Wen-bin DENG, Shao-sheng HUANG

(GSK CNC Equipment Co., Ltd., Guangzhou 510530, China)

Abstract: In order to improve the efficiency of gear machining, an automatic parametric programming system based on gear hobbing is presented in this paper. The mathematical model of the gear hobbing processing was established. The core of the method is inputting certain parameters like workpiece, hob cutter and process parameters through human-machine interface, which automatically generates NC code of gear hobbing by parameter processing module in support of the operation and processing database. The design of human-machine interface, arithmetic, and functional module was realized by custom macro program based on GSK 218MC CNC system. The application in machine tools validates high programming efficiency, high manufacturing accuracy and reliability of the arithmetic, improving the utilization efficiency of the hobbing machine and decreasing the professional technical threshold for operators, but also promoting the market competitive power of the national produced gear hobbing CNC system.

Key words: Automatic programming, Gear hobbing, Computer numerical control (CNC)

1 Introduction

Hobbing is regarded as one of the most accurate gear cutting process. But because of the demands for improved performance gears, it is essential to manufacture better quality gears, preferably without using a further finishing process, such as grinding. Hobbing machines have traditionally been designed using mechanical transmission systems, whereas the new generation machines are based on Computer Numerical Control (CNC) where the axes are synchronized using an “electronic gearbox” [1].

Parametric programming as a feature of modern CNC machines has the potential to bring higher efficiency to manufacturing industries. The application of parametric programming to CNC operations is possible in several ways. These include generating a single CNC program for parts with similar design, inventing macros for machining custom design features, and developing subprograms for a group of parts that are not similar in design but require similar machining operations. In all these applications, parametric programming can significantly reduce the part programming time and effort which in turn leads to shorter throughput and product development time [2].

CNC gear cutting machine mostly adopts the method of manual programming. Its disadvantages are: It needs programmers to have certain professional knowledge and vocational skills; it requires a lot of time for programming; In addition, once the programming has an error, it will affect the processing quality, which causes extended production cycle and low work efficiency. Automatic programming is using a computer to write NC codes for machine tools so that most of the work is finished by the computer. So it can greatly shorten the production time and the operation skills require fewer requirements for operators. Therefore, automatic programming technology research for gear hobbing machine has a realistic significance [3].

At present, most research work concentrate on tooth wear mechanisms and cutting forces evolution in the area of gear hobbing. They are focused on the physical mechanisms occurring at the cutting zone and during the chip removing process [4]. According to the literature, some authors have been interested to the hob geometry, the prediction and measurements of the cutting forces components, the chip formation and tool wear prediction during machining [5-6]. Additionally, several authors have developed various simulation codes to simulate the kinematics of the gear hobbing process, such as SPARTApro and HOB3D software [7-8]. Numerical models have been developed using Computer-Aided Design (CAD) [9] and Finite Element Analysis (FEA) [4].

Moreover, most of the hobbing machines use the high-end CNC controller such as Siemens 840D and FANUC 30i series with high cost for customers. It is developed by using the openness of the system to increase gear processing module [3, 10-11]. However, it is not useful for some small hobbing machine manufacturer and the retrofitting of traditional gear cutting machine or old CNC hobbing machine if adopting the high-end CNC controller due to the cost and developing ability. So it will be meaningful to develop the appropriate price controller and easy use for this kind of user. On the basis of it, we developed a professional system used for hobbing machine based on the GSK218MC controller.

The GSK218MC CNC system is a cost-effective product, which is developed by GSK CNC Equipment Co., Ltd. It has a good openness through secondary development by custom macro program. Processing gear like helical gear has many parameters. Changing the gear specifications requires re-establishing the machining program, and the NC programming is not intuitive. Human-machine interaction is poor. In order to solve the complicated problems of NC programming in processing different gears and improve processing efficiency, the human-machine interface of the GSK218MC CNC controller is customized by the custom macro program, making the basic parameters of gear to be put into the machine directly through the screen. Then, it generates the corresponding NC machining program and completes automation processing.

