A kind of Cycloid tooth profile profiling quantity optimization method based on matlab
Technical field
The present invention relates to the design and manufacture art field of Cycloidal Wheel, particularly relate to a kind of Cycloid tooth profile profiling quantity optimization method based on matlab.
Background technology
Planet cycloid speed reducer is a kind of application Gear Planet Transmission principle, adopts the reducing gear of cycloidal pin teeth engagement.Due to the distinct advantages of its advanced design, novel structure, obtain increasingly extensive application at aspects such as military project, space flight, metallurgy and lifting transportations.
Cycloidal pinion engaged pair is the core parts of planet cycloid speed reducer.Cycloid pair belongs to the poor internal gear group of a tooth, and the theoretic flank profil of gripping does not altogether have radial play, and the number of its meshing point equals the pinwheel number of teeth all the time, and its action line is a symmetrical closed curve.When practical application cycloid pinwheel planetary gear transmission system, in order to compensate foozle, be convenient to mounting or dismounting and guarantee lubricate, between cycloidal gear teeth and pinwheel tooth, must have back lash.Therefore, actual Cycloidal Wheel must be carried out correction of the flank shape, and rationally, correction of the flank shape is accurately to realize the important guarantee that cycloidal gear teeth transmission capacity is strong, operate steadily.
In current production practices, the correction of the flank shape of Cycloid tooth profile generally adopts and equidistantly adds the correction method that moves distance, and for equidistant, modification of moved distance amount, depends on workman's experience, needs validation trial.In theory, determining while equidistantly adding modification of moved distance amount, due to the method difference adopting, obtain a result also very not identical.Document [1] proposes by approaching modification of rotated angle cycloidal profile, obtains equidistantly adding modification of moved distance amount, and this kind of method just makes two kinds of profiles of tooth similar, and the normal direction gap of real decisions meshing quality is not etc., does not reach the requirement that improves meshing performance.Document [2] proposes transverse tooth thickness profiling quantity, and owing to not adopting optimum theory, result precision is low, does not reach request for utilization.Document [3] document [4] has provided application MATLAB Optimization Toolbox and has found the correction method equidistantly moving apart from best profiling quantity, but do not consider the position of engagement of Cycloidal Wheel, therefore, the profiling quantity of calculating can not be applied to actual production run, also can not think the best.
For the gear after processing, its general length that adopts common normal of testing is verified, in production engineering, conventionally need to draw cad figure, adopt the mode of approaching gradually to provide base tangent length.Document [5] proposes employing and asks transcendental equation to carry out, and easily occurs empty solution, loses solution phenomenon while still solving transcendental equation, and the length of common normal is also an approximate numerical value.
Above-mentioned document [1] to [5] is specially:
[1] Wang Qiucheng. the optimization [J] of the form of cycloidal gear tooth finishing. Zhejiang Polytechnic College journal, 1989,42 (1): 7-15.
[2] Zhang Lanyi, Qin Weiqian. the Primary Study [J] of cycloidal pinion engaged pair profile of tooth correction. Jilin Industry University journal, 1982, (4): 94-106.
[3] Jiao Wenrui, Kong Qinghua, Song Dechao etc., the optimal design [J] of Cycloid tooth profile correction of the flank shape. mechanical drive, 2009,33 (1): 41-43
[4] Jiao Wenrui, Kong Qinghua, Song Dechao etc., without the design [J] of tie-rod cycloidal pinion engaged pair profile modification. Tongji University's journal (natural science edition), 2010,38 (1): 108-112
[5] Xu Anping, wears a day tail, Qu Yuxia etc., and Cycloid tooth profile correction of the flank shape detection and base tangent length are calculated [J]. Hebei University of Technology's journal, 1997,26 (4): 56-59
Summary of the invention
Goal of the invention of the present invention is: for improving Cycloidal Wheel meshing quality, by analyzing the mathematical model of Cycloidal Wheel correction of the flank shape, propose a kind of MATLAB of application Optimization Toolbox the analytical approach that improves and optimizates Cycloid tooth profile.Try to achieve best correction of the flank shape angle by oil film thickness, and find the scope of optimum profiling quantity according to corner position in region of engagement, thereby draw best equidistant modification of moved distance flank profil; And then provide the Cycloid tooth profile profiling quantity optimization method based on matlab that a kind of computation period is short, transmission efficiency is high.
