毕业设计外文翻译原文

编号：

毕业设计(论文)外文翻译

（原文）

院（系）：应用科技学院

专业：机械设计制造及其自动化

学生姓名：邓瑜

学号：0501120501

指导教师单位：应用科技学院

姓名：黄小能

职称：

2009年 5 月20 日

The Injection Molding

The Introduction of Molds

The mold is at the core of a plastic manufacturing process because its cavity gives a part its shape. This makes the mold at least as critical-and many cases more so-for the quality of the end product as, for example, the plasticiting unit or other components of the processing equipment.

Mold Material

Depending on the processing parameters for the various processing methods as well as the length of the production run, the number of finished products to be produced, molds for plastics processing must satisfy a great variety of requirements. It is therefore not surprising that molds can be made from a very broad spectrum of materials, including-from a technical standpoint-such exotic materials as paper matched and plaster. However, because most processes require high pressures, often combined with high temperatures, metals still represent by far the most important material group, with steel being the predominant metal. It is interesting in this regard that, in many cases, the selection of the mold material is not only a question of material properties and an optimum price-to-performance ratio but also that the methods used to produce the mold, and thus the entire design, can be influenced.

A typical example can be seen in the choice between cast metal molds, with their very different cooling systems, compared to machined molds. In addition, the production technique can also have an effect; for instance, it is often reported that, for the sake of simplicity, a prototype mold is frequently machined from solid stock with the aid of the latest technology such as computer-aided (CAD) and computer-integrated manufacturing (CIM). In contrast to the previously used methods based on the use of patterns, the use of CAD and CAM often represents the more economical solution today, not only because this production capability is available pin-house but also because with any other technique an order would have to be placed with an outside supplier.

Overall, although high-grade materials are often used, as a rule standard materials are used in mold making. New, state-of-the art (high-performance) materials, such as ceramics, for instance, are almost completely absent. This may be related to the fact that their desirable characteristics, such as constant properties up to very high temperatures, are not required on molds, whereas their negative characteristics, e. g. low tensile strength and poor thermal conductivity, have a clearly related to ceramics, such as sintered material, is found in mild making only to a limited degree. This refers less to the modern materials and components

produced by powder metallurgy, and possibly by hot isocratic pressing, than to sintered metals in the sense of porous, air-permeable materials.

Removal of air from the cavity of a mold is necessary with many different processing methods, and it has been proposed many times that this can be accomplished using porous metallic materials. The advantages over specially fabricated venting devices, particularly in areas where melt flow fronts meet, I, e, at weld lines, are as obvious as the potential problem areas: on one hand, preventing the texture of such surfaces from becoming visible on the finished product, and on the other hand, preventing the microspores from quickly becoming clogged with residues (broken off flash, deposits from the molding material, so-called plate out, etc.). It is also interesting in this case that completely new possibilities with regard to mold design and processing technique result from the use of such materials.

A. Design rules

There are many rules for designing molds. These rules and standard practices are based on logic, past experience, convenience, and economy. For designing, mold making, and molding, it is usually of advantage to follow the rules. But occasionally, it may work out better if a rule is ignored and an alternative way is selected. In this text, the most common rules are noted, but the designer will learn only from experience which way to go. The designer must ever be open to new ideas and methods, to new molding and mold materials that may affect these rules.

B. The basic mold

1. Mold cavity space

The mold cavity space is a shape inside the mold, “excavated” in such a manner that when the molding material is forced into this space it will take on the shape of the cavity space and, therefore, the desired product. The principle of a mold is almost as old as human civilization. Molds have metals into sand forms. Such molds, which are still used today in foundries, can be used only once because the mold is destroyed to release the product after it has solidified. Today, we are looking for permanent molds that can be used over and over. Now molds are made from strong, durable materials, such as steel, or from softer aluminum or metal alloys and even from certain plastics where a long mold life is not required because the planned production is small. In injection molding the plastic is injected into the cavity space with high pressure, so the mold must be strong enough to resist the injection pressure without deforming.

