thermal deformation in machine tools - mcgraw-hill professional

About the EditorYoshimi Ito, Dr.-Eng., C Eng., FIET, is Professor Emeri-tus at the Tokyo Institute of Technology, immediate past vice president of the Engineering Academy of Japan, and past president of the Japan Society of Mechanical Engineers, Tokyo. The author of numerous engineering research papers and books, he is currently involved in the establishment of the Indian Institute of Information Technology, Design & Manufacturing, Jabalpur, India.

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvTable for Conversation . . . . . . . . . . . . . . . . . . . . . . . . . xix

1 Fundamentals in Design of Structural Body Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Necessities and Importance of Lightweighted Structure in Reduction of Thermal Deformation—Discussion Using Mathematical Models . . . . . . . . . . . . . . . . . . . . . 81.2 First-hand View for Lightweighted Structures with High Stiffness and Damping in Practice . . . . . . . . . . . . . . . . . . . . . . 19

1.2.1 Axi-symmetrical Confi guration—Portal Column (Column of Twin-Pillar Type) . . . 191.2.2 Placement and Allocation of Structural Confi guration Entities . . . . . . . . . . . . . . . 21

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2 What Is Thermal Deformation? . . . . . . . . . . . . . . . . 312.1 General Behavior of Thermal Deformation . . . 322.2 Estimation of Heat Sources and Their Magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.2.1 Estimation of Heat Source Position . . . . 382.2.2 Estimation of Magnitude of Heat Generation . . . . . . . . . . . . . . . . . . . . . . . . 39

2.3 Estimation of Thermal Deformation of Machine Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.3.1 Estimation of Thermal Deformation in General . . . . . . . . . . . . . . . . . . . . . . . . . 422.3.2 Thermal Deformation Caused by Inner Heat Sources . . . . . . . . . . . . . . . . . 432.3.3 Thermal Deformation Caused by Both Inner and Outer Heat Sources . . . . . . . . 46

2.4 Heat Sources Generated by Chips and Their Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.4.1 Mathematical Model of Chips . . . . . . . . 51

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2.4.2 Thermal Properties of Chips— Equivalent Thermal Conductivity and Contact Resistance . . . . . . . . . . . . . . 532.4.3 An Example of Heat Transfer from Piled Chips to Machine Tool Structure . . . . . . 582.4.4 Dissipation of Chips . . . . . . . . . . . . . . . . 60

2.5 Future Perspectives in Research and Development for Heat Sources and Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3 Structural Materials and Design for Preferable Thermal Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.1 Remedies Concerning Raw Materials for Structural Body Components . . . . . . . . . . . . . . 72

3.1.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . 773.1.2 Painting and Coating Materials . . . . . . . 853.1.3 New Materials . . . . . . . . . . . . . . . . . . . . . 87

3.2 Remedies Concerning Structural Confi gurations and Plural-Spindle Systems . . . 90

3.2.1 Non-Sensitive Structure . . . . . . . . . . . . . 953.2.2 Non-Constraint Structure . . . . . . . . . . . . 973.2.3 Deformation Minimization Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 1003.2.4 Plural-Spindle Systems—Twin-Spindle Confi guration Including Spindle-over- Spindle Type . . . . . . . . . . . . . . . . . . . . . . . 105

3.3 Future Perspectives in Research and Development for Structural Confi guration to Minimize Thermal Deformation . . . . . . . . . . 107

3.3.1 Two-Layered Spindle with Independent Rotating Function . . . . . . . . . . . . . . . . . . 1093.3.2 Selective Modular Design for Advanced Quinaxial-Controlled MC with Turning Function . . . . . . . . . . . . . . . . . . . . . . . . . . 111

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4 Various Remedies for Reduction of Thermal Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.1 Thermal Deformations and Effective Remedies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.2 Classifi cation of Remedies for Reduction of Thermal Deformation . . . . . . . . . . . . . . . . . . . . . 119

4.2.1 Separation of Heat Sources . . . . . . . . . . . 1204.2.2 Reduction of Generated Heat . . . . . . . . 123

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4.2.3 Equalization of Temperature Distribution . . . . . . . . . . . . . . . . . . . . . . . . 1284.2.4 Compensation of Thermal Deformations . . . . . . . . . . . . . . . . . . . . . . 131

4.3 Innovative Remedies for Minimizing Thermal Deformation in the Near Future . . . . 133References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

A.1 Separation of Heat Sources . . . . . . . . . . . 138 A.2 Reduction of Generated Heat . . . . . . . . 138 A.3 Equalization of Temperature Distribution . . . . . . . . . . . . . . . . . . . . . . . . 139 A.4 Compensation of Thermal Deformations . . . . . . . . . . . . . . . . . . . . . . 139 A.5 Optimization of Structural Design . . . . 140

5 Finite Element Analysis for Thermal Behavior . . . 1435.1 Numerical Computation for Thermal Problems in General . . . . . . . . . . . . . . . . . . . . . . 144

5.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 1445.1.2 Finite Element Method . . . . . . . . . . . . . . 1445.1.3 Finite Differences Method . . . . . . . . . . . 1475.1.4 Decision Making for the Selection of Methods . . . . . . . . . . . . . . . . . . . . . . . . 150

5.2 Procedure for Thermal Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 1515.2.2 Discretisation . . . . . . . . . . . . . . . . . . . . . . 1515.2.3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2.4 Assembling Components to an Entire Machine Tool Model . . . . . . . . . . . . . . . . 1555.2.5 Boundary Conditions . . . . . . . . . . . . . . . 1605.2.6 Loadcases . . . . . . . . . . . . . . . . . . . . . . . . . 1605.2.7 Linear and Non-Linear Thermal Computation . . . . . . . . . . . . . . . . . . . . . . 162

5.3 Determination of Boundary Conditions . . . . . 1625.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 1625.3.2 Convection Heat Transfer Coeffi cients . . . . . . . . . . . . . . . . . . . . . . . . 1665.3.3 Emission Coeffi cients and View Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1705.3.4 Heat Sources and Sinks . . . . . . . . . . . . . . 170

5.4 Thermomechanical Simulation Process . . . . . . 1745.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 174

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5.4.2 Serial Processing . . . . . . . . . . . . . . . . . . . 1745.4.3 Coupled Processing . . . . . . . . . . . . . . . . . 174

5.5 Future Perspectives in Research and Development for Thermal FEA . . . . . . . . . . . . . 175References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

6 Engineering Computation for Thermal Behavior and Thermal Performance Test . . . . . . . . . . . . . . . . . 179

6.1 Tank Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1806.2 Bond Graph Simulation to Estimate Thermal Behavior within High-Voltage and NC Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1846.3 Thermal Performance Testing . . . . . . . . . . . . . . 196References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

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Preface

Within a machine tool context, there are two crucial techno-logical issues. One is “thermal deformation” and the other is “chatter.” Since the 1940s, these two technological

subjects have been primary concerns in both production and utiliza-tion of technologies for machine tools. We have endeavored to estab-lish the effective remedies for the reduction of thermal deformation and suppression of chatter vibration from both academic research and practical applications. To our regret, even now the remedies available are not totally satisfactory. In other words, while thermal deformation and chatter are very old problems, they still present new technological challenges.