2 Mathematical model of automatic programming for gear hobbing

2.1 Methods of hobbing

There are several methods in which gears can be produced by the hobbing process, including radial hobbing, axial hobbing, simultaneous radial and axial feed hobbing method for gear hobbing. It is divided into conventional hobbing and climb hobbing based on axial feed [12]. In conventional type cutting, the hob is fed into the part in a direction that is in agreement with the tangential vector denoting the direction of hob rotation. Climb cutting takes place when the hob is fed into the part in a direction that opposes the tangential vector denoting the direction of hob rotation. And according to the technology requirements of the component can be divided into multiple cycle feeding ways. The choice of hobbing method is based on gear type, size and technical requirements, etc. Hobbing methods in detail are illustrated in Fig.1. Surface finish is usually the main factor to consider when selecting climb or conventional cutting. There is no rule, which can be applied to choose which method will produce a better surface finish for a specific job. In many cases, climb cutting has been applied to replace conventional cutting because a better finish obtained, with equivalent hob life and accuracy, provided the machine is rigid and no backlash.

Fig.1 Methods of hobbing

2.2 Coordinate system of hobbing machine

CNC machine tool coordinate system is defined by a right-handed Cartesian coordinate system. Each CNC machine tool has its own coordinate system. It is fixed and set by the machine maker. Fig.2 presents a schematic drawing of a 6-axis CNC hobbing machine [13], where axesX,YandZare the radial axis, the tool shifting axis, and the axial axis, respectively; axes A, B and C are the hob swivelling axis, the hob spindle axis and the work table axis, respectively.

Fig.2 Coordinate system of gear hobbing machine

2.3 Kinematic relation between CNC hobbing machine and its hob cutter

In the NC hobbing process, the hob has its own hob coordinate system, and there is also a workpiece coordinate system. Therefore, the conversion relationship between the hob coordinate system and the workpiece coordinate system must be determined before establishing the mathematical model. Coordinate system [Og:Xg,Yg,Zg] is attached to the workpiece while coordinate system [Od:Xd,Yd,Zd] is attached to the hob cutter (showed as Fig.3),Ydis the hob cutter axis, andλis the setting angle of hob cutter. Suppose the coordinates for the origin of hob cutter coordinates in the coordinate system of a workpiece as(L,0,Z0), whereLis the center distance between hob cutter and gear blank. Then the relation between hob cutter coordinates system and gear blank coordinate system can be obtained by applying coordinate transformation as follows.

(1)

Fig.3 Coordinate of hob cutter and gear blank

2.4 Hob settings calculation

Tool setting must be carried out before gear hobbing. The purpose of tool setting is to keep the correct relative position between the workpiece and the hob cutter’s edge, so as to make appropriate gear [14]. If the tool setting is inaccurate, it may occur the phenomena of tool-crashing, or lead to waste cutting time because the bigger distance between the cutter and gear blank. We take standard cylindrical gear as an example for research.

Using hob cutter to process cylindrical gear, there is a title angle between the hob axis and the workpiece end face, namely the installation angleλ. Tool setting is shown in Fig.4.Ris half of work gear diameter,tis cutting depth,Bis the gear width.

In terms of standard cylindrical gear, it is necessary to make the tool contact with the workpiece exactly (point A in Fig.4), and to make the tool outer diameter tangent with the depth line CD. Because the cross section is an ellipse at the tool setting point, it is reflected in Fig.3 that the elliptical short axis is tangent to the line CD. The radius of hob isr, and it is easy to obtainx1=R+r-tfrom Fig.4. The coordinate ofOdis(x1,z1). The curve equation of the elliptical cross section of hob cutter is as follows:

(2)

Point A is also belonging to the curve, substitutex=R,z=0 into the above equation, then we can get:

(3)

So we can obtain the hob setting coordinate is:

2.5 Hob trajectory and the key position

Determination of the swivel angle for hob cutter:

For manufacturing cylinder gears by hobbing, there are two variations depending on the helix angle directions of the hob cutter and the gear blank cylinder. Equi-directional hobbing is set when the helix angle directions of the hob and the gear blank are the same, while in the opposite case, counter-directional hobbing is applied. Hence, the hob-setting angleλgiven by

λ=|β|±|α|

(4)

Whereαis the lead angle of the hob andβis the helix angle of the gear (which is zero for spur gears). The positive sign is used above when the hob and gear helix angles are both of the opposite hand, while a negative sign denotes when they are both right-handed or both left-handed.

