Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B Calculator

Calculate Equivalent Mass MOI









Formula

The formula to calculate Equivalent Mass Moment of Inertia of Geared System (I) is:

\[ I = I_A + \frac{G^2 \cdot I_B}{\eta} \]

Where:

Definition

Equivalent Mass Moment of Inertia of Geared System with Shaft A and B is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.

Mass Moment of Inertia of mass attached to shaft A is a quantity expressing a body's tendency to resist angular acceleration.

Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of the number of teeth on the gear to that on the pinion.

Mass Moment of Inertia of mass attached to shaft B is a quantity expressing a body's tendency to resist angular acceleration.

Gear Efficiency is simply the ratio of output shaft power to the input shaft power.

How to calculate Equivalent Mass Moment of Inertia of Geared System

Let's assume the following values:

Using the formula:

\[ I = I_A + \frac{G^2 \cdot I_B}{\eta} \]

Evaluating:

\[ I = 18 + \frac{3^2 \cdot 36}{0.82} \]

The Equivalent Mass Moment of Inertia of Geared System is 413.121951219512 kg·m².

Equivalent Mass Moment of Inertia Conversion Chart

Mass Moment of Inertia (IA) Gear Ratio (G) Mass Moment of Inertia (IB) Gear Efficiency (η) Equivalent Mass Moment of Inertia (I)
10 2 30 0.7 181.428571428571445
10 2 30 0.75 170.000000000000000
10 2 30 0.8 160.000000000000000
10 2 30 0.85 151.176470588235276
10 2 32 0.7 192.857142857142861
10 2 32 0.75 180.666666666666657
10 2 32 0.8 170.000000000000000
10 2 32 0.85 160.588235294117624
10 2 34 0.7 204.285714285714306
10 2 34 0.75 191.333333333333343
10 2 34 0.8 180.000000000000000
10 2 34 0.85 169.999999999999972
10 2 36 0.7 215.714285714285722
10 2 36 0.75 202.000000000000000
10 2 36 0.8 190.000000000000000
10 2 36 0.85 179.411764705882348
10 2 38 0.7 227.142857142857167
10 2 38 0.75 212.666666666666657
10 2 38 0.8 200.000000000000000
10 2 38 0.85 188.823529411764696
10 2 40 0.7 238.571428571428584
10 2 40 0.75 223.333333333333343
10 2 40 0.8 210.000000000000000
10 2 40 0.85 198.235294117647044
10 3 30 0.7 395.714285714285722
10 3 30 0.75 370.000000000000000
10 3 30 0.8 347.500000000000000
10 3 30 0.85 327.647058823529392
10 3 32 0.7 421.428571428571445
10 3 32 0.75 394.000000000000000
10 3 32 0.8 370.000000000000000
10 3 32 0.85 348.823529411764696
10 3 34 0.7 447.142857142857167
10 3 34 0.75 418.000000000000000
10 3 34 0.8 392.500000000000000
10 3 34 0.85 369.999999999999943
10 3 36 0.7 472.857142857142890
10 3 36 0.75 442.000000000000000
10 3 36 0.8 415.000000000000000
10 3 36 0.85 391.176470588235247
10 3 38 0.7 498.571428571428612
10 3 38 0.75 466.000000000000000
10 3 38 0.8 437.500000000000000
10 3 38 0.85 412.352941176470551
10 3 40 0.7 524.285714285714334
10 3 40 0.75 490.000000000000000
10 3 40 0.8 460.000000000000000
10 3 40 0.85 433.529411764705856
10 4 30 0.7 695.714285714285779
10 4 30 0.75 650.000000000000000
10 4 30 0.8 610.000000000000000
10 4 30 0.85 574.705882352941103
10 4 32 0.7 741.428571428571445
10 4 32 0.75 692.666666666666629
