CN109582984A - 一种空心抛物线型变幅杆的设计方法 - Google Patents
一种空心抛物线型变幅杆的设计方法 Download PDFInfo
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Abstract
一种空心抛物线型变幅杆的设计方法,属于功率超声变幅杆设计领域。本解发明决了现有变幅杆设计方法均为实心结构,缺少空心结构以及实心放大倍数有限的问题。它包括以下步骤:步骤一、计算面积系数N、谐振长度Lp;步骤二、计算位移节点x0;步骤三、计算放大系数Mp;四、运用模拟软件依据步骤一至步骤三中给定的数据和计算的结果进行数值模拟,对空心超声变幅杆的设计进行优化。本发明适用于空心抛物线型超声变幅杆的设计。
Description
技术领域
本发明属于功率超声变幅杆设计领域,具体涉及一种空心抛物线型变幅杆的设计方法。
背景技术
功率超声在工业中应用十分广泛,超声变幅杆是超声波振动系统中一个重要的组成部分,它在振动系统中的主要作用是把机械振动的质点位移或速度放大,并将超声能量集中在较小的面积上聚能,因此也称超声变速杆或超声聚能器。超声变幅杆主要分为阶梯形、指数型、圆锥形、双曲线形等类型,在其它参数相同的情况下,阶梯形变幅杆的放大系数最大,其次是双曲线形变幅杆和指数型变幅杆圆锥形变幅杆的形状因数最大,其次是指数型。综合考虑形状因数和放大系数,指数型超声变幅杆要优于其它类型。目前,超声变幅杆多为实心设计,并且放大系数有限,在此基础上想获得更高的放大系数,唯有增大端面直径来获得更大的放大系数,这势必造成径向振动增大,反而制约了能量在小端的聚焦,进而影响功率超声装置的整体放大系数。而空心变幅杆,在不需要增大变幅杆端面直径的条件下,便可获得更大的放大系数。此外,在材料加工领域,常常需要空心超声变幅杆,例如,带中心孔的变幅杆可以实现旋转超声加工的中心供冷却液或气体,可使其具有良好的冷却和排屑效果。然而,,变幅杆设计方法缺少相关数学模型,而且没有完整的理论体系,为此,本发明提出了一种空心超声变幅杆的设计方法。
发明内容
本发明为了解决现有变幅杆设计方法均为实心结构,缺少空心结构的,以及实心超声变幅杆的放大系数有限的问题,提出了一种空心抛物线型变幅杆的设计方法。
一种空心抛物线型超声变幅杆的设计方法,它是按以下步骤实现的:
步骤一、变幅杆的母线选为抛物线型,设变幅杆大端面面积为S1,小端面面积为S2,圆柱形空心部分内圆面积为S0,D1为变幅杆的大端端面直径,D2为变幅杆的小端端面直径,D0为变幅杆的空心直径,振动频率为f,纵波波速为C。抛物线型空心变幅杆可以类比成实心抛物线型变幅杆,所以空心抛物线型变幅杆的面积函数为
(1)
式(1)中的 γ,j为抛物线变幅杆的系数,且
(2)
式(2)中N为面积系数,l p为谐振长度,且
(3)
其中频率方程为:
(4)
空心抛物线线变幅杆的直径函数为:
(5)
在已知、D2、D0、n、C、f时,联立公式(2)至公式(5)即可求出D1、l p、N,进而求出j;
步骤二、将步骤一中求得的l代入位移节点公式(6)中可求出位移节点x0,
(6)
步骤三、将步骤一中求得的N代入放大系数公式(7)中可求出计算出Mp:
(7)
步骤四、运用模拟软件依据步骤一至步骤三中给定的数据和计算的结果进行数值模拟,对空心超声变幅杆的设计进行优化。
附图说明
图1是一种空心抛物线型变幅杆的设计的示意图;
图2是空心直径为20mm的带法兰抛物线型变幅杆模拟结果图中的总位移云图;
图3是空心直径为20mm的带法兰抛物线型变幅杆模拟结果图中的节点位移图;
图4是实心抛物线型变幅杆模拟结果图中的位移云图;
图5是实心抛物线型变幅杆模拟结果图中的位移矢量云图(节点的)。
具体实施例
