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工程设计学报
Chinese Journal of Engineering Design  2024, Vol. 31 Issue (6): 810-822    DOI: 10.3785/j.issn.1006-754X.2024.04.112
Optimization Design     
Optimization design of metal structure of bridge crane based on structural function derivative coefficients
Qing DONG(),Tianxiang ZHANG,Qisong QI,Gening XU
School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
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Abstract  

Crane is one of the eight special equipment, the rationality of its structural design is crucial for the safe operation, quality improvement, and efficiency enhancement of the equipment. Therefore, an optimization design method of metal structure of bridge crane based on structural function derivative coefficients was proposed. Firstly, the interpretive structure model was used to accurately describe the interactions and influence relationships between different parts of the crane, the structure complexity of the crane was analyzed to identify and optimize the parameters that had a significant impact on the strength of metal structure of the crane. Secondly, based on the finite element simulation, the structural function derivative coefficients were combined with fitting functions to find the optimal combination of design parameters. Finally, a 300/100 t-30 m bridge crane was taken as an engineering example, and the mass of the whole crane was reduced by 2 035.113 kg through simulation, and the effectiveness of the proposed method was verified. The optimization design method of metal structure of crane based on structural function derivative coefficients solves the problem that the complex interactions between various parts of crane is ignored in the traditional optimization method, and can realize the lightweight design of metal structure on the basis of ensuring the safety of crane service.

Key words： interpretative structure model      structural functional derivative coefficient      optimization design      bridge crane      metal structure     
Received: 19 February 2024      Published: 31 December 2024
CLC:  TH 215  
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Qing DONG
Tianxiang ZHANG
Qisong QI
Gening XU
Cite this article:

Qing DONG,Tianxiang ZHANG,Qisong QI,Gening XU. Optimization design of metal structure of bridge crane based on structural function derivative coefficients. Chinese Journal of Engineering Design, 2024, 31(6): 810-822.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2024.04.112     OR     https://www.zjujournals.com/gcsjxb/Y2024/V31/I6/810


基于结构功能衍生系数的桥式起重机金属结构优化设计

起重机是八大特种设备之一，其结构设计的合理性对于设备安全运行、提质增效至关重要。为此，提出了一种基于结构功能衍生系数的桥式起重机金属结构优化设计方法。首先，利用解释结构模型准确描述了起重机不同零部件之间的相互作用和影响关系，分析了起重机结构的复杂性，识别出对起重机金属结构强度影响较大的参数并对其进行优化设计；其次，在有限元仿真的基础上，将结构功能衍生系数与拟合函数相结合，寻找出最佳的设计参数组合；最后，以300/100 t-30 m通用桥式起重机为工程实例，通过仿真使整机的质量减小了2 035.113 kg，验证了所提方法的有效性。基于结构功能衍生系数的起重机金属结构优化设计方法，解决了传统的优化方法中忽略了起重机各零部件之间复杂的相互作用的问题，可在确保起重机服役安全性的基础上实现其金属结构的轻量化设计。


关键词： 解释结构模型,  结构功能衍生系数,  优化设计,  桥式起重机,  金属结构 
Fig.1 Optimization design flow chart of metal structure of crane
Fig.2 Composition of crane
符号元素序号元素序号元素序号元素
S1主梁S8小车从动车轮组S15副横梁S22大车主起升电机
S2大车台车梁S9副小车架车轮组S16主起升定滑轮装配S23副起升定滑轮装配
S3大车连接梁S10

小车运行电机

（三合一）

S17主起升动滑轮装配S24副起升动滑轮装配
S4大车台车S18主吊钩组S25副吊钩组
S5大车车轮组S11小车台车S19

主起升卷

筒组

S26副起升卷筒组
S6

大车运行电机

（三合一）

S12小车架S27副减速器
S13副小车架S20主减速器S28副制动器
S7小车主动车轮组S14横梁S21主制动器S29大车副起升电机
Table 1 Elements of crane
Fig.3 Initial digraph of crane
元素序号可达集元素序号可达集元素序号可达集
S1{S1, S2, S3, S11, S12, S13}S12{S1, S2, S3, S11, S12, S13}S21

