CN103954494A - Mechanical performance testing method of oblique-coil springs - Google Patents

Abstract

The invention discloses a mechanical performance testing method of oblique-coil springs. The method comprises the following steps: firstly, establishing geometric parameter equations of a linear oblique-coil spring and an annular oblique-coil spring; secondly, drawing geometric models of the various oblique-coil springs according to the geometric parameter equations, introducing the geometric models into finite element software ANSYS to perform numerical simulation so as to obtain load-displacement curves before the oblique-coil springs work to reach a coil combination state when geometric parameters of the oblique-coil springs are regulated, changing the parameters so as to obtain the influences of the geometric parameters to the load-displacement curves, and carrying out experimental measurement on a sample so as to obtain load-displacement curves of the linear oblique-coil spring and the annular oblique-coil spring in practical work; and finally, comparing a finite element calculation result with an experimental measurement result to verify the reasonability of finite element calculation so as to verify the feasibility of the geometric parameter equations. According to the method, a production design optimization scheme of the oblique-coil springs is provided according to the experiment and the finite element calculation result, and the method has an innovative significance and wide application prospect.

Description

A kind of canted coil spring mechanic property test method

Technical field

The present invention relates to the technical field of canted coil spring mechanical property research, refer in particular to a kind of canted coil spring mechanic property test method.

Background technology

In plant equipment, the stability of connecting-piece structure performance and reliability are the emphasis that engineering circles is paid close attention to always, and canted coil spring is because its coil dimension is little, quantity is many, has very high through-current capability and good Technical Economy, thereby makes canted coil spring be particularly suitable for the design of web member.

Canted coil spring is compared with general positive coil spring, and its designs simplification, easy for installation in actual applications, contact point is many, conducts electricity very well, high current capacity, electronic and thermal stability is high, Electric Field Distribution is even, and juxtaposition metamorphose scope is compared with large and contact substantially constant weares and teares little, life cycle is long, fluting size is simple and easy to processing, and specification series can be joined the conducting rod of multiple diameter.Based on these features, have market widely as web member in power industry.

The manufacturing of canted coil spring is the patented technology of company of Basel of the U.S., the domestic current ripe production technology that also do not have, but due to external technical monopoly, limit the prodution and development of this product in China, domestic Counterfeit Item is because technology or technological problems cause existing in performance larger gap compared with imported product, be only 1/10 of same kind of products at abroad serviceable life, and because this product is one of vital part of primary cut-out, the market demand is most of dependence on import greatly.To this canted coil spring, design possesses some special knowledge domestic existing part technician, but great majority research is all relevant electric property aspect, and the research of mechanical property aspect relates to very few.Due to the size of canted coil spring, the magnitude of load being subject in the space geometry characteristic parameters such as angle of inclination and its course of work is closely related, thereby the life-span to its use has a certain impact, therefore research and development have an independent intellectual property right canted coil spring production technology and technology have great society and economic worth, also be a urgent task, spring is the element of stressed more complicated in mechanical component simultaneously, it is launched to research and also possess higher theory value.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art and shortcoming, a kind of reasonable, reliable, efficient canted coil spring mechanic property test method is provided, can directly provide theoretical direction for producing.

For achieving the above object, technical scheme provided by the present invention is: a kind of canted coil spring mechanic property test method, first, set up the geometric parameter equation of straight line canted coil spring and circular slanting coil spring; Secondly, draw the geometric model of all kinds of canted coil springs by geometric parameter equation, and import to and in finite element software ANSYS, carry out numerical simulation, the load-displacement curve of canted coil spring before work reaches doubling-up when adjusted its various geometric parameter, and by changing parameter, draw the impact of each geometric parameter on this load-displacement curve, derive the relation between geometric parameter by result of calculation, be experimental formula, obtain straight line canted coil spring and the load-displacement curve of circular slanting coil spring in real work by sample experiment test simultaneously; Finally, result of finite element and experimental results are contrasted, to verify the rationality of FEM (finite element) calculation, thus the feasibility of checking geometric parameter equation.

