometer (Shore hardness). Brussels, Belgium:

International Organization for Standardization.

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 2017a. Acoustics - Measurement of the

influence of road surfaces on traffic noise - Part 2: The Close-proximity method. Geneva,

Switzerland: International Organization for Standardization.

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 2017b. Acoustics - Measurement of the

influence of road surfaces on traffic noise - Part 3: Reference tyres. Geneva, Switzerland:

International Organization for Standardization.

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION 2018. Rubber, vulcanized or thermoplastic

- Determination of hardness - Part 4: Indentation hardness by durometer method (Shore

hardness). Geneva, Switzerland: International Organization for Standardization.

KRAGH, J., ANDERSEN, B. & ODDERSHEDE, J. 2010. Road Surface Texture - Low noise and low rolling

resistance: CPX trailer comparison - Copenhagen 2009. Copenhagen, Denmark: Danish Road

Directorate.

KUCHERSKII, A. M. & KAPOROVSKII, B. M. 1997. A promising method for measuring hardness of

rubbers. Polymer Testing, 16, 481-490.

LI, T., BURDISSO, R. & SANDU, C. 2018. Literature review of models on tire-pavement interaction noise.

Journal of Sound and Vibration, 420, 357-445.

MIX, A. & GIACOMIN, A. 2011. Standardized Polymer Durometry. Journal of Testing and Evaluation,

39, 696-705.

MOHAMED, M. I. & AGGAG, G. A. 2003. Uncertainty evaluation of shore hardness testers.

Measurement, 33 , 251-257.

ODDERSHEDE, J. & KRAGH, J. 2014. Changes in noise levels from Standard reference Test tyres due to

increasing tyre tread hardness. Forum Acusticum. Krakow, Poland.

PEETERS, B., REININK, F. & VLIET, W.-J. V. 2018. Close Proximity (CPX) Round Robin Test 2017.

Euronoise 2018. Crete, Greece, .

PETIK, F. 1983. Problems of hardness measurement. Measurement, 1, 24-30.

PETIK, F. 1990. Metrology of hardness: Past development and present state of the art. Measurement,

8, 42-44.

PIARC 2009. Specification for a standard test tyre for friction coefficient measurement of a pavement

surface: smooth test tyre.

QI, H. J., JOYCE, K. & BOYCE, M. C. 2003. Durometer Hardness and the Stress-Strain Behavior of

Elastomeric Materials. Rubber Chemistry and Technology, 76, 419-435.

SANDBERG, U. & EJSMONT, J. 2007. Influence of tyre tread rubber hardness on tyre/road noise

emission. Inter-Noise. Istanbul, Turkey.

SANDBERG, U. & GLAESER, K.-P. 2008. Effect of tyre wear on noise emission and rolling resistance.

Inter-Noise. Shanghai, China: Chinese Academy of Sciences. Institute of Acoustics.

SHERIF, H. A. & ALMUFADI, F. A. 2018. Polymer Modulus of Elasticity and Hardness From Impact Data.

Journal of Engineering Materials and Technology, 141, pp. 8.

SPETZ, G. 1993. Improving precision of rubber test methods: Part 1—Hardness. Polymer Testing, 12,

351-378.

WEHR, R., FUCHS, A. & AICHINGER, C. 2018. A combined approach for correcting tyre hardness and

temperature influence on tyre/road noise. Applied Acoustics, 134, 110-118.

Credit Author Statement

We, the authors, declare that the contribution of each author, according was as follows:

Tiago Vieira: Conceptualization, Methodology, Validation, Investigation, Writing – Original Draft,

Writing – Review & Editing, Visualization.

Joacim Lundberg: Conceptualization, Methodology, Validation, Investigation, Writing – Original Draft,

Writing – Review & Editing, Visualization.

Olle Eriksson: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing –

Original Draft, Writing – Review & Editing, Visualization.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal

relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be

considered as potential competing interests:

Highlights

The hardness drift is observed when measuring Shore hardness on pneumatic tyres

Both operator and instrument have significant impact on shore hardness results

Instantaneous shore hardness values should not be considered

... Mätprogrammet inkluderade två däck, fem operatörer och tre instrument. För fler detaljer se Vieira et al. (2020a) och Vieira (2020). ...

