伺服惯量计算

1、第十一章 附錄A11 附錄A11.1 如何選擇慣量合適之伺服馬達選擇慣量合適之伺服馬達。根據伺服馬達型錄所示，最大設定值可達10倍JMJL 根據一般經驗法則，設定值為5倍 JMJLJM = 馬達慣量 (可查伺服馬達型錄得知)JL = 負載慣量 (可由下一節之公式計算得知)ð實際上，JM×10時，馬達動作遲鈍，所以一般都調在5倍以下。11.1.1 負載慣量之計算1) 滾筒慣量伺服馬達 (a) 齒輪(c) 滾筒(b) 齒輪R圖11-1計算JL之公式：單位：kg.cm2，kg.m2×10-4說明：2) 台面慣量(a) 齒輪(b) 齒輪(c) 導螺桿(d) 台面伺服馬達R

2、圖11-2計算JL之公式：單位：kg.cm2，kg.m2×10-4說明：台面慣量：註：若已知 台面質量M、螺距P，可由查表11-1得台面慣量。導螺桿慣量：註：若已知 導桿直徑、導桿重量，可由查表11-2得導螺桿慣量。註：若已知 導桿直徑、導桿長度，可由查表11-3得導螺桿慣量。範例：假設1. a齒輪：100g，Æ40mm2. b齒輪：300g，Æ120mm3. 導螺桿：6kg，Æ20mm，導螺桿為pitch 54. 台面：60kg5. 齒數比為5：1計算a齒輪慣量：1/2MR2 = 1/2×0.1×(2)2=0.2 kg.cm2b齒輪

3、慣量：1/2MR2 = 1/2×0.3×(6)2=5.4 kg.cm2P22P：以cm為單位台面慣量：M（ ）2：60×（0.5cm÷6.2832）：0.380導螺桿慣量：參照表11-2為3伺服馬達慣量為：5.4 + 3 + 0.380(5)2+ 0.2 = 0.351 + 0.2 = 0.551 kg.cm211.2 如何選擇最適的馬達條件：負載最大半徑、最小半徑、負載重量、速度 (mm/分鐘)例：如何選擇捲繞機；鋁箔材料的張力馬達已知必要條件：40 mm240 mm鋁箔外徑：240 mm內圓直徑：40 mm重量：15 Kg捲取最快速度：20米/分鐘計

4、算：負載旋轉慣量公式：1/2 MR2 M (質量) R(半徑)所以：1/2 ×15 ×(12)21080 Kg.cm2 (轉子慣量)【因負載旋轉慣量 (轉子慣量) 太大，因此要用齒數比來減輕慣量。】最小圓周 ×轉速 (rpm)距離最小半徑40 mm ÷220 mm最小圓周2 ×3.1416 ×20125.66 mm125.66 mm ×rpm20000 mm rpm159.159【假設齒數比為6：1 (馬達轉6圈，鋁箔材料轉1圈)】1080 Kg.cm2 ÷62 (齒數比)230 Kg.cm2 (轉子慣量)以野力馬

5、達為例 (請參照野力馬達標準規格中的轉子慣量值)註：野力、三菱、.等馬達可承受5倍的轉子慣量因低慣量馬達；轉子慣量 ×5倍後均不合，因此選擇中慣量馬達中慣量1 KW、2000 rpm馬達的轉子慣量為7.82 Kg.cm27.82 Kg.cm2 ×539.1 Kg.cm2 39.1 Kg.cm230 Kg.cm2159.159 (rpm) ×6 (齒數比) 955 rpm 2000 rpm955 rpm ×2【因張力馬達須考慮追隨速度，而算出張力馬達 (rpm) 的2倍約等於馬達最大rpm為最佳的張力追隨速度。】所以選擇齒數比6比條件下，中慣量1 KW的馬

6、達表11-1 台面慣量 (.2，.m2 ×10-4)工作台重量 ()螺距pitch(mm)5010015020025030035040045050030.1140.2280.3420.4560.5700.6840.7980.9121.0261.14040.2030.4050.6080.8111.0131.2161.4181.6211.8242.02650.3170.6330.9501.2671.5831.9002.2162.5332.8503.16660.4560.9121.3681.8242.2802.7363.1923.6484.1044.55970.6211.2411.8622

