CN110569560A - A Stress Superposition Method of Mirror Topology Tangentially Loaded Ring - Google Patents

A Stress Superposition Method of Mirror Topology Tangentially Loaded Ring Download PDF

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CN110569560A
CN110569560A CN201910760441.4A CN201910760441A CN110569560A CN 110569560 A CN110569560 A CN 110569560A CN 201910760441 A CN201910760441 A CN 201910760441A CN 110569560 A CN110569560 A CN 110569560A
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stress
tangential
ring
force
radial
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王世宇
柳金龙
王哲人
李海洋
王姚志豪
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Tianjin University
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Abstract

The invention discloses a method for superposing mirror image topological tangential loaded ring stress, which comprises the following steps: establishing a static model of the circular ring under the action of single tangential concentrated force on the micro-segment of the circular ring; calculating a distribution function of the tangential stress and the radial stress of the ring under the action of single tangential concentrated force through a static model; and obtaining the distribution function of the tangential stress and the radial stress of the mirror topology tangential loaded ring by using an superposition method. Compared with the prior art, the method has the characteristics of innovation, high efficiency, accuracy, universality and the like. According to the method, the relationship between the distribution of the tangential concentration force and the stress distribution can be researched.

Description

一种镜像拓扑切向受载圆环应力叠加的方法A Stress Superposition Method of Mirror Topology Tangentially Loaded Ring

技术领域technical field

本发明涉及材料力学应力分布领域,尤其涉及一种镜像拓扑切向受载圆环应力叠加的方法。The invention relates to the field of mechanical stress distribution of materials, in particular to a method for stress superposition of a mirror image topology tangentially loaded circular ring.

背景技术Background technique

早在古代中国,环状结构就被劳动人民所使用,水车,也叫天车,是一种古老的提水灌溉工具,是古代中国劳动人民充分利用水力资源而发展出来的一种运转机械。水车的一周布置有水斗,在水车旋转的过程中,水斗取水以灌溉土地。水车可以简化为环状结构,而水斗取水产生的重力可以看成施加在环状结构上的切向力。研究施加在圆环上的切向力对圆环的应力分布是很有必要的,因为根据应力分布才能选择满足许用应力条件的材质以制造水车,这决定了取水量的高低。古代劳动人民主要靠经验来选取材料。而在现代工程应用中,我们主要研究的对象是啮合的齿轮、齿条及齿圈。齿轮在啮合的过程中,齿与齿之间会产生沿啮合线指向齿面的力,该力沿节圆切向方向的分力是施加在从动轮上的驱动力,驱动力的大小决定了正常工作载荷的大小。所以,研究切向受载圆环的应力分布,可以在齿轮的设计阶段进行指导。文献(R.G.Parker.A physical explanation for theeffectiveness of planet phasing to suppress planetary gear vibration.J.SoundVib,2000,236(4):561-573)根据作用于太阳轮和行星轮上的力,研究了行星相位在一定谐波下的啮合频率抑制行星齿轮振动的有效性。由于某些设计目的和装配的限制,行星齿轮之间的空间有时是不均匀的,失去了循环对称性,文献(J.Lin andR.G.Parker.Structured vibration characteristics ofplanetary gears withunequally spaced planets.J.Sound Vib,2000,233(5):921-928)分析了具有不等距行星轮系统的自由振动。目前,很多齿轮动力学的研究,没有考虑或者简化了圆环的应力分布问题,由于圆环应力分布分析技术的局限性,特别需要一种在切向集中力作用下圆环应力分布的分析方法。As early as in ancient China, the ring structure was used by the working people. The water wheel, also called the crane, is an ancient water-lifting irrigation tool. It is a kind of running machine developed by the ancient Chinese working people by making full use of water resources. . Water buckets are arranged around the waterwheel. During the rotation of the waterwheel, the water buckets draw water to irrigate the land. The water wheel can be simplified as a ring structure, and the gravity generated by the water bucket can be regarded as a tangential force exerted on the ring structure. It is necessary to study the tangential force applied on the ring to the stress distribution of the ring, because the material that satisfies the allowable stress conditions can be selected according to the stress distribution to manufacture the waterwheel, which determines the water intake. The ancient working people mainly relied on experience to select materials. In modern engineering applications, our main research objects are meshing gears, racks and ring gears. During the meshing process of the gears, a force will be generated between the teeth and directed to the tooth surface along the meshing line. The component force of this force along the tangential direction of the pitch circle is the driving force applied to the driven wheel. The magnitude of the driving force determines The size of a normal workload. Therefore, the study of the stress distribution of the tangentially loaded ring can be used as a guide in the design stage of the gear. The literature (R.G.Parker.A physical explanation for the effectiveness of planet phasing to suppress planetary gear vibration.J.SoundVib,2000,236(4):561-573) studies the planetary phase according to the force acting on the sun gear and planetary gear The effectiveness of the meshing frequency at certain harmonics to suppress planetary gear vibration. Due to certain design purposes and assembly constraints, the space between planetary gears is sometimes uneven, losing cyclic symmetry, literature (J.Lin and R.G.Parker.Structured vibration characteristics of planetary gears with unevenly spaced planets.J. Sound Vib, 2000, 233(5): 921-928) analyzed the free vibration of a planetary gear system with unequal distances. At present, many studies on gear dynamics do not consider or simplify the stress distribution of the ring. Due to the limitations of the analysis technology of the stress distribution of the ring, an analysis method for the stress distribution of the ring under the action of the tangential concentrated force is especially needed. .