The geometric parameter equation of the straight line canted coil spring of setting up, as follows:

1) line model equation

$\left\{\begin{array}{c}x\left(t\right)=a\×\cos (360\×n\×t)\\ y\left(t\right)=b\×\sin (360\×n\×t)\\ z\left(t\right)=l\×t+c\×\sin (360\×n\×t)\end{array}---\left(1\right)\right.$

In formula, a, b are respectively that canted coil spring cross section is two oval length semiaxis, and a>b, represents that xsect is circular section if a, b are identical; L is the length of linear state lower spring; C is for adjustable inclination, i.e. gradient, and in the time that c value is zero, straight line canted coil spring is for just enclosing volute spring; N is the number of turns of canted coil spring, gets positive integer; T is a continually varying parameter between 0 and 1;

2) solid model equation

Spring wire cross sectional dimensions is taken into account, under rectangular coordinate system, is set up the parametric equation of following single-coil spring taking the starting point of spring as true origin:

$\left\{\begin{array}{c}x\left(t\right)=(r_x-r_{\mathrm{\ω}})\sin \left(2\mathrm{\π\ωt}\right)\\ y\left(t\right)=(r_y-r_{\mathrm{\ω}})(1-\cos \left(2\mathrm{\π\ωt}\right))\\ z\left(t\right)=t+c/2(1-\cos \left(2\mathrm{\π\ωt}\right))\end{array}\right.---\left(2\right)$

In formula, r _xrepresent that 1/2 circle is wide; r _yrepresent that 1/2 circle is high; r _ωrepresent the radius of spring silk xsect; Obviously (r _x-r _ω) corresponding to a in above formula (1), (r _y-r _ω) corresponding to the b in formula (1); ω represents the number of turns in unit length, its pitch that represents reciprocal; C represents the width that inclines, and encloses the distance that withstands on axial dipole field compared with positive coil spring; T is parametric variable, what the angle here adopted is radian;

3) the solid model equation that contains inclination angle

The equation of the straight line canted coil spring of oval cross section

$s\left(t\right)=\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πt}\\ y\left(t\right)=\mathrm{Pt}-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\πt}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πt}\end{array}\right.---\left(3\right)$

In formula, t ∈ [0, n], P represents pitch; CA is the angle of triangle base center line and vertical line, in the time that CA gets zero, represents the positive coil spring of straight line; CW is wide for enclosing; CH is high for enclosing; WD is wire diameter.

The geometric parameter equation of the circular slanting coil spring of setting up, as follows:

1) parametric equation of canted coil spring radially

1.1) under circular cylindrical coordinate, set up radially canted coil spring equation:

$\left\{\begin{array}{c}r=r_0+a\×\cos (360\×n\×t)\\ \mathrm{\θ}=360\×t+c\×\cos (360\×n\×t)\\ z=b\×\sin (360\×n\×t)\end{array}\right.---\left(4\right)$

In formula, a, b are respectively length semiaxis, the parameter that c is adjustable inclination, and n is the number of turns, r ₀centered by distance, t is a continually varying parameter between 0 and 1;

1.2) under rectangular coordinate, set up radially canted coil spring equation

1.2.1) radially canted coil spring of clockwise direction:

$\begin{array}{c}{h}_{\mathrm{radial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(0,u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{C\; A}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(5\right)$

1.2.2) radially canted coil spring of counter clockwise direction:

$\begin{array}{c}{h}_{\mathrm{radial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(\mathrm{\π},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(6\right)$

2) parametric equation of axial canted coil spring

2.1) clockwise axial canted coil spring:

$\begin{array}{c}{h}_{\mathrm{axial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\cos 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(7\right)$

2.2) anticlockwise axial canted coil spring

$\begin{array}{c}{h}_{\mathrm{axial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(-\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\cos 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(8\right)$

In formula (5), (6), (7), (8), n is the number of turns, r ₀centered by distance, t is a continually varying parameter between 0 and 1, R for circle footpath, CA is the angle of triangle base center line and vertical line, CW for circle wide, CH for enclose high, WD is wire diameter.