{S1, S2, S3, S11, S12, S13, S14,

S16, S17, S18, S19, S20, S21}

S2{S1, S2, S3,S11, S12, S13}
S3{S1, S2, S3, S11, S12, S13}S13{S1, S2, S3, S11, S12, S13}S22

{S1, S2, S3, S11, S12, S13, S14,

S16, S17, S18, S19, S20, S21, S22}

S4{S1, S2, S3, S4, S11, S12, S13}S14

{S1, S2, S3, S11, S12, S13,

S14, S16, S17, S18}

S23{S1, S2, S3, S11, S12, S13, S15, S23, S24}
S5{S1, S2, S3, S4, S5, S11, S12, S13}S15

{S1, S2, S3, S11, S12, S13,

S15, S23, S24}

S24{S1, S2, S3, S11, S12, S13, S15, S23, S24}
S6

{S1, S2, S3, S4, S5, S6,

S11, S12, S13}

S16

{S1, S2, S3, S11, S12, S13,

S14, S16, S17, S18}

S25{S1, S2, S3, S11, S12, S13, S15, S23, S24, S25}
S7{S1, S2, S3, S7, S11, S12, S13}S17

{S1, S2, S3, S11, S12, S13,

S14, S16, S17, S18}

S26{S1, S2, S3, S11, S12, S13, S15, S23, S24, S26}
S8{S1, S2, S3, S8, S11, S12, S13}S18

{S1, S2, S3, S11, S12, S13,

S14, S16, S17, S18}

S27

{S1, S2, S3, S11, S12, S13, S15,

S23, S24, S26, S27}

S9

{S1, S2, S3, S9, S11, S12,

S13, S14, S16, S17, S18}

S19

{S1, S2, S3, S11, S12, S13,

S14, S16, S17, S18, S19}

S28{S1, S2, S3, S11, S12, S13, S15, S23,S24, S26, S27, S28}
S10{S1, S2, S3, S7, S10, S11, S12, S13}S20

{S1, S2, S3, S11, S12, S13,

S14, S16, S17, S18, S19, S20}

S29

{S1, S2, S3, S11, S12, S13, S15, S23,

S24, S26, S27, S28, S29}

S11{S1, S2, S3, S11, S12, S13}
Table 2 Reachable sets of elements of crane
元素序号先行集元素序号先行集
S1{S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29}S14{S9, S14, S16, S17, S18, S19, S20, S21, S22}
S15{S15, S23, S24, S25, S26, S27, S28, S29}
S2{S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29}S16{S9, S14, S16, S17, S18, S19, S20, S21, S22}
S17{S9, S14, S16, S17, S18, S19, S20, S21, S22}
S3{S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29}S18{S9, S14, S16, S17, S18, S19, S20, S21, S22}
S19{S19, S20, S21, S22}
S4{S4, S5, S6}S20{S20, S21, S22}
S5{S5, S6}S21{S21, S22}
S6{S6}S22{S22}
S7{S7, S10}S23{S15, S23, S24, S25, S26, S27, S28, S29}
S8{S8}S24{S15, S23, S24, S25, S26, S27, S28, S29}
S9{S9}S25{S25}
S10{S10}S26{S26, S27, S28, S29}
S11{S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29}S27{S27, S28, S29}
S12{S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29}S28{S28, S29}
S13{S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29}S29{S29}
Table 3 Preliminary sets of elements of crane
Fig.4 Hierarchy and interconnection relationships of crane parts based on ISM