7、.4823.1033.7244.3444.9655.5856.20680.8111.6212.4323.2424.0534.8635.6746.4857.2958.10691.0262.0523.0784.1045.1296.1557.1818.2079.23310.259101.2672.5333.8005.0666.3337.5998.86610.13211.39912.665111.5323.0654.5976.1307.6629.19510.72712.26013.79215.325121.8243.6485.4717.2959.11910.94312.76614.59016.4141

8、8.238132.1404.2816.4218.56210.70212.84214.98317.12319.26421.404142.4824.9657.4479.92912.41214.89417.37719.85922.34124.824152.8505.6998.54911.39914.24817.09819.94822.79725.64728.497163.2426.4859.72712.96916.21119.45422.69625.93829.18132.423173.6607.32010.98114.64118.30121.96125.62229.28232.94236.6021

9、84.1048.20712.31116.41420.51824.62128.72532.82836.93241.035194.5729.14413.71618.28822.86127.43332.00536.57741.14945.721205.06610.13215.19820.26425.33030.39635.46240.52845.59550.661215.58511.17116.75622.34127.92733.51239.09744.68350.26855.853226.13012.26018.39024.52030.65036.78042.91049.03955.16961.2

10、99236.70013.40020.10026.79933.49940.19946.89953.59960.29966.999247.29514.59021.88529.18136.47643.77151.06658.36165.65672.951257.91615.83123.74731.66339.57947.49455.41063.32671.24179.157268.56217.12325.68534.24742.80851.37059.93168.49377.05585.616279.23318.46627.69936.93246.16455.39764.63073.86383.09

11、692.329289.92919.85929.78839.71849.64759.57769.50679.43689.36599.2952910.65121.30331.95442.60653.25763.90874.56085.21195.863106.513011.39922.79734.19645.59556.99368.39279.79091.189102.59113.99表11-2 導桿慣量 (.2，.m2 ×10-4)導桿直徑 ()導桿重(Kg)2025303540455010.50.7811.1251.53122.5313.1251.50.751.1721.6882.2

12、9733.7974.688211.5632.2503.06345.0636.2502.51.251.9532.8133.82856.3287.81331.52.3443.3754.59467.5949.3753.51.752.7343.9385.35978.85910.938423.1254.5006.125810.12512.5004.52.253.5165.0636.891911.39114.06352.53.9065.6257.6561012.65615.6255.52.754.2976.1888.4221113.92217.188634.6886.7509.1881215.18818.

13、7506.53.255.0787.3139.9531316.45320.31373.55.4697.87510.7191417.71921.8757.53.755.8598.43811.4841518.98423.438846.2509.00012.2501620.25025.0008.54.256.6419.56313.0161721.51626.56394.57.03110.12513.7811822.78128.1259.54.757.42210.68814.5471924.04729.6881057.81311.25015.3132025.31331.25010.55.258.2031

14、1.81316.0782126.57832.813115.58.59412.37516.8442227.84434.37511.55.758.98412.93817.6092329.10935.9381269.37513.50018.3752430.37537.50012.56.259.76614.06319.1412531.64139.063136.510.15614.62519.9062632.90640.62513.56.7510.54715.18820.6722734.17242.18814710.93815.75021.4382835.43843.75014.57.2511.3281

15、6.31322.2032936.70345.313157.511.71916.87522.9693037.96946.87515.57.7512.10917.43823.7343139.23448.43816812.50018.00024.5003240.50050.00016.58.2512.89118.56325.2663341.76651.563178.513.28119.12526.0313443.03153.12517.58.7513.67219.68826.7973544.29754.68818914.06320.25027.5633645.56356.25018.59.2514.

