![](\"https:\/\/www.dongwubaike.cn\/fanhaowp-content\/uploads\/2022\/05\/20220515051110-62808b6ecc455.jpg\")
<\/a><\/p>\n\u6458 \u8981\uff1a\u4eba\u5b57\u9f7f\u884c\u661f\u9f7f\u8f6e\u4f20\u52a8\u7684\u7ed3\u6784\u5f62\u5f0f\u4f18\u52a3\u548c\u627f\u53d7\u590d\u6742\u7684\u5185\u3001\u5916\u90e8\u6fc0\u52b1\u56e0\u7d20\u76f4\u63a5\u5f71\u54cd\u5230\u4f20\u52a8\u7cfb\u7edf\u7684\u6027\u80fd\uff0c\u7814\u7a76\u9f7f\u8f6e\u7cfb\u7edf\u5728\u4f20\u9012\u52a8\u529b\u548c\u8fd0\u52a8\u4e2d\u7684\u632f\u52a8\u3001\u51b2\u51fb\u53ca\u566a\u58f0\u57fa\u672c\u89c4\u5f8b\u5f88\u91cd\u8981\u3002\u672c\u6587\u4ece\u52a8\u529b\u5b66\u6a21\u578b\u5efa\u7acb\u65b9\u6cd5\u3001\u6c42\u89e3\u65b9\u6cd5\u3001\u56fa\u6709\u632f\u52a8\u7279\u6027\u3001\u52a8\u529b\u5b66\u54cd\u5e94\u7279\u6027\u3001\u51cf\u632f\u964d\u566a\u4e0e\u5b9e\u9a8c\u7814\u7a76\u7b49\u65b9\u9762\u5bf9\u56fd\u5185\u5916\u76f8\u5173\u7814\u7a76\u8fdb\u884c\u4e86\u7efc\u8ff0\uff0c\u5e76\u5bf9\u672a\u6765\u7814\u7a76\u65b9\u5411\u8fdb\u884c\u4e86\u5c55\u671b\u3002<\/p>\n
\u5173\u952e\u8bcd\uff1a\u4eba\u5b57\u9f7f\u884c\u661f\u4f20\u52a8 \u52a8\u529b\u5b66\u6a21\u578b \u632f\u52a8\u7279\u6027 \u51cf\u632f\u964d\u566a<\/p>\n
Abstract\uff1aThe structural form of herringbone planetary gear transmission and the endurance of complex internal or external incentive factors directly affect the performance of the transmission system. It is necessary to study the basic laws of gear system’s vibration\uff0c impact and noise in transmitting power and motion. In the article five aspects are reviewed\uff0c including the establishment and solution methods of dynamic models\uff0c natural vibration characteristics\uff0c dynamic response characteristics\uff0c vibration and noise reduction and experimental research. The future research directions are also prospected.<\/p>\n
Key words\uff1aherringbone planetary gear transmission\uff0c dynamic model\uff0c vibration characteristics\uff0c vibration and noise reduction<\/p>\n
\u884c\u661f\u9f7f\u8f6e\u4f20\u52a8\u901a\u5e38\u5305\u62ec\u4e09\u79cd\u4f20\u52a8\u5f62\u5f0f\uff1a\u76f4\u9f7f\u3001\u659c\u9f7f\u3001\u4eba\u5b57\u9f7f\u3002\u4eba\u5b57\u9f7f\u884c\u661f\u4f20\u52a8\u56e0\u5177\u6709\u5de5\u4f5c\u53ef\u9760\u3001\u4f20\u52a8\u5e73\u7a33\u3001\u627f\u8f7d\u80fd\u529b\u5927\u3001\u7ed3\u6784\u7d27\u51d1\u3001\u4f20\u52a8\u6548\u7387\u9ad8\u3001\u91cd\u5408\u5ea6\u9ad8\u4ee5\u53ca\u8f74\u5411\u529b\u8f83\u5c0f\u7b49\u4f18\u70b9[1]\uff0c\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5175\u5668\u88c5\u5907\u3001\u8239\u8236\u91cd\u5de5\u3001\u822a\u7a7a\u3001\u6c7d\u8f66\u7b49\u4f20\u52a8\u9886\u57df\u3002\u7531\u4e8e\u4eba\u5b57\u9f7f\u884c\u661f\u9f7f\u8f6e\u4f20\u52a8\u7ed3\u6784\u5f62\u5f0f\u548c\u5de5\u4f5c\u73af\u5883\u8f83\u4e3a\u590d\u6742\uff0c\u5728\u5b9e\u9645\u5de5\u7a0b\u5e94\u7528\u4e2d\uff0c\u9f7f\u8f6e\u76f8\u4e92\u556e\u5408\u4ea7\u751f\u7684\u9ad8\u9891\u52a8\u6001\u529b\u5fc5\u7136\u4f1a\u5f15\u8d77\u632f\u52a8\u3001\u51b2\u51fb\u3001\u566a\u58f0\u3001\u8f7d\u8377\u7a81\u53d8\u7b49\u73b0\u8c61\uff0c\u4e25\u91cd\u964d\u4f4e\u4e86\u4eba\u5b57\u9f7f\u884c\u661f\u9f7f\u8f6e\u4f20\u52a8\u7684\u5de5\u4f5c\u6027\u80fd\u3001\u4f7f\u7528\u5bff\u547d\u548c\u53ef\u9760\u6027\u3002\u672c\u6587\u4e3b\u8981\u4ece\u52a8\u529b\u5b66\u6a21\u578b\u5efa\u7acb\u65b9\u6cd5\u3001\u6c42\u89e3\u65b9\u6cd5\u3001\u56fa\u6709\u7279\u6027\u3001\u52a8\u6001\u7279\u6027\u3001\u51cf\u632f\u964d\u566a\u4e0e\u5b9e\u9a8c\u7814\u7a76\u7b49\u65b9\u9762\u5bf9\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u52a8\u529b\u5b66\u7684\u7814\u7a76\u73b0\u72b6\u8fdb\u884c\u7efc\u8ff0\uff0c\u5e76\u5728\u73b0\u6709\u7814\u7a76\u57fa\u7840\u4e0a\u5bf9\u672a\u6765\u53ef\u80fd\u7684\u7814\u7a76\u65b9\u5411\u8fdb\u884c\u4e86\u5c55\u671b\u3002<\/p>\n
1 \u52a8\u529b\u5b66\u5efa\u6a21<\/p>\n
