The establishment of the coordinate system refers to the habit of gear meshing analysis. The following four coordinate systems are used in the tool and face gear machining process. The two fixed coordinate systems of the initial position of the tool S and the face gear 2 are: SS0-OSxS0yS0zS0 and S20. -O2x20y20z20; two moving coordinate systems SS-OSxSySzS and S2-O2x2y2z2 rotating together with the tool S and the face gear 2. Wherein, the coordinate origins OS and O2 are the intersections O of the two axes of the tool and the machined surface gear; zS0 and zS are the rotation axes of the tool; z20 and z2 are the rotation axes of the gears to be machined. Initially, yS0 coincides with z20, and xS0 coincides with x20. The angle between the coordinate axis zS0(zS) and z20(z2). Using s and 2 to indicate the angle at which the tool S and the machined surface gear 2 are rotated, respectively, there is a common basic conversion matrix between the following coordinate systems.
[MS0,S]=[MS,S0]T=cosS-sinS00sinScosS00010001(1)
1 Coordinate system for non-orthogonal face gear machining [M20, 2] = [M2, 20] T = cos2-sin200sin2cos200010001 (2)
[M20,S0]=[MS0,20]T=100cos-sin00sincos01(3)
In the above formulas, [MS0, S] represents the conversion from the coordinate system SS to the coordinate system SS0, and the rest can be analogized; the upper right corner T represents the transposition of the matrix.
At the same time, the following relationships can be obtained:
[M2,S0]=[MS0,2]T=[M2,20][M20,S0]=cos2cossin2-sinsin20-sin2coscos2-sincos20sincos01(4)
[M2,S]=[MS,2]T=[M2,S0][MS0,S]=cosScos2 cossinSsin2-sinScos2 coscosSsin2-sinsin20-cosSsin2 cossinScos2sinSsin2 coscosScos2-sincos20sinsinSsincosScos01(5)
2 Tool tooth surface equation 2 is the coordinate system used to represent the involute curve of the tool tooth surface, and corresponds to the coordinate system in 1 (zS is perpendicular to the paper surface), then the tool involute tooth surface vector r is easily obtained.
The equation is: r
S(uS,S)=[xSySzSt]T=rbS[sin(S0 S)-Scos(S0 S)]-rbS[cos(S0 S) Ssin(S0 S)]uS1(6)
2 In the parameter of the involute tooth surface, rbS is the base circle radius of the involute of the tool; uS is the axial direction (in the zS direction) of the point on the tooth surface of the tool; S is the angle parameter of the point on the involute of the tool. ; S0 is the angle parameter of the tool slot symmetry line to the starting point of the involute. uS and S are parameters of the involute tooth surface. The symbols in equation (6) correspond to the involutes on both sides of the tool slot - and! -! , S0 is determined by the following formula: S0=
In 2NS-invS(7), NS is the number of teeth of the tool; S is the tool pressure angle; invS is the involute function of the pressure angle S: invS=tanS- S(8) unit normal of the tooth surface of the tool n
S is: n
S=nSxnSynSz=r S|=cos(S0 S)-sin(s0 S)0(9)
3 The relative speed of the contact between the tooth surface of the tool and the gear of the machined surface is set to a point R (xS, yS, zS) on the tooth surface of the tool.
S is r
S=[xSy zS]T=xSiS ySjS zSkS(10)
Where i
S, jS and k
S is the unit vector of the SS coordinate axis. P point along with the speed of SS movement v
S is: v S=S(rS=SkS(r S(11)
Where S is the angular velocity at which the tool rotates. Speed ​​of point P along with S2 movement v
2 is: v 2= 2 (rS=2k2(r S(12)
In the formula, 2 is the angular velocity at which the surface gear is rotated. The relative velocity v (S, 2) of point P along with SS motion and S2 motion is:
v (S, 2) = v Sv 2 = (SkS-2k2) (rS (13)
The following relationship is given by equation (5): k
2=sinsinSiS sincosSjS coskS(14)
It is also assumed that the number of teeth of the tool and the face gear are NS and N2, respectively, and the gear ratio is qS2 or q2S, then: qS2=N2NS=S2=1q2S(15)
Substituting equations (14) and (15) into equation (13) yields v S,2=v(S,2)xv(S,2)yv(S,2)z=S-yS q2S(yScos-zSsincosS )xS q2S(-xScos zSsinsinS)q2Ssin(xScosS-ySsinS)(16)
4 The tooth surface equation of the non-orthogonal face gear is known from the gear meshing principle. The meshing condition of the two gear tooth faces is: n(v (S, 2) = 0 (17)
Substituting equations (9) and (16) into the above equation, the meshing equation between the tool and the machined surface gear can be obtained: f(uS, S, S)=rbS(1-q2Scos)-uSq2Ssincos=0(18) , =S(S0 S).
From the coordinate relationship between the coordinate system SS and the coordinate system S2 (5), the tooth surface equation of the machined surface gear is: r
2(uS,S,S)=[M2,S]r
S(uS,S)f(uS,S,S)=0(19) is obtained from equation (18): zS=uS=rbS(1-q2Scos)q2Ssincos(20) Substituting equations (5) and (20) The first formula in equation (19), and let A = sin0ScosB = cosSsinC = 1 - q2Scosq2Scos95r2 (S, S) = x2y2z2t = rbS (Acos2-Bcossin2-Csin2) - rbS (Asin2 Bcoscos2 Ccos2) - rbS (Bsin-Ccot In the formula 1 (21), 2 = q2SS.