... As indicated by Brown [41], the test results are affected by the operator, the time of application, and the deviations from perfectly elastic despite correct calibration and measurements according to the standard testing procedure. Spetz [42] examined the repeatability of hardness measurements on rubber materials and concluded that the operator was the main source of variability [43]. Thus, during the indentation experiments, hardness changes not only with the hold time but also with loading and unloading rate [44]. ...

The degradation of polymeric components is of considerable interest to the nuclear industry and its regulatory bodies. The objective of this work was the development of a methodology to determine the useful life—based on the storage temperature—of acrylonitrile O-rings used as mechanical sealing elements to prevent leakages in nuclear equipment. To this aim, a reliability-based approach that allows prediction of the use-suitability of different storage scenarios (that involve different storage times and temperatures) considering the further required in-service performance, is presented. Thus, experimental measurements of Shore A hardness have been correlated with storage variables (temperature and storage time). The storage (and its associated hardening) was proved to have a direct effect on in-service durability, reducing this by up to 60.40%. Based on this model, the inservice performance was predicted; after the first three years of operation the increase in probability of failure (POF) was practically insignificant. Nevertheless, from this point on, and especially, from 5 years of operation, the POF increased from 10% to 20% at approximately 6 years (for new and stored). From the study, it was verified that for any of the analysis scenarios, the limit established criterion was above that of the storage time premise considered in usual nuclear industry practices. The novelty of this work is that from a non-destructive test, like a Shore A hardness measurement, the useful life and reliability of O-rings can be estimated and be, accordingly, a decision tool that allows for improvement in the management of maintenance of safety-related equipment. Finally, it was proved that the storage strategies of our nuclear power plants are successful, perfectly meeting the expectations of suitability and functionality of the components when they are installed after storage.

• Prashant N. Awachat
• Vinayak Dakre

To decide genuinity of any measured value, one must know the values of various uncertainties related to the measuring instrument. The uncertainty depends upon type construction and condition of measuring instrument, it is also influenced by the measurement process. The condition of the instrument and its handling contribute to a greater extent in deciding the accuracy of results obtained. In the present investigation, an attempt is made to find out the value of various uncertainties associated with the charpy impact testing instrument. The instrument is used to find out the toughness of material which is one of the most important properties of a material. Hence, it very much essential to know the values of various uncertainties related to the charpy impact testing instrument. The various factors responsible for measurement uncertainty in Charpy impact testing was identified. After identification, uncertainty (vulnerability) associated with various parameters of Charpy impact testing was estimated by the standard method given in guideline for uncertainty measurement (GUM) handbook. Both type A and B uncertainty value are calculated and reported in the paper. Also, a detailed analysis is carried out to get the value of overall uncertainty and method for reducing uncertainty is described in the paper.

• Erik Bühlmann

Recent studies have provided for substantial improvements to measurements made by the Close-Proximity (CPX) method, intended for measurement of noise properties of road surfaces. These new findings were incorporated in the new standards published in 2017: the ISO 11819-2 (the CPX method) and Technical Specifications 11819-3 (about the reference tyres) as well as 13471-1 (about temperature corrections). This study, firstly, investigates the typical uncertainties associated with speed, ambient temperature and rubber hardness corrections. Secondly, the study evaluates to what degree the new standards improved the measurement method's repeatability by evaluating measurements that were undertaken on the same road surface at different times. Thirdly, the paper assesses the method's ability to predict the effect of road surfaces on roadside traffic noise by analysing the relationship with statistical pass-by measurements (SPB) undertaken on a large number of road surfaces within the same time frame. The study shows that the repeatability of CPX-measurements could be significantly improved by the new ISO standards, while some uncertainties associated with the properties of the test tyres remain. The study, moreover, provides evidence that overall and spectral road side traffic noise emissions can be reliably predicted by the CPX-method.

When assessing the acoustic quality of a road pavement with the close-proximity (CPX) or the on-board sound intensity (OBSI) method, the rubber hardness of the reference tire substantially affects the measurement. Practical experience shows that measurement tires can get significantly harder within a single measurement season. This is why one would like to normalize measurements to a reference rubber hardness. The recently published technical specification defining the reference tires for CPX measurements (ISO/TS 11819-3), therefore, includes a new correction for tire rubber hardness. Early experiences with this new correction procedure raised questions about its accuracy. This paper takes an in-depth look on the influence of tire rubber hardness on CPX measurements for both reference tires P1 and H1. It analyses existing and new data and summarizes the research from several scientific contributions on this topic. It provides evidence that the effect of rubber hardness is tire specific and that separate correction factors for the P1 and the H1 tires lead to accuracy gains and improved repeatability and reproducibility of the method. The study concludes by proposing a revised tire-specific approach for the tire rubber hardness correction of CPX measurement results.