\u52a8\u529b\u5b66\u6a21\u578b\u7684\u5efa\u7acb\u662f\u7814\u7a76\u4eba\u5b57\u9f7f\u884c\u661f\u9f7f\u8f6e\u4f20\u52a8\u7cfb\u7edf\u52a8\u529b\u5b66\u53ca\u52a8\u6001\u7279\u6027\u5206\u6790\u7684\u57fa\u7840\u3002\u6839\u636e\u4eba\u5b57\u9f7f\u884c\u661f\u9f7f\u8f6e\u52a8\u529b\u5b66\u5efa\u6a21\u65f6\u8003\u8651\u56e0\u7d20\u548c\u91c7\u7528\u65b9\u6cd5\u7684\u4e0d\u540c\uff0c\u4e00\u822c\u91c7\u7528\u4ee5\u4e0b\u4e24\u79cd\u65b9\u6cd5\u3002<\/p>\n
1.1 \u96c6\u4e2d\u8d28\u91cf\u5efa\u6a21\u6cd5<\/p>\n
\u96c6\u4e2d\u8d28\u91cf\u6cd5\u56e0\u5177\u6709\u53ef\u5feb\u901f\u7ec4\u5408\u3001\u5efa\u6a21\u8fc7\u7a0b\u76f8\u5bf9\u7b80\u5355\u3001\u8f93\u5165\u91cf\u8f83\u5c11\u53ca\u6613\u6c42\u89e3\u7b49\u4f18\u70b9\u800c\u5f97\u5230\u8f83\u5e7f\u6cdb\u7684\u5e94\u7528[2]\u3002\u6839\u636e\u5efa\u6a21\u65f6\u91c7\u7528\u7684\u81ea\u7531\u5ea6\u5f62\u5f0f\u4e0d\u540c\uff0c\u53ef\u5c06\u96c6\u4e2d\u8d28\u91cf\u6cd5\u6a21\u578b\u5206\u4e3a\u4e09\u79cd\uff1a\u7eaf\u626d\u6a21\u578b\u3001\u5f2f-\u626d\u8026\u5408\u6a21\u578b\u548c\u5e73\u79fb-\u626d\u8f6c\u6a21\u578b\u3002<\/p>\n
\u7eaf\u626d\u6a21\u578b\u662f\u6307\u53ea\u8003\u8651\u5404\u4e2a\u6784\u4ef6\u7684\u626d\u8f6c\u632f\u52a8\u7684\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5982\u56fe1\u6240\u793a\u3002\u7531\u4e8e\u8be5\u6a21\u578b\u8003\u8651\u7684\u81ea\u7531\u5ea6\u6570\u8f83\u5c11\uff0c\u504f\u79bb\u5b9e\u9645\u5de5\u4f5c\u60c5\u51b5\u8f83\u8fdc\uff0c\u56e0\u6b64\u5f88\u5c11\u4f7f\u7528\u3002\u5e73\u79fb-\u626d\u8f6c\u6a21\u578b\u540c\u65f6\u8003\u8651\u4e86\u5404\u4e2a\u6784\u4ef6\u7684\u626d\u8f6c\u548c\u5e73\u79fb\u81ea\u7531\u5ea6\uff0c\u5982\u56fe2\u6240\u793a\u3002\u8be5\u6a21\u578b\u7684\u52a8\u529b\u5b66\u4eff\u771f\u8f83\u4e3a\u51c6\u786e\uff0c\u4e14\u6a21\u578b\u76f8\u5bf9\u8f83\u7b80\u5355\uff0c\u4e0e\u5b9e\u9645\u60c5\u51b5\u4e5f\u8f83\u4e3a\u63a5\u8fd1\uff0c\u56e0\u6b64\u4f7f\u7528\u8f83\u591a\u3002\u5982\u535c\u5fe0\u7ea2\u7b49[3]\u5efa\u6a21\u65f6\u8003\u8651\u4e86\u592a\u9633\u8f6e\u3001\u884c\u661f\u8f6e\u548c\u5185\u9f7f\u5708\u7684\u626d\u8f6c\u4f4d\u79fb\u53ca\u5176\u5728\u7ad6\u76f4\u548c\u6c34\u5e73\u65b9\u5411\u4e0a\u7684\u6a2a\u5411\u4f4d\u79fb\u3002\u5f20\u9716\u9716\u7b49[4]\u5efa\u6a21\u65f6\u8003\u8651\u7684\u56e0\u7d20\u66f4\u591a\uff0c\u5305\u62ec\u5404\u6784\u4ef6\u7684\u626d\u8f6c\u4f4d\u79fb\u53ca\u5176\u6a2a\u5411\u3001\u8f74\u5411\u548c\u7eb5\u5411\u4f4d\u79fb\u3001\u504f\u5fc3\u8bef\u5dee\u3001\u5b89\u88c5\u8bef\u5dee\u3001\u652f\u6491\u521a\u5ea6\u548c\u8f6e\u9f7f\u95f4\u65f6\u53d8\u556e\u5408\u521a\u5ea6\u3002\u8d75\u6c38\u5f3a\u7b49[5]\uff0c\u5218\u632f\u5dde\u7b49[6]\u5728\u8be5\u6a21\u578b\u4e2d\u5f15\u5165\u4e86\u8026\u5408\u56e0\u5b50\uff0c\u7814\u7a76\u4e86\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u6a21\u6001\u8dc3\u8fc1\u73b0\u8c61\u3002\u6c88\u7a3c\u8015[7]\u5efa\u6a21\u65f6\u4e3b\u8981\u8003\u8651\u4e86\u8bef\u5dee\u3001\u9640\u87ba\u6548\u5e94\u3001\u963b\u5c3c\u53ca\u65f6\u53d8\u556e\u5408\u521a\u5ea6\u7b49\u5f71\u54cd\u56e0\u7d20\uff0c\u7814\u7a76\u4e86\u556e\u5408\u76f8\u4f4d\u5bf9\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u632f\u52a8\u7279\u6027\u7684\u5f71\u54cd\u3002\u66f9\u946b[8]\u5728\u5efa\u6a21\u65f6\u8003\u8651\u4e86\u9f7f\u5ed3\u4fee\u5f62\u548c\u9f7f\u5411\u4fee\u5f62\uff0c\u5206\u6790\u5bf9\u6bd4\u4e86\u9f7f\u8f6e\u4fee\u5f62\u524d\u540e\u5bf9\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u632f\u52a8\u566a\u58f0\u7684\u5f71\u54cd\u3002<\/p>\n
\u76f8\u5bf9\u4e0a\u8ff0\u4e24\u79cd\u6a21\u578b\uff0c\u5f2f-\u626d\u8026\u5408\u6a21\u578b\u8003\u8651\u4e86\u5404\u4e2a\u9f7f\u8f6e\u7684\u632f\u52a8\u81ea\u7531\u5ea6\uff0c\u5f71\u54cd\u56e0\u7d20\u66f4\u591a\uff0c\u6a21\u578b\u8026\u5408\u632f\u52a8\u66f4\u4e3a\u590d\u6742\uff0c\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u65b9\u7a0b\u7684\u6c42\u89e3\u548c\u5206\u6790\u4e5f\u66f4\u52a0\u56f0\u96be\uff0c\u4f46\u80fd\u591f\u5168\u9762\u5730\u53cd\u6620\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7279\u6027\uff0c\u5728\u7406\u8bba\u7814\u7a76\u65b9\u9762\u5e94\u7528\u8f83\u591a\u3002\u848b\u7acb\u51ac\u7b49[9]\u91c7\u7528\u5f2f-\u626d\u8026\u5408\u6a21\u578b