So the hob cutter must be tilted as a swiveling angle by the hob swiveling axis A. The trajectory of hob is 1→2→3→4→5 shown in the Fig.4 when the machine is processing. After starting process, the hob cutter starts from point (X0,Z0) to (X4,Z4) with rapid speed, then rotates the hob cutter, move to cutting position (X1,Z1) and starts to cut. When the hob cutter move to (X2,Z2), the gear blank will be finished and then return to position (X3,Z3), then returned to the starting position(X0,Z0), and then the total cutting process will be finished.

Obviously, the four key points (X1,Z1),(X2,Z2),(X3,Z3), (X4,Z4) are very important. Because they are not only related to the safety of machine and hob cutter, but also affect the gear processing precision. So how these coordinates are determined, we take the cylindrical gear as an example to calculate the relationship among them and work blank, hob cutter and fixture.

The contact position of tool setting is the actual cutting point. However, it tends to attach an allowance to the calculation coordinates in actual processing to avoid damaging hob cutter. In addition to ensure complete and easy to adjust, other positions also have a margin for their coordinates setting. Considering the margin used for correction, combined with Fig.4, and follow the last section of the hob setting. It is not difficult to calculate the key point coordinates as follows.

Coordinate of the key position 1:

(5)

Whereris half of the hob diameter,Ris the radius of work gear, Δx, Δzis the correction forXaxis andZaxis respectively.

Fig.4 Hob setting and trajectory calculation of hobbing

Coordinate of the key position 2:

(6)

Coordinate of the key position 3:

(7)

Wherelis the return stroke of the hob cutter in theXaxis, which is determined according to the machine tool, cutting tool and workpiece’s size.

Coordinate of the key position 4:

(8)

2.6 The kinematic relationship between hob cutter andworkpiece

Based on the kinematic relationship of the CNC hobbing machine mechanism, the relative velocity between the hob cutter and workpiece can be obtained.

Fig.5 The movement of the gear and hob when processing

During the hobbing process, there are four kinds of kinematic motion as showed in Fig.5 [15].

(1) Hob rotationNt(r/min);

(2) Rotation of the the gear blankNi(r/min);

(3) Axial feed hobbingVf(mm/min);

(4) Additional rotation of workpieceNf(r/min) to compensate for the axial motion of the hob relative to the tooth helices.

Because of the hob and workpiece is meshing movement, so the relationship between the hob and gear blank is:

Ni=KdNt/Zg

(9)

WhereKdis number of starts on hob,Zgis number of teeth of gear.

The kinematic motion between axial feeding movement of hob and gear blank is as follows:

Vf=faNw

(10)

Wherefais an axial feed rate of the hob per workpiece rotation andNwis the actual speed of the gear blank (r/min).

Additional rotation of the workpiece can be obtained since a helix makes one complete rotation in an axial distance equal to the leadPzof the gear. And axial feeding motion of hobVfwhen making helical gears by hobbing as

Nf=±Vf/Pz

(11)

In the above equation, the sign is determined by hobbing method. Climb hobbing: the positive sign is used above when the hob and gear helix angles are both of opposite hand, while a negative sign denotes when they are both right handed or both left handed; Conventional hobbing: the positive sign is used above when the hob and gear helix angles are both right handed or both left handed, while a negative sign denotes when they are both of opposite hand.

The lead of gear blankPzis calculated as

Pz=MnπZg/sinβ

(12)

WhereMnis the gear module andβis the helix angle of the gear.