Due to improvements in combustion-engines and use of electric-engines for cars, tyre noise has become the prominent noise source also at lower speeds. Models exist that simulate the noise produced by a rolling tyre, as do models that auralize different traffic situations from basic data. In this paper, a novel auralization method is introduced, with the purpose to enable synthesis of useful car pass-by sound signals for various situations. The method is based on an established model for tyre noise levels (SPERoN) that is combined with a validated auralization tool (LISTEN). In the LISTEN approach, source signals for tyre–road interaction and propulsion are produced from data based on recorded pass-by sounds. In the combined model, the tyre–road interaction data is shaped by the spectra estimated in SPERoN and synthesized back into a pass-by signal. The combined model is made to agree spectrally with measurements for a receiver at 7.5 m distance. Psychoacoustic judgments were used to compare the modelled signals with recorded signals, and the pass-by sounds for a given listener position showed promising quality and accuracy with respect to perceived pleasantness.

• Ulf Sandberg
• Jerzy Ejsmont

During its lifetime a tyre undergoes degradations due to mechanical wear and chemical ageing which affect not only durability and safety but also tyre/road noise emission. A parameter used to describe the noise-relevant ageing effect is tread rubber hardness expressed as Shore A values. During a tyre's lifetime, the rubber hardness of individual tyres may increase by up to 15 Shore A, which is equally large as new tyres may differ in hardness due to construction and material design. The hardness increase usually results in a noise emission increase, mainly at high frequencies; often up to 2-2.5 dB(A) in overall level per 10 units of Shore A increase. This means, e.g., that ageing of reference tyres must be avoided. Further, hardness is one of the most influential parameters when quieter tyres are designed. Finally, road traffic noise may be reduced if tyre ageing can be limited.

Recently, new reference test tyres have been specified by the ISO to be used for tyre/road noise measurements with the close-proximity (CPX) method. Various studies have provided evidence that tyre ageing is accompanied by significant and continuous changes in the noise emission properties. It is therefore essential to consider the changing state of reference tyres when carrying out tyre/road noise measurements using the CPX method. A reliable quantification of these ageing effects and their influence on noise emission levels requires that individual reference tyre sets are monitored over time. This study aims at investigating the ageing process of the new reference tyres SRTT and Avon AV4 during one measurement season. Measurements, which test the indentation resistance of tyre rubber with the type A durometer, were repeated on a monthly basis. This revealed substantial increases in rubber hardness during the 2012 measurement season, exceeding 3 units Shore A for the SRTT tyre and 6 units Shore A for the Avon AV4 tyre. This corresponded with a considerable rise in noise levels, suggesting that tyre ageing is a primary influencing factor when carrying out tyre/road noise measurements using the CPX method. The study provides a simple tyre specific model for estimating rubber hardness changes based on the number of measurement days. The evaluation of temperature data suggested that, due to the physical and environmental strain on in-service tyres, usage influences tyre ageing to a larger extent than standardised operational storage conditions. The data implies, moreover, that individual corrections for the CPX reference tyres SRTT and Avon AV4 are needed.

The present paper introduces a simple method to predict the modulus of elasticity and the hardness of polymeric materials that range from soft elastomers to hard plastics. Hertzian elastic impact model is used to define the relationship between the contact time duration and the maximum force of normal contact due to the impact of a hard sphere indenter with the tested polymer sample. It is shown that the adopted model and experimental method can be used as a tool for extracting the magnitude of the complex modulus of elasticity. Moreover, a new impact index is shown to be proportional to the polymer shore hardness. Theoretical and experimental results based on the force-time signals are consistent and show good correlation.

• Reinhard Wehr
• Andreas Fuchs
• Claus Aichinger

For the determination of the road surface influences on tyre/road noise, the standard ISO 11819-2 (International Organization for Standardization, 2017), also called "CPX-method" is used. There, tyre/road noise is measured with a dedicated measurement trailer and tyre. As various parameters, such as temperature, trailer design, shore hardness of the tyre, etc. have significant influences on the CPX levels, correction procedures to address these are described in the standard. Where currently the air temperature and the shore A hardness, measured under laboratory conditions, are used, a different approach is presented in this paper. Here, the tyre temperature is measured during the measurement run, and subsequently calculated to the in-situ shore A hardness. As this is assumed to be the dominating influence on tyre/road noise emission, a direct correlation between the in situ shore A hardness and the CPX levels is performed. Extensive measurements are presented, and the different correction procedures are analysed with regard to their repeatability. It will be shown that, within the limitations of the measurement setup, the combined correction of temperature and shore A hardness is feasible and may support the further development of the CPX method.

