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基于参数化的榫卯尺寸智能确定方法

汤琳 关惠元

汤琳, 关惠元. 基于参数化的榫卯尺寸智能确定方法[J]. 北京林业大学学报, 2021, 43(3): 145-154. doi: 10.12171/j.1000-1522.20200104
引用本文: 汤琳, 关惠元. 基于参数化的榫卯尺寸智能确定方法[J]. 北京林业大学学报, 2021, 43(3): 145-154. doi: 10.12171/j.1000-1522.20200104
Tang Lin, Guan Huiyuan. Intelligent method of determining dimension of mortise and tenon joint based on parameterization[J]. Journal of Beijing Forestry University, 2021, 43(3): 145-154. doi: 10.12171/j.1000-1522.20200104
Citation: Tang Lin, Guan Huiyuan. Intelligent method of determining dimension of mortise and tenon joint based on parameterization[J]. Journal of Beijing Forestry University, 2021, 43(3): 145-154. doi: 10.12171/j.1000-1522.20200104

基于参数化的榫卯尺寸智能确定方法

doi: 10.12171/j.1000-1522.20200104
基金项目: 南京工业职业技术大学引进人才专项科研项目(2020SKYJ01)
详细信息
    作者简介:

    汤琳,博士,讲师。主要研究方向:家具设计与工程。Email:106330176@qq.com 地址:210046 江苏省南京市秦淮区军农路14号南京工业职业技术大学天堂校区

    责任作者:

    关惠元,教授,博士生导师。主要研究方向:家具设计及理论、人体工程学、家具生产制造。Email:guanhuiyuan@njfu.com.cn 地址:210037 江苏省南京市玄武区龙蟠路159号南京林业大学家居与工业设计学院

  • 中图分类号: TS657

Intelligent method of determining dimension of mortise and tenon joint based on parameterization

  • 摘要:   目的  榫卯结构尺寸的确定是编写榫卯数控加工代码的前提,也是实现榫卯数控加工的基础,但现有的通过反复修改榫卯几何模型确定榫卯尺寸的方式,效率低、难度高,严重影响了榫卯数字化加工的发展。因此,有必要设计一种榫卯尺寸智能化确定的方法。  方法  以改良型格肩榫为例,首先利用参数化的设计思想,建立格肩榫的数学模型并提取了格肩榫尺寸参数;然后根据榫卯装配体零件的特征,基于装配约束,从位置关系和配合关系两个角度,建立格肩榫尺寸参数间的关系函数;再基于工艺约束,从数控加工方式、市场调研结果和工艺知识这3个方面,确定部分尺寸的取值范围和预设参考值,并建立尺寸参数与工艺约束间的关联函数;最后,以零件的断面尺寸为输入参数,整合关联函数、取值范围和预设参考值,建立尺寸参数关联函数表。  结果  通过建立榫卯数学模型,提取了榫卯各类尺寸参数;根据榫卯装配和工艺约束,成功建立了榫卯尺寸参数间的函数关联,并获取了尺寸参数的取值范围和预设推荐值;通过建立尺寸参数关联函数表,实现了只需输入榫卯零件的断面尺寸,系统就可以自动输出榫卯其他尺寸参数值。  结论  在装配和工艺两方面综合约束函数基础上建立的榫卯尺寸智能确定方法,是对榫卯工艺知识的数字化整理和重用,不仅能实现榫卯尺寸的智能确定,也为实现榫卯乃至实木加工的智能制造提供了基础条件。

     

  • 图  1  榫卯尺寸的智能化确定流程

    Figure  1.  Intelligent dimension determination flow of mortise and tenon joints

    图  2  格肩榫榫眼零件的几何模型

    Wm为榫眼材料断面宽度;Dm为榫眼材料断面厚度;Lm为榫眼中心距离端面在X方向位置;G为三角肩缺底边长度;A为椭圆榫眼的宽度;B为椭圆榫眼的长度;L为椭圆榫眼的深度;W1为三角肩缺的厚度;W2为榫眼偏置(三角肩缺下边线与椭圆榫眼上边线的距离);W3为椭圆榫眼左右边距;W4为榫眼下偏置(椭圆榫眼下边线于材料底面间的距离)。Wm is the width of mortise material, Dm is the thickness of mortise material, Lm is the distance between the center of mortise and the end face in X direction, G is the length of breach, A is the wide of mortise, B is the length of mortise, L is the depth of mortise, W1 is the thickness of triangular mortise, W2 is the offset of mortise (distance between the border-bottom of triangular mortise and border-top of mortise), W3 is the margins of mortise, and W4 is the under offset of mortise (distance between the border-bottom of mortise and the underside of material).

