ORIGINAL ARTICLE

A novel impact load model for tool-changer mechanismof spindle system in machine tool

Huipeng Shen1& Huimin Dong1 & Delun Wang1 & Yu Wu1

& Guanglei Wu1

Received: 21 March 2017 /Accepted: 14 August 2017 /Published online: 29 August 2017# Springer-Verlag London Ltd. 2017

Abstract In this paper, a novel impact load model for a tool-changer mechanism of spindle system in machine tool is pro-posed to determine the impact load of tool-changer duringunclamping tool. The tool-changer mechanism is composedof cam (frame), shift fork, headstock, and spindle system withcutter bar. In order to build the model, the working principlesof the tool-changer and the spindle system structure are brieflyintroduced, and the load transmitting path of spindle system isanalyzed. By combining the kinetostatic behavior and energyconservation law, the computational model to calculate theimpact load of tool-changer mechanism is established toobtain the theoretical result. Moreover, a transmitting modelof the impact load is set up to collect the experiment result inthe light of bolted connection equivalent model, which is inagreement with the impact load transmitting path. With thecomputational model, the theoretical result of impact loadcan be determined based on the motion of shift fork and cutterbar system constrained by both headstock movement and camcontour curve. Using the transmitting model, the experimentalresult of impact load can be calculated by measuring checkring strain. From the comparison of the theoretical and exper-imental results, it is found that the experimental measurementagrees well with theoretical analysis. This means that the builtmodel is valid, which can be used to predict the impact loadduring the unclamping tool process. This work aims toprovide some fundamental analysis for both the design ofthe spindle system and the selection of the spindle bearingsof high-performance machine tools.

Keywords Spindle system . Tool-changer mechanism .

Impact load . Computational model . Transmitting model .

Experiment

1 Introduction

With the development of the technology and the increasingdemand on the machine tools, the spindle system has been thekey component of the CNC machine tools. The motionprecision and structural stiffness of the spindle system playan important role for the processing quality and machiningefficiency, where the accurate duration of spindle system is acritical problem to be solved for the machine tool manufac-turers. Frequent maintenances on the spindle system notonly increase the usage costs but also decrease the productquality. A major issue to influence the working life of thespindle system lies in the damage and fatigue of the bear-ings, where in the reason causing these problems is that theloading conditions of the bearing cannot be accuratelyestimated. For the spindle system, the working life of thespindle bearings are mainly subjected to the impact loadduring the process of unclamping tool, as well as the work-ing load. Although tool-changer and spindle system work atthe different times, the impact load caused by tool-changerhas a significant influence to the spindle system precisionand lifetime.

In designing the spindle system and machine tools, andselecting spindle bearings, the cutting force [1, 2], thermalload [3–6], dynamics [7–10], preload force [11–13], and ma-chine stiffness [14, 15] of the spindle system, among others,have been extensively studied and considered in the literature.On the other hand, there are very few works on the determi-nation of the impact load between tool-changer and spindlesystem during unclamping tool. For instance, De Lacalle LL

* Delun Wangdlunwang@dlut.edu.cn

1 Dalian University of Technology, Dalian 116024, China

Int J Adv Manuf Technol (2018) 94:1477–1490DOI 10.1007/s00170-017-0960-3

et al. [16] introduced a new way for preparing CNC programsfor high-speed milling. In this work, it is shown that the CAMstage is of importance in high-speed milling. Two new sub-stages should be contained in the CAM stage. One of thenew sub-stages is that the related utilities should be used forassessing the cutting forces. And then cutting strategies areestablished aimed to minimize cutting forces. The other oneis that a virtual simulation of the process is put into effect toevaluate the possibility of collisions and undesired cuts canbe assessed. Sarhan AAD [17] pointed out that the error dueto the thermal change is a major error source that affects theaccuracy of CNC machine tools, which can take up to 70%of the total machining error. This paper presented anapproach to monitor the spindle error motions caused bythermal change more precisely by using displacement sen-sor system at different levels to construct an independentmodule measurement system of spindle. In order to im-prove the precision of the machine tool, Yang X et al. [18]combined the model with the tool path to build a surfacetopography model. Their research shows that the dynamicperformance of the spindle is the major aspect for thetexture generation. By investigating spindle optimization,dynamic finite element analysis of the optimized spindleshows better performance. For obtaining an accurate modelof the preloaded bearing system, Rabréau C et al. [19] fo-cuses on the axial spindle behavior. They formulated ananalytical model to compute the equilibrium condition ofthe shaft, rear sleeve, and bearing arrangement. In theirstudy, a good agreement between the theoretical and exper-imental results was achieved to show that the modelupdating strategy and the enriched model are valid.Salgado MA et al. [20] investigated the system stiffnessformed by the machine tool, shank and tool-holder, collet,and tool, which can be adopted to approximate a value closeto the real value than the cantilever beam model and eval-uate the proportion between the corresponding deflection ofthe tool and that corresponding to the rest of the system.

