## 留言板 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. 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. • 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 ($l$ )

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.

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 l ≥ Dm/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 ≤ A ≤ Dm/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/3When 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

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 = Wm – W1 – W2 – A u4 u4 = Ds – u1 – u2 – a
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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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