Carry out numerical simulation in finite element software ANSYS time, what adopt is beam element BEAM44 simulation, described beam element BEAM44 be a kind of have bear draw, press, the three-dimensional single shaft beam element of torsion and crooking ability, the each node in unit has six-freedom degree: the axially movable rotation of the translation of x, y, z direction and x, y, z, this unit allows to have asymmetric end face structure, and allow end face node to depart from cross section position of form center, in addition spring material is beryllium-bronze, getting elastic modulus is 1.3e5MPa, and Poisson ratio is 0.32;

For straight line canted coil spring, the boundary condition of employing is: a free end of spring applies axially, i.e. Z direction displacement constraint, and the lower end of spring applies X, the displacement of Y both direction, displacement is zero; The upper end of spring applies X, the displacement of Y both direction, and wherein directions X displacement is zero, the displacement of Y-direction, according to simulation changes in demand, applies different displacement load;

For the radially canted coil spring in circular slanting coil spring, the boundary condition of employing is: utilize outer ring all fixing; Inner ring hoop is removable, axial restraint, and radial loaded has been analyzed whole model;

For the axial canted coil spring in circular slanting coil spring, the boundary condition of employing is: circle top is radially fixing, axially applies displacement load, and hoop is removable; Circle bottom is all fixing; Sample elastic modulus is got 1.3e5MPa, and Poisson ratio gets 0.32;

Impact by each geometric parameter on load-displacement curve, derives the relation between geometric parameter through result of finite element, can obtain the experimental formula of following relevant canted coil spring parameter:

c＝λb?λ∈[0.45～0.53]

In formula, c is the width that inclines, and encloses the distance that withstands on axial dipole field compared with positive coil spring; B is the minor semi-axis of canted coil spring, encloses high.

In the time carrying out sample experiment test, sample is carried out on MTS testing machine to quasistatic compression test, to spring-like product load application to be measured, draw the relation curve of the load-displacement of spring in real work by MTS testing machine.

Adopt PRO/E software to set up the geometric model of canted coil spring, and select IGS form to export to and in finite element software ANSYS, carry out finite element analysis.

Compared with prior art, tool has the following advantages and beneficial effect in the present invention:

1, on the basis contrasting at experiment and finite element result, rationally set up the geometric parameter equation of canted coil spring, and utilized finite element to analyze each geometric parameter, obtained the Effect on Mechanical Properties of parameters to canted coil spring;

2, by test findings and finite element result contrast, draw the impact of each geometric parameter on load-displacement curve;

3, the Production design prioritization scheme that proposes by experiment canted coil spring with result of finite element, has innovative significance, is with a wide range of applications.

Brief description of the drawings

Fig. 1 a is one of solid model schematic diagram of the straight line canted coil spring of oval cross section.

Fig. 1 b be the straight line canted coil spring of oval cross section solid model schematic diagram two.

Fig. 2 a is the geometric model figure of straight line canted coil spring.

Fig. 2 b is the geometric model figure of radially canted coil spring.

Fig. 2 c is the geometric model figure of axial canted coil spring.

Fig. 3 a is the test loading figure of straight line canted coil spring.

Fig. 3 b is the test loading figure of circular slanting coil spring.

Fig. 4 a is the load-displacement curve figure of straight line canted coil spring test specimen 1.

Fig. 4 b is the load-displacement curve figure of straight line canted coil spring test specimen 2.

Fig. 5 is the load-displacement curve figure of circular slanting coil spring test specimen.

Fig. 6 a is test findings and the finite element result comparison chart of straight line canted coil spring.

Fig. 6 b is test findings and the finite element result comparison chart of circular slanting coil spring.

Embodiment

Below in conjunction with specific embodiment, the invention will be further described.

Canted coil spring mechanic property test method described in the present embodiment, its concrete condition is as follows:

1, understand classification and the structural attitude thereof of canted coil spring, have understanding clearly for its geometric parameter, then set up the geometric parameter equation of straight line canted coil spring and circular slanting coil spring.

1) the geometric parameter equation of straight line canted coil spring, as follows:

1.1) line model equation

$\left\{\begin{array}{c}x\left(t\right)=a\×\cos (360\×n\×t)\\ y\left(t\right)=b\×\sin (360\×n\×t)\\ z\left(t\right)=l\×t+c\×\sin (360\×n\×t)\end{array}---\left(1\right)\right.$

In formula, a, b are respectively that canted coil spring cross section is two oval length semiaxis, and a>b, represents that xsect is circular section if a, b are identical; L is the length of linear state lower spring; C is for adjustable inclination, i.e. gradient, and in the time that c value is zero, straight line canted coil spring is for just enclosing volute spring; N is the number of turns of canted coil spring, gets positive integer; T is a continually varying parameter between 0 and 1.