连接

序号

装配连接关系及尺寸符号参数传递关系符号
S22—S21主起升电机轴直径—联轴器孔径—制动器轴直径d1—Φ1—d2主起升电机输出轴转速—联轴器转速n1
S22—S12电机底座螺纹孔径—小车架固定孔径—小车架上盖板厚Φ2—Φ3—x14主起升电机转动产生力—小车架上盖板压力F1
S29—S28副起升电机轴直径—联轴器孔径—制动器轴直径d3—Φ4—d2副起升电机输出轴转速—联轴器转速n2
S29—S13电机底座螺纹孔径—小车架固定孔—小车架上盖板厚Φ5—Φ6—x14副起升电机产生的力—小车架上盖板压力F2
S21—S20联轴器孔径—减速器轴直径Φ1—d4联轴器转速—减速器输入轴转速n1
S21—S12减速器底座螺纹孔径—小车架固定孔径—小车架上盖板厚Φ8—Φ9—x14减速器转动产生的力—小车架上盖板压力F3
S6—S5大车运行电机轴直径—车轮组孔径d5—Φ10大车运行电机输出轴转速—车轮组转速n3
S28—S27副联轴器孔径—减速器孔径Φ11—Φ12副联轴器转速—减速器输入轴转速n2
S28—S13副制动器底座螺纹孔径—小车架固定孔径Φ13—Φ14副减速器转动产生的力—小车架上盖板压力F4
S20—S19主减速器输出轴直径—卷筒组孔径—卷筒轴直径d6—Φ15—d7起升减速器输出轴扭矩—卷筒扭矩M1
S5—S4大车车轮组螺纹孔直径—台车螺纹孔径—台车主副腹板厚Φ16—Φ17—x7大车车轮组支撑力—大车台车压力F5
S27—S26副减速器输出轴直径—副卷筒组孔径—副卷筒轴直径d8—Φ18—d9副起升减速器输出轴扭矩—副卷筒扭矩M2
S18—S17吊钩组孔径—主起升动滑轮组孔径—销轴直径Φ19—Φ20—d10起重量—钢丝绳抗拉强度G—σ1
S19—S17卷筒组卷筒半径—钢丝绳直经—定滑轮组滑轮半径r1—d11—r2钢丝绳上拉力—抗拉强度—抗压强度F6 —σ1—σ2
S19—S12卷筒组螺纹孔径—小车架螺纹孔径—小车架上盖板厚Φ21—Φ22—x14卷筒组压力—小车架上盖板支撑力F4
S10—S7小车运行电机轴直径—小车运行车轮组孔径d12—Φ23小车运行电机输出轴—车轮组转速n6
S4—S2大车台车连接孔径—台车梁连接孔径—销轴直径Φ24—Φ25—d13大车台车支撑力—台车梁压力F5
S9—S13副小车架车轮组螺纹孔径—副小车架螺纹孔径Φ26—Φ27副小车架车轮组支撑力—副小车架压力F7
S26—S24副卷筒组卷筒半径—钢丝绳直经—定滑轮半径r3—d14—r4副起升钢丝绳拉力—抗拉强度—卷筒抗压强度

F8—

σ3—σ4

S26—S13副卷筒组螺纹孔径—副小车架螺纹孔径Φ28—Φ29副卷筒组压力—副小车架上盖板支撑力F9
S25—S24副吊钩组孔径—副起升动滑轮组孔径—销轴直径Φ30—Φ31—d15副起重量—钢丝绳抗拉强度G2—σ3
S17—S16主起升动滑轮半径—钢丝绳直径—定滑轮半径r2—d11—r5主起升和吊钩组质量—钢丝绳抗拉强度G3—σ1
S16—S14主起升定滑轮孔径—滑轮轴直径—横梁孔径—横梁主腹板厚—横梁副腹板厚Φ32—d16—Φ33—x12—x13主起升和吊钩组滑轮组质量—钢丝绳抗拉强度—横梁抗拉强度G4—σ1—σ5
S14—S12横梁下盖板厚—小车基距—小车架上盖板厚x11—l1—x14横梁压力—小车架支撑力F10
S8—S11小车从动车轮螺纹孔径—台车螺纹孔径—台车主腹板厚Φ34—Φ35—x16小车从动车轮组支撑力—小车台车压力F11
S7—S1小车主动车轮组半径—大车主梁上盖板厚—轨距r6—x1—l2小车轮压/轨道摩擦系数—轨道摩擦力P1/u1—f
S2—S1大车台车梁螺纹孔径—大车主梁螺纹孔径—台车梁上盖板厚—主梁下盖板厚

Φ36—Φ37—

x5—x2

大车台车支撑力—主梁上产生的压力F12
S3—S2大车连接梁孔径—大车台车梁孔径—销轴直径—大车连接梁腹板厚—大车台车腹板厚

Φ38—Φ39—

d17—x7—x9

大车台车与连接梁运行过程中产生的推拉力F13
S24—S23副起升动滑轮半径—钢丝绳直径—定滑轮半径r7—d18—r8副起升和吊钩组质量—钢丝绳抗拉强度G5—σ3
S23—S15副起升定滑轮孔径—滑轮轴直径—副横梁孔径Φ40—d19—Φ41副起升量和吊钩组滑轮组质量—钢丝绳抗拉强度—横梁抗拉强度G6—σ3—σ6
S15—S13副横梁下盖板厚—小车基距—副小车架上盖板厚x11—l1—x14副横梁压力—副小车架支撑力F14
S12—S11小车架孔径—小车台车孔径—销轴直径—小车架主腹板厚—小车台车主腹板厚