As described above, the research on the impact load in theprocess of unclamping tool is rarely carried out. Moreover, itis very difficult for the machine tool manufacturer to get theactual value of impact load by the calculation or experiment inpractice. Therefore, it is necessary to study the impact load. Inthis paper, we focus on the impact load on the spindle systemand deal with the problem. The calculation and verificationprocess of the impact load is introduced as follows. Firstly, theworking principle of tool-changer and the spindle systemstructure are briefly introduced. And then, the theoreticalmodel for computational impact load is established throughthe combination of the kinetostatics and energy conservationlaw. Moreover, the impact load elastic transmitting model de-scribing load transmitting path is developed based on loadmodel of multiple connected members by bolted connection.Afterwards, the theoretical result of impact load is calculated

using the analytical model, according to the motion of cam,headstock, shift fork, and cutter bar system. Finally, the impactload is measured by a strain experiment with a quarter bridgesof strain gages. By comparing the theoretical and experimentresults, it is shown that the proposed impact load model fortool-changer mechanism of machine tool spindle system isvalid to predict the impact load during the process ofunclamping tool.

In the process of the research, it was found that themodel was related to cam contour curve, the headstockmotion, and the parameters of the tool-changer mecha-nism. With the prescribed conditions, the impact load canbe correctly calculated by the proposed model, whichmeans that the method can be used to optimize the designparameters to meet the required impact load effectively.Moreover, it will provide a scientific theoretical supportfor designing spindle system and selecting spindle bearingsof high-performance machine tools. To specially mention,the mechanical tool-changer studied in this paper is a majortype of that used in machine tools. The method formulatedcan be generalized to calculate the impact load for the sametype machine tool products.

2 Working principle of tool-changer

With the requirement of the product quality and machiningefficiency, automatic tool-changer has become a necessaryequipment of CNC machine tools. The working procedureof tool-changer mainly includes unclamping tool, ex-changing tool, and loading tool. In this procedure, tool-changer mechanism unclamps down the current cuttingtool from the spindle system, exchanges the used tooland new tool, and loads the new tool into the spindlesystem and the used tool into the tool magazine by tool-changer mechanism. As the impact load of unclampingtool has a significant influence to the spindle system inthe entire working processes of tool-changer, the processof unclamping tool is mainly researched. It should benoted that changing times of tool-changer are importantfor processing efficiency. However, this paper aims to cal-culate the impact load, and the changing times of a perfectcycle always kept unchanged which can meet the userrequirement for this type of machine tool.

2.1 Tool-changer mechanism

There are a number of variations of tool-changer mecha-nisms, such as hydraulic, pneumatic, and mechanical. Ofthem, a mechanical tool-changer mechanism is a major typein many machine tools. It is composed of a headstock, aframe, a cam, a shift fork, and a spindle system. Figure 1shows the tool-changer structure and sketch, where the

1478 Int J Adv Manuf Technol (2018) 94:1477–1490

headstock II is used as a driving link that moves up anddown, driven by a screw mechanism; cam is fixed on theframe I; shift fork III connects headstock II by revolute pairR2; and spindle system IV is installed on the headstock II bybolted connection.

In the process of unclamping tool, with headstock IImoving up, press roll R1 of shift fork III will contact withthe cam, the shift fork III will rotate about the circle centerof revolute pair R2, and press roll R3 will contact withcutterhead of spindle system IV. The process of unclampingtool is not completed until disc spring V is compressed to thelowest point. Obviously, the process of unclamping tool isachieved by the movement of shift fork and spindle systemrelative to the frame (cam).

2.2 Spindle system structure

The structure of spindle system IV is relatively complex, which isconsisted of disc spring 1, locknut 2, the end cover of rear bearing3, rear bearing 4, check ring 5, water jacket 6, head bearing 7, theend cover of head bearing 8, the flange of head bearing 9, sleeve10, mandrel 11, cutter bar 12, straight pin 13, cutter head 14, andsome other sealing devices, as shown in Fig. 2.

For achieving the unclamping tool and loading tool, the pre-load bearing and disc spring in spindle system are set. Bearing ispreloaded by means of a torque wrench, aiming to eliminatebearing clearance, improve motion stability of spindle system,and enhance spindle stiffness. Disc spring is preloaded by limitinginstallation dimension provides enough tensioning force to keepspindle work normally.

According to the tool-changer mechanism and the spindlesystem structure, as depicted in Figs. 1 and 2, respectively,while press roll R3 comes into contact with spindle systemIV to unclamp tool, cutter head 14 is pushed down; then cutterbar 12 moves down relative to headstock II, disc spring 1 isfurther compressed, mandrel 11 is stretched, and sleeve 10 is

relaxed. The impact load is transmitted to mandrel 11, locknut2, the end cover of rear bearing 3, rear bearing 4, check ring 5,and water jacket 6 in order. At last, the force is acted onheadstock II and frame I. In consequence of cutter bar 12when bound together with cutterhead 14 by straight pin 13,they have the same motion. For convenience, the whole ofcutter bar 12, straight pin 13, and cutterhead 14 is defined ascutter bar system. We are interested in the impact load actingon cutter bar system in the process of unclamping tool in thispaper. Therefore, the impact load model will be built and theverification experiment will be designed.