1.2) solid model equation

Spring wire cross sectional dimensions is taken into account, under rectangular coordinate system, is set up the parametric equation of following single-coil spring taking the starting point of spring as true origin:

$\left\{\begin{array}{c}x\left(t\right)=(r_x-r_{\mathrm{\ω}})\sin \left(2\mathrm{\π\ωt}\right)\\ y\left(t\right)=(r_y-r_{\mathrm{\ω}})(1-\cos \left(2\mathrm{\π\ωt}\right))\\ z\left(t\right)=t+c/2(1-\cos \left(2\mathrm{\π\ωt}\right))\end{array}\right.---\left(2\right)$

In formula, r _xrepresent that 1/2 circle is wide; r _yrepresent that 1/2 circle is high; r _ωrepresent the radius of spring silk xsect; Obviously (r _x-r _ω) corresponding to a in above formula (1), (r _y-r _ω) corresponding to the b in formula (1); ω represents the number of turns in unit length, its pitch that represents reciprocal; C represents the width that inclines, and encloses the distance that withstands on axial dipole field compared with positive coil spring; T is parametric variable, that the angle here adopts is radian (rad);

1.3) the solid model equation that contains inclination angle

The equation of the straight line canted coil spring of oval cross section

$s\left(t\right)=\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πt}\\ y\left(t\right)=\mathrm{Pt}-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\πt}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πt}\end{array}\right.---\left(3\right)$

Its parameters and inclination angle as shown in Fig. 1 a and Fig. 1 b, t ∈ [0, n], P represents pitch; CA is the angle of figure intermediate cam shape base center line and vertical line, in the time that CA gets zero, represents the positive coil spring of straight line; CW is wide for enclosing; CH is high for enclosing; WD is wire diameter; FA represents top rake, and BA represents back rake angle.

2) the geometric parameter equation of circular slanting coil spring, as follows:

2.1) parametric equation of canted coil spring radially

2.1.1) under circular cylindrical coordinate, set up radially canted coil spring equation:

$\left\{\begin{array}{c}r=r_0+a\×\cos (360\×n\×t)\\ \mathrm{\θ}=360\×t+c\×\cos (360\×n\×t)\\ z=b\×\sin (360\×n\×t)\end{array}\right.---\left(4\right)$

In formula, a, b are respectively length semiaxis, the parameter that c is adjustable inclination, and n is the number of turns, r ₀centered by distance, t is a continually varying parameter between 0 and 1.

2.1.2) under rectangular coordinate, set up radially canted coil spring equation

2.1.2.1) radially canted coil spring of clockwise direction:

$\begin{array}{c}{h}_{\mathrm{radial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(0,u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{C\; A}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(5\right)$

2.1.2.2) radially canted coil spring of counter clockwise direction:

$\begin{array}{c}{h}_{\mathrm{radial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(\mathrm{\π},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(6\right)$

2.2) the axial parametric equation of canted coil spring

2.2.1) clockwise axial canted coil spring:

$\begin{array}{c}{h}_{\mathrm{axial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\cos 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(7\right)$

2.2.2) anticlockwise axial canted coil spring

$\begin{array}{c}{h}_{\mathrm{axial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(-\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\cos 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(8\right)$

In formula (5), (6), (7), (8), n is the number of turns, r ₀centered by distance, t is a continually varying parameter between 0 and 1, R for circle footpath, CA is the angle of triangle base center line and vertical line, CW for circle wide, CH for enclose high, WD is wire diameter.

2, for geometric parameter equation, adopt PRO/E software to set up the geometric model of canted coil spring, as shown in Fig. 2 a, 2b, 2c, and select IGS form to import to and in finite element software ANSYS, carry out numerical simulation, the load-displacement curve of canted coil spring before work reaches doubling-up when adjusted its various geometric parameter, and by changing parameter, draw the impact of each geometric parameter on this load-displacement curve.Its concrete condition is as follows:

Carry out numerical simulation in finite element software ANSYS time, what adopt is beam element BEAM44 simulation, beam element BEAM44 be a kind of have bear draw, press, the three-dimensional single shaft beam element of torsion and crooking ability, the each node in unit has six-freedom degree: the axially movable rotation of the translation of x, y, z direction and x, y, z, this unit allows to have asymmetric end face structure, and allow end face node to depart from cross section position of form center, in addition spring material is beryllium-bronze, getting elastic modulus is 1.3e5MPa, and Poisson ratio is 0.32.