Φ42—Φ43—

d20—x16—x18

小车架压力—小车台车的支撑力F15
S11—S1小车台车下盖板厚—主梁上盖板厚—轨距x17—x1—l2从动小车轮组轮压/轨道摩擦系数—小车轨道摩擦力P2/u1—f
S13—S1副小车架下盖板厚—主梁上盖板厚—轨距x15—x1—l2副小车轮组轮压/轨道摩擦系数—小车轨道摩擦力P3/u1—f
S13—S11副小车架孔径—小车台车孔径销轴直径Φ44—Φ45—d21副小车架压力—小车台车的支撑力F16
Table 4 Interconnection relationships of crane parts
Fig.5 Schematic of key structural parameters of crane
结构参数初始值设计范围
桥架结构x12420~28
x22420~28
x3139~17
x4139~17
x53430~38
x62016~24
x73430~38
x8128~16
x92420~28
小车架结构x101612~20
x112016~24
x124036~44
x134036~44
x143632~40
x151612~20
x162420~28
x1753~7
x1853~7
Table 5 Design range of key structural parameters of metal structure of crane
结构序号

x1/

mm

x2/

mm

x3/

mm

x4/

mm

应力/MPa序号

x5/

mm

x6/

mm

x7/

mm

应力/MPa序号

x8/

mm

x9/

mm

应力/MPa
桥架结构1202099142.961030163096.411982098.586
220241313101.391130203498.632082498.585
32028171775.9612302438100.592182898.584
4242099135.811334163096.4422122098.578
52424131398.611434203498.6123122498.610
62428171757.1315342438100.4824122898.581
7282099139.231638163096.3225162098.595
82824131381.921738203498.5026162498.584
92828171756.5018382438100.3327162898.580
结构序号

x10/

mm

x11/

mm

x12/

mm

x13/

mm

应力/MPa序号

x14/

mm

x15/

mm

x16/

mm

应力/MPa序号

x17/

mm

x18/

mm

应力/MPa
小车架结构112163636147.8810321220158.101933131.08
212204040129.3011321624141.662035130.99
312244444149.9512322028147.742137130.79
416163636146.5013361220148.432253130.91
516204040130.5614361624130.562355130.56
616244444148.9615362028147.812457130.53
720163636145.3316401220134.682573130.85
820204040127.2617401624120.672675130.75
920244444151.9518402028147.862777130.44
Table 6 Maximum stress on metal structure of crane under different structural parameters
结构参数参数水平
V1V2V3
桥架结构x1101.3998.6181.92
x2135.8198.6157.13
x3139.2381.9256.50
x4139.2381.9256.50
x598.6398.6198.50
x696.4498.61100.48
x796.3298.50100.33
x898.5898.6198.58
x998.5898.6198.58
小车架结构x10129.30130.56120.67
x11146.50130.56147.81
x12145.33127.26151.95
x13145.33127.26151.95
x14141.66130.56120.67
x15148.43130.56147.81
x16158.10141.66147.74
x17130.99130.56130.44
x18130.91130.56130.53
Table 7 Maximum stress on metal structure of crane under different parameter levels
结构参数离差平方和影响因子
桥架结构x1241.70.022 6
x23099.90.289 8
x33639.50.340 1
x43639.50.340 1
x512.40.001 2
x619.812 10.001 9
x718.152 90.001 7
x812.70.001 2
x912.50.001 2
SST10 695.70
小车架结构x10372.650.131 5
x11241.920.0854
x12381.260.134 6
x13381.260.134 6
x14338.970.119 6
x15281.360.099 3
x16574.440.203 3
x17130.180.045 9
x18129.970.045 8
SST2 832.04
Table 8 Variance analysis of maximum stress on metal structure of crane
结构参数第1次优化值/mm单调增减情况第2次优化值/mm单调增减情况第3次优化值/mm单调增减情况第3次优化值/mm单调增减情况
桥架结构x124-24-24-24-
x223+22+21+20+
x314-14-14-14-
x414-14-14-14-
x534-34-34-34-
x620-20-20-20-
x734+34+34+34+
x812-12-12-12-
x924-24-24-24-
ΔDCM13.567 52.489 71.411 90.334 1
Y1/MPa102.177 5104.667 2106.079 1106.413 2
小车架结构x1015+141312
x1120-202020
x1239+383736
x1339+383736
x1435+343332
x1516+161616
x1624-242424
x175+555
x185+555
ΔDCM210.863 79.86218.860 57.858 9
Y2/MPa141.423 7151.285 8160.146 3168.005 2
Table 9 Optimization results of metal structure of crane
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