下面结合实施例对具体实施方式做进一步的说明,参见附图1,给定D1=52mm,D0=20mm,f=20KHz,材料选择45号钢,则C=5200m/s,n取一个波长,即n=260mm,公式(2)至公式(4),求得D2=32mm,lp=130mm ,N=1.921 ,γ= 0.0142,将求得l p、n代入位移节点公式(6)中,求得位移节点x0=39.1。将求得N代入放大系数公式(7)中,求得计算放大系数Mp= 11,用模拟软件依据上述给定的数据和求得的结果进行数值模拟,模拟结果见附图2和附图3,从附图2中可看到空心抛物线型变幅杆的模拟放大系数为6.44,从附图3中可看到空心抛物线型变幅杆的波的轴向性较好。
对照例
为了与实心抛物线型变幅杆的模拟放大倍数作比较,选取同样材质的45号钢,实心抛物线型变幅杆的设计尺寸均与实施例的设计尺寸相同,但变幅杆为实心结构,按照具体实施方式的步骤一至步骤四进行,所得模拟结果见附图4和附图5,从附图4中可看到实心抛物线型变幅杆的模拟放大系数为4.184 , 空心抛物线型变幅杆的模拟放大系数为6.44,反映的空心的抛物线型变幅杆要好实心的抛物线型变幅杆。
空心抛物线型变幅杆的模拟放大系数为抛物线指数型变幅杆的模拟放大系数1.5倍,远优于实心抛物线型变幅。此外,对比附图2和附图5可看出空心抛物线型变幅杆的波的轴向性比实心抛物线型变幅杆的波的轴向性好很多。
Claims (1)
1.一种空心抛物线型超声变幅杆的设计方法,它是按以下步骤实现的:
步骤一、变幅杆的母线选为抛物线型,设变幅杆大端面面积为S1,小端面面积为S2,圆柱形空心部分内圆面积为S0,D1为变幅杆的大端端面直径,D2为变幅杆的小端端面直径,D0为变幅杆的空心直径,振动频率为f,纵波波速为C抛物线型空心变幅杆可以类比成实心抛物线型变幅杆,所以空心抛物线型变幅杆的面积函数为:
(1)
式(1)中的 γ,j为抛物线变幅杆的系数,且
(2)
式(2)中N为面积系数,l p为谐振长度,且
(3)
其中频率方程为:
(4)
空心抛物线线变幅杆的直径函数为:
(5)
在已知、D2、D0、n、C、f时,联立公式(2)至公式(5)即可求出D1、l p、N,进而求出j;
步骤二、将步骤一中求得的l代入位移节点公式(6)中可求出位移节点x0,
(6)
步骤三、将步骤一中求得的N代入放大系数公式(7)中可求出计算出Mp:
(7)
步骤四、运用模拟软件依据步骤一至步骤三中给定的数据和计算的结果进行数值模拟,对空心超声变幅杆的设计进行优化。
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Cited By (2)
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CN110976260A (zh) * | 2019-11-25 | 2020-04-10 | 大族激光科技产业集团股份有限公司 | 变幅杆及换能系统 |
CN114102275A (zh) * | 2021-11-19 | 2022-03-01 | 南京航空航天大学 | 一种适用于齿轮超声振动辅助磨削的装置及其运行工艺 |
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Cited By (2)
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CN110976260A (zh) * | 2019-11-25 | 2020-04-10 | 大族激光科技产业集团股份有限公司 | 变幅杆及换能系统 |
CN114102275A (zh) * | 2021-11-19 | 2022-03-01 | 南京航空航天大学 | 一种适用于齿轮超声振动辅助磨削的装置及其运行工艺 |
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