惯量计算知识

1、1负载惯量之计算1)滚筒惯量计算Jl之公式：負載慣量Jl二(b)齒輪慣量齢(c)滾筒慣量(a)齒輪慣量(齒數比)2单位：kg.cm2, kg.m2xio-4说明:11. (a)齒輪，(b)齒輪滾筒皆為旋轉慣量：2MR22. M二質量,R=半徑3半曲小(b)齒輪數3. 齒數比=丽輪數上R1计算Jl之公式:2#負載慣量j _ (b)齒輪慣量-(c)導螺桿慣量-(d)台面慣量(齒數比)2 (a)齒輪慣量#单位：kg.cm2, kg.m2xio-4说明：11. (a)齒輪,(b)齒輪,(c)導螺桿，皆為旋轉慣量：qMR22. M二質量，R=半徑P 23. (d)為台面慣量=M ()2兀= 3.1416

2、4. M 質量，P =螺距,:台面惯量：人5. 齒數比二齒輪數(a)齒輪數注：若已知台面质量M、螺距P,可由查表2-1得台面惯量。导螺杆惯量:注：若已知导杆直径、导杆重量，可由查表2-2得导螺杆惯量。注：若已知导杆直径、导杆长度，可由查表2-3得导螺杆惯量。范例：假设 1. a 齿轮：100g, i40mm2. b 齿轮：300g, 一 120mm3. 导螺杆：6kg，“】20mm，导螺杆为 pitch 54. 台面：60kg5. 齿数比为5: 12 2 2计算a齿轮惯量：1/2MR = 1/2 X 0.1 X =0.2 kg.cm32 2 21/2MR = 1/2 X 0.3 X (6) =

3、5.4 kg.cm台面惯量：M (2P )* P:以cm为单位2nb齿轮惯量:#60X( 0.5cm- 6.2832)0.3804#导螺杆惯量:伺服马达惯量为:参照表11-1为3#5.4 + 3 + 0.38022+ 0.2 = 0.351 + 0.2 = 0.551 kg.cm(5)应用范例:条件：负载最大半径、最小半径、负载重量、速度（mm/分钟）例：如何选择卷绕机；铝箔材料的张力马达 已知必要条件：铝箔外径：240 mm内圆直径：40 mm重量：15 Kg卷取最快速度：20米/分钟计算：负载旋转惯量 公式：1/2 MR2 M （质量）R（半径）所以：1/2 X 15 X （12）2= 1

4、080 Kg.cm2 （转子惯量）【因负载旋转惯量 （转子惯量）太大，因此要用齿数比来减轻惯量。】最小圆周 X转速（rpm）=距离最小半径=40 mm十2= 20 mm最小圆周=2 X 3.1416 X 20= 125.66 mm125.66 mm X rpm= 20000 mmrpm= 159.159【假设齿数比为6： 1 （马达转6圈，铝箔材料转1圈）】1080 Kg.cm2 - 62 （齿数比）2= 30 Kg.cm2 （转子惯量）以SINANO马达为例（马达标准规格中的转子惯量值） 注：SINANO马达可承受5倍的转子惯量因低惯量马达；转子惯量X5倍后均不合，因此选择中惯量马达中惯量1

5、 KW、2000 rpm马达的转子惯量为 7.82 Kg.cm22 2 2 27.82 Kg.cm x 5= 39.1 Kg.cm39.1 Kg.cm 30 Kg.cm159.159 （rpm） x 6 （齿数比）=955 rpm 2000 rpm 955 rpm x 2【因张力马达须考虑追随速度，而算出张力马达（rpm）的2倍约等于马达最大rpm为最佳的张力追随速度。】所以选择齿数比6比条件下，中惯量1 KW的马达表 2-1 台面惯量(kg .cm 2,kg .m2 X10-4)工作台重量（kg）螺距pitch(mm)5010015020025030035040045050030.1140.

6、2280.3420.4560.5700.6840.7980.9121.0261.14040.203 :0.405:0.6080.8111.013P 1.2161.4181.6211.8242.02650.3170.6330.9501.2671.5831.9002.2162.5332.8503.16660.4560.912P 1.3681.8242.280:2.7363.1923.6484.1044.55970.6211.2411.8622.4823.1033.7244.3444.9655.5856.20680.8111.6212.4323.2424.0534.8635.6746.4857.29

7、58.10691.0262.0523.0784.1045.1296.1557.1818.2079.23310.259101.2672.5333.8005.0666.3337.5998.86610.13211.39912.665111.5323.0654.5976.1307.6629.19510.72712.26013.79215.325121.8243.6485.4717.2959.11910.94312.76614.59016.41418.238132.1404.2816.4218.56210.70212.84214.98317.12319.26421.404142.4824.9657.44