16、45320.81328.3283746.82857.813199.514.84421.37529.0943848.09459.37519.59.7515.23421.93829.8593949.35960.938201015.62522.50030.6254050.62562.500表11-3 導桿慣量 (.2，.m2 ×10-4)導桿直徑 (mm)導桿長(mm)1015202530354045502000.01530.07750.24500.59831.2412.2983.9216.2809.5724000.03060.15510.49011.19652.4814.5967.841

17、12.56019.1446000.04590.23260.73511.79483.7226.89511.76218.84128.7168000.06130.31010.98022.39304.9629.19315.68325.12138.28810000.07660.38771.22522.99136.20311.49119.60431.40147.86012000.09190.46521.47033.58957.44313.78923.52437.68157.43214000.10720.54271.71534.18788.68416.08827.44543.96267.00416000.1

18、2250.62031.96044.78609.92418.38631.36650.24276.57618000.13780.69782.20545.384311.16520.68435.28656.52286.14820000.15320.77532.45045.982512.40522.98239.20762.80295.72022000.16850.85292.69556.580813.64625.28143.12869.082105.29224000.18380.93042.94057.179014.88627.57947.04875.363114.86426000.19911.0079

19、3.18567.777316.12729.87750.96981.643124.43728000.21441.08553.43068.375517.36832.17554.89087.923134.00930000.22971.16303.67578.973818.60834.47458.81194.203143.58132000.24501.24053.92079.572019.84936.77262.731100.483153.15334000.26041.31814.165810.170321.08939.07066.652106.764162.72536000.27571.39564.

20、410810.768522.33041.36870.573113.044172.29738000.29101.47314.655811.366823.57043.66774.493119.324181.86940000.30631.55074.900911.965024.81145.96578.414125.604191.44142000.32161.62825.145912.563326.05148.26382.335131.885201.01344000.33691.70575.391013.161627.29250.56186.256138.165210.58546000.35231.7

21、8335.636013.759828.53252.86090.176144.445220.15748000.36761.86085.881114.358129.77355.15894.097150.725229.72950000.38291.93836.126114.956331.01357.45698.018157.005239.30111.3 如何計算變壓器的安培數一個 400W 的馬達。若實際效率為 100%，則此顆馬達實際為 400 ÷ 1 = 400VA (伏安)。若實際效率為 90%，則此顆馬達實際為 400 ÷ 0.9 = 444VA (伏安)。功率計算公式：

22、P = V (電壓) ×I (電流)安培數算法使用瓦數 (W)電壓 (220)計算安培33000VA單相 3000VA÷220V13.633000VA三相 3000VA÷【 ×220】7.87範例：捲繞機所需功率1. 400W馬達×9個 = 3600W2. 750W馬達×2個 = 1500W3. 點焊機一台 4A 【24V×4A = 96W】4. Born off .3A .35V【35V×3A = 105W】5. 控制器2台【5V×3A×2 = 30W】6. 24V POWER一個【24V&#

23、215;8A = 192W】5V±12VPOWER一個【5V×3 = 15W】【3600W1500W96W105W30W192W15W】×1.5 (經驗值) 8307VA 8307 = 1.732 (三相電壓) VI = 8307 ÷【1.732 × 415 (當地國電壓)】 11.55A註：12 的線可承受 8 安培的電流。11.4 被動 ENCODER被動 ENCODER含有兩項功能如下：(1) 同步裁剪 ( FLY CUT )1. 滾筒式同步裁剪2. 台車式同步裁剪 (如圖11-3)(2) 長度補償 (如圖11-4)11.4.1 被動 E

24、NCODER - 台車式同步裁剪 ( FLY CUT )被動ENCODER - 台車式同步裁剪的功能 (如圖11-3)。首先是物料送料不停,然後經由控制器X軸控制台車做裁剪動作。再經由控制器Y軸當被動ENCODER，令C145=1 Y軸為數顯模式，確認送料的長度,即可完成同步裁剪的動作。被動 ENCODER(Y軸)計算長度 C145 = 1 POWERHUST CNCMOTORENCODER滾輪物料（X軸）同步裁剪圖11-3 被動 ENCODER - 台車式同步裁剪 ( FLY CUT )11.4.2 被動 ENCODER - 長度補償被動ENCODER的另一個功能 - 長度補償 (如圖11-4)。材料經由皮帶送料，X軸控制滾輪帶動材料，來決定材料的長度。Y軸當被動ENCODER回授計算長度，即材料