A method and system for evaluating dry grip performance of a tire tread compound based on dynamic mechanical analysis (DMA)

Abstract

This invention relates to the field of tire material performance testing technology, and more particularly to a method and system for evaluating the dry grip performance of tire tread rubber based on Dynamic Mechanical Analysis (DMA). This invention performs linear baseline subtraction on the DMA tanδ-temperature curve, uses an α / α′ two-peak model for fitting, and calculates the peak area S. α S α′ And obtain the area ratio R α =S α / (S α +S α′ The results are rapidly determined based on a threshold (optimal: 0.35-0.60). The results are stable under conditions of 10Hz, 0.2%-0.3% strain, 2℃ / min, and -50 to 100℃. Compared with single-point indicators, it is more robust and transferable, and shows good consistency with actual vehicle dry braking / handling, making it suitable for rapid screening of formulations and processes.

Description

Technical Field

[0001] This invention relates to the field of tire material performance testing technology, and in particular to a method and system for evaluating the dry grip performance of tire tread rubber based on dynamic mechanical analysis (DMA). Background Technology

[0002] The grip performance of tire tread compound (both dry and wet) directly affects vehicle braking distance and handling safety. The EU / UN ECE R117 standard specifies testing and grading requirements for wet grip, rolling resistance, and rolling noise for C1 / C2 / C3 tires, but it does not provide alternative dry grip indicators at the material level that can be quickly assessed early in the R&D process. This forces companies to rely heavily on whole-tire prototypes and road / bench validation during the formulation screening stage, resulting in high timelines and costs. Domestic testing methods and technical guidelines primarily focus on rolling resistance and wet grip (such as the single-point test and result correlation method for rolling resistance in GB / T29040-2012, and the rolling resistance test for industrial vehicle tires in GB / T42356-2023), without providing a direct predictive path for "dry grip" at the material level.

[0003] At the materials science level, dynamic mechanical analysis (DMA) is a fundamental method for characterizing the viscoelastic response of rubber. It obtains the storage modulus E′′, loss modulus E′′, and loss factor tanδ = E′′ / E′ through small-amplitude vibration loading. When DMA is scanned with temperature, tanδ typically exhibits a series of peaks related to molecular relaxation (such as α-relaxation in the main glass transition segment and secondary relaxation), with the position and shape of each peak reflecting the contribution of different motion units or phase regions. This is clearly explained in domestic textbooks and technical documents; simultaneously, the national standard (GB / T40396-2021) for determining the glass transition temperature (Tg) of composite materials using DMA has been published, further standardizing the boundary conditions for testing and data interpretation.

[0004] In its R&D practices, the tire industry has long used tanδ as a "single-point or narrow-range" indicator of performance. Numerous Chinese patents explicitly link tanδ at different temperature points to specific performance characteristics in their specifications: for example, tanδ at 60℃ is used to characterize or compare rolling resistance; tanδ near 0℃ is often used as a material science indicator for wet grip; and some patents further use tanδ at 30℃ as an indicator of dry grip, thus establishing an empirical mapping between "0 / 30 / 60℃—wet / dry / rolling resistance". Specifically, Chinese invention patent CN114409980B explicitly states in the DMA section of its embodiments that "the tanδ value at 60℃ characterizes the rolling resistance of vulcanized rubber," and provides test conditions and an indexed comparison method; Chinese invention patent CN115128190A points out that "a higher tanδ at 0℃ indicates better wet resistance, and a lower tanδ at 60℃ indicates smaller hysteresis loss and thus lower rolling resistance"; CN111320733B directly defines "wet grip index—tanδ at 0℃, dry grip index—tanδ at 30℃, rolling resistance index—tanδ at 60℃," and provides multiple formulation comparison data and indices. The above disclosures demonstrate the commonality and operability of "single-point / narrow-range tanδ" in the evaluation of tire materials in China.

[0005] Besides the temperature point method, the industry also frequently uses formulation and structural methods to indirectly control the DMA curve to achieve performance balance. For example, reviews such as "Research Progress on Green Tire Raw Materials" show that the introduction of resin can increase the Tg of the tread compound and significantly raise the tanδ in the 0–20℃ range, which is beneficial for improving adhesion on wet roads. At the same time, it does not significantly increase tanδ energy consumption in the high-temperature range (70–80℃), thus alleviating the "wet grip-rolling resistance" conflict. Similar ideas are also reflected in several Chinese patents (such as controlling the styrene content of solution-polymerized styrene-butadiene rubber, introducing specific thermoplastic hydrocarbon resins / silane systems, etc.), the core objective of which is to adjust the viscoelastic characteristics in different temperature ranges to obtain the overall tire performance.