8、79.92912.41214.89417.37719.85922.34124.824152.8505.6998.54911.39914.24817.09819.94822.79725.64728.497163.2426.4859.72712.96916.21119.45422.69625.93829.18132.423173.660 :7.32010.98114.64118.30121.96125.62229.28232.94236.602184.1048.20712.31116.41420.51824.62128.72532.82836.93241.035194.5729.14413.716

9、18.28822.86127.43332.00536.57741.14945.721205.06610.13215.19820.26425.33030.39635.46240.52845.59550.661215.58511.17116.75622.34127.92733.51239.09744.68350.26855.853226.13012.26018.39024.52030.65036.78042.910 49.03955.16961.299236.700 :13.40020.10026.79933.49940.19946.899)53.59960.29966.999247.29514.

10、59021.88529.18136.47643.77151.06658.36165.65672.951厂257.91615.83123.74731.66339.57947.49455.41063.32671.24179.157268.56217.12325.68534.24742.80851.37059.93168.49377.05585.616279.23318.46627.69936.93246.16455.39764.63073.86383.09692.329289.92919.85929.78839.71849.64759.57769.50679.43689.36599.2952910

11、.65121.30331.95442.60653.25763.90874.56085.21195.863106.513011.39922.79734.19645.59556.99368.39279.79091.189102.59113.99表 2-2 导杆惯量(kg .cm 2,kg .m2 X10-4)导杆直径（伽）导杆重（Kg）2025303540455010.50.7811.1251.53122.5313.1251.50.751.1721.6882.29733.7974.688211.5632.2503.06345.0636.2502.51.251.9532.8133.82856.328

12、7.81331.52.3443.3754.59467.5949.3753.51.752.7343.9385.35978.85910.938423.1254.5006.125810.12512.5004.52.253.5165.0636.891911.39114.06352.53.9065.6257.6561012.65615.6255.52.754.2976.1888.4221113.92217.188634.6886.7509.1881215.188P 18.7506.53.255.0787.3139.9531316.45320.31373.55.4697.87510.7191417.719

13、21.8757.53.755.8598.43811.4841518.98423.438846.2509.00012.2501620.25025.0008.54.256.6419.56313.0161721.51626.56394.57.03110.12513.7811822.78128.1259.54.757.42210.68814.5471924.04729.6881057.81311.25015.3132025.31331.25010.55.258.20311.81316.0782126.57832.813115.58.59412.37516.8442227.84434.37511.55.

14、758.98412.93817.6092329.10935.9381269.37513.50018.3752430.37537.50012.56.259.76614.06319.1412531.64139.063136.510.15614.62519.9062632.90640.62513.56.7510.54715.18820.6722734.172P 42.18814710.93815.75021.4382835.43843.75014.57.2511.32816.31322.2032936.70345.313157.511.71916.87522.9693037.96946.87515.

15、57.7512.10917.43823.7343139.23448.43816812.50018.00024.5003240.50050.00016.58.2512.89118.56325.2663341.76651.563178.513.28119.12526.0313443.03153.12517.58.7513.67219.68826.7973544.29754.68818914.06320.25027.5633645.56356.25018.59.2514.45320.81328.3283746.82857.813199.514.84421.37529.0943848.09459.37

16、519.59.7515.23421.93829.8593949.35960.938201015.62522.50030.6254050.62562.500表 2-3 导杆惯量(kg .cm 2,kg .m2 X10-4)导杆直径(mm)导杆长(mm)10152025303540455012000.01530.07750.24500.59831.2412.2983.9216.2809.5724000.03060.15510.49011.19652.4814.5967.84112.56019.1446000.04590.23260.73511.79483.7226.89511.76218.8412

17、8.7168000.06130.31010.98022.39304.9629.19315.68325.12138.28810000.07660.38771.22522.99136.20311.49119.60431.40147.86012000.09190.46521.47033.58957.44313.78923.52437.68157.43214000.10720.54271.71534.18788.68416.08827.44543.96267.00416000.12250.62031.96044.78609.92418.38631.36650.24276.57618000.13780.

18、69782.20545.384311.16520.68435.28656.52286.14820000.15320.77532.45045.982512.40522.98239.20762.80295.72022000.16850.85292.69556.580813.64625.28143.12869.082105.29224000.18380.93042.94057.179014.88627.57947.04875.363114.86426000.19911.00793.18567.777316.12729.87750.96981.643124.43728000.21441.08553.43068.375517.36832.17554.89087.923134.00930000.22971.16303.67578.973818.60834.47458.81194.203143.581