发明内容Contents of the invention

本发明提供了一种镜像拓扑切向受载圆环应力叠加的方法,本发明针对切向受载圆环的应力分布问题,在圆环的微段上利用截面法建立静力学模型,采用叠加法来计算镜像拓扑切向受载圆环的应力分布,使所得结果更好地满足工程实际的需求,详见下文描述:The invention provides a method for stress superposition of a mirror-image topology tangentially loaded circular ring. The present invention aims at the stress distribution problem of a tangentially loaded circular ring. The method is used to calculate the stress distribution of the tangentially loaded ring in the mirror image topology, so that the obtained results can better meet the actual needs of the project. See the description below for details:

一种镜像拓扑切向受载圆环应力叠加的方法,所述方法包括以下步骤:A method for superimposing stress of a mirrored topological tangentially loaded ring, said method comprising the following steps:

在圆环的微段上建立单个切向集中力作用下圆环的静力学模型;Establish a static model of the ring under the action of a single tangential concentrated force on the micro-segment of the ring;

通过静力学模型计算单个切向集中力作用下圆环的切向应力和径向应力的分布函数;Calculate the distribution function of the tangential stress and radial stress of the ring under the action of a single tangential concentrated force through the static model;

利用叠加法,得到镜像拓扑切向受载圆环的切向应力以及径向应力的分布函数。Using the superposition method, the distribution functions of the tangential stress and the radial stress of the mirror topology tangentially loaded ring are obtained.

其中,所述静力学模型具体为:Wherein, the static model is specifically:

式中,θ为圆环上某质点的角度,Fef为切向集中力,Fff为虚拟支撑力,Fsf为径向内力,Ftf为切向内力,Mbm为弯矩。In the formula, θ is the angle of a particle on the ring, F ef is the tangential concentrated force, F ff is the virtual support force, F sf is the radial internal force, F tf is the tangential internal force, and M bm is the bending moment.

进一步地,所述单个切向集中力作用下圆环的切向应力和径向应力的分布函数具体为:Further, the distribution function of the tangential stress and radial stress of the ring under the action of the single tangential concentrated force is specifically:

式中,Ftfθ为切向应力,Fsfr为径向应力,A=bh为圆环的截面面积,h是径向厚度,b是轴向厚度。In the formula, F tfθ is the tangential stress, F sfr is the radial stress, A=bh is the cross-sectional area of the ring, h is the radial thickness, and b is the axial thickness.

进一步地,所述镜像拓扑切向受载圆环的切向应力以及径向应力的分布函数具体为:Further, the distribution function of the tangential stress and the radial stress of the mirrored topological tangentially loaded ring is specifically:

式中,N为切向集中力的个数,θi1,j1是第i1组中第j1个切向集中力的位置角。In the formula, N is the number of tangentially concentrated forces, θ i1, j1 is the position angle of the j 1 tangentially concentrated force in the i 1th group.