[0006] However, indicators based on single points or peak height have inherent limitations: First, single-point values ​​are easily affected by curve noise, baseline drift, and peak asymmetry; second, the operating temperature range in dry environments often spans the tail of the main glass transition segment and adjacent confined / interface-related energy dissipation processes (often referred to as "α′" or "shoulder peak" in engineering), making it difficult for single points to stably reflect the total energy dissipation contribution within the temperature range; third, changes in the microphase structure of the formulation (resin-rich phase, filler network, chain segment confinement, etc.) significantly affect the consistency of single-point interpretation, leading to deviations between actual vehicle results and "single-point predictions." In contrast, spectral decomposition around peak shape and characterizing the integrated contribution of energy dissipation using "area" is a common practice in various thermal / spectral analysis fields and better aligns with the physical picture of DMA curves where "multiple peaks correspond to multiple relaxations." Publicly available Chinese materials indicate that tanδ in DMA heating tests "presents a series of peaks, each corresponding to a specific relaxation process," providing a direct physical basis for subsequent peak decomposition and parameterization.

[0007] Currently, mainstream publicly available methods still use single-point / narrow-range tanδ (such as 0℃, 30℃, 60℃) or related indices as the material science characterization and formulation screening basis for "wet / dry / rolling resistance". However, there is no clear and reproducible publicly available threshold or process for using the "α and α′ two-peak decomposition" of the tanδ-temperature curve and the ratio of their peak areas as a rapid determination / grading measure of "dry grip". This gap echoes the existing system's "lack of a material-scale dry grip prediction path", indicating the need to introduce the spectral decomposition concept of DMA into the dry grip material science evaluation of tire tread compounds to improve the efficiency and consistency of early screening and decision-making in R&D. Summary of the Invention

[0008] The technical objective of this invention is to provide a method for evaluating the dry grip performance of tire tread rubber based on dynamic mechanical analysis (DMA). By performing linear baseline subtraction and α / α′ two-peak spectral decomposition on the DMAtanδ–temperature curve of the tread rubber, a quantitative index with the α peak area ratio Rα as the core is constructed, so as to achieve a rapid, robust and reproducible evaluation and classification of dry grip performance.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for evaluating the dry grip performance of tire tread rubber based on dynamic mechanical analysis (DMA) includes the following steps:

[0011] S1) Obtain the tanδ–temperature curve y(T) of the sample within the temperature range covering the glass transition region to the service temperature region;

[0012] S2) Perform first-order linear baseline subtraction on y(T) to obtain the processed curve y * (T);

[0013] S3) Using a two-peak model to... * (T) decomposes and fits to the α peak. With α′ peak The temperature at the center of the α peak Located on the material surface Within ±10℃, the center temperature of the α′ peak Located in the range of 0-40℃;

[0014] S4) Calculate the area of ​​peak α With α′ peak area ;

[0015] S5) Calculate the area ratio :

[0016] ;

[0017] and with As an indicator for determining or classifying the dry grip performance of the tread rubber;

[0018] In step S3, the fitting process uses a Gaussian or Voigt-type peak function and satisfies the goodness-of-fit threshold. Or the sum of squared residuals reaches a preset minimum value.

[0019] Preferably, the DMA test conditions are: frequency ,strain Heating rate 2°C / min, temperature range -50°C to 100°C, mechanical mode is tension or single shear.

[0020] Preferably, the linear baseline of step S2 is determined by the mean point of two reference intervals: the glassy low-temperature end and the rubbery high-temperature end.

[0021] Preferably, the two-peak fitting in step S3 uses: (i) Gaussian peak

[0022] ,

[0023] Where A is the peak amplitude, μ is the peak center temperature, σ is the Gaussian standard deviation, and T is the temperature variable;

[0024] Or (ii) the Voigt peak is a Gaussian-Lorentz type convolution:

[0025] ,

[0026] Among them, g V (T) is the Voigt peak function, G is the Gaussian kernel function, L is the Lorentz kernel function, and * indicates the convolution operation with respect to the variable T;

[0027] Global optimization is performed under multiple initial values ​​and multiple constraints to suppress local extrema.

[0028] Preferably, the peak area in step S4 is: when the peak function is Gaussian.

[0029] ,

[0030] Where S is the area of ​​a single Gaussian peak; A is the peak amplitude; σ is the Gaussian standard deviation; and π is the constant pi.

[0031] When the peak function is Voigt, the peak area is calculated using numerical integration or an approximate analytical expression.