The technical scheme that the present invention takes for the technical matters existing in solution known technology is:
A Cycloid tooth profile profiling quantity optimization method based on matlab, comprises the steps:
Step 1, according to the corner position of the Parameter Calculation Cycloid tooth profile of Cycloidal Wheel;
Step 2, according to oil film thickness, calculate best correction of the flank shape angle in conjunction with corner position;
Step 3,, modification of moved distance amount optimum equidistantly according to the optimizational function calculating of matlab;
Step 4, obtain the inspection parameter of convenient check.
As preferred version, the present invention has also adopted following technical scheme:
Described step 1 is specially:
First select the basic parameter of Cycloidal Wheel, described basic parameter comprises: Cycloidal Wheel number of teeth zc, pinwheel number of teeth zp, eccentric throw a, garden, Zhen Chi center radius of curvature rp, pin gear sleeve exradius rrp;
Then calculate the position of Cycloidal Wheel flex point; Described flex point is the concave, convex separation of curve; The detailed process of described calculating Cycloidal Wheel flex point is: establish f (x) in (a, b) continuously, curve is to any two points x1 in (a, b), x2, perseverance has
$f\left(\frac{{x}_{1}+{x}_{2}}{2}\right)\≤\frac{f\left({x}_{1}\right)+f\left({x}_{2}\right)}{2}$ , this curve is concave curve; If perseverance has
$f\left(\frac{{x}_{1}+{x}_{2}}{2}\right)\≥\frac{f\left({x}_{1}\right)+f\left({x}_{2}\right)}{2},$ This curve is convex curve; For this Cycloid tooth profile curve, curvilinear equation is f (x), if there is 1 x
_{n}, make
$f\left({x}_{n-1}\right)<\frac{f\left({x}_{n}\right)+f\left({x}_{n-2}\right)}{2}$ And
$f\left({x}_{n+1}\right)>\frac{f\left({x}_{n}\right)+f\left({x}_{n+2}\right)}{2},$ X
_{n}point is Cycloid tooth profile point of inflexion on a curve.
Described step 2 is specially:
Calculate best correction of the flank shape angle: Cycloidal Wheel is in the time of modification of rotated angle, and the corner Δ δ of flank profil each several part is identical, and the variation L of normal orientation is directly proportional to arm of force size,
wherein,
for pivoted arm is with respect to the corner of a certain Zhen Chi center radius vector, i.e. writing a Chinese character in simplified form of phase angle of meshing, k
_{1}for curtate ratio, k
_{1}=az
_{p}/ r
_{p};
according to given oil film thickness L, i.e. normal direction variation, calculates best correction of the flank shape angle Δ δ thus, thereby determines modification of rotated angle tooth curve.
Described step 3 is specially:
First determine the objective function that contains modification of equidistance amount Δ rrp and modification of moved distance amount Δ rp: according to tooth curve L1 after equidistant, modification of moved distance (x,
_{i}y
_{i}) with modification of rotated angle after tooth curve L2 (x,
_{i}, y,
_{i}) the most identical principle, y is worked as in order
_{i}=y,
_{i}(i=1,2,3 ... m) time, x
_{i}with x,
_{i}(i=1,2,3 ... m), all have gap, the divergence indicator of curve L1 and curve L2 can be weighed with the mean value of m some absolute value of the bias,
when F (Δ rrp, Δ rp) value hour, two curves are the most identical, its objective function is for asking the minimum value of F (Δ rrp, Δ rp);
Then determine constraint condition: according to the meaning of parameters and relation, determine the constraint condition of optimized variable;
Δ rrp<0, Δ rp<0, Δ rrp-Δ rp >=Δ j, wherein Δ j be the minimum tooth root distance that prevents tooth face agglutination from.