本发明提供的技术方案的有益效果是:The beneficial effects of the technical solution provided by the invention are:

1、本发明利用截面法在圆环的微段上建立静力学模型,求解单个切向集中力作用下圆环的应力分布;1. The present invention utilizes the section method to set up a statics model on the micro-section of the ring to solve the stress distribution of the ring under the action of a single tangential concentrated force;

2、本发明采用叠加法求解镜像拓扑切向受载圆环的应力分布;2. The present invention adopts the superposition method to solve the stress distribution of the mirror image topology tangentially loaded ring;

3、与现有方法相比,本发明具有创新、高效、准确和普适等特征。根据该方法可研究切向集中力的分布与应力分布之间的关系。3. Compared with the existing methods, the present invention has the characteristics of innovation, high efficiency, accuracy and universality. According to this method, the relationship between the distribution of tangential concentrated force and the stress distribution can be studied.

附图说明Description of drawings

图1为本发明提供的单个切向集中力作用下整环及微段上力的分布示意图;Fig. 1 is the distribution schematic diagram of whole ring and micro-section upper force under the action of single tangential concentrated force provided by the present invention;

其中,(a)为单个切向力作用下圆环上力的分布示意图;(b)为单个切向力作用下圆环微段上力的分布示意图。Among them, (a) is a schematic diagram of the force distribution on the ring under the action of a single tangential force; (b) is a schematic diagram of the distribution of the force on the micro-segment of the ring under the action of a single tangential force.

图2为本发明提供的旋转θk角的单个切向集中力作用下整环及微段上力的分布示意图;Fig. 2 is the distribution schematic diagram of the force on the whole ring and the micro-section under the action of the single tangential concentrated force of the rotation θ k angle provided by the present invention;

图3为本发明提供的单个切向力作用下圆环的切向和径向应力大小及其分布的示意图;Fig. 3 is the schematic diagram of the tangential and radial stress size and distribution thereof of the ring under the action of a single tangential force provided by the present invention;

其中,(a)为本发明提供的单个切向集中力作用下圆环的切向和径向应力分布的示意图;(b)为本发明提供的单个切向集中力作用下圆环的切向和径向应力大小的示意图;(c)为本发明提供的旋转θk角的单个切向集中力作用下圆环的切向和径向应力分布示意图。Wherein, (a) is the schematic diagram of the tangential and radial stress distribution of the ring under the action of a single tangential concentrated force provided by the present invention; and the schematic diagram of the radial stress magnitude; (c) is a schematic diagram of the tangential and radial stress distribution of the ring under the single tangential concentrated force of the rotation θ k angle provided by the present invention.

图4为本发明提供的镜像拓扑切向受载圆环的力的分布示意图。Fig. 4 is a schematic diagram of the force distribution of the mirror image topology tangential to the loaded ring provided by the present invention.

具体实施方式Detailed ways

为使本发明的目的、技术方案和优点更加清楚,下面对本发明实施方式作进一步地详细描述。In order to make the purpose, technical solution and advantages of the present invention clearer, the implementation manners of the present invention will be further described in detail below.

本发明实施例提出了一种适用性较强的专门针对镜像拓扑切向受载圆环应力叠加的方法。首先在圆环的微段上建立单个切向集中力作用下圆环的静力学模型,得到受载圆环的各内力分布,根据材料力学中内力和应力的关系,求出圆环在单个切向集中力作用下的应力分布,然后采用叠加法来计算镜像拓扑切向受载圆环的应力分布。本方法也可用于旋转电机的定转子以及微器件中的环形构件等典型周期结构的应力分布的求解。The embodiment of the present invention proposes a highly applicable method for stress superposition of tangentially loaded circular rings in mirror topology. First, the static model of the ring under the action of a single tangential concentrated force is established on the micro-segment of the ring, and the distribution of internal forces of the loaded ring is obtained. The stress distribution under the action of concentrated force is calculated, and then the superposition method is used to calculate the stress distribution of the mirror-image topological tangentially loaded ring. This method can also be used to solve the stress distribution of typical periodic structures such as stator and rotor of rotating electrical machines and ring components in micro-devices.

