Discussion on Simulation and Demonstration Inspection of Gear Cutting Gears


The gear-fan experiment is an important experiment in the principle of involute gear machining and the principle of meshing in the mechanical principle course. This experiment uses the gear model to simulate the process of machining the gear by the rack tool. However, due to the limitations of the experimental instrument and the experimental time, only two or three standard gears and displacement gears with a fixed modulus, number of teeth and pressure angle can be drawn. Tooth shape, the influence of parameters such as modulus, tooth number, pressure angle, tip height coefficient and head clearance coefficient on the tooth profile and base circle, tip circle and root circle radius cannot be demonstrated. In order to make up for the shortcomings of Fan Cheng's experiment, some schools have developed a virtual experiment of gear Fancheng using high-level programming language. The complete gear pattern can be parameterized on the computer, but only the virtual experiment of the rack tool processing gear is realized. There is no virtual experiment to achieve gear tool machining gears. The method not only dynamically simulates the process of machining the gears of the rack tool, but also solves the computer simulation problem of the gear processing gears. In the AutoCAD drawing environment, Fan Cheng's envelope graphics can be processed to obtain accurate gear profiles for 3D gear solid modeling.
1 The realization principle of the virtual experiment of gear tool machining gear The gear machining method is based on the principle that the conjugate tooth profiles are envelopes. The virtual vane experiment of the gear cutter machining gear can be divided into two steps: the formation of the gear cutter and the virtual machining of the gear.
1.1 The formation principle and implementation method of the gear cutter The contour of the gear cutter on the cutting surface is the same as the gear contour with the height of the tooth top increased by cm, and the diameter of the tip circle is da=da 2cm.
The precise contouring of the gear tool can be obtained by using the rack tool to machine the gear. The method first envelops the tooth profile of the gear cutter, and then extracts the envelope gear profile curve to obtain the gear cutter. As shown, the rack tool 1 is treated as a tile, and the B1 point on the rack is the pick point of the tile. The process of inserting the rack tool is equivalent to the involute line along the index circle of the tooth blank 2 along the B1 on the rack section line, inserting the rack tool block and rotating it around the O1 by a certain angle. (The sum of the angle between the pressure angle and the involute). The relationship with the E coordinate of the insertion point of the tool block is: xE=xO1 d(sin-cos)2yE=yO1 d(cos-sin)2 The half tooth of the rack is composed of three straight lines (A11A12, A13A15 and A16A18) It consists of two arcs (arc A12A13 and arc A15A16), and after obtaining a symmetrical pattern about the center line A18C2, a complete tooth is obtained. The remaining teeth can also be obtained by coordinate transformation. The coordinate system can determine the coordinates of the A11, A12, A13, A14, A15, A16, A17, A18 and pick-up points B1 on the teeth and the starting and ending angles of the two arcs A12A13 and A15A16.
Rack cutter tooth profile: l1=2(ha c)ml2=kmtan(2-)2l3=m4-(ha c)mtan, then A11(x11,y11)=[xO1,yO1 d2 (ha c)m] A12(x12,y12)=[x11-l3 l2,y11]A13(x13,y13)=[x11-l3-l2sin,y11-l2cos]A14(x14,y14)=[x11-l3 l2,y11-km] A15(x15, y15)=[x11-l3-(l1tan-l1sin), y11-(l1-l2cos)]A16(x16,y16)=[x11-l1tan-l3, y11-l1]A17(x17,y17) =[x11-l1tan-l3,y11-l1 km]A18(x18,y18)=[x11-m2,y11-l1]B1(xB1,yB1)=[xO1,yO1 d2] corresponding to the i-th wheel tooth The coordinates of the point Aij are: Aij(xij, yij)=[xij-(i-1)m-yij] (i=1, 2, Z0; j=1, 2, 8) the starting angle and termination of the arc Ai2Ai3 The angles are 2 and 2 respectively; the starting and ending angles of the arc Ai6Ai7 are 32, 32. respectively, the pressure angle; the m modulus; the d index circle diameter; the number of teeth of the Z0 rack cutter; Coefficient, = km. If the ordinate of the point Aij and the pickup point B1 is increased by a displacement amount, a gear tool of the displacement can be obtained.
