Chengzhe JIN,Chang GUO,Yun GAO

School of Mechanical Engineering,Shenyang Ligong University,Shenyang,People's Republic of China

Research on cutting vibration characteristics of face-milling involute gear

Chengzhe JIN*,Chang GUO,Yun GAO

School of Mechanical Engineering,Shenyang Ligong University,Shenyang,People's Republic of China

1.Introduction

Gear is one of the commonest and absolutely necessary driving members in various modern machinery and equipment.In recent years,the demand of gear has embodied a continuously rising tendency with the booming development of industries such as wind power,petroleum machinery,metallurgical and engineering machinery of China,[1].At present,the research on gear cutting machining is mainly concentrated in machining methods,such as gear hobbing,gear shaping,gear milling and gear grinding,etc.Through research of parametric design of hobbing cutter,Kim[2]et al.established an accurate hobbing cutter model,and analyzed the influence of errors existing in hobbing cutter design on gear machining.Jen-Ksieh[3]et al.used 3-dimension design software for 3-dimensional parameterization modeling of hobbing cutter,and completed the simulation of gear machining on the basis of modeling.Dimitriou[4]et al.invented a new type of hobbing cutter,which features excellent function for machining spur rack cutting tool.Bouzakis[5]have made in-depth research on the entire machining process of hobbing cutter,utilized finite elementmethod for analysis of formation and geometry of chip,tooth flank wearing mechanism and changing process of cutting force,and optimized geometric parameters of cutting tool during the process.Demidow[6]et al.researched the influence of angle of hobbing cutter upon tooth profile error of spur gear,discovering that positive rake angle has large influence upon it.Kawasaki[7]et al.established a tooth surface approximate mathematical model and analyzed the error between approximate model and the accuracy value,and the experiments were carried out using the machining center for cutting the large module gear.To a certain extent,traditional gear machining method no longer meets the increasing machining demand of gear,therefore it needs to make a breakthrough in machining mode of traditional gear machining method.In the present paper,a face-milling machining method is used for machining of involute gears.I.e.,use generalized milling cutters such as face milling cutter and ball-end milling cutter in CNC machine center and milling machine center,and complete cutting machining of gear through numerical control program so that cutting tools and manufacturing equipment are transformed from traditional specialization machining method to generalization,the production cost is reduced,and the use rate and production efficiency of machine tool are enhanced.The unavoidable cutting vibration problem always exists in cutting machining,and the vibration phenomenon in machining has very large influence upon machining qualityand production efficiency.In machining operations such as milling,broaching and gear shaping,a damped vibration may be generated repeatedly upon the start and end of cutting by cutting the edges.When frequency of intermittent cutting or integral multiple higher harmonic frequency approaches to the natural frequency of mechanical structure,a resonance phenomenon will occur,which imposes a substantial influence on cutting machining.Therefore,it is essential to perform vibration analysis.A rigid-flexible coupling virtual prototyping model of facemilling gear milling system was established so as to analyze the cutting vibration of face-milling gear.

2.Establishment of cutting vibration system model

A large module gear shaft(seeing the design parameters in Table 1)is selected as the research object,as shown in Fig.1.The material of gear shaft is 40CrNiMo,elastic modulus is 2.09E+11Pa,material density is 7870 kg/m3,and Poisson's ratio is 0.295.

A solid model of large module gear shaft and face-milling cutter was established using CATIA software,and was imported into ADAMS through data conversion.A clamping fixture and a driver unit were added,and a cutting tool gear milling machining simulation model was established,as shown in Fig.2.Point O is origin of coordinate system,Point A is the tip of single cutter tooth of facemilling cutter and does the feed motion following the cutting tool,and Point B is the center point of gear blank to be machined on a large module gear shaft.In accordance with actual motion situation,a dynamics simulation is performed for milling system simulation model.An immovable restraint is applied between gear and ground,and an immovable restraint is applied between cutting tool and clamping fixture.A driver unit is used to apply a movable restraint in direction Y in accordance with its motion relation,,and a straight line driving is set on the driver unit.A rotating restraint is applied between the clamping fixture and the driver unit,and a rotation driving is set.A load is applied through application of acting force.In summary,the rotating driving is to simulate the rotation of milling cutter,the straight line driving is to simulate the feed motion of workpiece[8],and the driver unit is used to drive the cutting tool to act upon workpiece so as to generate motion.

In ADAMS software,ADAMS/vibration module automatically establishes a linear digital prototype vibration model as per the mode of state space equation.The state space expression of linear time-invariant system can be expressed as

wherex-state variable of system;u-determined by input channel of system;y-determined by output channel of system;A(t)-system matrix;B(t)-control matrix;C(t)-output matrix;D(t)-direct transfer matrix.