For straight line canted coil spring, the boundary condition of employing is: a free end of spring applies axially, i.e. Z direction displacement constraint, and the lower end of spring applies X, the displacement of Y both direction, displacement is zero; The upper end of spring applies X, the displacement of Y both direction, and wherein directions X displacement is zero, the displacement of Y-direction, according to simulation changes in demand, applies different displacement load.

For canted coil spring radially, the boundary condition of employing is: utilize outer ring all fixing; Inner ring hoop is removable, axial restraint, and radial loaded has been analyzed whole model, and when simulation, still choosing canted coil spring wire diameter is 1.53mm (except while changing wire diameter parameter).

For axial canted coil spring, the boundary condition of employing is: circle top is radially fixing, axially applies displacement load, and hoop is removable; Circle bottom is all fixing; Sample elastic modulus is got 1.3e5MPa, and Poisson ratio gets 0.32.

For straight line canted coil spring, adopt and regulate the amplitude of inclining, the constant increase number of turns of pitch, change pitch, regulate major semi-axis, regulate minor semi-axis and regulate the mode of wire diameter to carry out parameter study.If obtain desirable unit support reaction, can mainly regulate the parameters such as wire diameter, pitch; If control the corresponding change in displacement of platform interval well, can mainly regulate the parameters such as width of inclining.

For circular slanting coil spring, adopt and regulate minor axis, regulate major axis, regulate wire diameter, regulate the mode of angle of inclination and adjusting joint distance to carry out parameter study.By comparison, the impact of same geometric parameter is consistent on the impact of dissimilar canted coil spring mechanical property.

Impact by each geometric parameter on load-displacement curve, derives the relation between geometric parameter through result of finite element, can obtain the experimental formula of following relevant canted coil spring parameter:

c＝λb?λ∈[0.45～0.53]

In formula, c is the width that inclines, and encloses the distance that withstands on axial dipole field compared with positive coil spring; B is the minor semi-axis of canted coil spring, encloses high.As can be seen from the above equation, can draw as long as provide the value of minor semi-axis b the width c value of inclining.Generally, in actual production, the length semiaxis of canted coil spring (or it is high to be called the wide circle of circle) is known, so can calculate the span of c by above formula.In this span, choose arbitrarily the complete geometric equation that a value just can obtain a canted coil spring.

By the impact research discovery of various parameters, the impact at angle of inclination is maximum.The change at angle of inclination not only changes the resemblance of canted coil spring, and its load-displacement curve form also changes a lot.Find by calculating above, the angle general control of hoop canted coil spring is comparatively desirable between 20-25 degree.

3, due to the special load-displacement curve of canted coil spring, if adopt load controlled loading more difficult, so locate to adopt MTS831.10Elastomer Test System testing machine to apply displacement load to straight line canted coil spring sample to be measured along short-axis direction, as shown in Figure 3 a, loading speed is 1mm/min, and maintains one minute after often applying one minute.The spring of having got two kinds of different sizes when test, design parameter is as shown in table 1 below.

Table 1

The sample of each specification carries out three same experiments, obtains the load-displacement curve of sample, as shown in Fig. 4 a and Fig. 4 b.

In addition, in order to analyze the mechanical property of circular slanting coil spring, sample is carried out on MTS to quasistatic compression experiment, apply displacement load along short-axis direction, as shown in Figure 3 b, loading speed is 0.2mm/min, and every loading stops half a minute for one minute, obtain the load-displacement curve of sample, as shown in Figure 5.When test, the concrete specification of the test specimen of circular slanting coil spring is as shown in table 2 below.

Table 2

Minor axis	Major axis	Inclination angle	Central diameter	The number of turns	Wire diameter
						4.2mm	4.8mm	20°	17mm	96	0.76mm

4, result of finite element and experimental results are contrasted, as shown in Fig. 6 a and Fig. 6 b.As can be seen from the figure, result of finite element and experimental result are comparatively identical, also just illustrated that the geometric parameter equation of setting up possesses theoretic feasibility for the description of canted coil spring, also illustrated that the simplification of boundary condition in FEM (finite element) calculation process is relatively reasonable, thereby verified the rationality of FEM (finite element) calculation simultaneously.

