Design and Control of the Natural Frequency of Brake Discs in the Aspect of the Gray Cast Iron Production Process
Abstract
:1. Introduction
2. Research Material and Research Methodology
3. Research Results and Discussion
3.1. Mechanical Properties Testing
3.2. Results of the Microstructural Tests
- -
- The graphite distribution was uniform—type A (70–75%) and interdendritic types D and E (19–26%);
- -
- The size of the graphite precipitates corresponded to the size patterns from number 3 to number 5. The largest share, over 90%, consisted of graphite precipitates corresponding to the length patterns 4 and 5 (from 60 to 250 μm);
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- The graphite precipitates had a straight flake shape and corresponded to pattern I.
3.3. Testing the Elastic Properties of Cast Iron Using the Ultrasonic Method
3.4. Simulations and Experimental Tests of the Natural Frequency of Brake Discs
3.5. Development of a Production Material Database
3.6. Predicting the Natural Frequency when Implementing a New Brake Disc
3.6.1. Design and Simulation Work
3.6.2. Experimental Verification of the Modal Simulation Results
3.7. Production Control of the Implemented Brake Disc
4. Summary and Concluding Statements
Final Statements
- An increase in the degree of saturation of eutectic cast iron from 0.87 to 1.01 resulted in a 21% reduction in Young’s modulus and a 10–11% reduction in the first natural vibration frequency of the brake discs.
- During the production cycle, even slight changes in the chemical composition of cast iron may affect the frequency stability of the discs. The high sensitivity of the first natural frequency to changes in the SC coefficient requires the use of high-quality input materials and strict process control at the stages of melting and modification of cast iron.
- The numerical prediction of the first natural frequency and the range of its changes are determined by the accuracy of the measurement of the elastic properties of cast iron. The ultrasonic method based on measuring the propagation speed of longitudinal and transverse waves allows for a quick and accurate determination of Young’s modulus and Poisson number of brake discs.
- For the analyzed brake disc geometries and cast iron grades (SC from 0.88 to 1.01), the relationships between the first natural frequency and Young’s modulus describe linear functions with direction coefficients ranging from 2.8 to 4.0 Hz/GPa
- Carrying out design and simulation work using the production material database is an effective method for optimizing the design of brake discs. The error of the numerical simulations of the first natural vibration frequency was on average below 1%.
- Control tests performed using I-MR cards confirmed both the effectiveness of the design and prediction of natural vibrations of brake discs, as well as the stability of the gray cast iron production and disc casting processes.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Disc Code | Outer Diameter [mm] | Inner Diameter [mm] | Thickness [mm] | Mass [kg] | |
---|---|---|---|---|---|
Disc 1 | 322 | 191 | 32 | 15 | |
Disc 2 | 380 | 221 | 34 | 19.9 |
Cast Iron Grade | Type of Chemical Composition | Chemical Composition, wt.% | Degree of Eutectic Saturation SC | Carbon Equivalent (CE) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C | Si | Mn | P | S | Cu | Cr | Mo | Ni | Sn | ||||
A | MIN | 3.25 | 1.70 | 0.50 | 0.00 | 0.05 | 0.10 | 0.13 | 0.00 | 0.00 | 0.00 | 0.87 | 3.78 |
OPT | 3.35 | 1.75 | 0.60 | - | 0.08 | 0.15 | 0.15 | - | - | - | 0.90 | 3.90 | |
MAX | 3.40 | 1.80 | 0.70 | 0.10 | 0.10 | 0.25 | 0.20 | 0.20 | 0.20 | 0.09 | 0.93 | 3.99 | |
B | MIN | 3.67 | 1.40 | 0.55 | 0.00 | 0.00 | 0.30 | 0.25 | 0.00 | 0.00 | 0.00 | 0.95 | 4.07 |
OPT | 3.70 | 1.45 | 0.60 | - | 0.08 | 0.32 | 0.25 | - | - | - | 0.97 | 4.12 | |
MAX | 3.72 | 1.50 | 0.70 | 0.10 | 0.15 | 0.35 | 0.35 | 0.15 | 0.10 | 0.09 | 0.98 | 4.16 | |
C | MIN | 3.70 | 1.60 | 0.50 | 0.00 | 0.00 | 0.15 | 0.13 | 0.00 | 0.00 | 0.00 | 0.98 | 4.18 |
OPT | 3.73 | 1.65 | 0.55 | - | 0.08 | 0.20 | 0.15 | - | - | - | 1.00 | 4.25 | |