Described step 4 is specially:
Adopt the majorized function Fmincon statement in matlab Optimization Toolbox, variable numerical value is optimized;
Normal distance when common normal refers to stride across n tooth between flank profil; The solution procedure of base tangent length, according to Cycloidal Wheel curvilinear equation based on the axisymmetric feature of x, based on actual measurement inspection method, if be even number across number of teeth n, in axisymmetric n/2 the Cycloidal Wheel of get-x direction of principal axis and x, peaked two times of Y coordinate is base tangent length; If peaked two times of Y coordinate is base tangent length in the Cycloidal Wheel of axisymmetric (n-1)/2 of while being odd number across number of teeth n, get+x direction of principal axis and x; When there is no common normal or when too large across the number of teeth, system reports an error.
Advantage and good effect that the present invention has are:
The present invention is by analyzing the mathematical model of Cycloidal Wheel correction of the flank shape, propose a kind of MATLAB of application Optimization Toolbox the analytical approach that improves and optimizates Cycloid tooth profile; Try to achieve best correction of the flank shape angle by oil film thickness, and find the scope of optimum profiling quantity according to corner position in region of engagement, thereby draw best equidistant modification of moved distance flank profil; Therefore greatly shortened the computation period of profile modification amount, guaranteed total number of teeth in engagement simultaneously simultaneously, thereby guaranteed the stability of transmission, transmission efficiency improves.
The present invention adopts and in matlab, optimizes statement objective function is optimized, and has overcome the defect by experience validation trial in traditional Cycloidal Wheel design process.
Accompanying drawing explanation
Fig. 1 is process flow diagram of the present invention.
Embodiment
For further understanding summary of the invention of the present invention, Characteristic, hereby exemplify following examples, and coordinate accompanying drawing to be described in detail as follows:
Refer to Fig. 1, a kind of Cycloid tooth profile profiling quantity optimization method based on matlab, comprises the steps:
Step 1, according to the corner position of the Parameter Calculation Cycloid tooth profile of Cycloidal Wheel; Detailed process is:
First select the basic parameter of Cycloidal Wheel, described basic parameter comprises: Cycloidal Wheel number of teeth zc, pinwheel number of teeth zp, eccentric throw a, garden, Zhen Chi center radius of curvature rp, pin gear sleeve exradius rrp;
Then calculate the position of Cycloidal Wheel flex point; Described flex point is the concave, convex separation of curve; The detailed process of described calculating Cycloidal Wheel flex point is: establish f (x) in (a, b) continuously, curve is to any two points x1 in (a, b), x2, perseverance has
$f\left(\frac{{x}_{1}+{x}_{2}}{2}\right)\≤\frac{f\left({x}_{1}\right)+f\left({x}_{2}\right)}{2}$ , this curve is concave curve; If perseverance has
$f\left(\frac{{x}_{1}+{x}_{2}}{2}\right)\≥\frac{f\left({x}_{1}\right)+f\left({x}_{2}\right)}{2},$ This curve is convex curve; For this Cycloid tooth profile curve, curvilinear equation is f (x), if there is 1 xn, makes
$f\left({x}_{n-1}\right)<\frac{f\left({x}_{n}\right)+f\left({x}_{n-2}\right)}{2}$ And
$f\left({x}_{n+1}\right)>\frac{f\left({x}_{n}\right)+f\left({x}_{n+2}\right)}{2}$ , xn point is Cycloid tooth profile point of inflexion on a curve.
Step 2, according to oil film thickness, calculate best correction of the flank shape angle in conjunction with corner position; Detailed process is:
Calculate best correction of the flank shape angle: Cycloidal Wheel is in the time of modification of rotated angle, and the corner Δ δ of flank profil each several part is identical, and the variation L of normal orientation is directly proportional to arm of force size,
wherein,
for pivoted arm is with respect to the corner of a certain Zhen Chi center radius vector, i.e. writing a Chinese character in simplified form of phase angle of meshing, k
_{1}for curtate ratio, k
_{1}=az
_{p}/ r
_{p};
according to given oil film thickness L, i.e. normal direction variation, calculates best correction of the flank shape angle Δ δ thus, thereby determines modification of rotated angle tooth curve.