[0032] As a preferred option, the determination of dry grip performance is based on Define the indicator and set tiered thresholds: when When, it is judged to have excellent grip performance on dry ground; when When the risk of decreased grip performance on dry ground increases, samples falling within the above range are considered areas for optimization.

[0033] Parallel reporting of α′ area percentage: , where R α′ The area ratio α′ is always equal to 1, and its sum with Rα is used as an equivalence evaluation index, and is compared with other indicators in prescription screening. Cross-validation.

[0034] Preferably, the method further includes quality control and robustness verification:

[0035] (a) Peak separation:

[0036] ,

[0037] Where D is the resolution; μ α ,μ α′ σ represents the center temperature of α and α′; α ,σ α′ The standard deviation of the corresponding peak;

[0038] (b) When the frequency changes At that time, the rate of change in area proportion ;

[0039] (c) Adaptively select the regularization strength based on the inflection point of the L-curve of the fitted residuals to avoid overfitting.

[0040] Furthermore, the present invention also provides a rapid evaluation system for dry grip performance of a method for performing the method, comprising:

[0041] The DMA test module is used to output the tanδ–temperature curve of the sample at a set frequency, strain, heating rate and temperature range.

[0042] The data processing unit / processor stores program instructions and is configured to: perform linear baseline subtraction; decompose and fit the curve under physical window constraints. and ;calculate and ;calculate ;

[0043] And perform judgment / grading output;

[0044] The human-computer interface is used to display the α / α′ fitting results, area and And quality control indicators and recommended formulation optimization directions.

[0045] Furthermore, the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the method.

[0046] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0047] This invention, by employing the aforementioned technical solution, performs linear baseline subtraction and α / α′ two-peak spectral decomposition on the DMAtanδ– temperature curve of the tread rubber under physical constraints, and uses the peak area ratio R... α As a core evaluation metric, it achieves an integrated characterization of the "temperature zone energy contribution" of dry soil gripping performance, significantly reducing the interference of curve noise, baseline drift, and peak shape changes on the conclusions compared to traditional single-point / peak height indicators. Through peak position windows, inter-peak separation, and frequency robustness checks, it ensures that the indicators are repeatable, comparable, and portable across formulations / processes. By setting R... α The threshold window enables rapid classification and risk warning of dry grip performance, thereby obtaining a relative ranking consistent with the actual vehicle's dry braking / handling in the early stage of formulation screening. This reduces the number of tire iterations and road tests, shortens the development cycle, reduces costs, and provides interpretable and quantifiable decision-making basis for targeted optimization of formulation and process. Attached Figure Description

[0048] Figure 1 The temperature curve is tanδ– (raw data).

[0049] Figure 2 Fit the two peaks after baseline subtraction (showing the α peak and α′ peak). Detailed Implementation

[0050] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0051] I. Overall Approach and Process

[0052] This invention provides a materials science evaluation method for dry grip performance based on dynamic mechanical analysis (DMA) temperature spectrum. The core idea is: to evaluate the dry grip performance of tread rubber samples... – The temperature curve undergoes first-order linear baseline subtraction. Under physical window constraints, the baseline-subtracted curve is decomposed into the main glass transition α peak and the confined / interface-related α′ peak. The areas of the two peaks are calculated separately to obtain the area ratio. Based on this, rapid determination and grading of dry soil grip is performed. The methodology includes: sample preparation → DMA testing → baseline subtraction → two-peak fitting → peak area calculation → area ratio calculation and grading → quality control and robustness verification → result output and formulation optimization.

[0053] II. Samples and Test Conditions

[0054] Sample: Cut strip-shaped samples from the tread masterbatch or small test pieces. The thickness is about 2 mm, the width is 5-10 mm, and the length is sufficient to meet the requirements of stable clamping and uniform heating.

[0055] Humidity conditioning: Let stand for 24 hours at 23℃ and 50% relative humidity.

[0056] DMA instrument and mode: either stretching or single-shear mode is acceptable; commercial DMA equipped with temperature control and small-amplitude linear scanning capability is preferred.

[0057] Recommended testing conditions:

[0058] Frequency: 10Hz (optional 3Hz and 30Hz retests for robustness verification);

[0059] Strain amplitude: 0.2%~0.3% (ensuring within the linear viscoelastic region);

[0060] Heating rate: 2℃ / min;

[0061] Temperature range: -50℃~100℃;

[0062] Output: –Temperature profile .

[0063] III. Data Processing and Model Setting

[0064] 1. Baseline subtraction

[0065] In the low-temperature end (glassy state, -50 to -30℃) and high-temperature end (rubbery state, 80 to 100℃) of the curve, small intervals of 5 to 10℃ are selected respectively, and mean or linear fitting is performed to construct a first-order linear baseline. The curve after baseline subtraction is obtained:

[0066] ;

[0067] This step is used to reduce the impact of end drift and slow background changes on subsequent fitting.