The above examples of implementation, only for preferred embodiment of the present invention, not limits practical range of the present invention with this, therefore the variation that all shapes according to the present invention, principle are done all should be encompassed in protection scope of the present invention.

Claims (6)

1. a canted coil spring mechanic property test method, is characterized in that: first, set up the geometric parameter equation of straight line canted coil spring and circular slanting coil spring; Secondly, draw the geometric model of all kinds of canted coil springs by geometric parameter equation, and import to and in finite element software ANSYS, carry out numerical simulation, the load-displacement curve of canted coil spring before work reaches doubling-up when adjusted its various geometric parameter, and by changing parameter, draw the impact of each geometric parameter on this load-displacement curve, derive the relation between geometric parameter by result of finite element, be experimental formula, obtain straight line canted coil spring and the load-displacement curve of circular slanting coil spring in real work by sample experiment test simultaneously; Finally, result of finite element and experimental results are contrasted, to verify the rationality of FEM (finite element) calculation, thus the feasibility of checking geometric parameter equation.

2. a kind of canted coil spring mechanic property test method according to claim 1, is characterized in that, the geometric parameter equation of the straight line canted coil spring of foundation is as follows:

1) line model equation

$\left\{\begin{array}{c}x\left(t\right)=a\×\cos (360\×n\×t)\\ y\left(t\right)=b\×\sin (360\×n\×t)\\ z\left(t\right)=l\×t+c\×\sin (360\×n\×t)\end{array}---\left(1\right)\right.$

In formula, a, b are respectively that canted coil spring cross section is two oval length semiaxis, and a > b, represents that xsect is circular section if a, b are identical; L is the length of linear state lower spring; C is for adjustable inclination, i.e. gradient, and in the time that c value is zero, straight line canted coil spring is for just enclosing volute spring; N is the number of turns of canted coil spring, gets positive integer; T is a continually varying parameter between 0 and 1;

2) solid model equation

Spring wire cross sectional dimensions is taken into account, under rectangular coordinate system, is set up the parametric equation of following single-coil spring taking the starting point of spring as true origin:

$\left\{\begin{array}{c}x\left(t\right)=(r_x-r_{\mathrm{\ω}})\sin \left(2\mathrm{\π\ωt}\right)\\ y\left(t\right)=(r_y-r_{\mathrm{\ω}})(1-\cos \left(2\mathrm{\π\ωt}\right))\\ z\left(t\right)=t+c/2(1-\cos \left(2\mathrm{\π\ωt}\right))\end{array}\right.---\left(2\right)$

In formula, r _xrepresent that 1/2 circle is wide; r _yrepresent that 1/2 circle is high; r _ωrepresent the radius of spring silk xsect; Obviously (r _x-r _ω) corresponding to a in above formula (1), (r _y-r _ω) corresponding to the b in formula (1); ω represents the number of turns in unit length, its pitch that represents reciprocal; C represents the width that inclines, and encloses the distance that withstands on axial dipole field compared with positive coil spring; T is parametric variable, what the angle here adopted is radian;

3) the solid model equation that contains inclination angle

The equation of the straight line canted coil spring of oval cross section

$s\left(t\right)=\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πt}\\ y\left(t\right)=\mathrm{Pt}-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\πt}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πt}\end{array}\right.---\left(3\right)$

In formula, t ∈ [0, n], p represents pitch; CA is the angle of triangle base center line and vertical line, in the time that CA gets zero, represents the positive coil spring of straight line; CW is wide for enclosing; CH is high for enclosing; WD is wire diameter.