圆环受镜像拓扑切向集中力的作用;该应力分布的叠加方法的基本特征在于:采用叠加法实现圆环的应力分布求解,具体步骤为:The ring is affected by the tangential concentration force of the mirror image topology; the basic feature of the superposition method of the stress distribution is that the stress distribution of the ring is solved by using the superposition method, and the specific steps are as follows:

(1)利用截面法,在圆环的微段上根据力和力矩平衡原理建立单个切向集中力作用下圆环的静力学模型:(1) Using the section method, the static model of the ring under the action of a single tangential concentrated force is established on the micro-segment of the ring according to the principle of force and moment balance:

式中,θ为圆环上某质点的角度,Fef为切向集中力,Fff为虚拟支撑力,Fsf为径向内力,Ftf为切向内力,Mbm为弯矩。In the formula, θ is the angle of a particle on the ring, F ef is the tangential concentrated force, F ff is the virtual support force, F sf is the radial internal force, F tf is the tangential internal force, and M bm is the bending moment.

图1为单个切向集中力作用时圆环及微段上力的分布图。如图1(a)所示,圆环中性圆的半径是R,径向厚度是h,轴向厚度是b,圆环在θ=0处受一个切向力集中Fef的作用,方向向下。为了便于研究,在圆环的一周,分布着均匀的虚拟支撑,虚拟支撑产生虚拟力Fff,方向向上,圆环在一个切向集中力、虚拟的转矩以及均布的虚拟力的作用下维持平衡。Figure 1 is the distribution diagram of the force on the ring and the micro-segment when a single tangential concentrated force acts. As shown in Figure 1(a), the radius of the neutral circle of the ring is R, the radial thickness is h, and the axial thickness is b. The ring is affected by a tangential force concentration F ef at θ=0, and the direction down. For the convenience of research, uniform virtual supports are distributed around the circle of the ring, and the virtual supports generate virtual force F ff , the direction is upward, and the ring is under the action of a tangential concentrated force, virtual torque and uniform virtual force maintain balance.

为了研究圆环在单个切向集中力下产生的应力分布,在圆环θ(θ∈(0,2π))处截取dθ的微段,采用截面法对微段进行受力分析,如图1(b)所示,O和O′分别是圆环的几何中心和微段的中点,Fsf、Ftf、Mbm和Ttm分别为径向内力、切向内力、弯矩和转矩。In order to study the stress distribution of the ring under a single tangential concentrated force, the micro-segment of dθ is intercepted at the ring θ(θ∈(0,2π)), and the force analysis of the micro-segment is carried out by using the section method, as shown in Figure 1 As shown in (b), O and O′ are the geometric center of the ring and the midpoint of the micro-segment, respectively, F sf , F tf , M bm and T tm are the radial internal force, tangential internal force, bending moment and torque, respectively .

(2)由于研究的是圆环的微段,dθ为微量,利用极限的思想,因此,含有微量的三角函数可以化简为:(2) Since the micro-segment of the ring is studied, dθ is a micro-quantity, and the idea of limit is used, therefore, the trigonometric function containing a micro-quantity can be simplified as:

(3)将式(4)-(7)代入式(1)-(3)中,化简可得:(3) Substituting formulas (4)-(7) into formulas (1)-(3) and simplifying can get:

dMbm=FsfRdθ (10)dM bm = F sf Rdθ (10)

(4)求径向内力的通解(4) Find the general solution of the radial internal force

由式(8)和(9)可得径向内力Fsf与切向集中力Fef的关系:The relationship between the radial internal force F sf and the tangential concentrated force F ef can be obtained from formulas (8) and (9):

式(11)是径向内力的二阶非齐次微分方程,由式(11)可得特征方程:Equation (11) is the second-order inhomogeneous differential equation of radial internal force, and the characteristic equation can be obtained from Equation (11):

λsf 2+1=0 (12)λ sf 2 +1=0 (12)

式中,λsf是特征方程的特征值,解之得λsf1,2=±i,i为虚数单位。In the formula, λ sf is the eigenvalue of the characteristic equation, and the solution is λ sf1,2 =±i, where i is the imaginary unit.