2. Number of cavities

Many molds, particularly molds for larger products, are built for only cavity space, but many molds, especially large production molds, are built with 2 or more cavities. The reason

for this is purely economical. It takes only little more time to inject several cavities than to inject one. For example, a 4-cavity mold requires only one-fourth of the machine time of a single-cavity mold. Conversely, the production increases in proportion to the number of cavities. A mold with more cavities is more expensive to build than a single-cavity mold, but not necessarily 4 times as much as a single-cavity mold. But it may also require a larger machine with larger platen area and more clamping capacity, and because it will use 4 times the amount of plastic, it may need a large injection unit, so the machine hour cost will be higher than for a machine large enough for the smaller mold.

3. Cavity shape and shrinkage

Th e shape of the cavity is essentially the “negative” of the shape of the desired product, with dimensional allowance added to allow for shrinking of the plastic. The shape of the cavity is usually created with chip-removing machine tools, or with electric discharge machining, with chemical etching, or by any new method that may be available to remove metal or build it up, such as galvanic processes. It may also be created by casting certain metals in plaster molds created from models of the product to be made, or by casting some suitable hard plastics. The cavity shape can be either cut directly into the mold plates or formed by putting inserts into the plates.

C. Cavity and core

By convention, the hollow portion of the cavity space is called the cavity. The matching, often raised portion of the cavity space is called the core. Most plastic products are cup-shaped. This does not mean that they look like a cup, but they do have an inside and an outside. The outside of the product is formed by the cavity, the inside by the core. The alternative to the cup shape is the flat shape. In this case, there is no specific convex portion, and sometimes, the core looks like a mirror image of the cavity. Typical examples for this are plastic knives, game chips, or round disks such as records. While these items are simple in appearance, they often present serious molding problems for ejection of the product. The reason for this is that all injection molding machines provide an ejection mechanism on the moving platen and the products tend to shrink onto and cling to the core, from where they are then ejected. Most injection molding machines do not provide ejection mechanisms on the injection side.

Polymer Processing

Polymer processing, in its most general context, involves the transformation of a solid (sometimes liquid) polymeric resin, which is in a random form (e.g., powder, pellets, beads), to a solid plastics product of specified shape, dimensions, and properties. This is achieved by means of a transformation process: extrusion, molding, calendaring, coating, thermoforming,

etc. The process, in order to achieve the above objective, usually involves the following operations: solid transport, compression, heating, melting, mixing, shaping, cooling, solidification, and finishing. Obviously, these operations do not necessarily occur in sequence, and many of them take place simultaneously.

Shaping is required in order to impart to the material the desired geometry and dimensions. It involves combinations of viscoelastic deformations and heat transfer, which are generally associated with solidification of the product from the melt.

Shaping includes: two-dimensional operations, e.g. die forming, calendaring and coating; three-dimensional molding and forming operations. Two-dimensional processes are either of the continuous, steady state type (e.g. film and sheet extrusion, wire coating, paper and sheet coating, calendaring, fiber spinning, pipe and profile extrusion, etc.) or intermittent as in the case of extrusions associated with intermittent extrusion blow molding. Generally, molding operations are intermittent, and, thus, they tend to involve unsteady state conditions. Thermoforming, vacuum forming, and similar processes may be considered as secondary shaping operations, since they usually involve the reshaping of an already shaped form. In some cases, like blow molding, the process involves primary shaping (pair-son formation) and secondary shaping (pair son inflation).

Shaping operations involve simultaneous or staggered fluid flow and heat transfer. In two-dimensional processes, solidification usually follows the shaping process, whereas solidification and shaping tend to take place simultaneously inside the mold in three dimensional processes. Flow regimes, depending on the nature of the material, the equipment, and the processing conditions, usually involve combinations of shear, extensional, and squeezing flows in conjunction with enclosed (contained) or free surface flows.