The root cause of difficulties lies in the holistic or synergistic influences of various factors in problems of thermal behavior and chatter. We must solve these problems from the viewpoint of the machine-tool-work system while considering the individual problem of the machine tool, the cutting tool, and the work; whereas, in modu-lar design and lightweighted structural design, the objective is the machine tool itself. Nevertheless, the better functionality and perfor-mance of a machine tool itself, the easier it is to establish effective remedies to reduce thermal deformation and suppress chatter.

Importantly, the fundamentals of thermal deformation are trans-parent considerably relative to those of chatter vibration. For exam-ple, thermal elongation is as commonly reported as it has always been and dominant in discussions of thermal deformation. (Academic research has so far concentrated on thermal contact resistance.) In contrast, a considerable number of factors that influence thermal behavior of a machine-tool-work system exist; e.g., heat dissipation capacity from the surface of the structural body component and from the rotating chuck. These factors play very complicated and mutually tangled roles in determining the thermal behavior of a system. As a result, we have not been able to establish perfectly effective remedies, although we can apply a large number of remedies for reducing ther-mal deformation in practice.

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It is desirable in an effective remedy that thermal behavior of a machine-tool-work system, or at least the machine tool itself, be esti-mated in the design stage. To meet such a desire, there are two crucial subjects to estimate authentically the thermal behavior of the machine tool: (1) dynamic and thermal boundary conditions of the machine tool and (2) heat dissipation capacity from the machine tool to the surrounding environment. Obviously, these two are important target subjects for academia, although corresponding research has not been active.

More specifically, there is a two-pronged perspective in consider-ing the thermal behavior of a machine tool:

1. Design principle for lightweighted structural body com-ponent; e.g., realization of a lightweighted structure by using a structural material with a smaller thermal expansion coefficient.

2. The NC machine tool benefits , on one hand, to reduce thermal deformation using compensation technology, but on the other hand, deteriorates the thermal characteristics of the machine tool by, for example, increasing heat sources.

Within the context of NC machine tools, we must pay special attention to a new horizon. First, the conventional MC (machining center) and TC (turning center); i.e., the most representative kinds of machine tools, can produce nearly all products necessary to maintain and advance human society. With the advance of NC technology and rapid changes in machining requirements, next, both quinaxial-controlled MC and TC of twin-spindle type; i.e., some advanced vari-ants of the conventional MC and TC, should be designed to fulfill simultaneously all three, or at least two of three, representative design attributes: those related to form-generating motion with higher speed, better machining accuracy, and heavier cutting capability. In accor-dance with the maxim-like design principle of the machine tool from earlier days, these attributes definitely conflict with one another, and the machine tool thus far has been generally designed with consider-ation of only one of these attributes. Designing for two or three of these attributes introduces a handful of new problems in the design sphere of the NC machine tool. Solving such conflicts is a crucial issue.

Keeping in mind the matters mentioned above, we can detail dis-advantageous features of NC technology as follows:

1. With prevailing the quinaxial-controlled MC, the monolithic part with a complex shape can be machined by one-chucking and using simultaneous quinaxial control. This may be considered complex-machining using various methods; e.g., turning, milling, drilling, and planing, and in due course, a

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large amount of heat will be generated. As a result, it becomes very complicated and difficult to estimate thermal deformation of quinaxial-controlled MC.

2. In NC machine tools in general, each traveling axis has its own driving motor, and thus NC machine tools have more driving motors than those in traditional machine tools, resulting in a greater amount of heat generation.

3. Some advanced NC machine tools should be designed with consideration of skillful fusion of two of three, or all three, representative attributes. Obviously, such a new design trend induces a new horizon in thermal deformation of NC machine tools.

This book describes primary concerns in reducing thermal defor-mation in machine tools. Specifically, a lightweighted structure can allow less thermal deformation than a heavyweight structure, and that is a necessary and inevitable precondition in the design for a structural body component. In this context, we must be aware that, even still, some machine tool engineers believe that heavyweight machine tools are welcomed by users. Next, the book covers the basics of thermal deformation together with the analytical expressions and design data for the estimation of the magnitude of heat generated, and determining the thermal boundary condition. The book goes on to specify remedies to reduce thermal deformation in practice from the perspective of both structural design and NC compensation tech-nology. It also introduces computational methods in the evaluation and estimation of thermal behavior, paying special attention to non-linearity in thermal behavior and testing in thermal behavior.

Further, this book can be regarded as a companion to ModularDesign for Machine Tools already published; both books deal with the design of structural body components and their joints.

The book consists of six chapters, and contributing authors for each chapter are as follows.

Chapter 1: “Fundamentals in Design of Structural Body Components” by Yoshimi Ito, Professor Emeritus of Tokyo Institute of Technology, Dr.-Eng., C Eng FIETChapter 2: “What is Thermal Deformation?—Estimation of Heat Sources and Thermal Deformation” by Nobuhiko Nishiwaki, Professor Emeritus, Dr.-Eng., and Dr. Eng., Sankei Hori, Tokyo University of Agricultural and TechnologyChapter 3: “Structural Materials and Design for Preferable Thermal Stability—Design Database Part 1” by Yoshimi ItoChapter 4: “Various Remedies for Reduction of Thermal Deformation—Design Database Part 2” Hidenori Shinno, Professor Dr.-Eng., Tokyo Institute of Technology

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Chapter 5: “Finite Element Analysis for Thermal Behavior” by Michael F. Zaeh, Professor Dr.-Ing and Dipl.-Ing., Tobias Maier of Technische Universität München Chapter 6: “Engineering Computation for Thermal Behavior and Thermal Performance Test” Section 6.1: “Tank Model” by Nobuhiko Nishiwaki and Sankei

Hori Section 6.2: “Bond Graph Simulation to Estimate Thermal

Behavior within High-Voltage and NC Controllers” by Sun-Kyu Lee, Professor Dr.-Eng., Gwangju Institute of Science and Technology, Korea

Section 6.3: “Thermal Performance Testing” by Yoshimi Ito

In summary, this book will provide systematically the reader with necessary, and valuable knowledge about thermal deformation in machine tools, ranging from the fundamentals through the remedies for reducing thermal deformation, to FEA (finite element analysis), and engineering methods in estimating thermal behavior, including thermal performance testing. In short, the book is extremely suitable for the continuing professional development of the mature engineer because each chapter depicts a firsthand view of pertinent research and development subjects.

Finally, contributing authors and the editor would like to express sincerest gratitude to their former editor, Mr. Soda, their current senior editor Mr. Penn, and Mr. Mulcahy, editorial assistant, all of McGraw-Hill, for their assistance in publishing the book. Also, the editor would like to express his sincerest gratitude to Dr. Ruth of the Universität Bremen for cooperating with the editor in getting the copyright permission for Chapters 1 and 3. Professor Zaeh would like to thank DFG (Deutsche Forschungsgemeinschaft) for its financial supports while carrying out a part of the research into thermal behav-ior of machine tools, and Professor Lee would like to join to express his sincerest gratitude to PhD student of GIST, Mr. Jung-Kyun Kim, for the production of the illustrations.

Editor Yoshimi Ito

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CHAPTER 1

Fundamentals in Design of Structural

Body Components

Yoshimi Ito

Production technology can create wealth for a nation, and its core is machine tool technology.