3 Impact load model of tool-changer mechanism

The impact load model of tool-changer mechanism to deter-mine the impact load contains both a computational modeland a transmitting model. The computational model is built

(a) Structure of tool-changer (b) Sketch of tool-changer

Fig. 1 Tool-changer mechanismof machine tool. a Structure oftool-changer. b Sketch of tool-changer

Fig. 2 Structure of spindle system

Int J Adv Manuf Technol (2018) 94:1477–1490 1479

for theoretical analysis, and the transmitting model isestablished for measuring the impact load to verify the former.

3.1 Computational model of impact load

From the previous description, the cutter bar system movesalong the Z direction relative to headstock. For establishingthe computational model, let the acceleration of the cutter barsystem be a12 at the instantaneous impacting; the kinetostaticanalysis of the tool-changer mechanism is conducted. For thecutter bar system, there are three forces on it, namely, theimpact load FR3 , preloading force F1 of disc spring 1 whichcan be obtained by the stiffness k1 and the compressionΔx ofdisc spring during the period of preloading, and inertia forceof cutter bar system, as shown in Fig. 3a. The equilibriumequation is expressed in Eq. (1).

FR3 þ F1 ¼ m12a12F1 ¼ −k1Δx

�; ð1Þ

where m12 is the mass of cutter bar system.For the cam shift forks system, there are three forces and an

inertia torque shown in Fig. 3b, the impact load F0R3

¼ −FR3 ,

the force of cam on the shift fork F0R1, the force of headstock

on shift fork F0R2, and inertia force. Due to the low stiffness of

the shift fork, the deformation of the shift fork is consideredshown in Fig. 3c. Henceforth, assuming the angular accelera-tion of shift fork is α at the impacting instant, the equilibriumequation is written as follows Eq. (2):.

F0R 3

þ F0R2cos α2 þ F

0R 1cos θ ¼ mIIIaIIIZ

F0R 2sin α2 þ F

0R1sin θ ¼ mIIIaIIIY

Jα ¼ R2R1 þΔR1r þΔR1tð Þ � F0R 1

þ R2R3 þΔR3r þΔR3tð Þ � F0R3;

8>>><>>>:

ð2Þ

where αR2 is the angle between the force F0R2

and Y direc-

tion, θ is the angle between cam profile with straight lineand Y direction, mIII is the mass of shift fork at center ofrevolute pair R2, aIIIY and aIIIZ are the acceleration of shiftfork barycenter along Y direction and Z direction, respec-tively, and J is the moment of inertia about revolute pairR2 of the shift fork. Moreover, R2R1 and R2R3, respec-tively, are the length vectors of R1R2 and R2R3 shift fork,and ΔR1r ,ΔR1t ,ΔR3r and ΔR3t are the corresponding radialand tangential deformations of R1R2 and R2R3 shift fork,respectively.

In accordance with material mechanics theory, the radialand tangential deformations of R1R2 and R2R3 shift fork inEq. (2) can be readily denoted in Eq. (3).

ΔR1r ¼ F0R 1

cos αR 1 R2R1j j.

EAR1R2ð Þ

ΔR1t ¼ F0R 1

sin αR 1 R2R1j j3.

3EIR1R2ð Þ

ΔR3r ¼ F0R 3

cos αR 3 R2R3j j.

EAR2R3ð Þ

ΔR3t ¼ F0R 3

sin αR 3 R2R3j j3.

3EIR2R3ð Þ

8>>>>>>>>><>>>>>>>>>:

; ð3Þ

where αR1 is the angle between the force F0R1

and R1R2 shift

fork;αR3 is the angle between the force F0R3

and R2R3 shift

fork; E is elastic modulus of shift fork; AR1R2 and AR2R3 are thecross section areas of R1R2 and R2R3 shift fork, respectively;IR1R2 and IR2R3 are the area moment of inertia about R1R2

and R2R3 shift fork, respectively.Based on energy conservation law, it is known that the

kinetic energy variation ΔT of shift fork and cutter barsystem equals to the potential energy variation ΔV of shiftfork caused by the impact force FR3 . Taking the deforma-tions in Fig. 3c into account, the kinetic energy variationΔT and the potential energy variation ΔV are derivedin Eq. (4).

ΔT ¼ ΔV

ΔT ¼ 1

2J ω1

2−ω22

� �þ 1

2m12 v1

2−v22� �

ΔV ¼ 1

2F

0R 1

þ k1Δx R2R3j jsin αR 3

R2R1j jsin αR 1

� �2R2R1j jcos2αR 1

EAR1R2

þ 1

2F

0R 1þ k1Δx R2R3j jsin αR 3

R2R1j jsin αR 1

� �2R2R1j j3sin2αR 1

3EIR1R2

þ 1

2F

0R3

þ k1Δx

� �2R2R3j jcos2αR 3

EAR2R3

þ 1

2F

0R 3

þ k1Δx

� �2R2R3j j3sin2αR 3

3EIR2R3

8>>>>>>>><>>>>>>>>:

; ð4Þ

where ω1, ω2, v1, and v2 are the angular velocity of theshift fork and linear velocity of the cutter bar system inthe process of unclamping tool, respectively, which can bedetermined by cam profile and the cutter bar system as

shown in Fig. 4, and meet the following relationship inEq. (5).