Step 3,, modification of moved distance amount optimum equidistantly according to the optimizational function calculating of matlab; Detailed process is:
First determine the objective function that contains modification of equidistance amount Δ rrp and modification of moved distance amount Δ rp: according to tooth curve L1 after equidistant, modification of moved distance (x,
_{i}y
_{i}) with modification of rotated angle after tooth curve L2 (x,
_{i}, y,
_{i}) the most identical principle, y is worked as in order
_{i}=y,
_{i}(i=1,2,3 ... m) time, x
_{i}with x,
_{i}(i=1,2,3 ... m), all have gap, the divergence indicator of curve L1 and curve L2 can be weighed with the mean value of m some absolute value of the bias,
when F (Δ rrp, Δ rp) value hour, two curves are the most identical, its objective function is for asking the minimum value of F (Δ rrp, Δ rp);
Then determine constraint condition: according to the meaning of parameters and relation, determine the constraint condition of optimized variable;
Δ rrp<0, Δ rp<0, Δ rrp-Δ rp >=Δ j, wherein Δ j be the minimum tooth root distance that prevents tooth face agglutination from.
Step 4, obtain the inspection parameter of convenient check.Detailed process is:
Adopt the majorized function Fmincon statement in matlab Optimization Toolbox, variable numerical value is optimized;
Normal distance when common normal refers to stride across n tooth between flank profil; The solution procedure of base tangent length, according to Cycloidal Wheel curvilinear equation based on the axisymmetric feature of x, based on actual measurement inspection method, if be even number across number of teeth n, in axisymmetric n/2 the Cycloidal Wheel of get-x direction of principal axis and x, peaked two times of Y coordinate is base tangent length; If peaked two times of Y coordinate is base tangent length in the Cycloidal Wheel of axisymmetric (n-1)/2 of while being odd number across number of teeth n, get+x direction of principal axis and x; When there is no common normal or when too large across the number of teeth, system reports an error.
Below in conjunction with concrete parameter, take Bai Li TianXing, the Tianjin 320s of transmission company limited be series products as example,
S1, input basic parameter: rp=114.5, rrp=5, Zp=40, a=2.2;
S2, the position of calculating Cycloid tooth profile knee point, for the calculating of objective function;
S3, rule of thumb give fixed oil film thickness, i.e. the normal direction variation L=0.015mm of Cycloidal Wheel, obtains best correction of the flank shape angle Δ δ,
For the calculating of objective function;
S4, determine objective function: before and after flex point in the scope of each 10 °, modification of rotated angle curve with equidistant, modification of moved distance curve is the most approaching, objective function is
get its minimum value, being minF (Δ rrp, Δ rp) is objective function.
S5, determine constraint condition, i.e. Δ rrp<0, Δ rp<0, Δ rrp-Δ rp >=Δ j, wherein Δ j be the minimum tooth root distance that prevents tooth face agglutination from, in this example, rule of thumb determine Δ j=0.025mm.
S6, utilize the majorized function Fmincon statement in matlab, final optimization pass result, Δ rrp=-0.037, Δ rp=-0.062;
S7, inspection parameter: in the time being 15 teeth across the number of teeth, base tangent length is 202.975.Can also input other across the number of teeth, calculate the length of common normal.
Above-described embodiment interpretation of result:
Analyze through cad, while adopting this equidistant profiling quantity and modification of moved distance amount to carry out tooth curve correction of the flank shape to Cycloidal Wheel, the number of teeth that simultaneously participates in engagement is 10, reaches 1/4 of the whole Cycloidal Wheel number of teeth.
Traditional empirical value is Δ rrp=-0.02, Δ rp=-0.07; Now the number of teeth of engagement is 6 simultaneously.
Computation period is short, and whole optimizing process completes within the very short time; Can directly calculate inspection parameter.
Above embodiments of the invention are had been described in detail, but described content is only preferred embodiment of the present invention, can not be considered to for limiting practical range of the present invention.All equalizations of doing according to the present patent application scope change and improve, within all should still belonging to patent covering scope of the present invention.