为了求解微分方程的通解,设该微分方程的一个特解为:In order to solve the general solution of the differential equation, let a special solution of the differential equation be:

Fsf *=θ(a1cosθ+b1sinθ)+a0 (13)F sf * =θ(a 1 cosθ+b 1 sinθ)+a 0 (13)

式中,a0、a1和b1均为实数。In the formula, a 0 , a 1 and b 1 are all real numbers.

将式(13)代入式(11)中,化简可得:Substituting formula (13) into formula (11), it can be simplified to get:

由待定系数法可得a0、a1和b1分别为:According to the undetermined coefficient method, a 0 , a 1 and b 1 can be obtained as:

a1=0 (16)a 1 =0 (16)

因此,微分方程的特解为:Therefore, the particular solution of the differential equation is:

由特征方程得到的特征值以及微分方程的一个特解,可得径向内力的通解为:From the eigenvalue obtained from the characteristic equation and a special solution of the differential equation, the general solution of the radial internal force can be obtained as:

式中,c1和c2为实数。In the formula, c 1 and c 2 are real numbers.

(5)求切向内力及弯矩的通解(5) Find the general solution of tangential internal force and bending moment

由式(8)、(10)和(19)可得:From formulas (8), (10) and (19), we can get:

(6)求径向变形的通解(6) Find the general solution of radial deformation

对于小曲率圆环,由材料力学的知识可知弯矩与径向变形的关系是:For small curvature rings, the relationship between bending moment and radial deformation is known from the knowledge of material mechanics:

式中,v为圆环的径向变形,E和I分别为圆环的弹性模量和转动惯量。In the formula, v is the radial deformation of the ring, and E and I are the elastic modulus and moment of inertia of the ring, respectively.

由式(10)、(11)和(22)可得径向变形的五阶非齐次微分方程:From equations (10), (11) and (22), the fifth-order inhomogeneous differential equation of radial deformation can be obtained:

由式(23)可得特征方程为:From formula (23), the characteristic equation can be obtained as:

λv 5+2λv 3v=0 (24)λ v 5 +2λ v 3v =0 (24)

解之得λv1=0,λv2,3=±i,λv4,5=±i,i为虚数单位。The solution is λ v1 =0, λ v2,3 =±i, λ v4,5 =±i, i is the imaginary unit.

为了求解微分方程的通解,设该微分方程的一个特解为:In order to solve the general solution of the differential equation, let a special solution of the differential equation be:

v*=θ2(a2cosθ+b2sinθ)+a0′θ (25)v * =θ 2 (a 2 cosθ+b 2 sinθ)+a 0′ θ (25)

式中,a0′、a2和b2均为实数。In the formula, a 0′ , a 2 and b 2 are all real numbers.

将式(25)代入式(23)中,化简可得:Substituting formula (25) into formula (23), simplification can get:

由待定系数法可得a0′、a2和b2分别为:According to the undetermined coefficient method, a 0′ , a 2 and b 2 can be obtained as follows:

a2=0 (28)a 2 =0 (28)

因此,微分方程的特解为:Therefore, the particular solution of the differential equation is:

由特征方程得到的特征值以及微分方程的一个特解,可得径向变形的通解为:From the eigenvalue obtained from the characteristic equation and a special solution of the differential equation, the general solution of the radial deformation can be obtained as:

式中,av1~av5均为实数。In the formula, a v1 ~a v5 are all real numbers.

(7)利用边界条件求各通解的系数(7) Use the boundary conditions to find the coefficients of each general solution

由材料力学知识可知,对于小曲率圆环,任意截面上的转角为:According to the knowledge of material mechanics, for a ring with small curvature, the rotation angle on any section for:

取圆环θ=0处的截面分析,切向内力为:Taking the section analysis of the ring at θ=0, the tangential internal force is:

由式(20)和(33)解得:From equations (20) and (33), we get:

圆环在θ=0处的转角均为零,由式(31)可知:The rotation angle of the ring at θ=0 is zero, and it can be known from formula (31):

由式(21)、(22)和(31)可知:From formulas (21), (22) and (31), it can be seen that:

圆环在θ=0和θ=π处,径向变形为0,由式(31)可知:At θ=0 and θ=π, the radial deformation of the ring is 0, as can be seen from formula (31):