v2−v1 ¼ ω2 R2R3j jsin αR 3 ð5Þ

1480 Int J Adv Manuf Technol (2018) 94:1477–1490

According to Eqs. (1) to (5), the theoretical impactload FR3 exerting to cutterhead of spindle system bypress roll R3 can be derived as shown below:

B11FR34−B12FR3

3 þ B13FR32−B14FR3 þ B15 ¼ 0 ð6Þ

where

A11 ¼ cos2αR 3 R2R3j jEAR2R3

þ sin2αR 3 R2R3j j33EIR2R3

!. cot2αR 1

EAR1R2 R2R1j j þR2R1j j3EIR1R2

� �

A12 ¼ J ω12−

v2−v1R2R3j jsin αR 3

� �2 !

þ m12 v12−v22

� � !. cot2αR 1

EAR1R2 R2R1j j þR2R1j j3EIR1R2

� �

A13 ¼ k1Δx R2R3j jsin αR 3 þ EAR1R2 R2R1j jtan αR 1

.2

A14 ¼ E2A2R1R2 R2R1j j2tan2αR 1

.4þ Jα

A15 ¼ EAR1R2 sin αR 1 sin αR 3 R2R1j j R2R3j jA16 ¼ AR1R2 sin αR 1cos αR 3 R2R1j j R2R3j jð Þ

.AR2R3

B11 ¼ A11 þ A16ð Þ2B12 ¼ 2A11 A11 þ 2A16ð Þk1Δx−3A11A15−2A15A16

B13 ¼ 2A11 3A11 þ A16ð Þk12Δx2−4A11A15k1Δxþ A215 þ 2A16 A14−A12−A2

13

� �þ 2A11 A213−A12 þ A14

� �B14 ¼ 4A3

11k13Δx3−2A11A15k12Δx2 þ 4A11 A14 þ A213−A12

� �k1Δxþ 2A15 A12 þ A2

13−A14

� �B15 ¼ A12−A2

13−A11k12Δx2 þ A14

� �2−4 A12A14−A11A14k12Δx2� �

8>>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>>:

: ð7Þ

Equation (6) represents the impact load model for compu-tational the impact load. It indicates the impact load dependson the cam contour curve, the headstock motion, materialproperty and geometrical dimensions of shift fork, thepreloaded length, and stiffness of disc spring. When theabovementioned parameters are given, the impact force canbe determined. Consequently, the model will provide a way tooptimize the abovementioned parameters to meet the requiredimpact load in the future.

3.2 Transmitting model of impact load

In this section, we are interested in the transmission processand the transmitting model of the impact load FR3 for testing

and verifying the computational model through experimentalapproach. For the convenience of clearly illustrating the loadpaths, all contact surfaces between adjacent parts are intro-duced by different letters when establishing the transmittingmodel of the impact load. The transmitting model of impactload is depicted in Fig. 5. In Fig. 5, the letters from A to M,respectively, stand for the contact surfaces between the eachtwo adjacent parts.

According to the spindle system structure, its load transmit-ting form is similar to the force model of bolted connection,and the difference of them lies in the number of connectedmembers. Therefore, the force model of multiple connectedmembers by bolted connection is built to describe the transmit-ting process of the impact load in spindle system. In the model,

(a) Mechanical model of cutter bar system (b) Mechanical model of cam shift forks system (c) The deformation of shift fork

Fig. 3 Mechanical model of the impact load. a Mechanical model of cutter bar system. b Mechanical model of cam shift forks system. c Thedeformation of shift fork

Int J Adv Manuf Technol (2018) 94:1477–1490 1481

mandrel is equal to bolt preloaded by locknut, and others in-cluding rear bearing, check ring, water jacket, sleeve, and headbearing are treated as multiple connected members, as shownin Fig. 5b. Here, each part can be replaced with the equivalentspring or dampers, where the elastic equivalent mechanicalmodel of spindle system has been established, as displayed inFig. 5c. It is noteworthy that locknut and the end cover of rearbearing are simplified as a spring k2 , 3, because of the sameforce applied to them.

When the locknut is not tightened, every connectedmember is in the natural state, as shown in Fig. 5b. After thelocknut (letterA) is tightened in torqueT0 by a torque wrench,mandrel is stretched, and the other parts are compressed. Atthe moment, the spindle system is not assembled in machinetool, and the equivalent model after tightening locknut isshown in Fig. 6.

In the light of Fig. 6b, the preloaded load FT0 caused bytorque T0 is applied to the position labeled by letterA. Then, itis transmitted to the position labeled by letter B by locknut.Letter B passes the force in order of B-C-A, B-J-K-L-F/G-A,andB-D-E-F/G-A. Therefore, the load transmittingmodel con-stitutes a set of equations after tightening locknut as Eq. (8).

FT0 ¼

k2;3 x02;3−x2;3

� �

k4 x04−x4

� �þ f1

k5 x05−x5

� �þ k10 x

010−x10

� �þ f1

k6 x06−x6

� �þ k10 x

010−x10

� �þ f1

k7 x07−x7

� �þ f1 þ f2

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

; ð8Þ

where ki is the stiffness of the corresponding part in Fig. 2, xi isthe natural length of the corresponding part, x

0i is the natural

length of the corresponding part after tightening locknut, and fiis the friction of the corresponding part damper after tighteninglocknut.