\u5206\u6790\u4e86\u7cfb\u7edf\u7684\u81ea\u7531\u632f\u52a8\u7279\u6027\u548c\u4e09\u79cd\u632f\u52a8\u6a21\u5f0f\uff1a\u884c\u661f\u8f6e\u7cfb\u632f\u52a8\u6a21\u5f0f\u3001\u661f\u5f62\u8f6e\u7cfb\u632f\u52a8\u6a21\u5f0f\u548c\u8026\u5408\u632f\u52a8\u6a21\u5f0f\u3002\u4efb\u83f2\u7b49[10]\u5efa\u7acb\u7684\u5f2f-\u626d-\u8f74\u8026\u5408\u6a21\u578b\u4e2d\u8003\u8651\u4e86\u5404\u6784\u4ef6\u7684\u9f7f\u5ed3\u8bef\u5dee\u3001\u5404\u6784\u4ef6\u5236\u9020\u504f\u5fc3\u8bef\u5dee\u3001\u9640\u87ba\u6548\u5e94\u3001\u8f74\u627f\u652f\u627f\u521a\u5ea6\u53ca\u65f6\u53d8\u556e\u5408\u521a\u5ea6\u7b49\u56e0\u7d20\u3002\u738b\u6d69\u98de[11]\u91c7\u7528\u7684\u5f2f-\u626d-\u8f74\u8026\u5408\u6a21\u578b\u4e2d\u8003\u8651\u4e86\u65f6\u53d8\u556e\u5408\u521a\u5ea6\u3001\u9f7f\u9762\u6469\u64e6\u3001\u8bef\u5dee\u548c\u9f7f\u4fa7\u95f4\u9699\u3002\u90b1\u7ea2\u53cb[12]\u8003\u8651\u4e86\u4e24\u4e2a\u659c\u9f7f\u8f6e\u8026\u5408\u800c\u6210\u7684\u556e\u5408\u521a\u5ea6\u6fc0\u52b1\u3001\u5916\u8f7d\u8377\u548c\u7efc\u5408\u556e\u5408\u8bef\u5dee\u6fc0\u52b1\uff0c\u5efa\u7acb\u4e86\u5f2f-\u626d-\u8f74\u8026\u5408\u6a21\u578b\uff0c\u5982\u56fe3\u6240\u793a\u3002Sondkar P[13]\u8003\u8651\u4e86\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u5404\u4e2a\u6784\u4ef6\u76846\u4e2a\u81ea\u7531\u5ea6\uff0c\u5efa\u7acb\u4e86\u5f2f-\u626d-\u8f74-\u6446\u8026\u5408\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5982\u56fe4\u6240\u793a\u3002<\/p>\n
1.2 \u6709\u9650\u5143\u5efa\u6a21\u6cd5<\/p>\n
\u6709\u9650\u5143\u5efa\u6a21\u5904\u7406\u8fc7\u7a0b\u5f88\u7e41\u7410\uff0c\u7f51\u683c\u5212\u5206\u662f\u5426\u5408\u7406\u5bf9\u6c42\u89e3\u7cbe\u5ea6\u4e0e\u8ba1\u7b97\u6548\u7387\u6709\u5f88\u5927\u5f71\u54cd\uff0c\u540c\u65f6\u8ba1\u7b97\u65f6\u95f4\u4e5f\u8f83\u957f\uff0c\u5bf9\u8ba1\u7b97\u673a\u8f6f\u786c\u4ef6\u7684\u8981\u6c42\u8f83\u9ad8\uff0c\u5728\u6280\u672f\u64cd\u4f5c\u4e0a\u96be\u5ea6\u8f83\u5927\u3002\u4f46Parker R G\u7b49[14]\u8ba4\u4e3a\u96c6\u4e2d\u8d28\u91cf\u6a21\u578b\u4e0e\u5b9e\u9645\u60c5\u51b5\u76f8\u5dee\u8f83\u5927\uff0c\u56e0\u800c\u91c7\u7528\u5efa\u6a21\u7cbe\u5ea6\u76f8\u5bf9\u8f83\u9ad8\u7684\u6709\u9650\u5143\u6a21\u578b\u3002\u76ee\u524d\uff0cANSYS\u8f6f\u4ef6\u5728\u4eba\u5b57\u9f7f\u8f6e\u884c\u661f\u8f6e\u7cfb\u6709\u9650\u5143\u5efa\u6a21\u4e2d\u5e94\u7528\u6700\u591a[15-17]\u3002\u6b64\u5916\uff0c\u51af\u5fd7\u521a\u7b49[18]\u5728NX MasterFEM\u4e2d\u5efa\u7acb\u4eba\u5b57\u9f7f\u8f6e\u526f\u7684\u6709\u9650\u5143-\u63a5\u89e6\u6a21\u578b\uff0c\u91c7\u7528\u516d\u9762\u4f53\u5355\u5143\u8fdb\u884c\u7f51\u683c\u5212\u5206\uff0c\u5206\u6790\u4e86\u7cfb\u7edf\u7684\u9759\u6001\u63a5\u89e6\u60c5\u51b5\u548c\u81ea\u7531\u632f\u52a8\u7279\u6027\u3002<\/p>\n
2 \u6a21\u578b\u6c42\u89e3\u65b9\u6cd5<\/p>\n
\u6839\u636e\u89e3\u7684\u5f62\u5f0f\u4e0d\u540c\uff0c\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u52a8\u529b\u5b66\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3\u65b9\u6cd5\u53ef\u5206\u4e3a\u4e24\u7c7b\uff1a\u89e3\u6790\u6cd5\u548c\u6570\u503c\u6cd5\u3002<\/p>\n
2.1 \u89e3\u6790\u6cd5<\/p>\n
\u89e3\u6790\u6cd5\u53ef\u4ee5\u6c42\u5f97\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\uff0c\u5728\u591a\u81ea\u7531\u5ea6\u7684\u5f31\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u65b9\u7a0b\u4e2d\u5e94\u7528\u8f83\u591a\u3002\u76ee\u524d\uff0c\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u52a8\u529b\u5b66\u5206\u6790\u4e2d\u4f7f\u7528\u7684\u89e3\u6790\u6cd5\u5305\u62ec\u5085\u91cc\u53f6\u7ea7\u6570\u6cd5[7\uff0c8\uff0c19]\u3001\u591a\u5c3a\u5ea6\u6cd5[2]\u3001\u6b27\u62c9\u578b\u79ef\u5206\u6cd5[6]\u7b49\u3002\u5176\u4e2d\uff0c\u5085\u91cc\u53f6\u7ea7\u6570\u6cd5\u548c\u591a\u5c3a\u5ea6\u6cd5\u6700\u5e38\u7528\u3002\u5085\u91cc\u53f6\u7ea7\u6570\u6cd5\u7531\u4e8e\u8fd0\u7b97\u91cf\u5c0f\u3001\u53ef\u540c\u65f6\u6c42\u89e3\u65f6\u57df\u89e3\u548c\u9891\u57df\u89e3\uff0c\u4e14\u6c42\u89e3\u901f\u5ea6\u5feb\u7b49\u7279\u70b9\uff0c\u5728\u5e73\u79fb-\u626d\u8f6c\u52a8\u529b\u5b66\u6a21\u578b[7\uff0c8]\u6c42\u89e3\u4e2d\u5f97\u5230\u5e7f\u6cdb\u5e94\u7528;\u591a\u5c3a\u5ea6\u6cd5\u7531\u4e8e\u80fd\u6c42\u89e3\u8017\u6563\u7cfb\u7edf\u7684\u8870\u51cf\u632f\u52a8\u3001\u5468\u671f\u8fd0\u52a8\uff0c\u4ee5\u53ca\u7cfb\u7edf\u7684\u7a33\u6001\u548c\u975e\u7a33\u6001\u54cd\u5e94\u7b49\uff0c\u5e38\u7528\u4e8e\u626d\u8f6c\u6a21\u578b[2]\u548c\u5f2f-\u626d\u8026\u5408\u52a8\u529b\u5b66\u6a21\u578b[20]\u3002\u6b64\u5916\uff0c\u6c42\u89e3\u7cfb\u7edf\u7684\u626d\u8f6c\u6a21\u578b[7]\u4e5f\u53ef\u7528\u6b27\u62c9\u578b\u79ef\u5206\u6cd5\u3002<\/p>\n