    Figure  2.  Geometrical model of modified lattice shoulder mortise

    图  3  格肩榫榫头零件的几何模型

    Ws为榫头材料断面宽度;Ds为榫头材料断面厚度;$ {L}_{\mathrm{s}} $为材料端面到榫头底面的距离;a为椭圆榫头的厚度;b为椭圆榫头的宽度;l为椭圆榫头的长度;u1为三角榫肩厚度;u2为榫头偏置;u3为椭圆榫头上下边距。Ws is the width of joint material, Ds is the thickness of joint material, Ls is the distance between the end face and the bottom of tenon, a is the thickness of tenon, b is the width of tenon, l is the length of tenon, u1 is the thickness of triangular tenon, u2 is the offset of tenon, and u3 is the margins of tenon.

    Figure  3.  Geometrical model of modified lattice shoulder tenon

    图  4  榫卯构件中的装配关系

    Figure  4.  Assembly relations in mortise and tenon joints

    图  5  榫卯位置配合关系(以格肩榫为例)

    Figure  5.  Position matching relationship of mortise-tenon (taking lattice shoulder tenon for example)

    图  6  格肩榫配合关系和关联尺寸参数

    A为榫眼宽度,B为榫眼长度,L为榫眼深度,a为榫头厚度,b为榫头宽度,l为榫头长度,ΔA为榫头厚度方向配合参数,ΔB为榫头宽度方向配合参数,ΔL为榫头长度方向配合参数。A is the width of mortise,B is the length of mortise,L is the depth of mortise,a is the thickness of tenon, b is the width of tenon,l is the length of mortise, ΔA is the fitting parameter of the thickness of mortise,ΔB is the fitting parameter of the width of mortise, and ΔL is the fitting parameter of the length of mortise.

    Figure  6.  Matching relationship and related dimension parameters of lattice shoulder tenon

    表  1  格肩榫的参数表

    Table  1.   Parameter lists of lattice shoulder tenon

    零件名称
    Component name
    断面尺寸参数
    Cross-section dimension parameter
    位置尺寸参数
    Location dimension parameter
    形状尺寸参数
    Form size parameter
    榫眼零件
    Mortise part
    材料宽度
    Material width $ {(W}_{\mathrm{m}}) $
    材料厚度
    Material thickness ($ {D}_{\mathrm{m}} $)
    榫眼位置
    Location of mortise ($ {L}_{\mathrm{m}} $)
    三角肩缺厚度
    Thickness of
    triangular mortise ($ {W}_{1} $)
    榫偏置
    Offset of mortise ($ {W}_{2} $)
    左右边距
    Margin between bottom ($ {W}_{3} $)
    下偏置
    Under offset ($ {W}_{4} $)
    肩缺底长
    Length of breach ($ G $)
    榫眼宽
    Width of mortise ($ A $)
    榫眼长
    Length of mortise ($ B $)
    榫眼深
    Depth of mortise ($ L $)
    榫头零件
    Tenon part
    材料宽度
    Material width ($ {W}_{\mathrm{s}} $)
    材料厚度
    Material thickness ($ {D}_{\mathrm{s}} $)
    三角榫肩厚度
    Thickness of
    triangular
    tenon ($ {u}_{1} $)
    榫偏置
    Offset of tenon ($ {u}_{2} $)
    上下边距
    Margin between bottom ($ {u}_{3} $)
    后偏置
    Back offset ($ {u}_{4} $)
    榫头厚
    Thickness of tenon ($ a $)
    榫头宽
    Width of tenon
    ($ b $)
    榫头长
    Length of tenon ($ l $)
    下载: 导出CSV