After the spindle system is assembled in machinetool, the disc spring has been preloaded in the forceF1. As water jacket connects headstock by bolted con-nection, the position constraint of the elastic equivalentmechanical model lies in letter K, as shown in Fig. 7a.Due to the structural constraints of the spindle system,the upper part of mandrel sustains tension and the lowerpart suffers pressure after the disc spring is preloaded.Analyzed the load path in detail, the preloaded load F1

is transmitted to letter I by cutter bar system. Then, it istransmitted to letterH by disc spring. LetterH passes the forceto both letter A and letter C by mandrel. Next, the force ofletter A is transmitted in order of A-B-J-K. And the force of

(a) Simplification of contact surface (b) Equivalent model by bolted connection (c) Elastic equivalent model

Fig. 5 Transmitting model of the impact load

Fig. 4 The relation between angular velocity and linear velocity

1482 Int J Adv Manuf Technol (2018) 94:1477–1490

letter K returns to letter M forming a force circuit by waterjacket, headstock, and frame. The rest is the same as the loadpath of letter A except that the force of letter C is transmittedto letter K in order of C-J-K. Then, the lengths of eachcorresponding spring are supposed to be x″2;3, x

″4, x

″5, x

″6, x

″7,

and x″10.During the period of unclamping tool, the mandrel is fur-

ther stretched and sleeve is relaxed with the compression ofdisc spring with the impact load FR3 . When the sleeve iscompletely relaxed, head bearing and sleeve will be unloaded.At the time, the equivalent model by bolted connection isshown in Fig. 7b, and the elastic equivalent mechanical modelis simplified as shown in Fig. 7c. The lengths of each corre-

sponding spring are denoted by x‴2;3, x‴4, and x

‴5. Moreover, the

friction of the corresponding c1 damper is f01.

From Fig. 7, the load transmitting model during the periodof unclamping tool is expressed as Eq. (9).

FR3 ¼

k2;3 x‴2;3−x″2;3

� �þ f

01

k4 x‴4−x″4

� �þ F1

k5 x‴5−x″5

� �þ F

01

8>>>>>>><>>>>>>>:

; ð9Þ

where F01 represents the residual preload.

In summary, when cutter bar system is pushed down andmandrel is further stretched, the compression of check ring

x‴5−x″5� �

is caused not only by FR3−F1ð Þ, but also by the

relaxed preload of sleeve. So the residual preload F01 is intro-

duced to calculate the impact load FR3 . According to Eq. (9),

(a) Equivalent model by bolted connection (b) Elastic equivalent model

Fig. 6 Equivalent model aftertightening locknut

(a) Of preloaded the disc spring (b) Equivalent model by bolted connection (c) Of completely relaxed sleeve

Fig. 7 Equivalent model during the period of unclamping tool

Int J Adv Manuf Technol (2018) 94:1477–1490 1483

rear bearing and check ring can be used to determine theimpact load FR3 by means of the design of experiments.Considering their structures, check ring is more suitable andconvenient to predict the impact load FR3 . Therefore, trans-mitting model of impact load FR3 is rewritten as Eq. (10).

FR3 ¼ F01 þ k5Δx5; ð10Þ

where Δx5 represents the compression of check ring duringthe period of unclamping tool.

As described above, the computational model and transmit-ting model of impact load have been established. In the fol-lowing section, according to the motion relationship amongcam, headstock, shift fork, and cutter bar system, the theoret-ical result of the impact load will be calculated using the com-putational model. And an experiment of the impact load willbe designed to verify the validity of the theoretical result bymeasured the check ring.

4 Theoretical analysis of impact load

Cam contour curve, the headstock motion, material propertyand geometrical dimensions of shift fork, the preloaded length,and stiffness of disc spring will be given to calculate the impactload, consistent with the practical application. According to theknown headstock motions, shift fork and cutterhead motionscan be worked out by their movement relationships. Andkinematic parameters about shift fork and cutterhead arecalculated. Then, the theoretical result of the impact load issolved using the computational model in Eq. (6).

4.1 R1 center effect of headstock motion

It is noteworthy that the cam in the tool-changer mechanism isdifferent from the traditional one. In the tool-changer mecha-nism, the cam was fixed on the frame. And shift fork had acomposite motion subject to the restriction of headstock

motion and cam profile. The cam contour curve consists oftwo cycloidal displacements, straight line, and dwell displace-ment, shown in Fig. 8c. In the unclamping tool process, pressroll R1 of shift fork contacts with the straight line segment ofcam contour curve, from press roll R3 of shift fork contactwith cutterhead of spindle system to the cutter unclamped.And a constant angular velocity motion of shift folk isachieved. Therefore, for determining the impact load, the ac-celeration and jerk of the cycloidal displacement are not takeninto account. The straight line BR0 of cam contour curve hasbeen taken as a main object of study in this paper.