2.2 \u6570\u503c\u6cd5<\/p>\n
\u6570\u503c\u79ef\u5206\u6cd5\u7531\u4e8e\u4e0d\u9650\u5236\u65b9\u7a0b\u7ec4\u7684\u81ea\u7531\u5ea6\u6570\u3001\u9636\u6570\uff0c\u4e14\u6c42\u89e3\u7cbe\u5ea6\u8f83\u9ad8\uff0c\u5728\u591a\u81ea\u7531\u5ea6\u7684\u5f3a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\u4e2d\u5f97\u5230\u4e86\u5f88\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u5176\u4e2d\uff0c\u9f99\u683c\u5e93\u5854\u6cd5\u662f\u4e00\u79cd\u5355\u6b65\u6570\u503c\u79ef\u5206\u6cd5\uff0c\u56e0\u5177\u6709\u8ba1\u7b97\u7cbe\u5ea6\u9ad8\u4e14\u53ef\u8c03\u3001\u8ba1\u7b97\u8fc7\u7a0b\u8f83\u7b80\u5355\u3001\u5bb9\u6613\u7ed9\u5b9a\u8ba1\u7b97\u6b65\u957f\u548c\u521d\u59cb\u503c\u7b49\u4f18\u70b9\uff0c\u5728\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u6a21\u578b\u6c42\u89e3\u4e2d\u5e94\u7528\u7684\u6700\u6210\u719f\uff0c\u6587\u732e[11-12\uff0c15-17]\u7b49\u4f7f\u7528\u8be5\u65b9\u6cd5\u6c42\u89e3\u4e86\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u6a21\u578b\u3002<\/p>\n
3 \u56fa\u6709\u7279\u6027<\/p>\n
3.1 \u81ea\u7531\u632f\u52a8\u7279\u6027<\/p>\n
\u7cfb\u7edf\u7684\u81ea\u7531\u632f\u52a8\u7279\u6027\u4e3b\u8981\u5305\u62ec\u4e24\u4e2a\u65b9\u9762\uff1a\u56fa\u6709\u9891\u7387\u548c\u632f\u578b\u3002\u5728\u8bbe\u8ba1\u9636\u6bb5\u7814\u7a76\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u56fa\u6709\u7279\u6027\uff0c\u6709\u52a9\u4e8e\u9884\u6d4b\u7cfb\u7edf\u7684\u632f\u52a8\u7279\u6027\uff0c\u4f7f\u6fc0\u52b1\u9891\u7387\u8fdc\u79bb\u7cfb\u7edf\u7684\u56fa\u6709\u9891\u7387\uff0c\u907f\u514d\u4ea7\u751f\u5171\u632f\uff0c\u4e3a\u8fdb\u4e00\u6b65\u7814\u7a76\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u52a8\u529b\u5b66\u7279\u6027\u5960\u5b9a\u57fa\u7840\u3002<\/p>\n
\u5218\u632f\u5dde\u7b49[6]\u91c7\u7528\u96c6\u4e2d\u53c2\u6570\u6cd5\u5efa\u7acb\u7684\u5e73\u79fb-\u626d\u8f6c\u6a21\u578b\uff0c\u5206\u6790\u5f97\u51fa\u7cfb\u7edf\u76843\u79cd\u632f\u52a8\u6a21\u5f0f\uff1a\u4e2d\u5fc3\u6784\u4ef6\u626d\u8f6c\u632f\u52a8\u6a21\u5f0f\u3001\u4e2d\u5fc3\u6784\u4ef6\u5e73\u79fb\u632f\u52a8\u6a21\u5f0f\u548c\u884c\u661f\u8f6e\u632f\u52a8\u6a21\u5f0f\u3002\u80e1\u745e\u5e06[17]\u5229\u7528\u6709\u9650\u5143\u6a21\u578b\u7814\u7a76\u4e86\u4e8c\u7ea7\u4eba\u5b57\u9f7f\u8f6e\u4f20\u52a8\u7cfb\u7edf\u7684\u524d8\u9636\u56fa\u6709\u9891\u7387\u548c\u632f\u578b\u56fe\u3002Khoozani\u7b49[21]\u91c7\u7528\u8003\u8651\u9640\u87ba\u6548\u5e94\u7684\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5206\u6790\u4e86\u7cfb\u7edf\u7684\u56fa\u6709\u7279\u6027\u3002\u5206\u6790\u8868\u660e\uff0c\u9640\u87ba\u6548\u5e94\u5728\u5178\u578b\u901f\u5ea6\u8303\u56f4\u5185\u5bf9\u7cfb\u7edf\u56fa\u6709\u9891\u7387\u7684\u5f71\u54cd\u4e0d\u5927\u3002Li\u7b49[22]\u7814\u7a76\u4e86\u4e24\u7ea7\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u632f\u52a8\u6a21\u5f0f\uff0c\u53ef\u5206\u4e3a3\u79cd\uff1a\u8026\u5408\u632f\u52a8\u6a21\u5f0f\u3001\u5dee\u52a8\u884c\u661f\u8f6e\u7cfb\u632f\u52a8\u6a21\u5f0f\u548c\u661f\u5f62\u8f6e\u7cfb\u632f\u52a8\u6a21\u5f0f\u3002Bu\u7b49[23]\u91c7\u7528\u6709\u9650\u5143\u6cd5\u548c\u7ebf\u6027\u89c4\u5212\u6cd5\u5206\u6790\u4e86\u7cfb\u7edf\u7684\u56fa\u6709\u7279\u6027\uff0c\u5f97\u51fa5\u79cd\u632f\u52a8\u6a21\u5f0f\uff1a\u626d\u8f6c-\u8f74\u5411\u632f\u52a8\u6a21\u5f0f\uff0c\u6a2a\u5411\u632f\u52a8\u6a21\u5f0f\uff0c\u884c\u661f\u8f6e\u626d\u8f6c\u632f\u52a8\u6a21\u5f0f\uff0c\u5185\u9f7f\u5708\u626d\u8f6c-\u8f74\u5411\u632f\u52a8\u6a21\u5f0f\u548c\u5185\u9f7f\u5708\u6a2a\u5411\u632f\u52a8\u6a21\u5f0f\u3002<\/p>\n