MAX | 3.75 | 1.70 | 0.75 | 0.08 | 0.10 | 0.25 | 0.25 | 0.10 | 0.10 | 0.09 | 1.01 | 4.29 |
Cast Iron Grade | Disc Code | Graphite | Metal Matrix | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Shape | Distribution, % | Length, % | Perlite, % | Ferrite, % | Cementite, % | ||||||
A | B | D–E | 5 | 4 | 3 | ||||||
A | Disc 1 | I | 71 | 4 | 25 | 59 | 36 | 5 | 93 | 6 | <1 |
Disc 2 | I | 75 | 4 | 21 | 63 | 31 | 6 | 95 | 4 | <1 | |
B | Disc 1 | I | 72 | 4 | 24 | 63 | 32 | 5 | 94 | 5 | <1 |
Disc 2 | I | 75 | 4 | 21 | 65 | 29 | 6 | 95 | 4 | <1 | |
C | Disc 1 | I | 72 | 4 | 24 | 70 | 24 | 6 | 93 | 6 | <1 |
Disc 2 | I | 76 | 3 | 21 | 74 | 22 | 4 | 95 | 4 | <1 |
Cast Iron Grade | Chemical Composition | Disc Code | Average Speed (mm/µs) | E (GPa) | E According to Chemical Composition (GPa) | Standard Deviation σ(E) | Poisson’s Number | Density, g/cm3 | |
---|---|---|---|---|---|---|---|---|---|
VL | VS | ||||||||
A | MIN | Disc 1 | 4.87 | 2.71 | 135 | 135 | 3.15 | 0.26 | 7.192 |
Disc 2 | 4.84 | 2.72 | 135 | ||||||
OPT | Disc 1 | 4.77 | 2.67 | 131 | 131.5 | 0.26 | 7.188 | ||
Disc 2 | 4.78 | 2.69 | 132 | ||||||
MAX | Disc 1 | 4.71 | 2.64 | 128 | 128 | 0.26 | 7.181 | ||
Disc 2 | 4.69 | 2.65 | 128 | ||||||
B | MIN | Disc 1 | 4.51 | 2.59 | 120 | 121 | 2.34 | 0.26 | 7.148 |
Disc 2 | 4.54 | 2.61 | 122 | ||||||
OPT | Disc 1 | 4.55 | 2.59 | 121 | 120.5 | 0.27 | 7.143 | ||
Disc 2 | 4.52 | 2.58 | 120 | ||||||
MAX | Disc 1 | 4.52 | 2.53 | 117 | 116.5 | 0.26 | 7.319 | ||
Disc 2 | 4.47 | 2.54 | 116 | ||||||
C | MIN | Disc 1 | 4.47 | 2.54 | 116 | 116 | 4.32 | 0.27 | 7.117 |
Disc 2 | 4.50 | 2.54 | 116 | ||||||
OPT | Disc 1 | 4.43 | 2.51 | 113 | 112.5 | 0.27 | 7.113 | ||
Disc 2 | 4.39 | 2.50 | 112 | ||||||
MAX | Disc 1 | 4.30 | 2.44 | 107 | 106.5 | 0.26 | 7.111 | ||
Disc 2 | 4.29 | 2.43 | 106 |
Cast Iron Grade | Chemical Composition | Disc Code | First Natural Frequency, Hz | Calculation Error, % | ||
---|---|---|---|---|---|---|
Experiment | Simulation | |||||
Average Value | Standard Deviation | |||||
A | OPT | Disc 1 | 1090 | 8.1 | 1098 | 0.73 |
Disc 2 | 780 | 5.2 | 781 | 0.13 | ||
MIN | Disc 1 | 1097 | 8.3 | 1106 | 0.82 | |
Disc 2 | 786 | 5.2 | 791 | 0.64 | ||
MAX | Disc 1 | 1059 | 8.0 | 1066 | 0.66 | |
Disc 2 | 765 | 5.1 | 769 | 0.52 | ||
B | OPT | Disc 1 | 1033 | 8.0 | 1042 | 0.87 |
Disc 2 | 742 | 5.1 | 748 | 0.27 | ||
MIN | Disc 1 | 1054 | 8.0 | 1060 | 0.57 | |
Disc 2 | 751 | 5.0 | 753 | 0.27 | ||
MAX | Disc 1 | 1034 | 7.8 | 1033 | 0.10 | |
Disc 2 | 733 | 5.0 | 735 | 0.81 | ||
C | OPT | Disc 1 | 1001 | 7.5 | 1016 | 1.50 |
Disc 2 | 724 | 4.8 | 725 | 0.14 | ||
MIN | Disc 1 | 1036 | 7.6 | 1031 | 0.48 | |
Disc 2 | 733 | 4.7 | 734 | 0.14 | ||
MAX | Disc 1 | 980 | 7.5 | 994 | 1.43 | |
Disc 2 | 708 | 4.6 | 706 | 0.28 | ||
Average calculation error | 0.63 |
Mode No | Natural Frequency, Hz | Difference, % | |
---|---|---|---|
Disc before Blade Modification | Disc after Blade Modification | ||
Mod I (0;2) | 706 | 770 | 8.3 |
Mod II (0;3) | 1676 | 1851 | 9.5 |
Mod III (0;4) | 2751 | 3066 | 10.3 |
Parameter | Predicted Value | Actual Value | Error, % | |
---|---|---|---|---|
Average Value | Standard Deviation | |||
Natural frequency, Hz | 770 | 765 | 5.1 | 0.65 |
Young’s modulus, GPa | 119 | 118.5 | 0.8 | 0.42 |
Tensile strength, MPa | 222.4 | 218 | 7.7 | 2.01 |
Hardness, HB | 202.9 | 204 | 6.1 | 0.53 |
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Zyska, A.; Bieroński, M.; Naplocha, K.; Popielarski, P. Design and Control of the Natural Frequency of Brake Discs in the Aspect of the Gray Cast Iron Production Process. Materials 2024, 17, 3490. https://doi.org/10.3390/ma17143490
Zyska A, Bieroński M, Naplocha K, Popielarski P. Design and Control of the Natural Frequency of Brake Discs in the Aspect of the Gray Cast Iron Production Process. Materials. 2024; 17(14):3490. https://doi.org/10.3390/ma17143490
Chicago/Turabian StyleZyska, Andrzej, Mariusz Bieroński, Krzysztof Naplocha, and Paweł Popielarski. 2024. "Design and Control of the Natural Frequency of Brake Discs in the Aspect of the Gray Cast Iron Production Process" Materials 17, no. 14: 3490. https://doi.org/10.3390/ma17143490