1 Gear Parametric Theory The gear mechanism is one of the most common transmission mechanisms. The involute cylindrical gears are divided into spur gears and helical gears. Accurate and rapid modeling is very important if the three-dimensional shape of the tooth profile of the gear is accurate or not, which will affect the analysis of finite element and dynamics. The parametric design of the involute cylindrical gear in the Pro/E environment allows for precise modeling.
To achieve the parametric design of the gear, first select the specific gear parameters; secondly, use the Pro/E modeling tool to create the model; finally, edit the model's program file to achieve the automated design.
(1) Pro/E program function: Pro/E system is developed by American PTC company, and the core modeling idea of ​​the system is parameterization. That is, parameterization between size and size, and the relationship between the constraints and features of the model can be established. After each model is built, the Pro/E system displays its program files in the form of a notepad. The essence of the program is that the system establishes the characteristics of each part of the model, and records the establishment process and the generated conditions in a specific program. The system, in turn, allows the user to edit the established program to control the features in the model. This article is to use this function, for the various types and applications of gear products, by editing the program file, and finally realize the human-computer interaction question and answer to change the mechanical parameters of the gear, so that the design has greater flexibility, reflecting Pro / E parameters The core concept of the design is to automate the design of new types of gears such as spur gears, helical gears, and herringbone gears to improve work efficiency.
(2) The information contained in the program text: After the model is established, the program window is opened, and the system will display the program content in the process of establishing the record model in the information window. The information window includes the process of establishing all the features of the part, parameter settings, dimensions, and relationships. In Pro/E, its program has a standard structure, generally the following five parts are displayed in order:! Title section: A total of three lines. It is automatically generated by the system, including version information, number of corrections, part model, etc.; prompt information part: used to set the prompt information for input. Mainly use this part to establish a good human-computer interaction interface. The data input of human-computer interaction is realized by adding a prompt message between INPUT and ENDINPUT; the relational part is used to set the relationship of the characteristics of the control model. Add control statements to the trait between the RELATIONS and ENDRELATIONS in the program; add the feature part and the mass attribute part: the readers of these two parts can refer to the other = reference.
(3) Involute equation: There are many kinds of tooth profile curves in theory. Commonly used are involute, cycloid, arc, etc. Among them, the involute profile is the most widely used. This article uses the involute curve as the tooth profile curve). According to the relevant geometric knowledge, the geometric meaning of the involute is that when a straight line (occurring line) is purely scrolled along a circumference (base circle), the trajectory of any point on the line is the involute of the circle, and the circle The diameter is rb, according to the formation process of the involute, you can get:
Rb=db/2; rb is the base circle radius theta=t90; t is the parameter of Pro/E, ranging from 0 to 1x=rbcos(theta) rbsin(theta) theta(pi/180); pi is the y =rbsin(theta)-rbcos(theta)theta(pi/180)z=0 This is the mathematical equation for the involute in Pro/E.
(4) Spiral involute tooth profile equation: According to the formation principle of the spiral involute profile, there is a straight line AA on the occurrence surface which is at a β_2 angle with the axis of the base cylinder, and the occurrence surface is pure along the base cylinder surface. When scrolling, the trajectory of this straight line A is the tooth profile surface of the helical gear, and the intersection of this tooth profile surface and the base cylinder is a spiral. From the geometric knowledge, the parametric equation of the spiral is:
Rb=db/2; rb is the radius of the base circle pb=rb/tan(beta_2); where pb is the lift of the helix x=rbcos(tB/pb180/pi)y=rbsin(tB/pb180/pi)
The specific reversal of z=tB can be found in the relevant literature.
(5) Determine the mechanical parameters of the gear: China has standardized production for the gear. The parameters describing the basic geometrical dimensions of the involute spur gear are tooth thickness B, number of teeth Z, pressure angle angle, modulus mn, and tooth height coefficient hax. The clearance coefficient cx, in which the standardization coefficient hax=1, cx=0.25 is specified in the standard spur gear. At the same time, the pressure angle angle on the index circle of the gear is in the national standard (GB/T1356-88). The standard value is specified as angle=20, but other cases are also used in some specific situations, such as gears with angle=14.5, 15, 22.5, 25, etc. In addition, the modulus of the gear is also standardized. The designer should select the modulus of the gear according to (GB/T1357-87). Before starting the modeling of the gear, the designer should first determine the number of teeth Z, the pressure angle, and the modulus mn. And the values ​​of hax and cx (the gears created in this paper are standard straight/helical gears, so hax=1, cx=0.25). For the helical gears, the displacement coefficient xn and the helix angle beta should be determined. Finally, the following others can be obtained. parameter:
Basic parameters of spur gear: number of teeth z: number of teeth z from the actual production and custom index circle diameter: d = mnz base circle diameter: db = dcos (angle) tip circle diameter: da = d 2ha tooth root diameter: df =d-2hf pressure angle z/cos(beta) base circle diameter: db=dcos(angle_2) tooth tip circle diameter: da=d 2ha tooth root circle diameter: df=d-2hf pressure angle: angle=20 tooth thickness: The tooth thickness B is determined by the actual production and the custom displacement coefficient xn: It is easy to see from the actual definition of 2 gear parametric design ideas. The tooth profile curves of the commonly used spur gears and helical gears are involute, but two The tooth surface of the spur gear is different, the tooth surface of the spur gear is perpendicular to the involute tooth profile, and the involute tooth profile of the helical gear is not perpendicular to the spiral line on the base cylinder. Therefore, in the process of creating the gear, the teeth of the spur gear can be made by the Pro/E stretching function, and the gear teeth of the helical gear are completed by the variable section scanning function in Pro/E, that is, a spiral and a vertical The straight line of the tooth surface scans the oblique gear teeth for the scanning line. The modeling is as follows: (1) When setting the parameters, set the type of GEAR to whether or not, the value of LEFT is positive or negative 1. Where is the parameter GEAR for the control modeling gear is spur gear or helical gear, the parameter LEFT is the control slope The left or right hand of the gear.
