CN103954494B - A kind of canted coil spring mechanic property test method - Google Patents

Abstract

The invention discloses 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, the geometric model of all kinds of canted coil spring is drawn by geometric parameter equation, and import in FEM-software ANSYS and carry out numerical simulation, the load-displacement curve of canted coil spring before work reaches doubling-up during its various geometric parameter adjusted, and by changing parameter, draw the impact of each geometric parameter on this load-displacement curve, obtain straight line canted coil spring and the load-displacement curve of circular slanting coil spring in real work by sample experiments 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 present invention proposes the Production design prioritization scheme of canted coil spring with result of finite element by experiment, has innovative significance, is with a wide range of applications.

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 due to its coil dimension little, quantity is many, has very high through-current capability and good Technical Economy, thus 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 structure simplifies in actual applications, easy for installation, 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 contact substantially constant comparatively greatly, weares and teares little, life cycle is long, fluting size is simple and easy to processing, and specification series, can join 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., domestic also do not have ripe production technology at present, but due to external technical monopoly, limit the prodution and development of this product in China, domestic Counterfeit Item causes in performance, there is larger gap compared with imported product due to technology or technological problems, be only 1/10 of same kind of products at abroad serviceable life, because this product is one of vital part of primary cut-out, the market demand is most of dependence on import greatly.Domestic existing portion of techniques personnel possess some special knowledge to the design of this canted coil spring, 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 be subject in the space geometry characteristic parameters such as angle of inclination and its course of work is closely related, thus the life-span that it uses is had a certain impact, therefore research and development have the canted coil spring production technology of independent intellectual property right and technology has great society and economic worth, also be a urgent task, spring is the element of stressed more complicated in mechanical component simultaneously, launches research also possess higher theory value to it.

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 being provided, directly providing 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, sets up the geometric parameter equation of straight line canted coil spring and circular slanting coil spring; Secondly, the geometric model of all kinds of canted coil spring is drawn by geometric parameter equation, and import in FEM-software ANSYS and carry out numerical simulation, the load-displacement curve of canted coil spring before work reaches doubling-up during its various geometric parameter adjusted, and by changing parameter, draw the impact of each geometric parameter on this load-displacement curve, the relation between geometric parameter is derived by result of calculation, i.e. experimental formula, obtains straight line canted coil spring and the load-displacement curve of circular slanting coil spring in real work by sample experiments 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 set 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 canted coil spring cross section is respectively two oval length semiaxis, a>b, if a, b are identical namely represent that xsect is circular section; L is the length of linear state lower spring; C is used to adjustable inclination, i.e. gradient, and when c value is zero, straight line canted coil spring is for just to enclose volute spring; N is the number of turns of canted coil spring, gets positive integer; T is a continually varying parameter between zero and one;

2) solid model equation

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

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

In formula, r _xrepresent 1/2 circle wide; r _yrepresent 1/2 circle 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 expression pitch reciprocal; C represents the width that inclines, and namely encloses the distance withstanding on axial dipole field compared with positive coil spring; T is parametric variable, what angle here adopted is radian;

3) the solid model equation containing 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, when 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 set up, as follows:

1) parametric equation of radial canted coil spring

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

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

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

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

1.2.1) the radial 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) the radial 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 zero and one, 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.

When carrying out numerical simulation in FEM-software ANSYS, what adopt is that beam element BEAM44 simulates, described beam element BEAM44 be a kind of have to bear draw, press, reverse and the three-dimensional single shaft beam element of crooking ability, the each node of unit has six-freedom degree: the rotation that the translation in x, y, z direction and x, y, z move axially, this unit allows to have asymmetric end face structure, and allow end face node to depart from cross-section centroid position, 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 the displacement of X, Y both direction, and displacement is zero; The upper end of spring applies the displacement of X, Y both direction, and wherein X-direction displacement is zero, and the displacement of Y-direction, according to simulation changes in demand, namely applies different displacement load;

For the radial canted coil spring in circular slanting coil spring, the boundary condition of employing is: utilize outer ring all to fix; Inner ring hoop is removable, axial restraint, and radial loaded analyzes whole model;

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

By the impact of each geometric parameter on load-displacement curve, derive the relation between geometric parameter through result of finite element, the experimental formula of following relevant canted coil spring parameter can be obtained:

c＝λbλ∈[0.45～0.53]

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

When carrying out sample experiments test, sample being carried out quasistatic compression test on MTS testing machine, by MTS testing machine to spring-like product load application to be measured, draws the relation curve of the load-displacement of spring in real work.