3.2 \u53c2\u6570\u7075\u654f\u5ea6\u5206\u6790<\/p>\n
\u53c2\u6570\u7075\u654f\u5ea6\u5206\u6790\u662f\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u56fa\u6709\u7279\u6027\u5206\u6790\u7684\u91cd\u8981\u90e8\u5206\uff0c\u53ef\u4ee5\u9884\u5148\u4e86\u89e3\u53c2\u6570\u53d8\u5316\u5bf9\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u4f20\u52a8\u7279\u6027\u53d8\u5316\u7684\u5f71\u54cd\uff0c\u5728\u8bbe\u8ba1\u9636\u6bb5\u5e2e\u52a9\u8bbe\u8ba1\u4eba\u5458\u66f4\u597d\u5730\u786e\u5b9a\u5404\u4e2a\u53c2\u6570\u503c\u3002<\/p>\n
\u535c\u5fe0\u7ea2\u7b49[3]\u7814\u7a76\u4e86\u8003\u8651\u9640\u87ba\u6548\u5e94\u540e\u8f6c\u901f\u5bf9\u5c01\u95ed\u5f0f\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u56fa\u6709\u9891\u7387\u7684\u5f71\u54cd\uff0c\u5373\u5dee\u52a8\u7ea7\u6a2a\u5411\u632f\u52a8\u6a21\u5f0f\u7684\u4e8c\u91cd\u56fa\u6709\u9891\u7387\u5728\u884c\u661f\u67b6\u8f6c\u901f\u5f71\u54cd\u4e0b\u4f1a\u5448\u73b0\u51fa\u5206\u5c94\u73b0\u8c61\uff0c\u4e14\u8f6c\u901f\u8d8a\u5927\u5206\u79bb\u8d8a\u8fdc\u3002\u738b\u6d69\u98de[11]\u7814\u7a76\u4e86\u9f7f\u9762\u6469\u64e6\u5bf9\u7cfb\u7edf\u632f\u52a8\u4f4d\u79fb\u7279\u6027\u7684\u5f71\u54cd\uff0c\u5782\u76f4\u4e8e\u556e\u5408\u7ebf\u65b9\u5411\u7684\u632f\u52a8\u5728\u9f7f\u9762\u6469\u64e6\u4f5c\u7528\u4e0b\u6709\u6240\u589e\u52a0\uff0c\u800c\u5728\u556e\u5408\u7ebf\u65b9\u5411\u6709\u6240\u51cf\u5c0f\uff0c\u4e14\u5176\u4f7f\u7cfb\u7edf\u8fdb\u5165\u6df7\u6c8c\u7684\u9891\u7387\u964d\u4f4e\uff0c\u4f46\u4e5f\u4f7f\u7cfb\u7edf\u7684\u6df7\u6c8c\u8fd0\u52a8\u5f97\u5230\u4e86\u6291\u5236;\u540c\u65f6\u53d1\u73b0\u4e24\u7aef\u659c\u9f7f\u8f6e\u526f\u9519\u4f4d\u5bf9\u7cfb\u7edf\u7684\u8f74\u5411\u632f\u52a8\u5f71\u54cd\u4e5f\u5f88\u660e\u663e\u3002\u848b\u8fdb\u79d1\u7b49[24]\u5bf9\u7cfb\u7edf\u632f\u52a8\u7279\u6027\u7684\u7814\u7a76\u8868\u660e\uff0c\u556e\u5408\u51b2\u51fb\u6fc0\u52b1\u548c\u521a\u5ea6\u6fc0\u52b1\u5bf9\u556e\u5408\u7ebf\u65b9\u5411\u7684\u632f\u52a8\u5f71\u54cd\u663e\u7740\uff0c\u5bf9\u8f74\u5411\u632f\u52a8\u5f71\u54cd\u8f83\u5c0f\uff0c\u800c\u8f74\u5411\u4f4d\u79fb\u6fc0\u52b1\u5bf9\u556e\u5408\u7ebf\u65b9\u5411\u548c\u6a2a\u5411\u7684\u632f\u52a8\u53ef\u4ee5\u5ffd\u7565\uff0c\u5bf9\u8f74\u5411\u632f\u52a8\u5f71\u54cd\u663e\u7740\u3002\u80e1\u745e\u5e06\u7b49[17]\u7528\u6709\u9650\u5143\u6a21\u578b\u7814\u7a76\u4e86\u8f74\u627f\u652f\u6491\u521a\u5ea6\u3001\u963b\u5c3c\u5bf9\u7cfb\u7edf\u632f\u52a8\u7279\u6027\u7684\u5f71\u54cd\uff0c\u7cfb\u7edf\u5404\u9636\u56fa\u6709\u9891\u7387\u968f\u7740\u8f74\u627f\u652f\u6491\u521a\u5ea6\u7684\u589e\u5927\u800c\u589e\u5927\uff0c\u4f46\u53d7\u963b\u5c3c\u7684\u5f71\u54cd\u4e0d\u5927\uff0c\u53ef\u5ffd\u7565\u3002<\/p>\n
3.3 \u6a21\u6001\u8dc3\u8fc1\u73b0\u8c61<\/p>\n
\u6a21\u6001\u8dc3\u8fc1\u73b0\u8c61\u662f\u6307\u5728\u7cfb\u7edf\u53c2\u6570\u53d8\u5316\u65f6\uff0c\u4e24\u6761\u6216\u591a\u6761\u56fa\u6709\u9891\u7387\u66f2\u7ebf\u8ddd\u79bb\u975e\u5e38\u63a5\u8fd1\u540e\u53c8\u4ee5\u8f83\u5927\u66f2\u7387\u5feb\u901f\u5206\u79bb\uff0c\u540c\u65f6\u7cfb\u7edf\u7684\u632f\u52a8\u6a21\u5f0f\u4e5f\u968f\u7740\u53d1\u751f\u663e\u7740\u53d8\u5316\u3002<\/p>\n
\u8d75\u6c38\u5f3a\u7b49[5]\u91c7\u7528\u5e73\u79fb-\u626d\u8f6c\u6a21\u578b\u5206\u6790\u4e86\u4e24\u7ea7\u4eba\u5b57\u9f7f\u884c\u661f\u7cfb\u7edf\u7684\u6a21\u6001\u8dc3\u8fc1\u73b0\u8c61\u548c\u4e0d\u540c\u632f\u52a8\u6a21\u5f0f\u4e0b\u56fa\u6709\u9891\u7387\u7684\u6a21\u6001\u8dc3\u8fc1\u51c6\u5219\uff0c\u5e76\u901a\u8fc7\u5b9e\u4f8b\u5bf9\u51c6\u5219\u7684\u6b63\u786e\u6027\u8fdb\u884c\u4e86\u9a8c\u8bc1\u3002\u5218\u632f\u5dde\u7b49[6]\u91c7\u7528\u5e73\u79fb-\u626d\u8f6c\u6a21\u578b\u5206\u6790\u4e86\u7cfb\u7edf\u7684\u56fa\u6709\u7279\u6027\uff0c\u4ece\u632f\u52a8\u6a21\u5f0f\u548c\u6a21\u6001\u80fd\u91cf\u89d2\u5ea6\u5206\u6790\u4e86\u6a21\u6001\u76f8\u4ea4\u73b0\u8c61\u548c\u6a21\u6001\u8dc3\u8fc