(2) Before using the variable section scanning function, create the involute section required for scanning. The section is created using the created involute and four basic circles.
(3) First create a spur gear, and after the first gear of the spur gear is successfully created, immediately open the program file, in the program file, record the beginning of the tooth program, that is, in the program: ADDFEATURE internal feature identification Add the control statement in front: IFGEAR==YES, add ENDIF at the end. Then save and return, and array the remaining teeth, so that the teeth of the array are in the control statement, and the array teeth are also set to The form of the parameter and added in the relation. Similarly, after the first tooth of the helical gear is created, the program file is also opened, and the control statement is added at the beginning of the record of the tooth program: IFGEAR==NO, at the end of the program: ENDIF.
(4) When creating the spiral equation, multiply the Y equation by lef, t is: y=rbsin(tB/pb180/pi)
The purpose of lef,t is to control whether the helical gear is left-handed or right-handed by the positive or negative left value.
(5) Set relationship relation base circle diameter da=d 2ha/tooth circle diameter df=d-2hf/tooth circle diameter ifhax>=1D=0.38mnendififhax<1D =0.46Mendif/
D is the radius at the root of the tooth profile, and the relationship is the radius endif of the cross-section tangent arc under different tooth height factors. (Note: some parameters are omitted above)
(6) Enter the following between INPUT and ENDINPUT in the program file:
INPUTGEARYES_NO"Please enter the gear to be created: (create the value of the spur gear: yes / create the value of the helical gear: no) "LEFTYES_NO" If the helical gear created is left-handed, please enter 1, otherwise enter -1"ZNUMBER" Enter the number of teeth Z according to the design: (the number of teeth should be less than 41) "MNUMBER" Please enter the modulus m: "ANGLENUMBER" according to the standardized modulus series table. Please enter the pressure angle: (the national standard pressure angle angle is 20, special Other values ​​can be used.) "HAXNUMBER" Please enter the tip height coefficient hax: (the value of the tip height coefficient of China's standardized gear is 1) "CXNUMBER" Please enter the headspace coefficient cx: (the value of China's standardized headspace coefficient) For the 0.25) "BNUMBER", please enter the thickness of the gear B"BETANUMBER". Please enter the helix angle of the gear of the helical gear BETA"ENDINPUT
3 different parameter values, Pro/E automatic modeling gear (1) when M=8, Z=35, angle=22.5, B=100, beta=18, hax=1.0, cx=0.25, xn=0, left When =1, the gear generated automatically by Prp/E is the left-hand helical gear shown.
(2) When M=8, Z=30, angle=20, B=100, beta=20, hax=1.0, cx=0.25, xn=0, left=1, the gears automatically generated by Prp/E are Right-hand helical gear shown.
(3) When M=8, Z=28, angle=20, B=100, hax=1.0, cx=0.25, xn=0, the spur gear shown in Fig. 3 is automatically generated by Pro/E.
(4) When M=8, Z=35, angle=22.5, B=100, beta=18, hax=1.0, cx=0.25, xn=0, left=1, the gear generated by Prp/E is 4 The herringbone gear shown.
4 Ending This paper proposes a new method for automatic modeling of other gear transformations to different parameter values ​​after creating a single gear template in Pro/E.
That is, by parameterizing the main parameters of the gear, and modifying the gear program file, inputting new parameters in the human-computer interaction interface to realize the automatic generation process of a spur gear backward helical gear, solving the previous Pro/E gear The limitations of modeling. From the creation idea proposed in this paper, when creating another model, as long as the model has certain similarities, the parameterization can be established numerically and the program file can be edited, so that the repeated modeling can be avoided to improve the design efficiency of the product.
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