[0068] 2. Decomposition of two-peak spectrum (α and α′)

[0069] Will Represented as the superposition of two peaks:

[0070] ;

[0071] The peak function can be a Gaussian or Voigt model.

[0072] Mount Gauss: ;

[0073] Voigt peak: the convolution of Gaussian and Lorentz peaks, suitable for samples with peak tails.

[0074] Physical window constraints (used to improve interpretability and reproducibility):

[0075] α peak center temperature Constrained by the apparent glass transition temperature of the material Within ±10℃;

[0076] α′ peak center temperature Constrained within the range of 0–40°C (limited / interface-related energy dissipation processes near the dry operating temperature zone of the tire).

[0077] Fitting Solution: A multi-starting-point global search combined with local least squares (e.g., the LM algorithm) is preferred. Initial values ​​can be estimated based on the approximate location of the main peak and the half-peak width. The goodness of fit should ideally satisfy the following: coefficient of determination. At the same time, check the randomness of the residuals to avoid systematic bias.

[0078] Interpeak separation: It is recommended to use ;

[0079] This serves as the minimum separation threshold, ensuring the stability of two-peak identification.

[0080] 3. Peak Area Calculation and Core Indicators

[0081] Area of ​​Gauss Peak: ;

[0082] Voigt peak area: numerical integration of the fitted peak over the temperature range (e.g., Simpson or Gaussian integration).

[0083] Key metrics:

[0084] in and These are the areas of peaks α and α′, respectively.

[0085] 4. Judgment and Classification

[0086] Based on experience and real-world vehicle comparisons, the following classification suggestions are provided:

[0087] A value between 0.35 and 0.60 indicates excellent grip performance on dry surfaces ("Excellent" window).

[0088] or The risk of decreased soil adhesion in dry land increases;

[0089] The remainder is the optimizable region.

[0090] And can report in parallel As an equivalent characterization quantity.

[0091] IV. Quality Control and Robustness Requirements

[0092] Frequency robustness: Retested at 3, 10, and 30 Hz. If these conditions are not met, prioritize checking clamping, sample thickness consistency, and thermal balance.

[0093] Repeatability: Prepare and test the same formulation independently at least three times, and report the mean and standard deviation. If RSD > 8%, the selection of baseline intervals and the setting of initial fitted values ​​should be reviewed.

[0094] Overfitting suppression: If necessary, mild regularization can be introduced or the Akaike Information Criterion (AIC) can be used to automatically select the best Gaussian and Voigt criteria to avoid introducing unnecessary peak complexity.

[0095] Failure handling: If If the results are substandard or the residuals show a systematic shift, the temperature range can be expanded appropriately, the baseline optimized, or the initial peak value adjusted, and the peak shape changed before recalculation.

[0096] V. Examples and Comparative Examples (using given experimental data)

[0097] Test conditions: frequency 10Hz, strain 0.25%, heating rate 2℃ / min, temperature range -50℃ to 100℃; Gaussian model preferred for two-peak model; goodness of fit. Resolution .

[0098] (a) Comparative Example A (low resin / low restriction)

[0099] Two-peak parameters: , =22℃; , =14℃.

[0100] area: (au), (au).

[0101] Indicators and Judgments: This is considered a risk (α′ is insufficient).

[0102] Related: The dry braking / handling relative indices in Table 1 are all based on 100, which is one of the lowest levels.

[0103] (II) Example 1 (10 phr of Tg resin)

[0104] Two-peak parameters: , =23℃; , =20℃.

[0105] area: , .

[0106] Indicators and Judgments: It was rated as excellent.

[0107] Related: Table 1 shows dry braking 104 and handling 103 (relative comparative A=100), which is consistent with the "Excellent" window.

[0108] (III) Example 2 (High Tg resin 15 phr)

[0109] Two-peak parameters: , =24℃; , =24℃.

[0110] area: , .

[0111] Indicators and Judgments: It was rated as excellent.

[0112] Related: Table 1 shows that dry braking 106 and handling 105 are superior to Example 1, consistent with the trend of the "Superior" window.

[0113] (iv) Example 3 (25 phr of excess resin)

[0114] Two-peak parameters: , =25℃; , =28℃.

[0115] area: , .

[0116] Indicators and Judgments: It was determined to be a risk (excessive energy consumption).

[0117] Related: Table 1 shows that dry braking is 98 and handling is 97, indicating a risk of heat fade and decreased grip.

