1 Introduction
2 Establishment of Modified Contact Force Model
2.1 Contact Deformation of Asperity
2.2 Modified Contact Stiffness Model
2.3 Modified Contact Force Model
3 Numerical Simulation of Modified Contact Force Model
3.1 Simulation Parameters of the Mechanism
3.2 Analysis of Contact Process under Different Restitution Coefficients
3.3 Analysis of Contact Process at Different Initial Velocities
3.4 Analysis of Contact Process for Different Amounts of Roughness
4 Comparative Analysis of Models
4.1 Comparative Analysis of Models under Different Clearance Sizes
4.2 Comparative Analysis of Models under Different Restitution Coefficients
5 Experiment Verification
5.1 Test Rig
Parameter | Values | Parameter | Values |
---|---|---|---|
Elastic modulus | 207 GPa | Equivalent mass | 0.85 kg |
Poisson ratio | 0.3 | Simulation clearance | 0.5 mm |
Surface roughness | 6.3 | Area scale coefficient | 0.05 |
Convex radius | 16.5 mm | Restitution coefficient | 0.46 |
5.2 Experimental Results and Analysis
Experiment no. | Measured initial velocity (m/s) | Measured contact force (N) | Theoretical contact force (N) | Relative error |
---|---|---|---|---|
1 | 0.131 | 258.18 | 234.5 | − 9.63% |
2 | 0.150 | 308.53 | 281.6 | − 9.56% |
3 | 0.241 | 499.00 | 533.4 | 6.38% |
4 | 0.299 | 711.06 | 708.6 | − 0.42% |
5 | 0.302 | 739.00 | 721.7 | − 2.50% |
6 | 0.351 | 935.00 | 881.4 | − 6.08% |
7 | 0.388 | 1089.17 | 1010 | − 7.82% |
8 | 0.400 | 1188.66 | 1087 | − 9.29% |
9 | 0.421 | 1250.00 | 1128 | − 7.30% |
10 | 0.427 | 1183.78 | 1150 | − 2.87% |
11 | 0.577 | 1661.07 | 1718 | 3.32% |
12 | 0.630 | 2035.22 | 1924 | − 5.77% |
13 | 0.735 | 2205.81 | 2365 | 6.77% |
14 | 0.818 | 2435.45 | 2703 | 9.91% |
15 | 0.882 | 2827.45 | 2994 | 5.58% |
16 | 0.970 | 3191.83 | 3391 | 5.90% |
17 | 0.989 | 3347.17 | 3477 | 3.74% |
18 | 1.044 | 3752.15 | 3722 | − 0.80% |
19 | 1.070 | 3812.87 | 3842 | 0.78% |
20 | 1.110 | 3934.63 | 4039 | 2.60% |
Experiment no. | Measured initial velocity (m/s) | Measured contact force (N) | Theoretical contact force (N) | Relative error |
---|---|---|---|---|
1 | 0.131 | 258.18 | 242.4 | − 6.1% |
2 | 0.150 | 308.53 | 288.5 | − 6.5% |
3 | 0.241 | 499.00 | 530.3 | 6.3% |
4 | 0.299 | 711.06 | 698.4 | − 1.8% |
5 | 0.302 | 739.00 | 707.2 | − 4.3% |
6 | 0.343 | 847.78 | 832.4 | − 1.8% |
7 | 0.388 | 1059.17 | 972.7 | − 8.2% |
8 | 0.411 | 1112.06 | 1048.0 | − 5.8% |
9 | 0.422 | 1128.54 | 1084.0 | − 3.9% |
10 | 0.427 | 1183.78 | 1100.0 | − 7.1% |
11 | 0.577 | 1661.07 | 1611.0 | − 3.0% |
12 | 0.624 | 1697.08 | 1778.0 | 4.8% |
13 | 0.633 | 1748.96 | 1812.0 | 3.6% |
14 | 0.735 | 2205.81 | 2188.0 | − 0.8% |
15 | 0.818 | 2435.30 | 2503.9 | 2.8% |
16 | 0.882 | 2827.45 | 2755.8 | − 2.5% |
17 | 0.970 | 3191.83 | 3102.5 | − 2.8% |
18 | 0.989 | 3347.17 | 3177.4 | − 5.1% |
19 | 1.044 | 3752.15 | 3399.4 | − 9.4% |
20 | 1.070 | 3812.87 | 3508.7 | − 8.0% |
21 | 1.110 | 3934.63 | 3677.1 | − 6.5% |
Experiment no. | Measured initial velocity (m/s) | Measured contact force (N) | Theoretical contact force (N) | Relative error |
---|---|---|---|---|
1 | 0.101 | 174.56 | 190.6 | 9.2% |
2 | 0.127 | 249.63 | 256.2 | 2.6% |
3 | 0.253 | 652.16 | 623.3 | − 4.4% |
4 | 0.262 | 624.69 | 651.8 | 4.3% |
5 | 0.297 | 746.77 | 766 | 2.6% |
6 | 0.305 | 822.75 | 792.8 | − 3.6% |
7 | 0.354 | 1044.31 | 959.2 | − 8.1% |
8 | 0.378 | 1011.05 | 1044.5 | 3.3% |
9 | 0.383 | 1084.9 | 1062.3 | − 2.1% |
10 | 0.391 | 1130.68 | 1090.9 | − 3.5% |
11 | 0.392 | 1036.99 | 1094.4 | 5.5% |
12 | 0.402 | 1197.2 | 1130.1 | − 5.6% |
13 | 0.419 | 1176.76 | 1190.7 | 1.2% |
14 | 0.423 | 1163.02 | 1204.9 | 3.6% |
15 | 0.448 | 1313.78 | 1297.7 | − 1.2% |
16 | 0.480 | 1448.97 | 1419.2 | − 2.1% |
17 | 0.484 | 1395.57 | 1434.5 | 2.8% |
18 | 0.499 | 1580.81 | 1491.5 | − 5.6% |
19 | 0.534 | 1752.62 | 1624.7 | − 7.3% |
20 | 0.556 | 1744.38 | 1709.5 | − 2.0% |
21 | 0.602 | 1909.18 | 1896.4 | − 0.7% |
22 | 0.619 | 1992.19 | 1965.7 | − 1.3% |
23 | 0.649 | 2171.33 | 2088 | − 3.8% |
24 | 0.735 | 2647.09 | 2443.3 | − 7.7% |
25 | 0.809 | 2629.39 | 2767.3 | 5.2% |
26 | 0.910 | 3074.65 | 3210.9 | 4.4% |
27 | 0.911 | 3275.15 | 3215.3 | − 1.8% |
28 | 0.925 | 3320.92 | 3276.7 | − 1.3% |
29 | 0.926 | 3533.94 | 3281.1 | − 7.2% |
30 | 0.930 | 3009.95 | 3298.7 | 9.6% |