Transforming the state variable mode in formulae.(1)into frequency domain,andusing Laplace transformation for formulae(1),we have

Table 1 Design parameters of large module gear shaft.

Fig.1.Part drawing of a large module gear shaft.

Fig.2.Part drawing of a large module gear shaft.

where I-nXn unit matrix.Let initial state X(s)be 0,the transfer function G(s)between input and output of system can be derived

Therefore,the system response Y(s)in frequency domain is derived

When the cutting vibration characteristics of large module gear shaft system are studied by using face-milling cutter,a force bearing of system should be accurately analyzed,and normally a model should be relevantly simplified.

Fig.3.System simplification diagram.

Analysis about force bearing of cutting tool during cutting machining is shown in Fig.3.In Fig.3,K(t)is a comprehensive engagement stiffness,e(t)is a tooth profile error,cvis a contact damping factor,θ1and θ2are the turning angle,T1and T2are driving moment.The condition of cutting tool cutting a gear is considered as an contact motion between two objects.When motion and load are transmitted,collision/impact exists in engagement process due to the phenomenon of development of contact between gear and cutting tool from no-contact to contact,and the direction of force between the gear and cutting toolwill change at this point.Under normal cutting conditions,the relative displacement along path of contact is positive,therefore the dynamic engagement force Fp(t)is positive number.As the comprehensive deformation is expressed by,then the dynamic tangential engagement force can be expressed as

With consideration of the influences of stiffness characteristics,backlash and rotation eccentricity mass of cutting tool,the resolution of force applied on gear along directions x and y of coordinate system is performed,and then the dynamic excitation force of system applied on a pitch point of cutting tool is expressed by the following expression:

where Fmxand Fmy-excitation forces along directions x and y at pitch point of cutting tool(N);

Fnxand Fny-excitation forces along directions x and y at pitch point of gear(N);

Pmand Pn-comprehensive reverse exciting force between cutting tool and gear(N.m);

mmand mn-lumped masses between cutting tool and gear(Kg);

emand en-eccentricities of cutting tool and gear(m);

3.Analysis of simulated results of cutting vibration

The cutting parametersof finish machining in cutting machining are normally small,and the vibration generated by cutting has a direct in fluence on machined surface quality,such as finished surface roughness and dimensional precision of work piece.Therefore,the vibration analysis plays an essential role for finish machining of large module gear shaft.Here a 30 mm-diameter carbide alloy face-milling cutting tool was chosen for simulation machining offace-milling gear,and a single factor experimental method was used to select the cutting parameters in combination with actual production and in accordance with"concise metal cutting manual"[9].The cutting vibration characteristics were studied with feed speed of 125 mm/min,cutting depth of 1 mm,and milling speeds of 38 m/min,78 m/min and 118 m/min. From milling force calculation formula[9],it can be derived that the main cutting force is 441.84N,the radial force is 353.47N,and the axial force is 220.92N at the milling speed of 38 m/min;the main cutting force is 383.12N,the radial force is 306.5N,and the axial force is 191.56N at the milling speed of 78 m/min;the main cutting force is 352.66N,the radial force is 282.13N,and the axial force is 176.33N at the milling speed of 118 m/min.

Pre-processing of model through the modules such as ADAMS/Aircraft,ADAMS/Car,ADAMS/Engine and ADAMS/View is the basis of vibration analysis of cutting machining of large module gear shaft.Only through accurate simulation analysis,it is possible to ensure the acquirement of results that are close to actual situations through the establishment of vibration analysis module and vibration analysis,and the generation of modal coordinates list based on final post-processing of results through ADAMS/PostProcessor,including plotting and dynami display of forced vibration and frequency response function[10].As the excitation force of system comes from the milling force of milling cutter,the magnitude of cutting force is normally taken as the amplitude of sinusoidal excitation force,and the tip of milling cutter is taken as the excitation point of system.Generally speaking,an output port is used to test data.Large module gear shaft is a flexible object in simulation,its vibration deformation degree mainly depends on its motion degree,therefore,the type of output channel can be selected as displacement type,i.e.,center line of work piece is selected as output point,and the displacements along three directions of X,Y and Z and spatial direction are taken as output channels.

Under the excitation of force or moment of forces,the tip of cutting tool is taken as a point of action of excitation,and the center point of work piece is taken as an output point.look up modal information of system and plot frequency response curve.The modal information as shown in Fig.4 was acquired.It can be found from the modal coordinates in Fig.5 that the mode which has the largest influence on system vibration response is the second order mode due to existence of damp.It is also allowed to acquire the transfer function of system by looking up the power spectrum density function curve and the transfer function curve or the calculated results from the amplitude frequency response curve.

Fig.4.System modal information.

Fig.5.System modal information.