1\u73b0\u8c61\u5bf9\u4f20\u52a8\u7279\u6027\u7684\u5f71\u54cd\uff0c\u5e76\u901a\u8fc7\u5b9e\u4f8b\u9a8c\u8bc1\u4e86\u7ed3\u8bba\u7684\u6b63\u786e\u6027\u3002\u4efb\u83f2[10]\u91c7\u7528\u5f2f-\u626d-\u8f74\u8026\u5408\u6a21\u578b\u5206\u6790\u4e86\u7cfb\u7edf\u7684\u81ea\u7531\u632f\u52a8\u7279\u6027\u548c\u6a21\u6001\u8dc3\u8fc1\u73b0\u8c61\u3002\u5728\u6a21\u6001\u8dc3\u8fc1\u70b9\uff0c\u53c2\u6570\u53d8\u5316\u4f1a\u5f15\u8d77\u7cfb\u7edf\u56fa\u6709\u9891\u7387\u3001\u632f\u52a8\u6a21\u5f0f\u3001\u6a21\u6001\u548c\u80fd\u91cf\u7684\u7a81\u7136\u53d8\u5316\uff0c\u4ece\u800c\u5f71\u54cd\u4e86\u7cfb\u7edf\u7684\u52a8\u6001\u7279\u6027\u53ca\u964d\u4f4e\u4e86\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u3002\u5728\u52a8\u6001\u8bbe\u8ba1\u4e2d\uff0c\u5e94\u4f7f\u7cfb\u7edf\u7684\u53c2\u6570\u5c3d\u53ef\u80fd\u5730\u8fdc\u79bb\u6a21\u6001\u8dc3\u8fc1\u70b9\u6240\u5bf9\u5e94\u7684\u53c2\u6570\u503c\u3002<\/p>\n
4 \u52a8\u6001\u7279\u6027<\/p>\n
4.1 \u5747\u8f7d\u7279\u6027\u5206\u6790<\/p>\n
\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u5728\u5b9e\u9645\u4f20\u52a8\u4e2d\uff0c\u7531\u4e8e\u5236\u9020\u8bef\u5dee\u3001\u5b89\u88c5\u8bef\u5dee\u3001\u67d4\u6027\u652f\u6491\u548c\u6784\u4ef6\u5f39\u6027\u53d8\u5f62\u7b49\u53c2\u6570\u7684\u5f71\u54cd\uff0c\u4f7f\u5f97\u5747\u5300\u5206\u5e03\u7684\u5404\u884c\u661f\u8f6e\u56e0\u53d7\u8f7d\u4e0d\u5747\u800c\u4ea7\u751f\u632f\u52a8\u3001\u51b2\u51fb\u548c\u566a\u58f0\uff0c\u5f71\u54cd\u7cfb\u7edf\u7684\u4f7f\u7528\u5bff\u547d\u3002\u56e0\u6b64\uff0c\u5404\u884c\u661f\u8f6e\u95f4\u7684\u5747\u8f7d\u7279\u6027\u662f\u4eba\u5b57\u9f7f\u884c\u661f\u4f20\u52a8\u7cfb\u7edf\u9700\u8981\u89e3\u51b3\u7684\u91cd\u8981\u95ee\u9898\u3002<\/p>\n
\u5f20\u9716\u9716\u7b49[4]\u91c7\u7528\u5e73\u79fb-\u626d\u8f6c\u8026\u5408\u6a21\u578b\uff0c\u7814\u7a76\u4e86\u556e\u5408\u76f8\u4f4d\u5bf9\u7cfb\u7edf\u5747\u8f7d\u7684\u5f71\u54cd\uff0c\u5e76\u7528\u8bd5\u9a8c\u9a8c\u8bc1\u7406\u8bba\u5206\u6790\u7684\u6b63\u786e\u6027\u3002Ren\u7b49[25]\u5206\u6790\u4e86\u5236\u9020\u8bef\u5dee\u53ca\u6784\u4ef6\u6d6e\u52a8\u5bf9\u7cfb\u7edf\u5747\u8f7d\u7279\u6027\u7684\u5f71\u54cd\u3002\u5206\u6790\u8868\u660e\uff0c\u5236\u9020\u8bef\u5dee\u53ca\u6784\u4ef6\u6d6e\u52a8\u5bf9\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u5747\u8f7d\u7279\u6027\u5f71\u54cd\u663e\u7740\uff0c\u4e14\u6784\u4ef6\u6d6e\u52a8\u53ef\u4ee5\u660e\u663e\u6539\u5584\u7cfb\u7edf\u7684\u5747\u8f7d\u7279\u6027\u3002\u738b\u6210\u7b49[26]\u57fa\u4e8e\u4eba\u5b57\u9f7f\u8f6e\u627f\u8f7d\u63a5\u89e6\u5206\u6790\u3001\u8f6e\u9f7f\u63a5\u89e6\u5206\u6790\uff0c\u5f97\u5230\u4eba\u5b57\u9f7f\u8f6e\u5747\u8f7d\u7279\u6027\u7684\u7406\u8bba\u8ba1\u7b97\u65b9\u6cd5\uff0c\u5e76\u901a\u8fc7\u8bd5\u9a8c\u6d4b\u91cf\u5bf9\u6bd4\u9a8c\u8bc1\u4e86\u8be5\u65b9\u6cd5\u7684\u6b63\u786e\u6027\u3002<\/p>\n
4.2 \u52a8\u6001\u54cd\u5e94<\/p>\n
\u556e\u5408\u76f8\u4f4d\u3001\u8bef\u5dee\u3001\u8f6c\u901f\u7b49\u56e0\u7d20\u5bf9\u7cfb\u7edf\u7684\u52a8\u6001\u54cd\u5e94\u5f71\u54cd\u663e\u7740\uff0c\u5bf9\u5176\u8fdb\u884c\u7814\u7a76\u53ef\u4ee5\u51cf\u5c0f\u7cfb\u7edf\u7684\u52a8\u6001\u4f20\u9012\u8bef\u5dee\uff0c\u964d\u4f4e\u7cfb\u7edf\u7684\u632f\u52a8\u3001\u51b2\u51fb\u548c\u566a\u58f0\u3002\u57282001\u5e74\uff0cAjmi\u7b49[27]\u57fa\u4e8e\u6b27\u62c9\u6881\u5355\u5143\u5efa\u7acb\u768424\u81ea\u7531\u5ea6\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5206\u6790\u4e86\u4eba\u5b57\u9f7f\u8f6e\u7cfb\u7edf\u7684\u52a8\u6001\u54cd\u5e94\u3002Dong\u7b49[28]\u63d0\u51fa\u4e86\u80fd\u591f\u66f4\u51c6\u786e\u63cf\u8ff0\u4eba\u5b57\u9f7f\u8f6e\u4f20\u52a8\u52a8\u6001\u54cd\u5e94\u7684Timoshenko\u6881\u5355\u5143\u52a8\u529b\u5b66\u5efa\u6a21\u7406\u8bba\uff0c\u5e76\u642d\u5efa\u4e86\u5c01\u95ed\u529f\u7387\u6d41\u5f0f\u632f\u52a8\u8bd5\u9a8c\u53f0\u6765\u9a8c\u8bc1\u8be5\u6a21\u578b\u7406\u8bba\u7684\u6b63\u786e\u6027\u3002Guo\u7b49[29]\u57fa\u4e8e\u7cfb\u7edf\u7684\u5e7f\u4e49\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