10 4 32 0.8 650.000000000000000
10 4 32 0.85 612.352941176470495
10 4 34 0.7 787.142857142857224
10 4 34 0.75 735.333333333333371
10 4 34 0.8 690.000000000000000
10 4 34 0.85 649.999999999999886
10 4 36 0.7 832.857142857142890
10 4 36 0.75 778.000000000000000
10 4 36 0.8 730.000000000000000
10 4 36 0.85 687.647058823529392
10 4 38 0.7 878.571428571428669
10 4 38 0.75 820.666666666666629
10 4 38 0.8 770.000000000000000
10 4 38 0.85 725.294117647058783
10 4 40 0.7 924.285714285714334
10 4 40 0.75 863.333333333333371
10 4 40 0.8 810.000000000000000
10 4 40 0.85 762.941176470588175
11 2 30 0.7 182.428571428571445
11 2 30 0.75 171.000000000000000
11 2 30 0.8 161.000000000000000
11 2 30 0.85 152.176470588235276
11 2 32 0.7 193.857142857142861
11 2 32 0.75 181.666666666666657
11 2 32 0.8 171.000000000000000
11 2 32 0.85 161.588235294117624
11 2 34 0.7 205.285714285714306
11 2 34 0.75 192.333333333333343
11 2 34 0.8 181.000000000000000
11 2 34 0.85 170.999999999999972
11 2 36 0.7 216.714285714285722
11 2 36 0.75 203.000000000000000
11 2 36 0.8 191.000000000000000
11 2 36 0.85 180.411764705882348
11 2 38 0.7 228.142857142857167
11 2 38 0.75 213.666666666666657
11 2 38 0.8 201.000000000000000
11 2 38 0.85 189.823529411764696
11 2 40 0.7 239.571428571428584
11 2 40 0.75 224.333333333333343
11 2 40 0.8 211.000000000000000
11 2 40 0.85 199.235294117647044
11 3 30 0.7 396.714285714285722
11 3 30 0.75 371.000000000000000
11 3 30 0.8 348.500000000000000
11 3 30 0.85 328.647058823529392
11 3 32 0.7 422.428571428571445
11 3 32 0.75 395.000000000000000
11 3 32 0.8 371.000000000000000
11 3 32 0.85 349.823529411764696
11 3 34 0.7 448.142857142857167
11 3 34 0.75 419.000000000000000
11 3 34 0.8 393.500000000000000
11 3 34 0.85 370.999999999999943
11 3 36 0.7 473.857142857142890
11 3 36 0.75 443.000000000000000
11 3 36 0.8 416.000000000000000
11 3 36 0.85 392.176470588235247
11 3 38 0.7 499.571428571428612
11 3 38 0.75 467.000000000000000
11 3 38 0.8 438.500000000000000
11 3 38 0.85 413.352941176470551
11 3 40 0.7 525.285714285714334
11 3 40 0.75 491.000000000000000
11 3 40 0.8 461.000000000000000
11 3 40 0.85 434.529411764705856
11 4 30 0.7 696.714285714285779
11 4 30 0.75 651.000000000000000
11 4 30 0.8 611.000000000000000
11 4 30 0.85 575.705882352941103
11 4 32 0.7 742.428571428571445
11 4 32 0.75 693.666666666666629
11 4 32 0.8 651.000000000000000
11 4 32 0.85 613.352941176470495
11 4 34 0.7 788.142857142857224
11 4 34 0.75 736.333333333333371
11 4 34 0.8 691.000000000000000
11 4 34 0.85 650.999999999999886
11 4 36 0.7 833.857142857142890
11 4 36 0.75 779.000000000000000
11 4 36 0.8 731.000000000000000
11 4 36 0.85 688.647058823529392
11 4 38 0.7 879.571428571428669
11 4 38 0.75 821.666666666666629
11 4 38 0.8 771.000000000000000
11 4 38 0.85 726.294117647058783
11 4 40 0.7 925.285714285714334
11 4 40 0.75 864.333333333333371
11 4 40 0.8 811.000000000000000
11 4 40 0.85 763.941176470588175
12 2 30 0.7 183.428571428571445
12 2 30 0.75 172.000000000000000
12 2 30 0.8 162.000000000000000
12 2 30 0.85 153.176470588235276
12 2 32 0.7 194.857142857142861