The above maxim is just as relevant now as it was years ago. As widely known, the machine tool has been contrived, developed, deployed, and improved to rationally produce both commercial

and defense supplies in accordance with the changing requirements of human society. As a result, we had more than 100 kinds of the tradi-tional machine tools, which were classified into around eight major families (e.g., lathe, milling and boring machine, grinding machine, and gear cutting machine).1 Some of these had already disappeared after finishing their roles (e.g., car wheel lathe for the steam locomo-tive), whereas we have a certain number of new comers with the advent of the information technology-related society (e.g., ultra-precision turning machine, for finishing the polygon mirror in the laser printer).

For the sake of understanding such a technological inheritance, Figs. 1-1, 1-2, and 1-3 depict, respectively, the families of the engine lathe, turret lathe (one of the subfamilies of engine lathe), and the pur-pose-oriented machine tools for ordnance production in 1960s. In the year 2000 and beyond, the lathe family can be fully replaced with the NC turning machine and TC (turning center), and apart from the work machined by the special purpose-oriented kinds (e.g., gun boring

1In general, the machine tool can be classified into the metal cutting machine tool and the metal working (plastic forming) machine tool.

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2 C h a p t e r O n e

Ram type (Capstan lathe in United Kingdom)

Saddle type (Combination type in United Kingdom)

Cross sliding type

Flat type (Scheu type)

Drum type (Pittler type)

Vertical turret lathe

Warner and Swasey type (Spindle with built-in-motor type)

Turret lathes

(variant)

Note: Novel kinds of lathes generally took the names of the company that first

contrived them. In this figure, underlining indicates these company names.

FIGURE 1-2 Turret lathe classifi cation.

machine with rifling function and stock lathe), the ordnance can be produced by the conventional NC machine tool such as shown (in part) in Fig. 1-3. Importantly, we can display a similar scenario in the case of the machine tool for the rolling stock production as will be, for example, shown in Fig. 1-5.

FIGURE 1-1 Engine lathe classifi cation in the 1960s.

Note: Novel kinds of lathes generally took the names of the company that first contrived them.

In this figure, underlining indicates these company names.

Engine lathes

Vertical lathe(vertical boring and turning mill)

Bench lathe

Engine lathe

Face lathe Automatic face lathe

Lathe with multiple-cutting edge

Tool room lathe

Ultra-precision lathe (diamond lathe)

Turret lathe

Automatic lathe

Automatic (screw cutting)machine Multiple-spindle

type

Single-spindletype

Brown and Sharpe type

Swiss type (headstocktraveling type)

Acme type

Gildemeister type

Open type

Portal type Roll lathe

Thread cutting lathe

Deep hole boring lathe

Crank shaft lathe, cam shaft lathe, crank pin lathe

Lathes for rolling stock

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F u n d a m e n t a l s i n D e s i g n o f S t r u c t u r a l B o d y C o m p o n e n t s 3

Stock copying lathe

Shell turning machine

Cartridge (case) lathe

Turret seat facing machine(for warship)

Gun boring and rifling machine

Gun drilling machine

Hull processing machine

Special purpose-oriented machinetools for ordnanceproduction

Formed thread cutting machine—Saw-like threadfor motor tube in rocket(air to ground)

6-axis horizontal breech processingmachine (variant of transfer line)

Thread cutting machine—Saw-like or “plectrum-like” thread in sabot of penetratorfor tank weapon system

Still using in the 1990s

Replaced by NC turning machine and TC in the 1990s

9-axis controlled NCplanomiller of portal type

Not used anymore

Variant of gun drillingmachine for civil supplies

Note: The other terminology for “Saw-like thread” is “buttress thread.”

FIGURE 1-3 Machine tools for ordnance production and their replacement by conventional NC machine tools.

Boring machine 1 unitMain spindle dia.: 80 mm

Radial drilling machine 2 unitsMain spindle dia.: 50 mm Milling machine 2 units

Multiple-axis upright drilling machine 2 units

MC 2 units

Traditional machine tools

FIGURE 1-4 Replacement of form-generating functions of a group of traditional machine tools with MC. (By Kessler)

Importantly, the number of machine tool kinds has been greatly reduced due to the prevalence of the NC machine tool. Figure 1-4 demonstrates how efficiently, even in the 1970s, the NC machine tool can replace several traditional machine tools by taking MC (Machining Center) of first stage development as an example [1-1]. As can be

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seen, MCs of two units can take over the form-generating functions so far performed by one unit of the boring machine, two units of the radial drilling machine, two units of the milling machine, and two units of the multiple-axis upright drilling machine. In the year 2000 and beyond, such functionality integrations have become even more efficient and dense.

Although there are fewer kinds of machine tools than ever before in the era of the NC machine tool, in fact, we have still a considerable number of kinds of machine tool. In short, the NC machine tool can be classified into three categories at present: (1) conventional type; (2) purpose-effective type by simplifying the structural configura-tion, functionality, and performance of the conventional type2; and (3) special purpose-oriented type, such as gun drilling machine, hyp-oid gear generator, and guideway grinding machine.

Importantly, Fig. 1-5 shows an MC of portal type (i.e., five-face pro-cessing machine, being engaged in railroad crossing machining). In fact, this is one of the examples for replacing the traditional purpose- oriented machine tool, (i.e., rail planer of the past) with the conventional MC. In contrast, Fig. 1-6 shows an example of a junior machine—CNC (Computerized NC) portal MC of rail type (Main motor: 100 HP, Main spindle speed in max.: 10,000 r/min, Portal width: 110 inches)3. As can be

2We used to call the purpose-effective type the junior machine, although it was first employed as a commercial name.3At present, this kind is called the old-fashioned MC of gantry type, because of its characteristic feature in configuration and form-generating function.

FIGURE 1-5 Railroad crossing being machined by fi ve-face processing machine around 1997. (Courtesy of Werkzeugmaschinenfabrik Waldrich Coburg GmbH)

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NC controllerTurret

Main spindle

Splash guard(panel cover)

FIGURE 1-7 A representative conventional TC—Type LB, Okuma-make, 2009. (Courtesy of Okuma)

seen, the machine base is simplified by replacing it with the twin-rail, where the basic length of the rail is 192 inches and the rail is extensible every 144 inches. In addition, the number of the control axes can be chosen as either three or five.

Figures 1-7 and 1-8 are the utmost representatives of TC and MC, which have prevailed across nearly all industrial and industrializing

FIGURE 1-6 CNC portal MC of rail type—Type 30V, Cincinnati Milacron-make, 1995.

Travelinggantry

Cross rail

Spindle head

Base of twin-rail type

Note: Simplification in base by replacing it with twin-rail.

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Splash guard

Spindle head

ATC

Base

Main spindle

NC controller

FIGURE 1-8 A representative conventional MC—vertical type, Type MB, Okuma-make, 2009. (Courtesy of Okuma)

Traveling columnMain spindle

ATC

Table of trunnion type

Main spindle speed in max.: 4,000 or 6,000 r/minMain motor: 40 or 50 HP

FIGURE 1-9 A quinaxial-controlled MC of trunnion type—Type TC, Cincinnati Milacron-make, 1995.

nations. In fact, these kinds have a considerable number of variants to enhance competitiveness in the worldwide market, and their pro-duction volume is increasing almost daily. Within such an MC, the most leading- edge types are the quinaxial-controlled MC (shown in Fig. 1-9) and mill-turn. Although the MC shown in Fig. 1-9 is obsolete Cop

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as a quinaxial-controlled MC, it is very convenient to understand the table of trunnion type. In fact, the table is compact in the year 2000 and beyond.