小曲率圆环,由无延展假设可知,圆环在(0,π)上的切向变形量u=0,由式(31)可知:For a small curvature ring, it can be known from the assumption of no extension, the tangential deformation of the ring on (0, π) is u = 0, and it can be known from formula (31):

由式(34)和(36)-(38)可知:From equations (34) and (36)-(38), it can be seen that:

因此,受单个切向集中力作用时,圆环的径向内力、切向内力、弯矩以及径向变形分别为:Therefore, under the action of a single tangential concentrated force, the radial internal force, tangential internal force, bending moment and radial deformation of the ring are respectively:

由材料力学中内力与应力的关系及式(41)-(42)可知,圆环的切向应力和径向应力分别为:From the relationship between internal force and stress in material mechanics and formulas (41)-(42), it can be known that the tangential stress and radial stress of the ring are respectively:

式中,A为圆环的截面面积。In the formula, A is the cross-sectional area of the ring.

(8)应力的叠加(8) Superposition of stress

如图2所示,圆环在θ=θk处受一个切向集中力Fef的作用,在圆环的一周分布着与集中力相平衡的虚拟力,与图1(a)相比,切向力和虚拟力的大小分别相等,方向分别旋转θk角。As shown in Figure 2, the ring is affected by a tangential concentrated force F ef at θ=θ k , and a virtual force that is balanced with the concentrated force is distributed around the ring. Compared with Figure 1(a), The magnitudes of the tangential force and the virtual force are respectively equal, and the directions are rotated by θ k angle respectively.

图3(a)是在单个切向集中力作用下圆环的切向应力和径向应力的分布图,其大小如图3(b)所示。图3(c)是由图3(a)旋转θk角之后得到的切向应力和径向应力的分布图。Figure 3(a) is the distribution diagram of the tangential stress and radial stress of the ring under the action of a single tangential concentrated force, and its size is shown in Figure 3(b). Figure 3(c) is the distribution diagram of the tangential stress and radial stress obtained after rotating the angle θ k in Figure 3(a).

由于在单个切向集中力的作用下,圆环的切向应力和径向应力的周期为2π,设式(45)和(46)的傅里叶级数展开式为:Since the period of the tangential stress and radial stress of the ring is 2π under the action of a single tangential concentrated force, the Fourier series expansions of equations (45) and (46) are:

式中,分别为:In the formula, and They are:

由将式(49)-(51)化简并代入式(47)可得:By simplifying formulas (49)-(51) and substituting them into formula (47), we can get:

由将式(52)-(54)化简并代入式(48)可得:By simplifying formulas (52)-(54) and substituting them into formula (48), we can get:

切向集中力旋转θk角之后,圆环的切向应力和径向应力的分布也应该旋转相同的角度,即:After the tangential concentrated force is rotated by θ k angle, the distribution of tangential stress and radial stress of the ring should also be rotated by the same angle, namely:

式中,θk为第一个集中力旋转到第k个集中力时的旋转角。In the formula, θ k is the rotation angle when the first concentrated force rotates to the kth concentrated force.

如图4所示,圆环的一周受到N个切向集中力的作用,这N个切向集中力被分为2组,采用镜像拓扑的布置形式,如图Gi1(i1=1,2)所示,每组N/2个,如图Li1,j1(i1=1,2,j1=1,2,...N/2)所示。θi1,j1描述的是第i1组中第j1个集中力的位置角,θ2,j1=θ1,j1+π。利用叠加法,当圆环受到N个切向集中力作用时,设第一个切向集中力作用在θ=0处,圆环的切向应力和径向应力分别为:As shown in Figure 4, the circle of the ring is affected by N tangentially concentrated forces, and these N tangentially concentrated forces are divided into two groups, and the arrangement form of mirror topology is adopted, as shown in Figure G i1 (i 1 =1, As shown in 2), each group has N/2 pieces, as shown in Figure L i1,j1 (i 1 =1,2,j 1 =1,2,...N/2). θ i1,j1 describes the position angle of the j 1st concentrated force in the i 1th group, θ 2,j1 = θ 1,j1 +π. Using the superposition method, when the ring is subjected to N tangential concentrated forces, assuming that the first tangential concentrated force acts at θ=0, the tangential stress and radial stress of the ring are respectively:

综上所述,本发明实施例提供了一种镜像拓扑切向受载圆环应力叠加的方法。该方法在圆环的微段上建立静力学模型,采用截面法得到受载圆环的内力,根据内力与应力之间的关系求出受载圆环的应力分布,利用叠加法,得到镜像拓扑受载圆环的应力分布,显著提高了圆环应力计算的准确性、效率以及普适性,更好地满足了工程实际的需求。To sum up, the embodiment of the present invention provides a method for stress superposition of mirror topology tangentially loaded rings. This method establishes a static model on the micro-segment of the ring, uses the section method to obtain the internal force of the loaded ring, calculates the stress distribution of the loaded ring according to the relationship between the internal force and the stress, and uses the superposition method to obtain the mirror image topology. The stress distribution of the loaded ring significantly improves the accuracy, efficiency and universality of the stress calculation of the ring, and better meets the actual needs of the project.

本领域技术人员可以理解附图只是一个优选实施例的示意图,上述本发明实施例序号仅仅为了描述,不代表实施例的优劣。Those skilled in the art can understand that the accompanying drawing is only a schematic diagram of a preferred embodiment, and the serial numbers of the above-mentioned embodiments of the present invention are for description only, and do not represent the advantages and disadvantages of the embodiments.

以上所述仅为本发明的较佳实施例,并不用以限制本发明,凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within range.

Claims (4)

1.一种镜像拓扑切向受载圆环应力叠加的方法,其特征在于,所述方法包括以下步骤:1. a method for superposition of mirror image topology tangentially loaded circular stress, is characterized in that, described method comprises the following steps: 在圆环的微段上建立单个切向集中力作用下圆环的静力学模型;Establish a static model of the ring under the action of a single tangential concentrated force on the micro-segment of the ring; 通过静力学模型计算单个切向集中力作用下圆环的切向应力和径向应力的分布函数;Calculate the distribution function of the tangential stress and radial stress of the ring under the action of a single tangential concentrated force through the static model; 利用叠加法,得到镜像拓扑切向受载圆环的切向应力以及径向应力的分布函数。Using the superposition method, the distribution functions of the tangential stress and the radial stress of the mirror topology tangentially loaded ring are obtained. 2.根据权利要求1所述的一种镜像拓扑切向受载圆环应力叠加的方法,其特征在于,所述静力学模型具体为:2. the method for a kind of mirror image topology tangential loaded ring stress superposition according to claim 1, is characterized in that, described statics model is specifically: 式中,θ为圆环上某质点的角度,Fef为切向集中力,Fff为虚拟支撑力,Fsf为径向内力,Ftf为切向内力,Mbm为弯矩。In the formula, θ is the angle of a particle on the ring, F ef is the tangential concentrated force, F ff is the virtual support force, F sf is the radial internal force, F tf is the tangential internal force, and M bm is the bending moment. 3.根据权利要求2所述的一种镜像拓扑切向受载圆环应力叠加的方法,其特征在于,所述单个切向集中力作用下圆环的切向应力和径向应力的分布函数具体为:3. the method for a kind of mirror image topology tangentially loaded circular ring stress superposition according to claim 2, is characterized in that, the distribution function of the tangential stress of circular ring under the action of described single tangential concentrated force and radial stress Specifically: 式中,Ftfθ为切向应力,Fsfr为径向应力,A=bh为圆环的截面面积,h是径向厚度,b是轴向厚度。In the formula, F tfθ is the tangential stress, F sfr is the radial stress, A=bh is the cross-sectional area of the ring, h is the radial thickness, and b is the axial thickness. 4.根据权利要求3所述的一种镜像拓扑切向受载圆环应力叠加的方法,其特征在于,所述镜像拓扑切向受载圆环的切向应力以及径向应力的分布函数具体为:4. the method for the stress superposition of a kind of mirror image topology tangentially loaded circular ring according to claim 3, is characterized in that, the distribution function of the tangential stress of described mirror image topology tangentially loaded circular ring and radial stress is specific for: 式中,N为切向集中力的个数,θi1,j1是第i1组中第j1个切向集中力的位置角。In the formula, N is the number of tangentially concentrated forces, θ i1, j1 is the position angle of the j 1 tangentially concentrated force in the i 1th group.
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