[0118] (v) Comparative Example B (High Fill / Poor Interface)

[0119] Two-peak parameters: , =21℃; , =12℃.

[0120] area: , .

[0121] Indicators and Judgments: This is considered a risk (α′ is insufficient).

[0122] Related: Table 1 shows dry braking 99 and handling 98, which is consistent with the judgment.

[0123] Table 1. Real Vehicle / Bench Test Frame Correlation (Comparative Example A=100)

[0124]

[0125] Summary of Examples: Examples 1 and 2 All were within the "excellent" range of 0.35 to 0.60, and showed a positive improvement in the overall tire dry braking / handling relative index; Comparative Examples A and B and Example 3 Samples with values ​​greater than 0.70 or less than 0.35 were identified as risk samples. Real-vehicle / bench indicators also showed performance degradation or thermal decay tendency, verifying the effectiveness and consistency of the method.

[0126] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

Claims

1. A method for evaluating the dry grip performance of tire tread rubber based on dynamic mechanical analysis (DMA), characterized in that, Includes the following steps: S1) Obtain the tanδ–temperature curve y(T) of the sample within the temperature range covering the glass transition region to the service temperature region; S2) a first order linear baseline subtraction is performed on y(T) to obtain a processed curve y * (T); S3) Using a two-peak model to... * (T) decomposes and fits to the α peak. With α′ peak The temperature at the center of the α peak Located on the material surface Within ±10℃, the center temperature of the α′ peak Located in the range of 0-40℃; S4) Calculate the area of ​​peak α With α′ peak area ; S5) Calculate the area ratio : ; and with As a criterion for determining and classifying the dry grip performance of the tread rubber; in step S3, the fitting adopts a Gaussian or Voigt-type peak function and meets the goodness-of-fit threshold. Or the sum of squared residuals reaches a preset minimum value.

2. The method according to claim 1, characterized in that, The dynamic mechanical analysis and testing conditions are as follows: frequency is... , adapt to The heating rate is 2℃ / min, the temperature range is -50℃ to 100℃, and the mechanical mode is tension or single shear.

3. The method according to claim 1 or 2, characterized in that, The linear baseline of step S2 is determined by the mean point of two reference intervals: the glassy low-temperature end and the rubbery high-temperature end.

4. The method according to claim 1, characterized in that, The two-peak fitting method used in step S3 is: (i) Gauss Peak for: ， Where A is the peak amplitude, μ is the peak center temperature, σ is the Gaussian standard deviation, and T is the temperature variable; Or (ii) The Voigt-type peak function is a convolution of Gaussian and Lorentz types: ， wherein g V (T) is a Voigt peak function, G is a Gaussian kernel function, L is a Lorentz kernel function, and * denotes a convolution operation with respect to the variable T; Global optimization is performed under multiple initial values ​​and multiple constraints to suppress local extrema.

5. The method according to claim 1, characterized in that, Peak area in step S4: When the peak function is Gaussian, ， Where S is the area of ​​a single Gaussian peak; A is the peak amplitude; σ is the Gaussian standard deviation; and π is the constant pi. When the peak function is Voigt, the peak area is calculated using numerical integration or an approximate analytical expression.

6. The method according to claim 1, characterized in that, The determination of dry grip performance is based on Define the indicator and set tiered thresholds: when When, it is judged to have excellent grip performance on dry ground; when When the risk of decreased grip performance on dry ground increases, samples falling within the above range are considered areas for optimization. Parallel report of α′ peak area percentage: , where R α′ The area ratio of peak α′ is related to R. α The sum of these values ​​is always 1, serving as an equivalence evaluation index, and is used in prescription screening in conjunction with... Cross-validation.

7. The method according to claim 1, characterized in that, This method further includes quality control and robustness checks: (a) Peak separation: ， Where D is the resolution; μ α ,μ α′ These are the center temperatures of the α peak and the α′ peak, respectively; σ α ,σ α′ These are the standard deviations of the corresponding peaks; (b) When the frequency changes At that time, the rate of change in area proportion ; (c) Adaptively select the regularization strength based on the inflection point of the L-curve of the fitted residuals to avoid overfitting.

8. A rapid evaluation system for dry grip performance of any one of claims 1-7, characterized in that, include: The DMA test module is used to output the tanδ–temperature curve of the sample at a set frequency, strain, heating rate and temperature range. The data processing unit stores program instructions and is configured to: perform first-order linear baseline subtraction; decompose and fit the curve under physical window constraints. and ;calculate and ;calculate ; It performs judgment and graded output; the human-computer interaction interface is used to display the fitting results of α peak and α′ peak, area and And quality control indicators and recommended formulation optimization directions.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-7.

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