More specifically, the mill-turn is a synergy of the quinaxial-controlled MC and turning function or a synergy of TC and milling function. Figure 1-10 shows a typical example of the mill-turn based on the quinaxial-controlled MC of trunnion type in the 2000s. As exemplified by the mill-turn, it is very interesting that we have a new horizon in the thermal engineering problem with the advent of a new kind. In the mill-turn of trunnion type, the table placed within the trunnion and supported by the cross-tapered bearing can be continuously rotated similar to a vertical turning machine by the direct drive motor. As will be stated in Chapter 3, the mill-turn has more heat sources than those in the quinaxial-controlled MC. In addition, the cross-tapered roller bearing runs with large frictional loss caused by its rotating mechanism, and duly generates much magnitude of heat as compared with that in other rolling bearings. Figure 1-11 further illustrates the extent to which various methods should be used in machining of a rotational part, and obviously, the mill-turn based on TC can handle all of these machining methods. As a result, TC can benefit the integration of machining processes, although dynamic and thermal loading becomes in turn very com-plex. In this case, the mill-turn has the spindle with indexing function and turret column, on which the turning tool and milling cutter are mounted back-to-back to each other.

FIGURE 1-10 A quinaxial-controlled MC with turning function—Type MU, Okuma-make, 2009. (Courtesy of Okuma)

Spindle head

Cross railMain spindle

NC controller

Continuouslyrotatable tableplaced withintrunnion

Splash guard

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Threading

Keyway slotting

Cylindrical turning(turn top)

End milling

Slot drilling

Drilling and tapping

Drilling

Boring

Facing (face end)

Facing (face head)

Side milling

Face milling

FIGURE 1-11 A sample workpiece machined by mill-turn.

In short, the conventional TC and MC are a primary concern when discussing the thermal behavior of machine tools nowadays; however, these kinds have the integrated functionality and perfor-mance, which were performed by each individual kind in the past as already shown in Fig. 1-4. As can be readily seen, thus, the static, dynamic, and thermal behavior of the conventional TC and MC are very complicated as compared with that of the traditional kind. This integration of functions results in complex structural design challenges.4

1.1 Necessities and Importance of Lightweighted Structure in Reduction of Thermal Deformation—Discussion Using Mathematical Models

Notwithstanding considerable variation in the kind of the machine tool and also the complexity of the structural configuration, in general, two fundamental relationships exist between the structural stiffness and the machining performance, as follows:

4As widely recognized, TC and MC can be considered the kinds, in which the multifarious functions and wide capabilities of the lathe, drilling machine, boring machine, and milling machine are integrated in a machine as a whole. In addition to TC and MC, we now have grinding center (GC) and gear production center. In the former, nearly all the kinds within the grinding machine family are integrated within a machine as a whole, whereas in the latter the hobbing machine, gear shaper, gear honing machine, and gear grinder are integrated within a machine as a whole.

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1. The static stiffness is in the closest relation to the geometrical accuracy of the finished part as compared with other charac-teristic indicators. For instance, the machining accuracy is subjected to the relative deflection between the work and the cutting tool, which is caused by the static component of the cutting force, self-weight of traveling structural component, and so on.

2. The dynamic stiffness is in the closest relation to the surface quality of the finished part, and also the anti-chatter vibration characteristics as compared with other characteristic indicators.

In the structural design of the machine tool, the first priority is thus to provide the machine as a whole with the highest static stiffness as possible on the basis of the Design Principle of Allowable Deflection.Nearly all industrial products are designed on the basis of the DesignPrinciple of Allowable Stress, and the typical exceptions from this princi-ple are the machine tool and, in part, the ordnance systems. Figure 1-12 demonstrates what the essential difference between these two design principles is and in short, the diameters of the cantilever are 22 mm and 70 mm in accordance with the design principles of allowable stress and deflection, respectively. In this calculation, the safety ratewas employed; however, the safety rate is not the prevailing terminol-ogy currently, but officially, the safety factor of old fashion is correct, where the allowable stress can be determined using the tensile strength. In contrast, the safety factor is prevailing at present, which can be facilitated by the fatigue strength (endurance limit).

Although there is such a large difference, the machine tool should be designed as compactly as possible (equivalent to other

Cantilever

l = 200 mm

P = 100 kgf

Maximum bending stress σmax = Pl/zm

Maximum deflection δmax = Pl3/3EI

where, zm = Section modulus

I = Second moment of area (moment of inertia)

E = Young’s modulus

When the material of cantilever is S45C (as per JIS), the tensile strength is around 60 kgf/mm . By assuming the safety rate to be 3, the allowable stress yields to 20 kgf/mm . As a result, d must be around 22 mm.2

2

In the cases of machine tools and certain kinds of ordnance, at issue is the allowable deflection. Thus, d yields to around 70 mm (around 0.6 kgf/mm2), when the allowable deflection is 1/100 mm.

φ d

FIGURE 1-12 Differing features in designs of allowable defl ection from allowable stress.


industrial products), because the machine tool is an industrial prod-uct and operated by human beings. As can be easily understood, a root cause of difficulties in machine tool design lies in the realiza-tion of a compact machine, while keeping with the Design Principle of Allowable Deflection.5

After the fulfillment of satisfactory static stiffness, then, the machine tool should be designed to have the acceptable dynamic stiffness. To understand the prerequisite for the design of the dynamically rigid structure, thus, a theoretical background will be stated herein. In fact, a simplified model of the machine tool is the mechanical vibration sys-tem with one degree of freedom as shown in Fig. 1-13. By assuming Fand x to be the external dynamic load and corresponding deflection, the dynamic stiffness Kd yields to

K F x Md n= = − +0 02 2 2 2 24/ ( )ω ω ε ω (1-1)

where 2ε = cd/M ωn

2 = k/M x = x0 sin (ωt – ϕ) t = time

5A considerable number of famous books relate to the structural design of machine tools. Although the books listed below were published decades ago, the essential features of structural design have not changed, and these books are a helpful reference. Atscherkan, N. S. Werkzeugmaschinen–Berechnung und Konstruktion Band 1, VEB

Verlag Technik, Berlin, 1961. Koenigsberger, F. Berechnungen, Konstruktionsgrundlagen und Bauelemente spanender

Werkzeugmaschinen, Springer-Verlag, Berlin, 1961. Koenigsberger, F., & Tlusty J. Machine Tool Structures Volume 1, Pergamon Press,

Oxford, 1970.

In addition, JMTBA has published the two books related to the structural design of machine tools as follows. Thus, structural design will be covered only briefly within this chapter.

JMTBA. Design of Machine Tools–Fundamentals, 1998. JMTBA. Design of Machine Tools–Applications, 2003.