Adopt PRO/E software to set up the geometric model of canted coil spring, and select IGS form to export in FEM-software ANSYS to 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 that experiment and finite element result contrast, rationally establish the geometric parameter equation of canted coil spring, and utilize finite element to analyze each geometric parameter, obtain the Effect on Mechanical Properties of parameters to canted coil spring;

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

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

Accompanying drawing explanation

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

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

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

Fig. 2 b is the geometric model figure of radial 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, its geometric parameter is had and is familiar with clearly, 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 canted coil spring cross section is respectively two oval length semiaxis, a>b, if a, b are identical namely represent that xsect is circular section; L is the length of linear state lower spring; C is used to adjustable inclination, i.e. gradient, and when c value is zero, straight line canted coil spring is for just to enclose volute spring; N is the number of turns of canted coil spring, gets positive integer; T is a continually varying parameter between zero and one.

1.2) solid model equation

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

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

In formula, r _xrepresent 1/2 circle wide; r _yrepresent 1/2 circle 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 expression pitch reciprocal; C represents the width that inclines, and namely encloses the distance withstanding on axial dipole field compared with positive coil spring; T is parametric variable, that angle here adopts is radian (rad);

1.3) the solid model equation containing 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 illustrated in figs. ia and ib, t ∈ [0, n], P represents pitch; CA is the angle of figure intermediate cam shape base center line and vertical line, when 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 radial canted coil spring

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

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

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

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

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

When carrying out numerical simulation in FEM-software ANSYS, what adopt is that beam element BEAM44 simulates, beam element BEAM44 be a kind of have to bear draw, press, reverse and the three-dimensional single shaft beam element of crooking ability, the each node of unit has six-freedom degree: the rotation that the translation in x, y, z direction and x, y, z move axially, this unit allows to have asymmetric end face structure, and allow end face node to depart from cross-section centroid position, 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 the displacement of X, Y both direction, and displacement is zero; The upper end of spring applies the displacement of X, Y both direction, and wherein X-direction displacement is zero, and the displacement of Y-direction, according to simulation changes in demand, namely applies different displacement load.

For radial canted coil spring, the boundary condition of employing is: utilize outer ring all to fix; Inner ring hoop is removable, axial restraint, and radial loaded analyzes whole model, and still choosing canted coil spring wire diameter during simulation is 1.53mm (except during change wire diameter parameter).

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

For straight line canted coil spring, adopt and regulate 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.To obtain desirable unit support reaction, mainly wire diameter can be regulated, the parameters such as pitch; To control well, the corresponding change in displacement of platform is interval, mainly can 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 angle of inclination and regulate the mode of pitch to carry out parameter study.By comparison, the impact of impact on dissimilar canted coil spring mechanical property of same geometric parameter is consistent.

By the impact of each geometric parameter on load-displacement curve, derive the relation between geometric parameter through result of finite element, the experimental formula of following relevant canted coil spring parameter can be obtained:

c＝λbλ∈[0.45～0.53]

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

Found by the influence research of various parameter, 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.Found by calculating above, the angle general control of hoop canted coil spring is ideal between 20-25 degree.

3, due to the special load-displacement curve of canted coil spring, more difficult according to load controlled loading, so place adopts MTS831.10ElastomerTestSystem 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 often applies to maintain one minute after one minute.Got the spring of two kinds of different sizes during 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 figures 4 a and 4b.

In addition, in order to analyze the mechanical property of circular slanting coil spring, sample is carried out quasistatic compression experiment on MTS, displacement load is applied along short-axis direction, as shown in Figure 3 b, loading speed is 0.2mm/min, and often loading stops half a minute in one minute, obtain the load-displacement curve of sample, as shown in Figure 5.During 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 figures 6 a and 6b.As can be seen from the figure, result of finite element and experimental result are comparatively identical, also the geometric parameter equation just describing foundation possesses theoretic feasibility for the description of canted coil spring, also illustrate that the simplification of boundary condition in FEM (finite element) calculation process is relatively reasonable simultaneously, thus demonstrate the rationality of FEM (finite element) calculation.