The actual rotation speed of workpieceNwis:

Nw=Ni+Nf

(13)

Substitute Eqs. (9) and (11) into Eq. (13). Then we can get the kinematic movement relationship between hob cutter and workpiece:

(14)

And substitute Eq. (14) into Eq. (10), axial feeding speed of hob cutter can be obtained as follows:

Vf=faNw=-faKdNt/[Zg(1±fa/Pz)]

(15)

Specially, when processing spur gear, becauseNf=0, then

Vf=faNw=faNi=faKdNt/Zg

(16)

3 Automatic programming system design for gear hobbing

3.1 Automatic programming system overall design

Although there are many kinds of gears and cutting tools, and their profile curve are quite complex, yet on the part drawings, the description of them is concise. The gears and tools can be expressed clearly with limited characteristic parameters. On the other hand, it has stringent transmission relationship between spindle and work table during gear machining. So the gear machining codes can be generated automatically after the related parameters are set. According to the above analysis, the parameters needed for CNC gear hobbing programming are divided into three groups: gear parameters, hob cutter parameters and cutting process parameters.

The automatic programming system is based on parameterization, and the NC program is generated according to the relevant parameters. It has a simple and convenient operation, friendly interface, and many other advantages. Furthermore, according to the function of automatic programming system setting including parameter settings and parameter validation, the corresponding file and parameter management function also require development in order to know the detail information for gear blank: program save, delete, open, edit and parameters save, etc. According to these needs, the automatic programming system is designed as shown in Fig.6.

3.2 Parameter input and processing

Through the above analysis for gear machining, hob cutter, gear blank and cutting process is easy to describe with some common characteristics, such as module, number of teeth, lead angle, etc. Regarding different types of gear, such as drum gear, spur gear, etc., a few characteristics of parameters can be added to describe it. So we can use parametric features to represent all kinds of gears to achieve automatic programming. The user interface developed by the macro program is shown in Fig.7. It mainly covers three parts related to gear cutting by hobbing.

Fig.6 Frame of automatic programming system

Fig.7 User interface of an automatic programming system for hobbing

(1) Interface of workpiece parameters

This part mainly includes work gear type, module of work gear, number of teeth, helix angle (right helix gear input positive value, left helix gear input negative value) and gear width. When the input parameter type or value beyond the limit condition, the system will present alarm message according to the results of the validation, then the operator can modify the input data to meet the conditions. Cutting tools and cutting parameters settings interface also has the check function.

(2) Interface of hob cutter parameters

The main parameters include: hob radius, number of teeth (starts) on hob and lead angle (right-handed hob input positive value, left-handed hob input negative value).

(3) Interface of cutting cycle parameters

The main cutting parameters include: spindle speed, cutting depth, feeding rate, cutting times (one-cut, two-cut or more), cutting method (climb hobbing, conventional hobbing), tool offset and related parameters for hob shift, etc.

Therefore, an operator only needs to input the basic parameters described by the drawing of a gear, then the NC program will be generated automatically. Moreover, we also simplified the cutting process by parameterization. So this system can improve efficiency for manufacturing gear even the operator has less knowledge about gear cutting.

Fig.8 Hobbing machines are equipped with GSK218MC CNC system

Fig.9 Gear samples are made by the present system

4 Test and application

We have used the automatic programming system for a new 6-axis hobbing machine made by a manufacturer from Korea and some second-hand machines retrofitting replaced from FANUC CNC system for the end-users. Fig.8 is the photos showing the application for a new machine and an old retrofitting machine. Moreover, Fig.9 illustrates gear samples of helix gear and spur gear manufactured by the machines which are shown in Fig. 8 via the automatic programming system presenting in this paper.

For the application, we also have tested the process parameters like cutting times, cutting method and hob shift, etc. And the end-users are satisfied for this programming system after used for their machines in a factory because of easy to operate, meeting their accuracy and reliability.

5 Conclusions

The mathematical model on automatic programming of gear hobbing was established in this paper. We presented an automatic parametric programming method that can generate NC codes for gear hobbing automatically by inputting certain parameters based on hob, gear, technics and operation for CNC hobbing machines. The design of human-machine interface and arithmetic was realized on the basis of the secondary development of more economical CNC system GSK218MC. Finally, the application of machine tools for end-users showed high programming efficiency and high manufacturing accuracy, and is easy to operate and reliability.