Dampingcapacity

Spring constant(static stiffness)

x

kcd

F = F0 sin ω t

MMass

FIGURE 1-13Mathematical model of machine tools—Replacement to mechanical vibration system of one degree of freedom.


Cutting time

Cut

ting

forc

e

Dyn

amic

com

pone

nt

Stat

ic c

ompo

nent

Fluc

tuat

ion

com

pone

nt

Two cutting edges being engagedOne cutting edge beingengaged

0

FIGURE 1-14 Defi nition of static, dynamic, and fl uctuation components in cutting force.

At issue is the dynamic stiffness near resonance point, and thus by substituting ω with ωn, Eq. (1-1) can be written as

K c k Md d= / (1-2)

In short, the high dynamic stiffness can be achieved by (1) increasing the damping capacity cd, (2) increasing the static stiffness, and (3) reduc-ing the mass M. As a matter of course, a lightweighted structure is pri-mary concern to increasing the dynamic stiffness. In other words, we can expect a structure with both much higher static and higher dynamic stiff-ness by employing the lightweighted structure.

In this context, to what extent must we consider static and dynamic loading? As widely known, the leading loads are the self-weight of the structural body component, self-weight of the workpiece, forced excita-tion load caused by the unbalance in the rotating component, driving force in the spindle head, and cutting force. Of these, the cutting force is dominant in small- and medium-sized machine tools. As shown in Fig. 1-14, cutting force comprises three components—static, dynamic, and fluctuation. In due course, there is a considerable heat generation while cutting and grinding the workpiece, and in the cutting, the temperature rises up to 800°C, most of which is accumulated within the swarf.6

6Swarf is one of the British technical terms to represent the chip in American English; however, the term swarf is very convenient to classify itself into various shapes, ranging from the tangled formation of long helices (bushy swarf), through broken chips and short helices, to dust and sludge. In discussing the thermal engineering problem in machining, the shape and size of the swarf are crucial, and thus we use the term swarf within this book. Gough, P. J. C., (ed) Swarf and Machine Tools, Hutchinson of London, 1970.


Q

hdz

s

z

0

l

0 400 800

10

20

30

40

The

rmal

exp

ansi

on, ∆

z (µ

m)

Height of side wall, h (mm)

s = 30 mm

20 mm

10 mm

5 mm

θu

α = 5 kcal/m2 h°Cλ = 45 kcal/mh°CβGG = 10.6 µm/m°Cθu = 20°CθF = 30°Cl s

θF

FIGURE 1-15 A simplifi ed mathematical model for side wall of structural body components in machine tools. (By Opitz and Schunck)

Similar to dynamic stiffness, the thermal behavior can be dis-cussed by using a simplified model shown in Fig. 1-15. In short, the thinner a side wall of the structural body component, the smaller is its thermal expansion as shown in the calculation diagram of Fig. 1-15 [1-2]. More specifically, assuming that the side wall is heated at its bottom surface by the heat sources Q (i.e., temperature θF), and that the heat dissipation from both of the sides can be ignored, the thermal expansion ∆z is given by

∆z = {[βθF]/[em∗ + e –m∗]}{[h/m∗][e–m∗(1 – z∗) – em∗(1 – z∗) – e–m∗ + em∗]} (1-3)

where m∗ = Biot number and can be written as ( )2 2α λh /( )sλ = Thermal conductivityα = Thermal convection coefficientβ = Coefficient of thermal expansion (in Fig. 1-15, the value

for gray cast iron is given)z∗ = z/h

As can be readily seen, thermal expansion becomes smaller with the larger m∗. This means, the thin-walled structure which is a prereq-uisite for realizing the lightweighted structure, shows, in principle, the least thermal deformation.

Having in mind the design principle of basic requirement for the machine tool mentioned above, a facing problem is clarifying the objective components in designing the machine tool. Figure 1-16 shows an outline of the core components in the machine tool


structure. Obviously, the large-sized component, i.e., structural body component, is the design objective for the lightweighted structure, and it is very convenient for the designer to understand to what extent the lightweighted structure is to be in reality in practice. For the ease of understanding, first, Figs. 1-17 and 1-18 demonstrate the representative structural body components within the conventional TC and MC in the year 2010, and then Table 1-1 shows some data of s/DR, which is an index to estimate whether or not the structural body component is lightweighted. In short, the ratio s/DR ranges from 0.03 to 0.07, and thus the lightweighted structure in the machine tool can be, in principle, regarded as a quasi-lightweight structure by nature, as compared with that of aircraft.7

The three leading remedies to realize the lightweighted structure are as follows:

1. From the structural material point of view, use of steel welded structure, structural body component made of light alloy, and so on.

2. From the overall structural configuration point of view, use of structural body component with closed cross-sectional

7In referring to automobiles and aircraft, it is common to use the term lightweightstructure; however, the machine tool engineer has employed the term lightweighted structure to characterize the essential feature in the structural design, aiming at realization of the lightweight structure based on the design principle of allowable deflection. Thus, the term lightweight-oriented structure is more suitable. In addition, the values of s/DR shown in Table 1-1 were obtained from the traditional machine tool; however, these values are available for the year 2000 and beyond.

Structuralcomponents

Conventionalparts

Joint between both the large-sized components

Attachments (e.g.,jigs and fixtures)

Large-sized(structural body) components

Small-sizedcomponents

Bed, base, column, cross beam,headstock, underarm, main spindle,and so on

Shafts (power transmission shaft, feed rod, spline shaft, and so on)GearsBearingsOil sealsOthers

In general, standardized parts

Stationary and sliding joints

Chucks, centers, mandrels, ATC, and so on

Lea

ding

com

pone

nts

in m

achi

ne to

ol s

truc

ture

s

FIGURE 1-16 Leading components in machine tool structures.


Portal column(column of twin-pillar type)

Saddle

Cross slideHeadstock

Bed

Tool spindle head ofswiveling type

Traveling ram

FIGURE 1-17 Representative structural body components in TC—Type NT, 2009. (Courtesy of Mori Seiki)

Table-saddle

Portal column

Spindle

Spindle head

Spindle head-saddle

Base

FIGURE 1-18 Representative structural body components in horizontal MC—Type NH 4000, 2009. (Courtesy of Mori Seiki)


configuration and large cross-sectional moment of inertia in both the casting and the welded structures.

3. From the structural configuration entity (element) point of view, rational allocation and placement of rib, connecting rib, annular stay, partition, double-wall, and cell in both the cast-ing and the welded structures.

In short, the structural body component should be designed in accordance with the Design Principle of Allowable Deflection together with fulfilling the requirement of light selfweight.

Ideally, the small-sized component such as the power transmis-sion shaft and gear, shown in Fig. 1-19, should be designed on the basis of Principle of Endurance Limit.8 This can also benefit to be the lightweighted and compact dimensional structure in reality, resulting in one of the indirect remedies to reduce the thermal deformation. When employing the Principle of Endurance Limit, the basic necessity is to replace the small-sized component with a new one in accordance with its design life. Figure 1-19 illustrates the spindle head, which is designed per either the Design Principle of Allowable Deflection or Principle of Endurance Limit.9 In short, the machine tool should be designed by the preferable combination of or leverage between these two principles.