Fig.6 shows log magnitude-frequency characteristics curve,in which the longitudinal coordinates are expressed with L(ω)=20logA(ω)in unit of decibel(dB).Through vibration analysis,the frequency response curve in frequency scope of 0.1-1000 Hz of face-milling gear cutting machining systemwas acquiredin ADAMS post-processing module.The maximum response in direction X is at frequency of 109.6478 Hz;the maximum response in direction Y is at frequency of 301.9952 Hz;and the maximum response in direction Z is at frequency of 109.6478 Hz;the peak value is reached at 301.9952 Hz in spatial direction,and the vibration amplitude generated at this point is 0.0034 mm.Therefore,during finish machining of face-milling gear,it is necessary to prevent cutting vibration frequency generated by system at 109.6478 Hz and 301.9952 Hz through adoption of measures such as adjustment of cutting parameters and other technique equipment.A cutting machining system of face-milling gear was established,for which the internal vibration sources of all parts of machine tool,the external vibration sources outside machine tool,and the vibration influence caused due to damp between structural members of machine tool are ignored,and the ground is taken as fixing object.The output coordinates were converted as Logarithmic coordinate,and a 3-dimensional curved surface was used for more instinctive display of frequency response in all directions,as shown in Fig.7.

Fig.7.Frequency response of three dimensional surface.

Fig.8 shows the frequency responses at point B of work piece in all directions at the milling speeds of 38 m/min,78 m/min and 118 m/min.Frequency responses of center point B of work piece in all directions increases with the increase in milling speed.It shows that the higher the milling speed(i.e.,the rotation speed of spindle)is,the more prominent the generated cutting vibration is.As shown in the frequency response curves in Fig.8,the response of work piece is the largest in direction Y in scanning frequency range of 0.1-1000 Hz,indicating that the dynamic stiffness of work piece in direction Y is the smallest,the root cause is mainly due to the fact that work piece is subjected to the milling force action of milling cutter in direction Y during machining.Cutting vibration during finish machining has a substantial in fluence on the quality of machining surface,such as surface roughness and dimension accuracy of work piece.It is allowed to reduce the in fluence of vibration on machining quality by optimizing the cutting parameters and improving the technological equipment.

4.Summary

Fig.6.Frequency responses of work piece at milling speed of 38 m/min.

Fig.8.Frequency responses of work piece at different milling speeds.

The traditional gear processing method has failed to meet the growing demand for gears to a certain extent.this process prove end milling method can be used to machine the involute gears.That in the CNC milling machining center by general end milling cutter,the ball end mill cutter,through the CNC programming complete machining of gear,so that cutting tools and manufacturing equipment are transformed form traditional specialization machining method to generalization,and reduce the production cost.

A solid model of a large module gear shaft and face-milling cutter was established using UG software,and was imported to ADAMS through data conversion,and the clamping fixture and driver unit were added and assembled,so that the cutting tool gear milling machining simulation model was acquired.With consideration of the influences of stiffness characteristics,backlash and cutting tool rotation eccentricity mass,the expression of system dynamic excitation force applied on the pitch point of cutting tool derived acquired,and,was used for cutting vibration analysis as input excitation.

Using ADAMS software finish machining vibration analysis of large module gear based on fast sine sweep method,it is deduced that the displacement of the workpiece in each direction within the scope of response analysis to produce the frequency of maximum response,Y direction on the response maximum dynamic stiffness minimum.The influence of cutting vibration on the machined surface quality and machining accuracy can be reduced by optimizing the cutting parameters and improving the technological equipment and other methods.

Acknowledgement

This paper is financially supported by Natural Science Foundation of Liaoning Province(20170540778),People's Republic of China.

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A R T I C L E I N F O

Article history:

12 December 2016

in revised form

24 April 2017

Accepted 22 May 2017

Available online 26 May 2017

Gear

Face-milling

Vibration

ADAMS

Traditional machining methods,such as gear hobbing,gear shaping and gear milling,etc,are commonly used for cutting machining of gear tooth profile,which cannot meet huge machining demand of gears to a certain extent.This article proposes to utilize a face-milling machining method in involute gear machining,which can be used to reduce production cost effectively.Cutting vibration generated during cutting machining has a direct effect on the machining accuracy and machined surface quality of workpiece.Therefore,it is desiderated to perform in-depth research regarding this issue.ADAMS software was used to establish a rigid-flexible coupling virtual prototyping model of face-milling gear milling system and a cutting vibration system model.Cutting vibration analysis was performed for face-milling gear by adopting quick sine frequency sweep method,so that the frequency response characteristics of workpiece in three directions X,Y and Z and space were acquired.The research results will provide reference and theoretical foundation for actual application of face-milling gear machining technology.

?2017 The Authors.Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail addresses:jinchengzhe71@163.com(C.JIN),1019419919gc@gmail.com(C.GUO),GY13609821670@163.com(Y.GAO).

Peer review under responsibility of China Ordnance Society.