The thermo-mechanical history experienced by the polymer during flow and solidification results in the development of microstructure (morphology, crystallinity, and orientation distributions) in the manufactured article. The ultimate properties of the article are closely related to the microstructure. Therefore, the control of the process and product quality must be based on an understanding of the interactions between resin properties, equipment design, operating conditions, thermo-mechanical history, microstructure, and ultimate product properties. Mathematical modeling and computer simulation have been employed to obtain an understanding of these interactions. Such an approach has gained more importance in view of the expanding utilization of computer design/computer assisted manufacturing/computer aided engineering (CAD/CAM/CAE) systems in conjunction with plastics processing.

It will emphasize recent developments relating to the analysis and simulation of some important commercial process, with due consideration to elucidation of both thermo-

mechanical history and microstructure development.

As mentioned above, shaping operations involve combinations of fluid flow and heat transfer, with phase change, of a visco-elastic polymer melt. Both steady and unsteady state processes are encountered. A scientific analysis of operations of this type requires solving the relevant equations of continuity, motion, and energy (I. e. conservation equations).

Injection Molding

Many different processes are used to transform plastic granules, powders, and liquids into final product. The plastic material is in moldable form, and is adaptable to various forming methods. In most cases thermoplastic materials are suitable for certain processes while thermosetting materials require other methods of forming. This is recognized by the fact that thermoplastics are usually heated to a soft state and then reshaped before cooling. Theromosets, on the other hand have not yet been polymerized before processing, and the chemical reaction takes place during the process, usually through heat, a catalyst, or pressure. It is important to remember this concept while studying the plastics manufacturing processes and the polymers used.

Injection molding is by far the most widely used process of forming thermoplastic materials. It is also one of the oldest. Currently injection molding accounts for 30% of all plastics resin consumption. Since raw material can be converted by a single procedure, injection molding is suitable for mass production of plastics articles and automated one-step production of complex geometries. In most cases, finishing is not necessary. Typical products include toys, automotive parts, household articles, and consumer electronics goods,

Since injection molding has a number of interdependent variables, it is a process of considerable complexity. The success of the injection molding operation is dependent not only in the proper setup of the machine variables, but also on eliminating shot-to-shot variations that are caused by the machine hydraulics, barrel temperature variations, and changes in material viscosity. Increasing shot-to-shot repeatability of machine variables helps produce parts with tighter tolerance, lowers the level of rejects, and increases product quality ( i.e., appearance and serviceability).

The principal objective of any molding operation is the manufacture of products: to a specific quality level, in the shortest time, and using a repeatable and fully automatic cycle. Molders strive to reduce or eliminate rejected parts, or parts with a high added value such as appliance cases, the payoff of reduced rejects is high.

A typical injection molding cycle or sequence consists of five phases:

1 Injection or mold filling

2 Packing or compression

3 Holding

4 Cooling

5 Part ejection

Injection Molding Overview

Process

Injection molding is a cyclic process of forming plastic into a desired shape by forcing

the material under pressure into a cavity. The shaping is achieved by cooling (thermoplastics) or by a chemical reaction (thermosets). It is one of the most common

and versatile operations for mass production of complex plastics parts with excellent dimensional tolerance. It requires minimal or no finishing or assembly operations. In addition to thermoplastics and thermosets, the process is being extended to such

materials as fibers, ceramics, and powdered metals, with polymers as binders.

Applications

Approximately 32 percent by weight of all plastics processed go through injection molding machines. Historically, the major milestones of injection molding include the invention of the reciprocating screw machine and various new alternative processes, and the application of computersimulation to the design and manufacture of plastics parts.

Development of the injection molding machine

Since its introduction in the early 1870s, the injection molding machine has undergone significant

modifications and improvements. In particular, the invention of the reciprocating screw machine hasrevolutionized the versatility and productivity of the thermoplastic injection molding process.

Benefits of the reciprocating screw

Apart from obvious improvements in machine control and machine functions, the major development for the injection molding machine is the change from a plunger mechanism to a reciprocating screw. Although the plunger-type machine is inherently simple, its popularity was

limited due to the slow heating rate through pure conduction only. The reciprocating screw can

plasticize the material more quickly and uniformly with its rotating motion, as shown in Figure 1. Inaddition, it is able to inject the molten polymer in a forward direction, as a plunger.