The above examples of implementation is only present pre-ferred embodiments, not limits practical range of the present invention with this, therefore the change that all shapes according to the present invention, principle are done, all should be encompassed in protection scope of the present invention.

Claims (4)

1. a canted coil spring mechanic property test method, is characterized in that: first, sets up the geometric parameter equation of straight line canted coil spring and circular slanting coil spring; Secondly, the geometric model of all kinds of canted coil spring is drawn by geometric parameter equation, and import in FEM-software ANSYS and carry out numerical simulation, the load-displacement curve of canted coil spring before work reaches doubling-up during its various geometric parameter adjusted, and by changing parameter, draw the impact of each geometric parameter on this load-displacement curve, the relation between geometric parameter is derived by result of finite element, i.e. experimental formula, obtains straight line canted coil spring and the load-displacement curve of circular slanting coil spring in real work by sample experiments 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; Wherein, the geometric parameter equation of the straight line canted coil spring of foundation, as follows:

1) line model equation

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

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

2) solid model equation

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

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

In formula, r _xrepresent 1/2 circle wide; r _yrepresent 1/2 circle 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 expression pitch reciprocal; C represents the width that inclines, and namely encloses the distance withstanding on axial dipole field compared with positive coil spring; T is parametric variable, what angle here adopted is radian;

3) the solid model equation containing inclination angle

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

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

In formula, t ∈ [0, n], p represents pitch; CA is the angle of triangle base center line and vertical line, when 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 set up, as follows:

1) parametric equation of radial canted coil spring

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

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

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

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

1.2.1) the radial canted coil spring of clockwise direction:

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

1.2.2) the radial canted coil spring of counter clockwise direction:

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

2.2) anticlockwise axial canted coil spring

$\begin{array}{c}{h}_{axial}\left(t\right)=Rot(\mathrm{\θ},u_x)\·\[Rot(-\frac{\mathrm{\π}}{2},u_y)e\left(t\right)+r_0\]\\ =\left\{\begin{array}{c}x\left(t\right)=\frac{1}{2}(CH-WD)\cos 2\mathrm{\π}nt\\ y\left(t\right)=-\frac{1}{2}(CW-WD)\sin \left(CA\right)\cos 2\mathrm{\π}nt\cos 2\mathrm{\π}n+\[-\frac{1}{2}(CW-WD)\sin 2\mathrm{\π}nt+R\]\sin 2\mathrm{\π}n\\ z\left(t\right)=\frac{1}{2}(CW-WD)\sin \left(CA\right)\cos 2\mathrm{\π}nt\sin 2\mathrm{\π}n+\[-\frac{1}{2}(CW-WD)\sin 2\mathrm{\π}nt+R\]\cos 2\mathrm{\π}n\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 zero and one, 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. a kind of canted coil spring mechanic property test method according to claim 1, it is characterized in that: when carrying out numerical simulation in FEM-software ANSYS, what adopt is that beam element BEAM44 simulates, described beam element BEAM44 is that one has to bear and draws, pressure, the three-dimensional single shaft beam element of torsion and crooking ability, the each node of unit has six-freedom degree: x, y, the translation in z direction and x, y, z-axis is to the rotation of movement, this unit allows to have asymmetric end face structure, and allow end face node to depart from cross-section centroid position, 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 the displacement of X, Y both direction, and displacement is zero; The upper end of spring applies the displacement of X, Y both direction, and wherein X-direction displacement is zero, and the displacement of Y-direction, according to simulation changes in demand, namely applies different displacement load;

For the radial canted coil spring in circular slanting coil spring, the boundary condition of employing is: utilize outer ring all to fix; Inner ring hoop is removable, axial restraint, and radial loaded analyzes whole model;

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

By the impact of each geometric parameter on load-displacement curve, derive the relation between geometric parameter through result of finite element, the experimental formula of following relevant canted coil spring parameter can be obtained:

c＝λbλ∈[0.45～0.53]

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

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

4. 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 selects IGS form to export in FEM-software ANSYS to carry out finite element analysis.