1.2 Principle and Implementation of Gear Tool Machining Gear When the gear cutter is used to machine gears, the relative motion of the gear cutter and the machined gear is equivalent to the cutter pitch circle being tangent to the indexing circle of the machined gear and purely rolling. In the middle, 1 is a gear cutter, 2 is a gear to be machined, and the contour curve of the tool 1 is taken as a tile, and the center is taken as a pickup point. Then, the process of machining the gear by the gear cutter is equivalent to inserting a gear cutter block rotating at a certain angle on a circle having a radius of a with O2 as a center. When the insertion point is O11, the gear cutter has a revolution angle and a rotation angle. The relationship of each parameter is as follows: a=r1 r2 xmO2=(xO2,yO2)=[xO2,yO2-a]O11=(xO11,yO11)=[xO2 acos(2 ),yO2 asin(2 )]=(1 Z2Z1 2 program design 2.1 program flow chart According to the realization principle of the gear tool processing gear virtual fan experiment analyzed above, the VB language is used for the secondary development of AutoCAD, and the gear tool machining gear virtual experiment program gear Fancheng CAD is compiled. flow chart.
(a) Main program flow chart (b) Create rack tool block program flow chart (c) Rack tool machining gear tool subroutine flow chart d) Rack tool machining gear flow. 2 Partial Source Program Description 2.2.1 Connecting AutoCAD with VB for AutoCAD Secondary Development Based on the new ActiveX automation interface technology, VB programming is used to control and manipulate AutoCAD. Through the VB project reference menu, in the reference dialog box. By selecting the AutoCAD2000 typelibrary item, VB can reference the AutoCAD object library. Add the following code to the VB form code to start running AutoCAD.
Dim gear CADasapplicationPrivateSubform-loadonErrorResumeNextSet gear CAD=GetObject(,autocad.application)IfErrThenErr.ClearSet gear CAD=CreateObject(autocad.application)IfErrThenMsgBox (Cannot run AutoCAD, please check if AutoCAD is installed) ExitSubEndIf gear CAD.Visible=TrueEndSub2.2.2 Block creation and reference In this program, the gear cutter wheel blank, rack tool and gear tool are set as the block. The rack tool block is taken as an example to explain the creation and reference of the block.
Define the block object of the rack tool and the insertion point of the block DimBlockobjAsAcadBlockDiminsertpnt(0To2)AsDouble Here, the statement that omits the definition of other variables assigns the pick point of the block, and creates the block object of the rack tool DaoJuBlockinsertpnt(0)=XB11( 0):insertpnt(1)=YB11(0):insertpnt(2)=0SetBlockobj=Gear CAD.ActiveDocument.Blocks.Add(insertpnt,DaoJuBlock) The program for forming the rack tool block with the number of teeth Z0 Fori=0ToZ0 A parameter and an assignment statement are added to the tool block object to add a line segment and an arc SetlineobjA11A12=Blockobj.AddLine(startpointA11A12,endpointA11A12)SetArcobjO1=Blockobj.AddArc(CenterO1,radius,StartangleO1,EndangleO1) to mirror the line segment and the arc, and obtain A complete tooth SetlineobjA11A12M=lineobjA11A12.Mirror(point1,point2)SetArcobjO11=ArcobjO1.Mirror(point1,point2)Nexti inserts the tool block, insertpntB is the insertion point, and si is the rack tool block.
2.2.3 Creation and use of layers In order to facilitate the control of AutoCAD graphic objects, different graphic objects are created in different layers, such as gear tool layer, gear wheel blank layer, gear tool layer and other layers. . For example, after the gear cutter is wrapped with the rack and the gear tool contour curve is extracted, the gear cutter layer is closed, and only the gear cutter and the wheel blank are displayed on the drawing interface of the AutoCAD, which facilitates the next gear cutter block. The creation and processing of gears and other operations. The following describes the creation of layers, setting them as current layers, and turning off layers.
Define layer DimlayerLUNPI1AsAcadLayer gear cutter wheel blank 1 layer, DimlayerCTDAOJUAsAcadLayer rack tool layer DimlayerCLDAOJUAsAcadLayer gear cutter layer DimlayerCHILUNAsAcadLayer processed gear contour layer Create layer SetlayerCTDAOJU=Gear CAD.ActiveDocument.Layers.Add(Rack cutter layer) SetlayerLUNPI1= Gear CAD.ActiveDocument.Layers.Add (Board 1 layer) SetlayerCLDAOJU=Gear CAD.ActiveDocument.Layers.Add (Gear cutter layer) Set the layer color layerCTDAOJU.Color=acRed rack tool layer layer color layerCLDAOJU.Color =acGreen gear cutter layer layer color setting the tooth blank 1 layer is the current layer gear CAD.ActiveDocument.ActiveLayer=layerLUNPI1 turns the round blank 1 round.
