1 Three-dimensional modeling of involute gears in ANSYS environment In the ANSYS environment, cylindrical gear solid modeling can be achieved by one of the following methods:
(1) In the working coordinate system, the tooth blank is generated according to the known parameters of the gear, the new coordinate system is defined based on the end face of the tooth blank and the center thereof, and the cogging contour cutting entity is generated in the newly defined coordinate system, and then according to the tooth The circumferential array feature of the groove rotates the array of cogging contours to cut the entity and then applies Boolean subtraction (...
The >>Booleans>>subtract) operation generates all the slots.
(2) Generate a complete gear end face (planar) body and hub body based on known parameters, then stretch into a gear tooth entity, and then generate a rotation through rotation, entity fusion (Merge) or Boolean operation Gear entity.
(3) According to the known parameters, a fan-shaped entity containing a complete tooth (including the tooth profile, the tooth gap) and the hub is generated, and then completed by a series of operations such as rotation copying and physical fusion.
This article uses the third method of solid modeling.
2 Involute Helical Gear Profile Forming Method The tooth profile surface of the helical gear is an involute helicoid, which can be seen as a curved surface formed by numerous involutes arranged along a spiral. Therefore, the key to modeling is to determine the exact involute, transition curve and spiral.
2.1 Drawing of the involute of the end face (1) The polar coordinate equation of the involute is:
Ri=rb/cosi"i=invi=tani-i(1)
Where: αi - pressure angle of each point; rb-base circle radius; ri-angle of any point on the involute; θi - involute angle. See 1.
(2) Gear tooth thickness formula: si=srir-2ri(invi-inv)(2)
Where: si- each point corresponds to the tooth thickness of the circle; s-indexed circular tooth thickness, for standard spur gear s=m/2 (the helical gear is the end face modulus mt); r-division circle radius; ri- The diameter of any point on the line;
I-pressure angle at each point; α-index round normal pressure angle.
(3) The central angle corresponding to different tooth thicknesses is i: i=si2r=s2r-(invi-inv)(3)
(4) The Cartesian coordinate equation of the involute can be expressed as: xi=ricosiyi=risini
(4) According to the coordinates on the arbitrary circle, the key points on the involute tooth profile are generated, and the spline fitting generates the end face involute.
2.2 The construction method of the spiral line According to the geometric relationship of the spiral line, if the helical gear is developed along its indexing cylindrical surface, the geometric relationship of the indexing circular spiral line can be obtained: tanβ=πd/l(5)
Where: β is the indexing circle helix angle; d is the index circle diameter; l is the lead, that is, the distance that the helix rises around the index circle one week later.
According to the known gear thickness, a pitch circular spiral of a corresponding length is drawn. The method of drawing the base circular spiral or the spiral on any cylindrical surface is also the same, and only needs to be transformed into the spiral angle and diameter on the cylindrical surface, and the conversion method is described in Reference [1].
According to the above method, a three-dimensional meshing model of an involute helical gear of an automobile transmission is established in the actual engineering practice of this paper (2). The basic parameters are as follows.
3APDL programming realizes parameterization of involute helical gear in ANSYS environment. The APDL language can be used to establish a parameter exchange interface directly in the ANSYS environment to realize the interaction of related parameters.
The main contents of the APDL program are as follows:
(1) The main command stream forming the involute *DIM, X,, 12! Define two arrays to define the generated points *DIM, Y,, 12(a) When the radius of the root circle is less than the radius of the base circle: rf<rb*DO,i,1,12! Cycle to calculate the coordinates on any circle ri=rb+(ra-rb)*(i-1)/11ai=Acos(rb/ri)! Calculate the pressure angle on any circle invai=tan(ai)-aigamai=pi/(2*z)-(invai-inva)! The arbitrary circle corresponds to the center angle of the tooth thickness x(i)=ri*cos(gamai)! Calculate the coordinates of each point on the involute y(i)=ri*sin(gamai)*ENDDO/PREP7! Enter the pre-processor *DO, i, 1, 12! Generate key points k, i, x(i), y(i)*ENDDO(b) on the involute profile when the root radius is greater than the base radius: rf>rb*SET, af, Acos( Rb/rf)! Root root pressure angle *SET, invaf, tan(af)-af*SET, gamaf, pi/(2*z)-(invaf-inva)! Calculate the center angle corresponding to the root tooth thickness *SET, x(1), rf*cos(gamaf)! Calculate the tooth root coordinate *SET, y (1), rf * sin (gamaf) * DO, i, 1, 11! From 1-11 cycles, the cycle calculates the coordinates on an arbitrary circle ri=rf+r1+(ra-(rf+r1))*(i-1)/10i=i+1ai=Acos(rb/ri)invai=tan(ai)-aigamai=pi /(2*z)-(invai-inva)! The angle of the center of the arbitrary scallop thickness x(i)=ri*cos(gamai)! Calculate arbitrary circular coordinates y(i)=ri*sin(gamai)*ENDDO
(2) The main command flow for forming a spiral *AFUN, DEG! The unit for changing the angle is degrees *set,pz,(2*pi*r)/tan(beta)! Calculate the spiral lead *set, q, (360*b)/pz! The helix angle corresponding to the tooth width 20*DIM, u,, 5! Define two arrays to define the generated points *DIM,v,,5*set,u(1),0*set,v(1),0*DO,i,1,4! Cycle the coordinates of each point on the spiral u(i+1)=i*q/4v(i+1)=i*b/4*ENDDO/PREP7! Enter the pre-processor CSYS, 1! Activate the current coordinate system as the cylindrical coordinate system *DO, i, 1, 5! The key points k, i, r, u(i), v(i)*ENDDO of the loop generation spiral are edited in the system's text editor with the extension. Mac macro file is saved.
This example saves it as mygear.
Mac, you can call the macro file by commanding "*USEmygear". Or you can save it in the format of a text file and load it through the menu form. Click “File>ReadInputFrom†to pop up a file loading dialog box. Select the text file (defined in this example as mygear.txt) and click OK. Multiple parameters appear. Enter the dialog box (3), assign it through the multi-parameter input dialog box, click OK to generate the tooth shape and finite element model of the corresponding parameter values.
4 Conclusions Based on the parametric modeling technology of APDL language, the geometric model of standard involute helical gear and the parametric design of 3D finite element model are realized. After the parametric modeling of the gear is completed, when the similar gear is redesigned, the completed gear design macro program can be directly called, and the corresponding parameters can be modified to quickly and accurately draw the standard involute helical gear.
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