u7814\u7a76\u5f97\u51fa\u968f\u7740\u884c\u661f\u8f6e\u504f\u5fc3\u8bef\u5dee\u7684\u53d8\u5316\uff0c\u7cfb\u7edf\u5448\u73b0\u51fa\u5355\u5468\u671f\u3001\u500d\u5468\u671f\u3001\u51c6\u5468\u671f\u548c\u6df7\u6c8c\u8fd0\u52a8\u73b0\u8c61\u3002Kang[30]\u91c7\u7528\u7406\u8bba\u548c\u5b9e\u9a8c\u65b9\u6cd5\u5bf9\u4eba\u5b57\u9f7f\u8f6e\u526f\u52a8\u6001\u54cd\u5e94\u7684\u7814\u7a76\u8868\u660e\uff0c\u5b89\u88c5\u76f8\u89d2\u5bf9\u7cfb\u7edf\u7684\u626d\u8f6c\u548c\u6a2a\u5411\u632f\u52a8\u5f71\u54cd\u663e\u7740\uff0c\u6307\u51fa\u7cfb\u7edf\u5efa\u6a21\u65f6\u5e94\u8003\u8651\u8f74\u548c\u8f74\u627f\u652f\u6491\u67d4\u6027\u56e0\u7d20\u7684\u5f71\u54cd\u3002<\/p>\n
\u9f7f\u8f6e\u4f20\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u4e92\u556e\u5408\u9762\u4e4b\u95f4\u4f1a\u4ea7\u751f\u5927\u5c0f\u548c\u65b9\u5411\u5747\u53d1\u751f\u5468\u671f\u6027\u53d8\u5316\u7684\u6469\u64e6\u529b\uff0c\u5f62\u6210\u7684\u975e\u8c10\u6ce2\u578b\u6fc0\u52b1\u5bf9\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7279\u6027\u6709\u91cd\u8981\u5f71\u54cd\u3002Liu\u7b49[31]\u91c7\u7528\u542b\u6709\u6469\u64e6\u548c\u9f7f\u5f62\u8bef\u5dee\u6fc0\u52b1\u7684\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5206\u6790\u4e86\u6469\u64e6\u548c\u8bef\u5dee\u6fc0\u52b1\u5bf9\u4eba\u5b57\u9f7f\u8f6e\u7cfb\u7edf\u52a8\u6001\u54cd\u5e94\u7684\u5f71\u54cd\u3002\u5206\u6790\u8868\u660e\uff0c\u6469\u64e6\u5bf9\u4eba\u5b57\u9f7f\u8f6e\u53d8\u901f\u8fc7\u7a0b\u7684\u52a8\u6001\u7279\u6027\u5f71\u54cd\u663e\u7740\uff0c\u5f53\u5ffd\u7565\u9f7f\u5f62\u8bef\u5dee\u6fc0\u52b1\u65f6\uff0c\u5f71\u54cd\u5c24\u4e3a\u663e\u7740;\u76f8\u5bf9\u6052\u5b9a\u6469\u64e6\u56e0\u6570\uff0c\u53d8\u6469\u64e6\u56e0\u7d20\u63d0\u9ad8\u4e86\u6469\u64e6\u7684\u6ce2\u52a8\uff0c\u964d\u4f4e\u4e86\u6469\u64e6\u963b\u5c3c\u6548\u5e94\u3002<\/p>\n
5 \u51cf\u632f\u964d\u566a\u4e0e\u5b9e\u9a8c\u7814\u7a76<\/p>\n
\u4e3a\u4e86\u4f7f\u4eba\u5b57\u9f7f\u884c\u661f\u4f20\u52a8\u5728\u5de5\u4f5c\u8f6c\u901f\u4e0b\u7684\u556e\u5408\u9891\u7387\uff08\u6216\u556e\u5408\u9891\u7387\u6574\u6570\u500d\uff09\u8fdc\u79bb\u7cfb\u7edf\u7684\u56fa\u6709\u9891\u7387\uff0c\u907f\u514d\u7cfb\u7edf\u4ea7\u751f\u5171\u632f\uff0c\u63d0\u9ad8\u7cfb\u7edf\u7684\u5bff\u547d\u3001\u5de5\u4f5c\u6027\u80fd\u548c\u53ef\u9760\u6027\u3002\u76ee\u524d\uff0c\u5f88\u591a\u5b66\u8005\u5bf9\u8f6e\u9f7f\u4fee\u5f62\u51cf\u632f\u964d\u566a\u7684\u6709\u6548\u6027\u8fdb\u884c\u4e86\u7b97\u4f8b\u548c\u8bd5\u9a8c\u9a8c\u8bc1\u3002<\/p>\n
Wang\u7b49[32]\u91c7\u7528\u4e09\u6bb5\u629b\u7269\u7ebf\u7684\u9f7f\u6761\u9f7f\u5ed3\uff0c\u5728\u9ad8\u901f\u9f7f\u8f6e\u5b9e\u9a8c\u53f0\u4e0a\u901a\u8fc7\u4f20\u52a8\u8bef\u5dee\u6d4b\u91cf\u7cfb\u7edf\u5bf9\u4e00\u5bf9\u9f7f\u8f6e\u7684\u4f20\u52a8\u8bef\u5dee\u8fdb\u884c\u6d4b\u91cf\uff0c\u5f97\u51fa\u9f7f\u5ed3\u4fee\u5f62\u80fd\u663e\u7740\u964d\u4f4e\u7cfb\u7edf\u7684\u632f\u52a8\u548c\u566a\u58f0\uff0c\u9a8c\u8bc1\u4e86\u8be5\u4f18\u5316\u65b9\u6cd5\u7684\u6709\u6548\u6027\u3002Wang\u7b49[33]\u63d0\u51fa\u4e86\u57fa\u4e8e\u4f20\u52a8\u8bef\u5dee\u7684\u516d\u9636\u591a\u9879\u5f0f\u51fd\u6570\u4f18\u5316\u8bbe\u8ba1\u65b9\u6cd5\uff0c\u5e76\u901a\u8fc7\u5b9e\u4f8b\u5bf9\u91c7\u7528\u8be5\u65b9\u6cd5\u4f18\u5316\u540e\u7684\u4eba\u5b57\u9f7f\u8f6e\u8fdb\u884c\u51cf\u632f\u964d\u566a\u5206\u6790\uff0c\u9a8c\u8bc1\u4e86\u8be5\u65b9\u6cd5\u7684\u6709\u6548\u6027\u3002Chapron\u7b49[34]\u91c7\u7528\u9057\u4f20\u7b97\u6cd5\u4f18\u5316\u540e\u7684\u9f7f\u8f6e\uff0c\u5206\u6790\u4e86\u4fee\u5f62\u9f7f\u8f6e\u5bf9\u8f6c\u901f\u548c\u8d1f\u8f7d\u7684\u7075\u654f\u5ea6\u3002\u5206\u6790\u8868\u660e\uff0c\u77ed\u4fee\u5f62\u9f7f\u8f6e\u5bf9\u964d\u4f4e\u52a8\u6001\u8f7d\u8377\u6700\u6709\u6548\u3002\u8d3e\u8d85\u7b49[35]\u4ee5\u9f7f\u9762\u95ea\u6e29\u6700\u5c0f\u3001\u9f7f\u9762\u8f7d\u8377\u5747\u5300\u5206\u5e03\u548c\u627f\u8f7d\u4f20\u52a8\u8bef\u5dee\u5e45\u503c\u6700\u5c0f\u4e3a\u4f18\u5316\u76ee\u6807\u8fdb\u884c\u7814\u7a76\uff0c\u5f97\u51fa\uff0c\u4fee\u884c\u540e\uff0c\u627f\u8f7d\u4f20\u52a8\u8bef\u5dee\u5e45\u503c\u663e\u7740\u4e0b\u964d\uff0c\u6709\u6548\u6539\u5584\u4e86\u9f7f\u9762\u8f7d\u8377\u5206\u5e03\uff0c\u9a8c\u8bc1\u4e86\u4f18\u5316\u8bbe\u8ba1\u65b9\u6cd5\u7684\u53ef\u9760\u6027\u3002<\/p>\n