The cam profile and the headstock motion are provided asknown parameters by the machine tool manufacturer.According to Fig. 8a, themotions of headstock drags the centerof revolute pair R2 of shift fork up or down directivity, withwhich influences the center point of press roll R1 (point B

′) bycam contour. In order to give the numerical value about camcontour and the headstock motion, the coordinate system B′YZis set up with the center of R1 (pointB

′) shown in Fig. 8b. In thecoordinate system B′YZ, it is known that the coordinates of B′,R

00, R

′, C′, and O are respectively (0, 0), (4.3776, 13.4729),(6.2130, 25.0610), (6.213, 97.0610), and (−31.2870,25.0610) with the unit of millimeter from the machine toolmanufacturer. The angle θ between line BR0 of cam contourcurve and Y direction is 72°. The circle radiuses of press roll R1and R3, respectively, are denoted by rR1 ¼ 17:5 mm andrR3 ¼ 11 mm. According to the knowns, in coordinate systemB′YZ, cam straight line segment can be calculated as Eq. (11).

y0 ¼ z

0cot θ z

B0≤z

0≤z

R00

!ð11Þ

For simplification, let assume that a fixed position B″ existson headstock, and the same position as B′ on headstock whilethe shift fork and the cam do not contact. By integrating thecam contour curve into the kinematic parameters of headstock,

(a) (b) (c)

Fig. 8 Cam contour curve

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Z-motion trajectory of the fixed position B″ on headstock isworked out in coordinate system B′YZ from t0 = 0 s to tT =1.1575 s, as shown in Eq. (12). The coefficients of each sec-tion in Eq. (12) are listed in Table 1.

z ¼ ait2 þ bit þ ci ti≤ t < tiþ1ð Þ ð12Þ

4.2 Shift fork motion

From Fig. 1, the motion of shift fork is in accordance with Z-motion trajectory of headstock before shift fork contacts withcam. But after shift fork contacts with cam, press roll R1 ofshift fork moves along cam profile. The straight line BR0 ofcam profile is crucial to calculate the impact load.

Figure 9 shows shift fork motion condition when shift forkcontacts with the point B of cam contour curve. The initialangle α0 is 18.5001° between R1R2 shift fork and Z directionbefore shift fork contacts with cam. The initial angle β0 is11.5392° between R2R3 shift fork and Y direction before shiftfork contacts with cam. After shift fork contacts with cam, theangle between R1R2 shift fork and Z direction is α1. The anglebetween R2R3 shift fork and Y direction is β1. The Y and Zdisplacement variation of press roll R1 areΔy andΔz. The Zdisplacement variation of press roll R3 is Δz′.

Δy ¼ R1R2j j sin α0−sin α1ð ÞΔz

0 ¼ R2R3j j sin β1−sin β0ð Þα0 þ β0 ¼ α1 þ β1

8<: ð13Þ

Moving along cam profile B′R′0, the center of press roll R1

is not only in cam contour curve B′R′0 but also in a dynamic

circle around revolute pair R2 (70.71298, z2). So Y-motion y1and Z-motion z1 along cam profile B′R′

0 is subject to the fol-lowing kinematic constraints in Eq. (13).

y1 ¼ z1cot θ

y1−yR2

� �2 þ z1−z2ð Þ2 ¼ R1R2j j2y2 ¼ R1R2j jsin α0

z2 ¼ z− R1R2j jcos α1

y1 ¼ R1R2j j sin α0−sin α1ð Þ

8>>>><>>>>:

ð14Þ

When press roll R1 moves on the point R00, the coordi-

nate of R00 is (4.3776, 13.4729) with the unit of mm in the

coordinate system B′YZ and the angle α1 between the R1R2

shift fork and Z direction equals 17.3173°. Then, the co-

ordinates of R00 and the angle α1 are put into Eq. (14) to

gain z = 13.4729 mm. Next, the time tR00moving on the

point R00 can be solved using Eq. (12). The calculation

result is that tR01equals 0.790085 s. So the time interval

moving along cam contour curve B′R′0 is from 0.70925 to

0.790085 s.

4.3 Cutter bar system motion

For cutter bar system, the point at the position that press rollR3 contacts with cutterhead is used to describe cutter barsystem motion. When press roll R3 moves 2.6 mm alongthe negative Z direction relative to headstock, shift fork justcontacts with cutterhead. Assumed the contact time is tR3 ,the cutterhead motion is in accordance with headstock be-fore the time tR3 . At the time tR3 , the Z displacement

Table 1 Z-motion trajectory coefficients of headstock

i ti (s) ti + 1 (s) ai bi ci i ti (s) ti + 1 (s) ai bi ci

1 0 0.0250 10,000 0 −333.3468 9 0.9393 0.9402 −10,000 18,802.6667 −8818.85362 0.0250 0.6600 0 500 −339.5968 10 0.9402 0.9485 10,000 −18,804 8859.4136

3 0.6600 0.6850 −10,000 13,700 −4695.5968 11 0.9485 1.0002 0 166.6667 −137.74134 0.6850 0.6933 10,000 −13,700 −4688.9032 12 1.0002 1.0085 −10,000 20,170.6667 −10,141.74175 0.6933 0.8110 0 166.6667 −118.2079 13 1.0085 1.0335 10,000 −20,170 10,200.3757