Development of the injection molding process

The injection molding process was first used only with thermoplastic polymers. Advances in the

understanding of materials, improvements in molding equipment, and the needs of specific industrysegments have expanded the use of the process to areas beyond its original scope. Alternative injection molding processes

During the past two decades, numerous attempts have been made to develop injection molding

processes to produce parts with special design features and properties. Alternative processes derivedfrom conventional injection molding have created a new era for additional applications, more designfreedom, and special structural features. These efforts have resulted in a number of processes,including:

Co-injection (sandwich) molding

Fusible core injection molding)

Gas-assisted injection molding

Injection-compression molding

Lamellar (microlayer) injection moldin

Live-feed injection molding

Low-pressure injection molding

Push-pull injection molding

Reactive molding

Structural foam injection molding

Thin-wall molding

Computer simulation of injection molding processes

Because of these extensions and their promising future, computer simulation of the process has alsoexpanded beyond the early "lay-flat," empirical cavity-filling estimates. Now, complex programs simulate post-filling behavior, reaction kinetics, and the use of two materials with different properties, or two distinct phases, during the process.

The Simulation section provides information on using C-MOLD products.Among the Design topicsare several examples that illustrate how you can use CAE tools to improve your part and molddesign and optimize processing conditions.

Co-injection (sandwich) molding

Overview

Co-injection molding involves sequential or concurrent injection of two different but compatible polymer melts into a cavity. The materials laminate and solidify. This process produces parts that have a laminated structure, with the core material embedded between

the layers of the skin material. This innovative process offers the inherent flexibility of

using the optimal properties of each material or modifying the properties of the molded part.

FIGURE 1. Four stages of co-injection molding. (a) Short shot of skin polymer melt (shown in dark green)is injected into the mold. (b) Injection of core polymer melt until cavity is nearly filled, as shown in (c). (d)Skin polymer is injected again, to purge the core polymer away from the sprue.

Fusible core injection molding

Overview

The fusible (lost, soluble) core injection molding process illustrated below produces

single-piece, hollow parts with complex internal geometry. This process molds a core

inside the plastic part. After the molding, the core will be physically melted or chemically dissolved, leaving its outer geometry as the internal shape of the plastic part.

FIGURE 1. Fusible (lost, soluble) core injection molding

Gas-assisted injection molding

Gas-assisted process

The gas-assisted injection molding process begins with a partial or full injection of

polymer melt into the mold cavity. Compressed gas is then injected into the core of the polymer melt to help fill and pack the mold. This process is illustrated below.

FIGURE 1. Gas-assisted injection molding: (a) the electrical system, (b) the hydraulic system, (c) the control panel, and (d) the gas cylinder.

Injection-compression molding

Overview

The injection-compression molding process is an extension of conventional injection molding. After a pre-set amount of polymer melt is fed into an open cavity, it is compressed, as shown below. The compression can also take place when the polymer is

to be injected. The primary advantage of this process is the ability to produce dimensionally stable, relatively stress-free parts, at a low clamp tonnage (typically 20 to 50 percent lower).

Lamellar (microlayer) injection molding

Overview

This process uses a feedblock and layer multipliers to combine melt streams from dual injection cylinders. It produces parts from multiple resins in distinct microlayers, as shown in Figure 1 below. Combining different resins in a layered structure enhances a number of properties, such as the gas barrier property, dimensional stability, heat resistance, and optical clarity.

Live-feed injection molding

Overview

The live-feed injection molding process applies oscillating pressure at multiple polymer entrances to cause the melt to oscillate, as shown in the illustration below. The action of the pistons keeps the material in the gates molten while different layers of molecular or fiber orientation are being built up in the mold due to solidification. This process provides a means of making simple or complex parts that are free from voids, cracks, sink marks, and weld-line defects.