12 2 32 0.75 182.666666666666657
12 2 32 0.8 172.000000000000000
12 2 32 0.85 162.588235294117624
12 2 34 0.7 206.285714285714306
12 2 34 0.75 193.333333333333343
12 2 34 0.8 182.000000000000000
12 2 34 0.85 171.999999999999972
12 2 36 0.7 217.714285714285722
12 2 36 0.75 204.000000000000000
12 2 36 0.8 192.000000000000000
12 2 36 0.85 181.411764705882348
12 2 38 0.7 229.142857142857167
12 2 38 0.75 214.666666666666657
12 2 38 0.8 202.000000000000000
12 2 38 0.85 190.823529411764696
12 2 40 0.7 240.571428571428584
12 2 40 0.75 225.333333333333343
12 2 40 0.8 212.000000000000000
12 2 40 0.85 200.235294117647044
12 3 30 0.7 397.714285714285722
12 3 30 0.75 372.000000000000000
12 3 30 0.8 349.500000000000000
12 3 30 0.85 329.647058823529392
12 3 32 0.7 423.428571428571445
12 3 32 0.75 396.000000000000000
12 3 32 0.8 372.000000000000000
12 3 32 0.85 350.823529411764696
12 3 34 0.7 449.142857142857167
12 3 34 0.75 420.000000000000000
12 3 34 0.8 394.500000000000000
12 3 34 0.85 371.999999999999943
12 3 36 0.7 474.857142857142890
12 3 36 0.75 444.000000000000000
12 3 36 0.8 417.000000000000000
12 3 36 0.85 393.176470588235247
12 3 38 0.7 500.571428571428612
12 3 38 0.75 468.000000000000000
12 3 38 0.8 439.500000000000000
12 3 38 0.85 414.352941176470551
12 3 40 0.7 526.285714285714334
12 3 40 0.75 492.000000000000000
12 3 40 0.8 462.000000000000000
12 3 40 0.85 435.529411764705856
12 4 30 0.7 697.714285714285779
12 4 30 0.75 652.000000000000000
12 4 30 0.8 612.000000000000000
12 4 30 0.85 576.705882352941103
12 4 32 0.7 743.428571428571445
12 4 32 0.75 694.666666666666629
12 4 32 0.8 652.000000000000000
12 4 32 0.85 614.352941176470495
12 4 34 0.7 789.142857142857224
12 4 34 0.75 737.333333333333371
12 4 34 0.8 692.000000000000000
12 4 34 0.85 651.999999999999886
12 4 36 0.7 834.857142857142890
12 4 36 0.75 780.000000000000000
12 4 36 0.8 732.000000000000000
12 4 36 0.85 689.647058823529392
12 4 38 0.7 880.571428571428669
12 4 38 0.75 822.666666666666629
12 4 38 0.8 772.000000000000000
12 4 38 0.85 727.294117647058783
12 4 40 0.7 926.285714285714334
12 4 40 0.75 865.333333333333371
12 4 40 0.8 812.000000000000000
12 4 40 0.85 764.941176470588175
13 2 30 0.7 184.428571428571445
13 2 30 0.75 173.000000000000000
13 2 30 0.8 163.000000000000000
13 2 30 0.85 154.176470588235276
13 2 32 0.7 195.857142857142861
13 2 32 0.75 183.666666666666657
13 2 32 0.8 173.000000000000000
13 2 32 0.85 163.588235294117624
13 2 34 0.7 207.285714285714306
13 2 34 0.75 194.333333333333343
13 2 34 0.8 183.000000000000000
13 2 34 0.85 172.999999999999972
13 2 36 0.7 218.714285714285722
13 2 36 0.75 205.000000000000000
13 2 36 0.8 193.000000000000000
13 2 36 0.85 182.411764705882348
13 2 38 0.7 230.142857142857167
13 2 38 0.75 215.666666666666657
13 2 38 0.8 203.000000000000000
13 2 38 0.85 191.823529411764696
13 2 40 0.7 241.571428571428584
13 2 40 0.75 226.333333333333343
13 2 40 0.8 213.000000000000000
13 2 40 0.85 201.235294117647044
13 3 30 0.7 398.714285714285722
13 3 30 0.75 373.000000000000000
13 3 30 0.8 350.500000000000000
13 3 30 0.85 330.647058823529392