In order to facilitate the simulation in Matlab, the surface gear equation is expressed in the coordinate system shown in 3. That is: rt(S,S)=[Mt,2]r2(S,S)(22)
In the formula [Mt, 2] represents the transformation matrix from the coordinate system S2 to St, ie: [Mt, 2] = 10cossinrSm0-sincosrSmcot01 (23)
Where rSm is the distance between the face gear tip and the tool. Equation (22) can be further written as: r
(S,S)=xtytzt=x2y2cos z2sin rSm-y2sin z2cos rSmcot1=rbS(Acos2-Bcossin2-Crsin2)-rbScos[Asin2 Bcos(cos2 tan2) C(cos2-1)] rSmrbSsin[Asin2 Bcos(cos2-1) C (cos2 cot2)] rSmcot1(24)
The other coordinate system of the 3 face gear tooth surface 5 Matlab simulates the real tooth surface before the tooth surface of the face gear is generated. First, the basic parameters of the face gear, ie the number of teeth z, the modulus m, the angle of the axis, the pressure angle, etc., are determined. Then use MATLAB programming to calculate the maximum outer diameter Rmax and the minimum inner diameter Rmin of the face gear. From equation (21), the equation of the face gear tooth surface is an equation containing two parameters of s and s. The generation of the tooth surface can be divided into the following four steps: 1) Let y2 = c (c is a constant) can obtain the relationship equation s=f(s) between s and s; 2) Find the range of s according to the meshing condition, Take n discrete values ​​to obtain the corresponding n s values; 3) substitute the corresponding s and s values ​​into the tooth surface equation of the face gear to obtain the coordinates of n discrete points, which can be Synthesize a curve; 4) Take different y2 values ​​to obtain m curves, through which the tooth surface of the face gear can be fitted.
The tooth surface of the face gear has a tooth root transition surface in addition to the working tooth surface, and the tooth root transition surface is formed by the intersection of the tool tip circle and the tooth profile. The equation form and the generation process are similar to the working tooth surface and can be obtained in the same way. Combine the working flank with the transition surface to obtain a one-sided flank of the complete face gear.
6Pro/E non-orthogonal face gear model is drawn in MATLAB to calculate the discrete coordinate points of the face gear flank and output it to a suffix named. Txt file, then change its suffix name. Ib,l to form the data point files needed to model in Pro/E. The calculated discrete coordinate points can form a curve li in Pro/E. The specific steps are: insert the model reference curve from the file, select the default coordinate system, and select the desired one. For ibl files, you can get 3 splines through these points. Change the value of i to get different y2 values, and use the same method to get other curves. Finally, these curves form a tooth surface of one tooth of the face gear. The specific steps are: insert the curved surface from the spline curve, select the curve that has been formed one by one, and keep the default setting after the point is selected to obtain the face gear. One tooth face and the other tooth face can be obtained by mirroring.
According to the principle of face gear shaping, the face gear teeth are plane along the axial direction (ie, the upper and lower bottom surfaces), and the front and rear sides (ie, the faces near the inner and outer diameters of the face gear) are cylindrical surfaces. It is easy to form one tooth of the face gear, and then copy it in the circumferential direction to obtain all the teeth of the face gear. Finally, a hollow cylinder is formed according to the inner and outer diameters of the face gear as the unmachined face gear. In part, the height depends on the height of the face gear blank. Combining the two can obtain the geometric model of the required non-orthogonal face gear teeth, and finally form the geometric model of the non-orthogonal face gear.
A non-orthogonal face gear model with a cross-angle of 100) is given by (c) as shown in FIG.
7 Summary Through the derivation of the tooth surface equation of the non-orthogonal surface gear, and the preparation of the relevant program, the non-orthogonal surface gear tooth surface model of the relevant parameters is simulated and simulated. And through the introduction of the relevant data points generated by the program into Pro/E, the establishment of the entire non-orthogonal surface gear model is completed. In order to prepare for the strength analysis and dynamic characteristics analysis of non-orthogonal face gears in the future.
Mobile Concrete Batching Plant
This product(concrete batching plant) is equipped with the storage, batching, conveying, stirring, control and other devices of various raw materials required for precast concrete, and various aggregates, powders, admixtures, water, etc. A complete set of equipment for supplying concrete in a concentrated manner than by a mixer.
Features of concrete batching plant
1.The overall steel structure of the mixing station is made of high-quality steel, which has high overall structural strength and strong stability.
2.The mixing machine adopts the twin-shaft forced mixing main machine, which has strong mixing performance, uniform mixing and high productivity.
3.Excellent pneumatic components, electrical components, etc.; to ensure the reliability of the equipment, accurate metering performance.
4.Each maintenance and repair site is provided with a walking platform or a check ladder, and has sufficient operation space. Easy maintenance and repair
Mobile Concrete Batching Plant,Yhzs25 Mobile Concrete Mixing Plant,Yhzs50 Mobile Concrete Mixing Plant,Yhzs75 Mobile Concrete Mixing Plant
Shandong Zeyu Heavy Industry Science and Technology Co.,Ltd. , https://www.sdstabilizedsoilmixingplant.com