8The high-quality design can be facilitated with the Load Distribution Diagram across the Whole Product Life; however, such a diagram is not obtainable, because the user may run the machine tool under multifarious loading conditions, which are far beyond the designer’s estimation in the design stage.9The spindle head shown in Fig. 1-19 is based on that of horizontal MC of Heckert-make in 1993 (Type CWK); however, it is not obvious whether or not this MC is designed using the Principle of Endurance Limit. The illustration is used here by the courtesy of Heckert.

Company Kinds and components s/DR

A Vertical boring machine Column 0.025~0.06

B Horizontal boring machine Column 0.027~0.037

C Planing machine Cross rail 0.067

D Planing machine Column 0.039

E Lathe Bed 0.060

s: Side wall thickness DR: Representative dimension, e.g., height of cross rail and outer diameter of round column

TABLE 1-1 Ratio s/DR for Several Structural Body Components


More specifically, Table 1-2 enumerates the leading attributes, which can be detailed the kernel of the design principle mentioned above as the design guide, and which should be fully considered in the design of the structural body component. In addition, Table 1-3 shows other leading design attributes from the aspect of the utiliza-tion technology of the machine tool, and these may be considered the indirect influencing factor to the thermal behavior of the machine tool. For instance, the allowable spindle torque in maximum may govern the heat generation in the spindle head.

Summarizing, the lightweighted structure with thin walls is rec-ommended to reduce the thermal deformation; however, in the design practice, we cannot realize the satisfactory reduction of thermal deformation by only using the lightweighted structure. As a result, there are myriad remedies for reducing the thermal deformation in the machine tool, which will be covered in Chaps. 3 and 4.

To this end, Fig. 1-20 shows an outstanding bed structure for the copying lathe in the 1970s, in which both the bending and torsional stiffness are simultaneously larger than those in other lathes [1-3]. In general, the bed of the lathe and its variants can be designed to be rigid against either bending or torsional loading. In the reinforcement of the torsional stiffness, the closed-sectional configuration with cir-cular-like stiffening element can facilitate an amazing increased rigidity, although we have certain difficulty in its production, espe-cially in casting. Thus a cost-effective remedy is to use the cylindrical pipe available commercially. Figure 1-21 shows such an example,

AC motor Power transmission: “Endurance Limit” design

Quill and main spindle:“Allowable Deflection” design

FIGURE 1-19 Leverage between two design principles for allowable defl ection and endurance limit.


1. Lightweighted structure with allowable static and dynamic stiffness

– Suitable placement and allocation of structural configuration entities (e.g., rib, connecting rib, partition, and double-wall)

– Consideration of directional orientation effects in stiffness2. High bending and torsional stiffness as possible – For bending stiffness, the cross-sectional second moment

should be large. – For torsional stiffness, the closed cross-sectional configuration

is the utmost desirable.3. In the structural body component with guideway, its material,

dimension, and shape should be determined to guarantee the durability of guiding accuracy, and also to prevent the deformation caused by clamping force.

4. Extremely meticulous design for the reduction of thermal deformation

– When the component generating large heat sources is installed within the structural body

– When serving the machine on the heavy or high-speed cutting – When the machine has the panel cover, by which the heat

dissipation capability is deteriorated5. Structural configuration with ease of swarf disposal – Structural body component of chip-flow type (slant bed type)6. Design for machine tool joint with large stiffness and for high

accuracy assembly – Joint with assembly accuracy-secured type together with

guaranteeing the reproducibility

TABLE 1-2 Leading Design Attributes for Structural Body Components

TABLE 1-3 Function, Performance, and Dimensional Specifications in Direct Relation to Machine Tool Utilization Technology

Allowable spindle torque in maximum (allowable cutting area in max.) and its corresponding rotational speedAllowable work loading capacity of table in maximum (allowable work weight between both the centers in max.)Maximum machining spaceKinds of tapers at spindle nose and center holeStandards for cutting tools and work holding devices


Structural configurationentity of box-beam type: For enhancementof bending stiffness

Structural configuration entity with round cross-section:For enhancement oftorsional stiffness

Tool slide

Base(underpinning bed)

Bed

Copying tool slide

Template holder

FIGURE 1-20 A desirable bed confi guration in copying lathe. (By Frank)

Guideways

Cylindrical pipesPartitions placedat certain intervals

Partitions placedat certain intervals

Main spindle rotational speed in max.: 7,000 r/min, Main motor: 7.5 kW

FIGURE 1-21 Base of high torsional rigidity using through-pipe structure—In horizontal MC of Mori Seiki-make, Type MH-400, 1989.

where the base of horizontal MC is cast together with using the through-pipe structure. Importantly, these design guides were established already in the 1960s and after then, such a structural configuration shown in Fig. 1-20 is regarded as common sense in machine tool design.


1.2 First-hand View for Lightweighted Structures with High Stiffness and Damping in Practice In the structural design of a machine tool as a whole, as described in the preceding section, we must first design such structural body com-ponents shown in Fig. 1-16 as lightweighted structures as possible, and then pay special attention to the joint between both the structural body components. At the joint, the major design problem is the thermal con-tact resistance; often the overall behavior of the machine tool depends on the joint design.10

Due to greater complexities in the thermal deformation than those in the static and dynamic stiffness, the structural body component is at least designed to have the satisfactory stiffness, and in certain cases simultaneously provides the preferable thermal characteristics from the structural configuration (e.g., axi-symmetrical configuration). Obvi-ously, the machine tool as a whole often shows poor thermal character-istics, and thus the designer must consider further active and passive remedies, such as separation of heat source, cooling method of the machine, and compensation method based on the NC technology, for the improvement of such unfavorable characteristics.

Although such active and passive remedies are dominant, the basic design requirement is to realize the lightweighted structural body component from the raw material aspect and also from the con-figuration and dimensional design. In designing the lightweighted structure, furthermore, other primary concerns are to prevent (1) the local deformation (2) distortion of the cross-section, and (3) membrane vibration (i.e., drum effects) within the structural body component. These may influence considerably the deterioration of guiding accu-racy of the traveling structural body component, which is in direct proportion to the machining accuracy. As a result, it is common for the structural body component to be formed as a box- and stab-like beam with various structural configuration entities, for example, rib, con-necting rib etc, to enhance the static and dynamic stiffness.

In the following, some quick notes will be given to clarify the design requirement in the configuration, by which the structure becomes thermally stable.

1.2.1 Axi-symmetrical Configuration—Portal Column (Column of Twin-Pillar Type)

In discussing the control and minimization of thermal deformation, it has been recommended to prevent bending deformation, torsional

10Regarding the detail of the machine tool joint, refer to the book Modular Design for Machine Tools, which was already published by McGraw-Hill as a companion of this book.


deformation, and distortion. In fact, simple elongation can enhance the controllability of thermal deformation. Within this context, a desirable structural configuration is that of portal column, specifically called col-umn of twin-pillar type, such as shown in Fig. 1-22.11 Figure 1-22 illus-trates the plain view of the jig boring machine, and obviously, the column of twin-pillar type contains the spindle head between the two pillars. As can be seen, the machine is of axi-symmetrical configuration to the longitudinal axis of the main spindle, and thus it may be expected to have only the simple thermal elongation, even when thermal defor-mation occurs. In contrast, Fig. 1-23 shows the column, specifically called column of single-pillar type, in a horizontal boring and milling machine. In the column of single-pillar type, the spindle head is placed, as shown in Fig. 1-23, at the column slideways, similar to a bartizan, and

11With the advent of the MC of horizontal type, the column of twin-pillar type has become one of the very popular structural body components. In contrast, there is confusion in the terminology. We have employed the term portal column for that shown in Fig. 1-22, i.e., that so-called portal-like column; however, we have other kinds of machine tools called, for example, planomiller of portal column (double column) type, large-sized MC of portal column type, and five-face processing machine of portal column type. To avoid unnecessary confusion and misunderstanding, thus, the column of twin-pillar type is employed within this book, if necessary.