Low-pressure injection molding

Overview

Low-pressure injection molding is essentially an optimized extension of conventional injection molding (see Figure 1). Low pressure can be achieved by properly programming the screw revolutions per minute, hydraulic back pressure, and screw speed to control

the melt temperature and the injection speed. It also makes use of a generous gate size or

a n reduce umber of valve gates that open and close sequentially to reduce the flow length. The

packing stage is eliminated with a generally slow and controlled injection speed. The benefits of low-pressure injection molding include a reduction of the clamp force tonnage requirement, less costly molds and presses, and lower stress in the molded parts.

Push-pull injection molding

Overview

The push-pull injection molding process uses a conventional twin-component injection system and a two-gate mold to force material to flow back and forth between a master injection unit and a secondary injection unit, as shown below. This process eliminates

weld lines, voids, and cracks, and controls the fiber orientation.

Reactive molding

Processing

Major reactive molding processes include reactive injection molding (RIM), and composites processing, such as resin transfer molding (RTM) and structural reactive injection molding (SRIM).

The typically low viscosity of the reactive materials permits large and complex parts to be molded

with relatively lower pressure and clamp tonnage than required for thermoplastics molding. relatively For example, to make high-strength and low-volume large parts, RTM and SRIM can be used to include a preform made of long fibers. Another area that is receiving more attention than ever before is the encapsulation of microelectronic IC chips.

The adaptation of injection molding to these materials includes only a small increase in temperature in the feed mechanism (barrel) to avoid pre-curing. The cavity, however, is usually hot enough to initiate chemical cross-linking. As the warm pre-polymer is forced into the cavity, heat is added from the cavity wall, from viscous (frictional) heating of the flow, and from the heat released by the reacting components. The temperature of the part often exceeds the temperature of the mold. When the reaction is sufficiently advanced for the part to be rigid (even at a high temperature) the cycle is complete and the part is ejected.

Design considerations

The mold and process design for injection molding of reactive materials is much more complex

because of the chemical reaction that takes place during the filling and post-filling stages. For instance, slow filling often causes premature gelling and a resultant short shot, while fast filling

could induce turbulent flow that creates internal porosity. Improper control of mold-wall temperature and/or inadequate part thickness will either give rise to moldability problems during

injection, or cause scorching of the materials. Computer simulation is generally recognized as a

more cost-effective tool than the conventional, time-consuming trial-and-error method for tool and

process debugging.

Structural foam injection molding

Overview

Structural foam molding produces parts consisting of solid external skin surfaces surrounding an inner cellular (or foam) core, as illustrated in Figure 1 below. This process

is suitable for large, thick parts that are subject to bending loads in their end-use application. Structural foam parts can be produced with both low and high pressure, with

nitrogen gas or chemical blowing agents.

Thin-wall molding

Overview

The term "thin-wall" is relative. Conventional plastic parts are typically 2 to 4 mm thick. Thin-wall designs are called "advanced" when thicknesses range from 1.2 to 2 mm, and "leading-edge" when the dimension is below 1.2 mm. Another definition of thin-wall molding is based on the flow-length-to-wall-thickness ratios. Typical ratios for these

thin-wall applications range from 100:1 to 150:1 or more.

Typical applications

Thin-wall molding is more popular in portable communication and computing equipment, which

demand plastic shells that are much thinner yet still provide the same mechanical strength as conventional parts.

Processing

Because thin-wall parts freeze off quickly, they require high melt temperatures, high injectio speeds, and very high injection pressures if multiple gates or sequential valve gating are not an optimized ram-speed profile helps to reduce the pressure requirement.

Due to the high velocity and shear rate in thin-wall molding, orientation occurs more readily help minimize anisotropic shrinkage in thin-wall parts, it is important to pack the part adequately while the core is still molten.

Injection molding machine

Components

For thermoplastics, the injection molding machine converts granular or pelleted raw

plastic into final molded parts via a melt, inject, pack, and cool cycle. A typical injection molding machine consists of the following major components, as illustrated in Figure 1 below.