• Tan Li
• Ricardo Burdisso
• Corina Sandu

Tire-pavement interaction noise (TPIN) becomes dominant at speeds above 40 km/h for passenger vehicles and 70 km/h for trucks. Several models have been developed to describe and predict the TPIN. However, these models do not fully reveal the physical mechanisms or predict TPIN accurately. It is well known that all the models have both strengths and weaknesses, and different models fit different investigation purposes or conditions. The numerous papers that present these models are widely scattered among thousands of journals, and it is difficult to get the complete picture of the status of research in this area. This review article aims at presenting the history and current state of TPIN models systematically, making it easier to identify and distribute the key knowledge and opinions, and providing insight into the future research trend in this field. In this work, over 2000 references related to TPIN were collected, and 74 models were reviewed from nearly 200 selected references; these were categorized into deterministic models (37), statistical models (18), and hybrid models (19). The sections explaining the models are self-contained with key principles, equations, and illustrations included. The deterministic models were divided into three sub-categories: conventional physics models, finite element and boundary element models, and computational fluid dynamics models; the statistical models were divided into three sub-categories: traditional regression models, principal component analysis models, and fuzzy curve-fitting models; the hybrid models were divided into three sub-categories: tire-pavement interface models, mechanism separation models, and noise propagation models. At the end of each category of models, a summary table is presented to compare these models with the key information extracted. Readers may refer to these tables to find models of their interest. The strengths and weaknesses of the models in different categories were then analyzed. Finally, the modeling trend and future direction in this area are given.

• A. N. Gent

This chapter describes basic concepts and behavior associated with rubber elasticity. The single most important property of elastomers is their ability to undergo large elastic deformations, that is, to stretch and return to their original shape in a reversible way. The essential requirement for a substance to be rubbery is that it consists of long flexible chainlike molecules. Some type of permanent structure is necessary to form a coherent solid and prevent liquid like flow of elastomer molecules. This requirement is usually met by incorporating a small number of intermolecular chemical bonds (crosslinks) to make a loose three-dimensional molecular network. Such crosslinks are generally assumed to form in the most probable positions, that is, so that the long sections of molecules between them have the same spectrum of end-to-end lengths as a similar set of un-cross linked molecules would have.

• H.J. Qi
• K. Joyce
• Mary C. Boyce

The Durometer hardness test is one of the most commonly used measurements to qualitatively assess and compare the mechanical behavior of elastomeric and elastomeric-like materials. This paper presents nonlinear finite element simulations of hardness tests which act to provide a mapping of measured Durometer Shore A and D values to the stress-strain behavior of elastomers. In the simulations, the nonlinear stress-strain behavior of the elastomers is first represented using the Gaussian (neo-Hookean) constitutive model. The predictive capability of the simulations is verified by comparison of calculated conversions of Shore A to Shore D values with the guideline conversion chart in ASTM D2240. The simulation results are then used to determine the relationship between the neo-Hookean elastic modulus and Shore A and Shore D values. The simulation results show the elastomer to undergo locally large deformations during hardness testing. In order to assess the potential role of the limiting extensibility of the elastomer on the hardness measurement, simulations are conducted where the elastomer is represented by the non-Gaussian Arruda-Boyce constitutive model. The limiting extensibility is found to predict a higher hardness value for a material with a given initial modulus. This effect is pronounced as the limiting extensibility decreases to less than 5 and eliminates the one-to-one mapping of hardness to modulus. However, the durometer hardness test still can be used as a reasonable approximation of the initial neo-Hookean modulus unless the limiting extensibility is known to be small as is the case in many materials, such as some elastomers and most soft biological tissues.

Posted by: isaiahkamelssa.blogspot.com

Source: https://www.researchgate.net/publication/341047627_Evaluation_of_uncertainty_on_Shore_hardness_measurements_of_tyre_treads_and_implications_to_tyreroad_noise_measurements_with_the_Close_Proximity_method