Side wall

Partition

Rib

Slideway

Double-wallconfiguration

Slideway

Gib

Spindle head

Main spindle

Aperture

FIGURE 1-22 Column of twin-pillar type with double-wall confi guration in jig boring machine—Type 75N, Dixi-make, 1960s.


thus has enough open space around it.12 Conceptually, such an open space may assist the heat dissipation from the spindle head, whereas the main spindle should be located far from the slideways, and the spindle head itself is in the form of the cantilever. Obviously, this configuration is very far from the axis-symmetry and thus the main spindle is liable to deform by the relatively large moment including thermal effects, result-ing in the complicated thermal deformation.

In retrospect, the column of single-pillar type prevailed in the era of the traditional machine tool apart from the jig boring machine of horizontal type. In fact, the twin-pillar type was first employed to the column structure of the jig boring machine of horizontal type to ensure the desirable thermal stability, because the jig boring machine is for precision and ultra-precision machining.

Summarizing, the column of twin-pillar type has opposite charac-teristics as compared with those in the column of single-pillar type, and can enhance the functionality and performance of the conventional MC of horizontal type to a larger extent by simultaneously using the double-wall configuration to each pillar as will be stated later.

1.2.2 Placement and Allocation of Structural Configuration Entities

As already stated, the structural body component is, in principle, of box- and stab-like beam, and in due course should be of closed cross-sectional

12In the era of the traditional machine tool, such an open space is capable of allocating various handles, levers, measuring devices, and so on, and thus very helpful for the ease of operation.

Connecting rib withannular stay

Slideways forspindlestock

Column

Spindlestock

Annular stay

Cross-sectional view of column

Horizontal boring and milling machineof table type (Ikegai Iron Works-make, Type DA2115T in the 1960s)

RibDiameter of boring spindle: 115 mmMain motor: AC 4P 15 kW

Side wall

FIGURE 1-23 Structural confi guration entities in column of single-pillar type.


type. For reasons of installing electric and electronic equipment, driving motor, gearbox, and so on within the structural body component, how-ever, there are a considerable number of apertures. In due course, the aperture reduces the stiffness of the structural body component, and thus the structural configuration entities can help the structural body component recover from the stiffness deterioration.13 In addition, the structural configuration entity can nearly eliminate the drum effect.

To better define the structural configuration entity and its place-ment, the column with such entities was shown in Figs. 1-22 and 1-23. Although these illustrations appear to be outdated, such structural configuration entities have been, in principle, employed till today, and as will be clear from these illustrations, the structural body com-ponent can be reinforced satisfactorily by providing the structural configuration entities reasonably, maintaining the box- and stab-like beam as the basic configuration.

In the following section, some quick notes for each entity will be stated.

Rib and Connecting RibThe rib is a very popular structural configuration entity and in general its effective height is less than 1.5 times the side wall thickness. Importantly, the connecting rib appears to be the partition in certain cases, and the combination of the rib placed along the lon-gitudinal axis and connecting rib greatly improves the rigidity of the structural body component. Figure 1-24 illustrates a typical rib place-ment within the bed of the CNC lathe in the 1990s, and in fact, the rib can facilitate the further reinforcement for the stiffness of the struc-tural body component, which has already nearly acceptable stiffness by achieving the configuration with closed cross-section and for large second moment of inertia.14

The annular stay also further enhances the rigidity, as shown in Fig. 1-23, and thus there have been a considerable number of valuable contrivances so far. Figure 1-25 reproduces such a contrivance called ample ribbing, which was employed by Köllmann in the 1960s.

Double-wall ConfigurationFigure 1-26 shows a typical double-wall configuration, and as can be readily seen, the side wall of the bed is not monolithic, but consists of a structural configuration entity with two thin solid walls, which encircles a small room, called a cell [1-4]. Ideally, the walls and bottom

13The aperture should be furthermore placed from the viewpoint of the fettle of the core sand.14The rib configuration is very similar to the cooling fin in the personal computer, and thus the design knowledge in the machine tool sphere could be transferred to the information device industry. Regarding such a technology transfer, refer to Sec. 6-2, which discusses the heat sink at cabinets for power supplies and also the thermal problem of CPU of NC.


plate will encircle the cell, resulting in the enclosed cross-sectional configuration; however, the aperture should be placed at intervals of certain distance to fettel the core sand, although the torsional stiffness deteriorates to a certain extent.

Importantly, the double-wall configuration has prevailed since the 1960s, and still to this day, it is fundamental knowledge in structural

Rib in verticaldirection

Connecting rib placedat certain intervals(a kind of partition)

Side wall

FIGURE 1-25 Special rib confi guration—Ample ribbing in column of planomiller, 1962. (By Köllmann)

Bed guideways

Side wall

Aperture for fettling

Partition

Ribs

Through-hole

FIGURE 1-24 Rib placement in bed of CNC lathe—Type TU, Ikegai Iron Works-make, 1994.


design engineering. As a result, we take for granted the advantage of double-wall configuration; Fig. 1-27 compares static and dynamic characteristics between single-wall and double-wall configurations reported by the PERA in 1968 [1-5]. Although the data are old, both

Structural configuration entity: Double-wall

Aperture forfettling

FIGURE 1-26 Typical double-wall confi guration in automatic lathe—Heid-make, 1959.

Bending stiffness (kgf/µm)

About I-I

13.9

19.3

Old design

New design

About II-II

14.5

20.0

Torsional stiffness(×10 m-kgf/rad)

0.29

0.43

6

Frequency (cycles/sec.)

Bending about I-I

118

114

Bending about II-II

130

127

Torsion

86.5

95.5

Old design

New design


Damping ratio (×10 )–3

1.18

9.17

0.99

11.0


3.1

3.36



I

II

Core sand

Old design(connecting ribof Warren type)

New design(connecting ribof Vierendeel-liketype)

I

II

FIGURE 1-27 Comparison of static and dynamic characteristics between lathe beds with single-wall and double-wall confi gurations. (By PERA)


the beds for the experiment are not the same configuration, and the double-wall configuration uses the beneficial aspects of the core sand for the increase of damping, it is very easy to understand the superi-ority of the double-wall structure from Fig. 1-27.