6 0.8110 0.8193 −10,000 16,386.6667 −6695.4179 14 1.0335 1.1325 0 500 −480.84687 0.8193 0.8202 10,000 −16,386 6730.1781 15 1.1325 1.1575 −10,000 23,150 −13,306.40938 0.8202 0.9393 0 16.6667 3.9913

Fig. 9 Shift fork motion at inversion headstock

Int J Adv Manuf Technol (2018) 94:1477–1490 1485

variation of press roll R3is Δz

0tR3ð Þ ¼ 2:6 mm. After the

time tR3 , there is Δz′ difference of the Z displacement be-tween cutterhead and headstock. Using Eqs. (12) and (13),

the time tR3 can be calculated which equals 0.749870 s. Asa consequence, the cutterhead motion z3 is expressed inEq. (15).

z3 ¼ z − R1R2j jcos α0 þ R2R3j jsin β0 þΔz0tR3ð Þ þ rR3

� �t0≤ t≤ tR3ð Þ

z3 ¼ z − R1R2j jcos α0 þ R2R3j jsin β0 þΔz0tR3ð Þ þ rR3

� �− Δz

0−Δz

0tR3ð Þ

� �tR3 < t≤ t

R0

!

z3 ¼ z − R1R2j jcos α0 þ R2R3j jsin β0 þΔz0tR3ð Þ þ rR3

� �− Δz

0tR0ð Þ−Δz

0tR3ð Þ

� �tR0< t≤ tT

!

8>>>>>>>>><>>>>>>>>>:

ð15Þ

4.4 Theoretical result of impact load

Based on the previous analysis, the impact load FR3 can besolved when the kinematic parametersv1, v2,ω1, and α arecalculated. Since the motion about cutterhead and head-stock are the independent functions, the velocities v1 andv2 of the cutterhead can be worked out by infinitesimalmethod, as derived in Eqs. (16) and (17). By the same to-ken, the kinematic parameters ω1 and α can be computedfrom by Eq. (13). All of the parameters for calculating theimpact load FR3 are listed in Table 2. According to Table 2,the theoretical result of the impact load, which is equal to4027.04 N, can be solved by the computational modelof Eq. (6).

v1 ¼ z3 tR3ð Þ−z3 tR3−Δtð ÞΔt

ð16Þ

v2 ¼ z3 tR3 þΔtð Þ−z3 tR3ð ÞΔt

ð17Þ

5 Experiment design of impact load

In accordance with Eq. (10), a simple method to measure theimpact load FR3 is to obtain the structural stiffness k5 of checkring and its deflectionΔx5. However, due to the sealing struc-ture of the spindle system, it is difficult, even impossible, toobtain directly the check ring deformation at the moment ofunclamping tool. Therefore, this section adopts strain experi-ment approach to measure the impact load FR3 based on theHooke’s law as expressed in Eq. (18). The Eq. (10) is rewrittenin a new expression of Eq. (19).

F ¼ kεε ð18Þ

FR3 ¼ F01 þ k

05ε5 ð19Þ

where F is the tested force, kε is the coefficient between strainand force of the tested part, ε is the tested strain, k

05 is the

coefficient between strain and force of check ring, and ε5 isthe strain of check ring at the time of unclamping tool,respectively.

1486 Int J Adv Manuf Technol (2018) 94:1477–1490

Table 2 The parameters about computational the impact load

Parameter Value Unit Parameter Value Unit Parameter Value Unit

m12 1.4 kg |R1R2| 222.8542 mm α0

18.5001 °

J 3.2 × 105 kg mm2 |R2R3| 255.6487 mmβ

0

11.5392 °

E 2.1 × 105 MPa v1 166.6667 mm/s α1

17.9047 °

rR311 mm v2 102.8413 mm/s

β1

12.1346 °

AR1R2

1.7930 × 103 mm2 ω1 −0.2554 rad/s αR1

54.0953 °

AR2R3

2.1653 × 103 mm2 α 0.0211 rad/s2 αR3

77.8654 °

IR1R2

2.5512 × 106 mm4

Δz0tR3ð Þ 2.6 mm θ 72 °

IR2R3

7.7935 × 105 mm4 Δx −7.66 mm k1 426.389 N/mm

In order to calculate the impact load FR3 , F01 and k

05 of

check ring should be measured by the experiment calibration.Then, the impact load FR3 is calculated used transmittingmodel by testing strain ε5. So the task of this section is to

design an experiment to determine F01, k

05, and test strain ε5

of check ring.

5.1 Experiment scheme

This experiment adopts wireless strain system to obtain k05 and

ε5 by a quarter bridges of strain gages. In order to ensure auniform load distribution exerting to each part and the integ-rity of strain gauges at the process of installing spindle system,the experiment needs to process check ring and water jacket.

Processing check ring is to attach strain gauges, and pro-cessing water jacket is to measure strain gauges and connecttest instruments. The letters A and B respectively representthe processed positions of check ring and water jacket, asshown in Fig. 10. The four processed facets of check ringare shown in Fig. 11.