13 3 32 0.7 424.428571428571445
13 3 32 0.75 397.000000000000000
13 3 32 0.8 373.000000000000000
13 3 32 0.85 351.823529411764696
13 3 34 0.7 450.142857142857167
13 3 34 0.75 421.000000000000000
13 3 34 0.8 395.500000000000000
13 3 34 0.85 372.999999999999943
13 3 36 0.7 475.857142857142890
13 3 36 0.75 445.000000000000000
13 3 36 0.8 418.000000000000000
13 3 36 0.85 394.176470588235247
13 3 38 0.7 501.571428571428612
13 3 38 0.75 469.000000000000000
13 3 38 0.8 440.500000000000000
13 3 38 0.85 415.352941176470551
13 3 40 0.7 527.285714285714334
13 3 40 0.75 493.000000000000000
13 3 40 0.8 463.000000000000000
13 3 40 0.85 436.529411764705856
13 4 30 0.7 698.714285714285779
13 4 30 0.75 653.000000000000000
13 4 30 0.8 613.000000000000000
13 4 30 0.85 577.705882352941103
13 4 32 0.7 744.428571428571445
13 4 32 0.75 695.666666666666629
13 4 32 0.8 653.000000000000000
13 4 32 0.85 615.352941176470495
13 4 34 0.7 790.142857142857224
13 4 34 0.75 738.333333333333371
13 4 34 0.8 693.000000000000000
13 4 34 0.85 652.999999999999886
13 4 36 0.7 835.857142857142890
13 4 36 0.75 781.000000000000000
13 4 36 0.8 733.000000000000000
13 4 36 0.85 690.647058823529392
13 4 38 0.7 881.571428571428669
13 4 38 0.75 823.666666666666629
13 4 38 0.8 773.000000000000000
13 4 38 0.85 728.294117647058783
13 4 40 0.7 927.285714285714334
13 4 40 0.75 866.333333333333371
13 4 40 0.8 813.000000000000000
13 4 40 0.85 765.941176470588175
14 2 30 0.7 185.428571428571445
14 2 30 0.75 174.000000000000000
14 2 30 0.8 164.000000000000000
14 2 30 0.85 155.176470588235276
14 2 32 0.7 196.857142857142861
14 2 32 0.75 184.666666666666657
14 2 32 0.8 174.000000000000000
14 2 32 0.85 164.588235294117624
14 2 34 0.7 208.285714285714306
14 2 34 0.75 195.333333333333343
14 2 34 0.8 184.000000000000000
14 2 34 0.85 173.999999999999972
14 2 36 0.7 219.714285714285722
14 2 36 0.75 206.000000000000000
14 2 36 0.8 194.000000000000000
14 2 36 0.85 183.411764705882348
14 2 38 0.7 231.142857142857167
14 2 38 0.75 216.666666666666657
14 2 38 0.8 204.000000000000000
14 2 38 0.85 192.823529411764696
14 2 40 0.7 242.571428571428584
14 2 40 0.75 227.333333333333343
14 2 40 0.8 214.000000000000000
14 2 40 0.85 202.235294117647044
14 3 30 0.7 399.714285714285722
14 3 30 0.75 374.000000000000000
14 3 30 0.8 351.500000000000000
14 3 30 0.85 331.647058823529392
14 3 32 0.7 425.428571428571445
14 3 32 0.75 398.000000000000000
14 3 32 0.8 374.000000000000000
14 3 32 0.85 352.823529411764696
14 3 34 0.7 451.142857142857167
14 3 34 0.75 422.000000000000000
14 3 34 0.8 396.500000000000000
14 3 34 0.85 373.999999999999943
14 3 36 0.7 476.857142857142890
14 3 36 0.75 446.000000000000000
14 3 36 0.8 419.000000000000000
14 3 36 0.85 395.176470588235247
14 3 38 0.7 502.571428571428612
14 3 38 0.75 470.000000000000000
14 3 38 0.8 441.500000000000000
14 3 38 0.85 416.352941176470551
14 3 40 0.7 528.285714285714334
14 3 40 0.75 494.000000000000000
14 3 40 0.8 464.000000000000000
14 3 40 0.85 437.529411764705856
14 4 30 0.7 699.714285714285779
14 4 30 0.75 654.000000000000000
14 4 30 0.8 614.000000000000000