    表  2  格肩榫常见尺寸范围

    Table  2.   Common size range of lattice shoulder tenon

    零件名称 Component name尺寸类型 Dimension type尺寸范围 Range of size/mm常用尺寸 Commonly used size/mm
    材料尺寸 Material size $ {W}_{\mathrm{m}} $$ {W}_{\mathrm{s}} $ 13 ~ 74 24、30、32、42
    $ {D}_{\mathrm{m}} $$ {D}_{\mathrm{s}} $ 9 ~ 65 28、30、35、42
    格肩 Lattice shoulder $ {u}_{1}$$ {W}_{1} $ 4 ~ 12,以5 ~ 8内居多
    4−12,far more prevalent in 5−8
    6
    榫头尺寸 Tenon size a 4 ~ 13,以6 ~ 8内居多
    4−13,far more prevalent 6−8
    6、7、8
    b 13 ~ 74
    28、32、33
    u2 6 ~ 8 8
    注:调研对象为108组格肩榫。Note: 108 groups of lattice shoulder tenons are investigated.
    下载: 导出CSV

    表  3  部分榫卯尺寸的工艺知识和等价关联函数

    Table  3.   Technological knowledge and equal dependent function of mortise and tenon joint

    工艺知识
    Process knowledge
    等价关联函数
    Equivalent correlation function
    备注
    Remark
    欠榫负拉力
    A short tenon takes less strain
    lDm/2 l为榫头长度,Dm为榫眼厚度
    l is the mortise length, and Dm is the thickness of mortise material
    强卯弱榫
    Strong tenon and weak mortise
    Dm/4 ≤ ADm/3.5 A为榫眼宽度
    A is the tenon width
    小格肩肩高居半则蠢
    Small lattice shoulder height is less than half width of material
    h ≤ 0.5Dm,推荐值h = Dm/3
    When h ≤ 0.5Dm, recommended value h = Dm/3
    h为小格肩肩高
    h is the small lattice shoulder height
    边距厚以5 ~ 6 mm为宜
    Recommended value of margin thickness is 5−6 mm
    W1 = 5 mm$ \cup $W1 = 6 mm W1为榫边距
    W1 is the margin thickness
    平分双榫抗力更强
    Double tenon structure has stronger tensile force
    a ≥ 25 mm,推荐双榫结构;b ≥ 40 mm,推荐双榫结构
    If a ≥ 25 mm, double tenon structure is recommended; if b ≥ 40 mm, double tenon structure is recommended
    a为榫头厚度,b为榫头宽度
    a is tenon thickness, and b is tenon width
    下载: 导出CSV

    表  4  榫卯尺寸参数关联函数表(以格肩榫为例)

    Table  4.   Relevant function table of dimension parameters (taking lattice shoulder tenon for an example)

    参数类型
    Parameter type
    参数名
    Parameter name
    取值范围或系统内部预设值
    Value range and preset value/mm
    用户输入参数
    Input parameter from user
    Ws, Wm, Ds, Dm 13 ≤ Ws ≤ 74,13 ≤ Wm ≤ 74,9 ≤ Ds ≤ 65,9 ≤ Dm ≤ 65
    Lm 榫眼中心距端头距离的设计值
    Design value of the distance between middle of tenon and end
    预设参数(系统允许用户修改预设值)
    Preset value (system allows users to
    modify the default value)
    W1 W1 = 6,4 ≤ W1 ≤ 12
    u2 u2 = 8
    u3 u3 = 0.5
    A A = 8
    ΔA 榫头厚度方向上配合参数库
    Library of fit parameter in the mortise thickness direction
    ΔB 榫头宽度方向上配合参数库
    Library of fit parameter in the mortise width direction
    ΔL ΔL = −2
    因变参数
    Dependent parameter
    G G = Ws
    B B = Ws – 1 – 0.5ΔB
    L L= Dm – 2
    u1 u1= W1
    W2 W2 = u2 + 0.5ΔA
    a a = A – ΔA,4 ≤ a ≤ 13
    b B = B – ΔB,13 ≤ b ≤ 74
    l l = L – ΔL
    W3 W3 = u3 + 0.5ΔB
    W4 W4 = WmW1W2A
    u4 u4 = Dsu1u2a
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-11-10
  • 修回日期:  2021-01-02
  • 网络出版日期:  2021-03-03
  • 刊出日期:  2021-04-16

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