layerLUNPI1.LayerOn=False3 Program function and operation The upper left window is the CAD window of the main window of the program. The window is divided into upper and lower parts, which respectively realize the parameter input and control of the rack tool processing gear and the gear tool processing gear. The upper part is provided with 8 parameter input text boxes, which can input the rack tool tooth number Z0, the machined gear tooth number Z1, the modulus m, the pressure angle, the tooth top clearance coefficient c, the tip height coefficient ha, the displacement coefficient x and the transition circle. The angular curvature coefficient k, using the scroll bar to set the incremental value of the gear rotation angle. And set the gear to machine the gear, remove the wheel blank and help the three buttons. The lower part is provided with two parameter input text boxes, which can input the gear tooth number Z2 and the displacement coefficient x, and also set the gear tool block name input text box to provide the called tool block for the program. Use the scroll bar to set the incremental value of the gear rotation angle. And set up the confirmation, machine the gears with gears, remove the wheel blanks and exit the four buttons.
Gear Fancheng CAD program main window and AutoCAD drawing window When the gear Fancheng CAD window is started, first start running AutoCAD. If you can't start AutoCAD, the MsgBox dialog box will pop up: Cannot run AutoCAD, please check if AutoCAD is installed. After the parameters are input, click on the rack processing gear button to enclose the gear tool contour in the AutoCAD drawing environment according to the parameters set by the gear vane CAD window, and mark the circle radius of the gear cutter. The AutoCAD drawing window shows the envelope pattern of the gear tool determined by parameters Z0=16, Z1=12, m=10,=20, c=0.25, ha=1, x=0, k=0.2,=4.
When you click to clear the wheel blank button, you can close the layer where the wheel blank of the machined gear tool is located. When creating a gear tool block, the gear tool tip circle should be retained in the envelope diagram. Use the BOUNDARY command to extract the contour curve. Then use the FILLET command to obtain the gear tool tip transition fillet. Finally, the center of the gear cutter is Pick the point and set the gear tool contour curve to a tile. The gear tool pattern in a is a pattern extracted from the gear tool envelope and subjected to a transition fillet process; (b) an enlarged tooth profile of the gear tool. At this point, the operation of machining the gear tool with the rack tool has been completed, and then the gear tool contour curve in (a) is set as a block, and the name is named cldj, which is the virtual experiment for the gear tool of the next gear tool. ready.
When the number of teeth Z2 of the machined gear and the displacement coefficient x are input in the program window, the incremental value of the gear rotation angle is set, and the block name cldj of the called gear tool is input, and the confirmation button is clicked, and then the rack is used. The machining gear is twisted and can be parameterized in the drawing environment of AutoCAD. The dynamic tool is used to process the gears and finally envelop the contour of the machined gears. The contour curve of the machined gear can also be obtained by the method of obtaining the contour profile of the gear tool as described in the foregoing. The process of calling the cldj gear tool block simulation to machine the gears with the number of teeth Z2=8 and the displacement coefficient x=0 is shown. (a) is the initial positional relationship between the tool and the machined gear wheel blank, (b) is a momentary pattern in the process of machining, and (c) is the gear contour pattern enclosed by the gear tool, (d) ) is the contour curve of the machined gear extracted from (c). Changing the value of the displacement coefficient x can show the effect of x on the tooth profile. (a) and (b) show gear tooth profiles in which the number of teeth Z2 = 8 and the coefficient of displacement x are 0 and 0.5, which are processed by the cldj gear cutter.
4 Conclusions This virtual experiment uses VB to carry out the secondary development of AutoCAD. The influence of the displacement coefficient x on the tooth shape is parameterized in the drawing environment of AutoCAD. The dynamic simulation of the racking gear and gear tool processing gear is realized, showing the modulus, The influence of the parameters such as the number of teeth, the pressure angle, the height coefficient of the tip and the coefficient of the head gap on the tooth profile and the base circle, the tip circle and the root circle radius clearly show the gear top cut and root cut phenomenon. The research principle, gear cutting, the formation of the tooth profile curve and the gear meshing principle are of great significance.
Since the precise tooth profile of the gear can be obtained in AutoCAD, it provides the basis for the 3D solid modeling of the gear. It is of great significance to the finite element analysis of gears and the animation of gear transmission, the assembly of virtual prototypes and motion simulation.

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