3. a kind of canted coil spring mechanic property test method according to claim 1, is characterized in that, the geometric parameter equation of the circular slanting coil spring of foundation is as follows:

1) parametric equation of canted coil spring radially

1.1) under circular cylindrical coordinate, set up radially canted coil spring equation:

$\left\{\begin{array}{c}r=r_0+a\×\cos (360\×n\×t)\\ \mathrm{\θ}=360\×t+c\×\cos (360\×n\×t)\\ z=b\×\sin (360\×n\×t)\end{array}\right.---\left(4\right)$

In formula, a, b are respectively length semiaxis, the parameter that c is adjustable inclination, and n is the number of turns, r ₀centered by distance, t is a continually varying parameter between 0 and 1;

1.2) under rectangular coordinate, set up radially canted coil spring equation

1.2.1) radially canted coil spring of clockwise direction:

$\begin{array}{c}{h}_{\mathrm{radial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(0,u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{C\; A}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(5\right)$

1.2.2) radially canted coil spring of counter clockwise direction:

$\begin{array}{c}{h}_{\mathrm{radial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(\mathrm{\π},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\cos 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(6\right)$

2) parametric equation of axial canted coil spring

2.1) clockwise axial canted coil spring:

$\begin{array}{c}{h}_{\mathrm{axial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\cos 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(7\right)$

2.2) anticlockwise axial canted coil spring

$\begin{array}{c}{h}_{\mathrm{axial}}\left(t\right)=\mathrm{Rot}(\mathrm{\θ},u_x)\·[\mathrm{Rot}(-\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\cos 2\mathrm{\πnt}\\ y\left(t\right)=-\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\cos 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\sin 2\mathrm{\πn}\\ z\left(t\right)=\frac{1}{2}(\mathrm{CW}-\mathrm{WD})\sin \left(\mathrm{CA}\right)\cos 2\mathrm{\π}\mathrm{nt}\sin 2\mathrm{\πn}+[-\frac{1}{2}(\mathrm{CH}-\mathrm{WD})\sin 2\mathrm{\πnt}+R]\cos 2\mathrm{\πn}\end{array}\right.\end{array}---\left(8\right)$

In formula (5), (6), (7), (8), n is the number of turns, r ₀centered by distance, t is a continually varying parameter between 0 and 1, R for circle footpath, CA is the angle of triangle base center line and vertical line, CW for circle wide, CH for enclose high, WD is wire diameter.

4. a kind of canted coil spring mechanic property test method according to claim 1, it is characterized in that: carry out numerical simulation in finite element software ANSYS time, what adopt is beam element BEAM44 simulation, described beam element BEAM44 is that one has to bear and draws, press, the three-dimensional single shaft beam element of torsion and crooking ability, the each node in unit has six-freedom degree: x, y, the translation of z direction and x, y, the axially movable rotation of z, this unit allows to have asymmetric end face structure, and allow end face node to depart from cross section position of form center, in addition spring material is beryllium-bronze, getting elastic modulus is 1.3e5MPa, Poisson ratio is 0.32,

For straight line canted coil spring, the boundary condition of employing is: a free end of spring applies axially, i.e. Z direction displacement constraint, and the lower end of spring applies X, the displacement of Y both direction, displacement is zero; The upper end of spring applies X, the displacement of Y both direction, and wherein directions X displacement is zero, the displacement of Y-direction, according to simulation changes in demand, applies different displacement load;

For the radially canted coil spring in circular slanting coil spring, the boundary condition of employing is: utilize outer ring all fixing; Inner ring hoop is removable, axial restraint, and radial loaded has been analyzed whole model;

For the axial canted coil spring in circular slanting coil spring, the boundary condition of employing is: circle top is radially fixing, axially applies displacement load, and hoop is removable; Circle bottom is all fixing; Sample elastic modulus is got 1.3e5MPa, and Poisson ratio gets 0.32;

Impact by each geometric parameter on load-displacement curve, derives the relation between geometric parameter through result of finite element, can obtain the experimental formula of following relevant canted coil spring parameter:

c＝λb?λ∈[0.45～0.53]

In formula, c is the width that inclines, and encloses the distance that withstands on axial dipole field compared with positive coil spring; B is the minor semi-axis of canted coil spring, encloses high.

5. a kind of canted coil spring mechanic property test method according to claim 1, it is characterized in that: in the time carrying out sample experiment test, sample is carried out on MTS testing machine to quasistatic compression test, to spring-like product load application to be measured, draw the relation curve of the load-displacement of spring in real work by MTS testing machine.

6. a kind of canted coil spring mechanic property test method according to claim 1, is characterized in that: adopt PRO/E software to set up the geometric model of canted coil spring, and select IGS form to export to and in finite element software ANSYS, carry out finite element analysis.