\u9664\u4e86\u8f6e\u9f7f\u4fee\u5f62\u5916\uff0c\u9f7f\u8f6e\u7bb1\u4f53\u7ed3\u6784\u7684\u4f18\u5316\u8bbe\u8ba1\u4e5f\u80fd\u6709\u6548\u7684\u5bf9\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u8fdb\u884c\u51cf\u632f\u964d\u566a\u3002Zhang\u7b49[36]\u5229\u7528\u6709\u9650\u5143\u6cd5\u5206\u6790\u5f97\u51fa\u4f18\u5316\u540e\u4eba\u5b57\u9f7f\u8f6e\u51cf\u901f\u5668\u7684\u632f\u52a8\u548c\u566a\u58f0\u6709\u6240\u964d\u4f4e\u3002<\/p>\n
6 \u7814\u7a76\u5c55\u671b<\/p>\n
\u4e3a\u8bbe\u8ba1\u51fa\u632f\u52a8\u5c0f\u3001\u566a\u58f0\u4f4e\u7684\u4eba\u5b57\u9f7f\u884c\u661f\u9f7f\u8f6e\u7cfb\u7edf\uff0c\u5e94\u7d27\u5bc6\u7ed3\u5408\u5b9e\u9645\u5de5\u4f5c\u60c5\u51b5\u548c\u7814\u7a76\u76ee\u6807\uff0c\u7efc\u5408\u8003\u8651\u5404\u79cd\u6fc0\u52b1\u56e0\u7d20\u3001\u7cfb\u7edf\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5206\u6790\u548c\u4f18\u5316\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7279\u6027\u3002\u57fa\u4e8e\u6587\u4e2d\u56fd\u5185\u5916\u5df2\u53d6\u5f97\u7814\u7a76\u6210\u679c\uff0c\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u9762\u6709\u5f85\u8fdb\u884c\u6df1\u5165\u7814\u7a76\uff1a<\/p>\n
\uff081\uff09\u4eba\u5b57\u9f7f\u8f6e\u8f6e\u9f7f\u7684\u6e29\u5ea6\u573a\u5206\u5e03\u4e0e\u53d8\u5316\u89c4\u5f8b\u3002\u73b0\u6709\u6587\u732e\u5728\u8be5\u7406\u8bba\u65b9\u9762\u8fd8\u672a\u89c1\u7814\u7a76\uff0c\u6240\u4ee5\u6709\u5f85\u7814\u7a76\u3002<\/p>\n
\uff082\uff09\u590d\u5408\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u52a8\u529b\u5b66\u7279\u6027\u3002\u76ee\u524d\u5bf9\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u7814\u7a76\u4e3b\u8981\u4ee5\u5355\u6781\u4e3a\u4e3b\uff0c\u5c11\u6570\u7814\u7a76\u4e3a\u4e24\u7ea7\u4f20\u52a8\u3002\u76f8\u6bd4\u5355\u6781\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\uff0c\u590d\u5408\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7ed3\u6784\u66f4\u52a0\u590d\u6742\uff0c\u9700\u8981\u8003\u8651\u7684\u5f71\u54cd\u56e0\u7d20\u66f4\u591a\uff0c\u6240\u4ee5\u7814\u7a76\u590d\u5408\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u52a8\u529b\u5b66\u7279\u6027\u5f88\u91cd\u8981\u3002<\/p>\n
\uff083\uff09\u8003\u8651\u51b2\u51fb\u548c\u6cb9\u819c\u521a\u5ea6\u7684\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u52a8\u529b\u5b66\u7279\u6027\u3002\u556e\u5408\u51b2\u51fb\u548c\u6cb9\u819c\u521a\u5ea6\u662f\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u632f\u52a8\u7684\u91cd\u8981\u6fc0\u52b1\u56e0\u7d20\uff0c\u76ee\u524d\u5728\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u8fd8\u6bd4\u8f83\u5c11\u3002<\/p>\n
\uff084\uff09\u57fa\u4e8e\u53ef\u9760\u6027\u7684\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u52a8\u529b\u5b66\u7279\u6027\u3002\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7684\u53ef\u9760\u6027\u662f\u8861\u91cf\u7cfb\u7edf\u4f20\u52a8\u8d28\u91cf\u7684\u91cd\u8981\u6307\u6807\uff0c\u76f4\u63a5\u5f71\u54cd\u4e86\u7cfb\u7edf\u7684\u5bff\u547d\u7279\u5f81\u3002<\/p>\n
\uff085\uff09\u4eba\u5b57\u9f7f\u884c\u661f\u8f6e\u7cfb\u7edf\u7684\u51cf\u9707\u964d\u566a\u63a7\u5236\u3002\u9f7f\u8f6e\u7684\u556e\u5408\u521a\u5ea6\u3001\u652f\u6491\u521a\u5ea6\u3001\u8bef\u5dee\u3001\u6784\u4ef6\u7684\u5f39\u6027\u53d8\u5f62\u7b49\u6fc0\u52b1\u56e0\u7d20\u7684\u53d8\u5316\u80fd\u5f15\u8d77\u9f7f\u8f6e\u7684\u591a\u79cd\u632f\u52a8\uff0c\u5e76\u901a\u8fc7\u8f74\u3001\u8f74\u627f\u5c06\u632f\u52a8\u4f20\u9012\u7ed9\u7bb1\u4f53\uff0c\u4ece\u800c\u5f15\u8d77\u9f7f\u8f6e\u51cf\u901f\u5668\u7684\u632f\u52a8\u3002<\/p>\n
\u53c2\u8003\u6587\u732e\uff1a<\/p>\n
[1]Amendola J. Single vs double helical gears[J]. Turbomachinery International\uff0c 2006\uff08Sep\/Oct\uff09.<\/p>\n
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