14 4 30 0.85 578.705882352941103
14 4 32 0.7 745.428571428571445
14 4 32 0.75 696.666666666666629
14 4 32 0.8 654.000000000000000
14 4 32 0.85 616.352941176470495
14 4 34 0.7 791.142857142857224
14 4 34 0.75 739.333333333333371
14 4 34 0.8 694.000000000000000
14 4 34 0.85 653.999999999999886
14 4 36 0.7 836.857142857142890
14 4 36 0.75 782.000000000000000
14 4 36 0.8 734.000000000000000
14 4 36 0.85 691.647058823529392
14 4 38 0.7 882.571428571428669
14 4 38 0.75 824.666666666666629
14 4 38 0.8 774.000000000000000
14 4 38 0.85 729.294117647058783
14 4 40 0.7 928.285714285714334
14 4 40 0.75 867.333333333333371
14 4 40 0.8 814.000000000000000
14 4 40 0.85 766.941176470588175
15 2 30 0.7 186.428571428571445
15 2 30 0.75 175.000000000000000
15 2 30 0.8 165.000000000000000
15 2 30 0.85 156.176470588235276
15 2 32 0.7 197.857142857142861
15 2 32 0.75 185.666666666666657
15 2 32 0.8 175.000000000000000
15 2 32 0.85 165.588235294117624
15 2 34 0.7 209.285714285714306
15 2 34 0.75 196.333333333333343
15 2 34 0.8 185.000000000000000
15 2 34 0.85 174.999999999999972
15 2 36 0.7 220.714285714285722
15 2 36 0.75 207.000000000000000
15 2 36 0.8 195.000000000000000
15 2 36 0.85 184.411764705882348
15 2 38 0.7 232.142857142857167
15 2 38 0.75 217.666666666666657
15 2 38 0.8 205.000000000000000
15 2 38 0.85 193.823529411764696
15 2 40 0.7 243.571428571428584
15 2 40 0.75 228.333333333333343
15 2 40 0.8 215.000000000000000
15 2 40 0.85 203.235294117647044
15 3 30 0.7 400.714285714285722
15 3 30 0.75 375.000000000000000
15 3 30 0.8 352.500000000000000
15 3 30 0.85 332.647058823529392
15 3 32 0.7 426.428571428571445
15 3 32 0.75 399.000000000000000
15 3 32 0.8 375.000000000000000
15 3 32 0.85 353.823529411764696
15 3 34 0.7 452.142857142857167
15 3 34 0.75 423.000000000000000
15 3 34 0.8 397.500000000000000
15 3 34 0.85 374.999999999999943
15 3 36 0.7 477.857142857142890
15 3 36 0.75 447.000000000000000
15 3 36 0.8 420.000000000000000
15 3 36 0.85 396.176470588235247
15 3 38 0.7 503.571428571428612
15 3 38 0.75 471.000000000000000
15 3 38 0.8 442.500000000000000
15 3 38 0.85 417.352941176470551
15 3 40 0.7 529.285714285714334
15 3 40 0.75 495.000000000000000
15 3 40 0.8 465.000000000000000
15 3 40 0.85 438.529411764705856
15 4 30 0.7 700.714285714285779
15 4 30 0.75 655.000000000000000
15 4 30 0.8 615.000000000000000
15 4 30 0.85 579.705882352941103
15 4 32 0.7 746.428571428571445
15 4 32 0.75 697.666666666666629
15 4 32 0.8 655.000000000000000
15 4 32 0.85 617.352941176470495
15 4 34 0.7 792.142857142857224
15 4 34 0.75 740.333333333333371
15 4 34 0.8 695.000000000000000
15 4 34 0.85 654.999999999999886
15 4 36 0.7 837.857142857142890
15 4 36 0.75 783.000000000000000
15 4 36 0.8 735.000000000000000
15 4 36 0.85 692.647058823529392
15 4 38 0.7 883.571428571428669
15 4 38 0.75 825.666666666666629
15 4 38 0.8 775.000000000000000
15 4 38 0.85 730.294117647058783
15 4 40 0.7 929.285714285714334
15 4 40 0.75 868.333333333333371
15 4 40 0.8 815.000000000000000
15 4 40 0.85 767.941176470588175
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