5.2 Experiment calibration

The purpose of experiment calibration is to confirm F01 and k

05

to accomplish transmitting model of the impact load in

Eqs. (10) and (19). The coefficient k05 is achieved by the mea-

sured relationship between force and strain of check ring. And

the coefficient F01 is gained by measured the relation between

(a) Experiment design scheme (b) Spindle system after processing

Fig. 10 Experimental setup

Fig. 11 Calibration experimentof check ring

Int J Adv Manuf Technol (2018) 94:1477–1490 1487

force and strain of spindle system. The following contents willintroduce the process of experiment calibrations.

(1) Experiment calibration of check ring

After attaching strain gauges in the four processed facets ofcheck ring, the experiment loads of check ring are measuredby force sensor and experiment strains are measured bywireless strain system, as shown in Fig. 11. For the repeat-ability of the experiment and the reliability of the test data,the same process of the calibration experiment is repeatedten times for check ring. The experiment results are shownin Fig. 12.

In Fig. 12, horizontal and vertical axes respectively repre-sent experiment loads of check ring and the average strain dataof the four processed facets every time. It can be concludedfrom the Fig. 12 that the calibration experiment is repeatableand the experiment loads are linearly related to strain. Becauseof the experimental errors, the ideal evenness of load distribu-tion cannot be realized. Therefore, the ten experimental resultsare similar, but not identical. According to experiment

calibration curve, the strain and force coefficient k05 of check

ring, which is equals to −31.6676 N/με, is fitted out.

(2) Experiment calibration of spindle system

In order to get the coefficient F01 and simulate the same

load environment, the transmitting model of the impact loadin Eq. (10) is determined by calibration experiment of spindlesystem. After attaching strain gauge in terms of 5.1 and 5.2sections, spindle system is assembled. Then, test devices areconnected for experiment preparation. Next, the component ofspindle system is fixed to a press machine, as shown in Fig.13. Based on actual installation of spindle system and thepractical condition of unclamping tool, the experimental loadF is applied by rotating the hand wheel of the press machine,as shown in Fig. 13. And the numerical values of experimentload are recorded by three force sensors, which are axis-symmetrically placed at the flange of head bearing.

On the basis of test results in Fig. 14, the relationshipbetween tested strains and forces follows a linear functionapproximately. The transmitting model of impact load in

Fig. 12 Experiment calibration curve of check ring

Fig. 13 Calibration experimentof spindle system

Fig. 14 Experiment calibration curve of spindle system

1488 Int J Adv Manuf Technol (2018) 94:1477–1490

Eq. (10) or (19) is determined by the curve fitting method andthe experiment calibration result of spindle system. And it iswritten out in Eq. (20) like Eqs. (10) and (19). The coefficient

F01, which is equal to 2398.6 N, is fitted out.

FR3 ¼ 2398:6−31:6676ε5 ð20Þwhere ε5 is an average strain data of the four processed facetsfor check ring.

5.3 Experiment measurement

After the experiment calibration, spindle system is installed onmachine tool to measure the impact load, as shown in Fig. 15.The check ring strains of the four measured facets are −75.55,−60.19, −57.96, and −60.21 με, respectively. The average ofthe fourmeasured strains is equal to −63.4775 με. As a result,the experiment result of impact load is calculated as 4408.78N by Eq. (20).

5.4 Experiment result analysis

As mentioned above, theoretical and experiment results of theimpact load are respectively 4027.04 and 4408.78 N, whichmeans that the theoretical analysis and measurement experi-ment have a good agreement. The theoretical result is about8.66% smaller than the experimental one, which is acceptable.On the other hand, the reasons introducing the experimenterror are very complex, such as the effects of environmenttemperature and thermal load. The result shows that the ex-periment result can verify the validation of the theoreticalanalysis model about the impact load and the theoretical anal-ysis model of the impact load is able to predict the impact loadduring the process of unclamping tool.

6 Conclusions

In this paper, an impact load model of tool-changer mech-anism and an experiment measurement method are

developed. The following conclusions are drawn fromthe presented work:

(1) The impact load model of tool-changer mechanism wasbuilt by combining kinetostatics with energy conserva-tion law together with the structure and load transmittingpath of spindle system. It handled the problem of thedetermination of the impact load between tool-changerand spindle system during unclamping tool. The theoret-ical analysis agreed well with experimental measurementfor a mechanism with specified parameters. Using theimpact load model, or according to the impact load, thelifetime of spindle bearing and spindle system can beevaluated.

(2) An experimental measuring method was proposed byload transmitting path to obtain the load. It has beenproved to be an effective approach of testing impact loadin the tool-changer mechanism. And it can be used tovalidate theoretical model and to calculate the impactload in the same machine tool products. This methodcan be generalized to other load tests.

(3) The proposedmethod canwork efficiently and predict theimpact load, which can provide a reasonable load condi-tion and some fundamental analysis to design the spindlesystem as well as the selection of spindle bearings to-wards high-performance machine tools. Furthermore, itwill provide a way to optimize the parameters of tool-changer mechanism to meet the required impact load inthe future.

Acknowledgements The support by the National Natural ScienceFoundation of China (No. 51375065) is gratefully acknowledged.

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