On the strength of the reinforcement effect of the double-wall configuration without increasing the weight, in general, the conven-tional MC of horizontal type has been designed using the column of twin-pillar type, in which each pillar is, as mentioned already, of dou-ble-wall configuration. The column of twin-pillar type is more suit-able for realizing the symmetrical structural configuration than the column of single-pillar type as exemplified by the traveling posture of the spindle head. In fact, the spindle head can travel between two pillars without showing unfavorable overhang of the main spindle. In addition, it may be considered that a structure with geometrical symmetry is one of the pre-conditions to engineer the preferable char-acteristics of the machine tool to a various extent. Importantly, the column of twin-pillar type is suitable for the design of a thermally symmetrical structure, although a fatal disadvantage is the heat accu-mulation around the spindle head in certain cases, which is derived from the closed space encircled by the pillar and panel cover.

In contrast, the conventional MC of vertical type has been designed using some variants of the column with double-wall con-figuration, because of differing traveling motion of the spindle head, i.e., non-necessity of or difficulty in traveling between two pillars. Figure 1-28(a) shows a representative configuration of the vertical MC. The front wall of the column is of double-wall configuration, so that the guiding accuracy can be guaranteed for various loading to a large extent. In this case, there is less attention to the thermal defor-mation apart from the geometrical symmetry for X-axis. Within this context, Korea Machine Tools Manufacturing contrived a noteworthy variant by replacing the inside wall with five cylindrical connecting stays as shown in Fig. 1-28(b), which are placed at certain intervals along the longitudinal axis of the column. This may be called a sim-plified double-wall structure, and we can expect the considerable reduction of the production cost by eliminating troublesome fettling.

Although the same story is available for other column structures, the horizontal MC for precision machining consists, in nearly all cases, of the column of twin-pillar type, and is often designed using the slideway of eight-face constraint type (eight-face wrap-around to column guideways). As widely known, the slideway is, in principle, designed using the six-face constraint type, and it is the acceptable guiding accuracy in reality. In fact, the eight-face constraint type can facilitate to bring the best guiding accuracy in fruition, although the production cost jumps. Supposedly, the slideway of eight-face con-straint type includes a serious thermal problem caused by the dif-fering thermal contact resistance between both the slideways. More specifically, as shown in Fig. 1-29 the slideway placed closer to the


x

x

Column slideways


(a)

FIGURE 1-28 Variants of double-wall structural confi guration entity.(a) Vertical MC-oriented double-wall confi guration—Type VG, Hitachi Seiki-make, 1980s (b) Simplifi ed double-wall confi guration in column of fi ve-face processing machine—Korea Machine Tools Manufacturing, 1998.

(b)

1,500

2,00

0

1,000

φ 20

0

Ribs and stays are placed similar to that of Fig. 1-23

Column slideways

Cylindrical connectingstay placed at certainintervals along longitudinaldirection of column

150

60


feed screw should have its fitting tolerance adjusted to be tighter than that of the other slideway, to achieve more precise guiding accuracy by greatly decreasing the fluctuation in yawing, pitching, and rolling moments.

In fact, we can obtain outstanding guiding accuracy by employ-ing the eight-face constraint type; however, there remains something to be seen in its thermal behavior. In addition to it, the MC shown in Fig. 1-29 consists of the column of twin-pillar type, and each pillar is of double-wall configuration. Supposedly, there might be several effective remedies to obtain the stable thermal characteristics. For example, we can observe the relatively large space between the pillar with slideway of full tight fitting and the main motor, and it may imply the necessity for more heat dissipation capacity than that of the other side. Obviously, the tight fitting means low thermal contact resistance, resulting in better heat conductance than loose fitting.

Cellular ConfigurationBecause fettling is not required, the welded box-like structure can be fabricated extremely using the cell entity (small compartment), where the cell entity consists of the small room enclosed by the partition. In other words, the box-like structural body component can be formed as an integration of certain number of compartments without having apertures, and thus we can obtain the rigid structure without local deformation [1-6]. In contrast, the cellular structure without the aper-ture is likely to accumulate the heat, resulting in the non-uniform tem-perature distribution across the whole structural body component.

FIGURE 1-29 Eight-face constraint slideway in MC—Hitachi-Seiki-make, 1990s.

Full tight fitting for leading guiding referenceNote: The opposite is in relatively tight fitting for secondary guiding reference

Spindle

Quill

Main motorFeed screw

Column of twin-pillar type

Double-wall structural configuration entity

Spindle head

Column slideway


In consideration of the noteworthy advantages in both the rigid-ity enhancement and the heat dissipation caused by the flow of air through the apertures, the cellular configuration with much less number of apertures has been employed also in the casting structure as exemplified by the base of the horizontal MC, although we must carry out the dirty and tedious work for fettling. Figure 1-30 shows an outstanding base structure with the cellular configuration,15 in which the base appears to be a variant of the double-wall configura-tion. In fact, the partition can be regarded as the connecting rib when the cell is small or narrow. In 2000, the Dah Lih of Taiwan produced a horizontal MC (Type MCH) within which the base consists of the cel-lular entities similar to that of Hitachi Seiki-make; however, the cen-ter cell has, dare to say, the connecting rib instead of the partition. In addition, the spindle head is designed using the slideways of eight-face wrap-around to the column.

In retrospect, Lorenz employed the cellular configuration in the casting column of the gear shaping machine in the 1960s, as shown in Fig. 1-31. As can be seen, the cellular configuration is obviously one of the variants in the double-wall configuration. However, in the Lorenz case, the cross-sectional configuration becomes more complicated by

15The MC can be extremely characterized by the hardened steel guideway, which is produced by fusion-like casting, resulting in the monolithic structure.

FIGURE 1-30 Cellular structural confi guration entity in base of horizontal MC—Type HG 500 of Hitachi Seiki-make, 1988.

Guideways made of hardenedsteel: H C more than 60

Main body of basemade of cast iron

Main spindle speed in max.: 4,500 r/minAllowable spindle torque in max.: 92 kgf-m (18.5 kW)

R

Cell 1

Cell 2 Cell 3

Partition


Axis for pendulum-like motion of main spindle (for pinion cutter)

Partition

Rib

Aperture


FIGURE 1-31 Rigid column in gear shaping machine: A representative placement of structural confi guration entities—Type LS of Lorenz-make, 1960s.

providing a considerable number of stiffening ribs, partitions, and apertures in order to realize the rigid column. In contrast, the thermal behavior appears to be very complicated, although we have not any evidence.

References[1-1] Kessler, C. “Wandel der Fertigungstechnik in der elektrotechnischen

Industrie.” ZwF, 1979; 74–6: 273.[1-2] Opitz, H., & Schunck, J. “Untersuchung über den Einfluß thermisch bed-

ingter Verformungen auf die Arbeitsgenauigkeit von Werkzeugmaschinen.” Forschungsberichte des Landes Nordrhein-Westfalen 1966, Nr. 1781, Westdeutscher Verlag.

[1-3] Frank, J. “Guß für Werkzeugmaschinen.” Industrie-Anzeiger, 1971; 93–42: 981–985.

[1-4] Graz, R. M. “Österreichische Werkzeugmaschinen auf der 6. Europäischen Werkzeugmaschinen-Ausstellung.” Werkstatt und Betrieb, 1959; 92–9: 699–705.

[1-5] The PERA. Machine Tool Structures—Survey of Literature on Machine Tool Structures, Part 2. Report No. 172, Jan. 1968.

[1-6] Bobek, K., et al. “Stahleichtbau von Maschinen.” Springer Verlag, 1955.

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