Machine function

Injection molding machines can be generally classified into three categories, based on machine

function:

General-purpose machines

Precision, tight-tolerance machines

High-speed, thin-wall machines

Auxiliary equipment

The major equipment auxiliary to an injection molding machine includes resin dryers, materials-handling equipment, granulators, mold-temperature controllers and chillers, part-removal robots, and part-handling equipment.

Automated surface ?nishing of plastic injection mold steel with spherical

grinding and ball burnishing processes

Abstract This study investigates the possibilities of automated spherical grinding and ball burnishing surface ?nishing processes in a freefor m surface plastic injection mold steel PDS5 on a CNC machining center. The design and manufacture of a grinding tool holder has been accomplished in this study.The optimal surface grinding parameters were determined usingTaguchi’s orthogonal array method f or plastic injection moldingsteel PDS5 on a machining center. The optimal surface grinding parameters for the plastic injection mold steel PDS5 were

the combination of an abrasive material of PA Al2O3, a grinding speed of 18 000 rpm, a grinding depth of 20 μm, and a feed of 50 mm/min. The surface roughness R a of the specimen can be improved from about 1.60 μm to 0.35 μm by using the optimal parameters for surface grinding. Surface roughness R a can befurther improved from about 0.343 μm to 0.06 μm by using the ball burnishing process with the optimal burnishing parameters.Applying the optimal surface grinding and burnishing parame-ters sequentially to a ?ne-milled freeform surface mold insert,the surface roughness R a of freeform surface region on the tested part can be improved from about 2.15 μm to 0.07 μm.

Keywords Automated surface ?nishing · Ball burnishing process · Grinding process ·Surface roughnes s · Taguchi’s method

1 Introduction

Plastics are important engineering materials due to their speci?c characteristics, such as corrosion resistance, resistance to chemicals, low density, and ease of manufacture, and have increasingly replaced metallic components in industrial applications. Injection molding is one of the important forming processes for plastic products. The surface ?nish quality of the plastic injection mold is an essential requirement due to its direct effects on the appearance of the plastic product. Finishing processes such as grinding, polishing and lapping are commonly used to improve the surface ?nish.

The mounted grinding tools (wheels) have been widely used in conventional mold and die ?nishing industries. The geometric model of mounted grinding tools for automated surface ?nishing processes was introduced in [1]. A ?nishing process model of spherical grinding tools for automated surface ?nishing systems was developed in [2]. Grinding speed, depth of cut, feed rate, and wheel properties such as abrasive material and abrasive grain size, are the dominant parameters for the spherical grinding process, as shown in Fig. 1. The optimal spherical grinding parameters for the injection mold steel have not yet been investigated based in the literature.

In recent years, some research has been carried out in determining the optimal parameters of the ball burnishing process (Fig. 2). For instance, it has been found that plastic deformation on the workpiece surface can be reduced by using a tungsten carbide ball or a roller, thus improving the surface roughness, surface hardness, and fatigue resistance [3–6]. The burnishing process is accomplished by machining centers [3, 4] and lathes [5, 6]. The main burnishing parameters having signi?cant effec ts on the surface roughness are ball or roller material,burnishing force, feed rate, burnishing speed, lubrication, and number of burnishing passes, among others [3]. The optimal surface burnishing parameters for the plastic injection mold steel PDS5 were a combination of grease lubricant, the tungsten carbide ball, a burnishing speed of 200 mm/min, a burnishing force of 300 N, and a feed of 40 μm [7]. The depth of penetration of the burnished surface using the optimal ball burnishing parameters was about 2.5 microns. The improvement of the surface roughness through burnishing process generally ranged between 40% and 90% [3–7].

The aim of this study was to develop spherical grinding and ball burnishing surface ?nish processes of a freeform surface plastic injection mold on a machining center. The ?owchart of automated surface ?nish using spherical grinding and ball burnishing processes is shown in Fig. 3. We began by designing and manufacturing the spherical grinding tool and its alignment device for use on a machining center. The optimal surface spherical grinding parameters were determined by utilizing a Taguchi’s orthogonal array method. Four factors and three corresponding levels were then chosen for the Taguchi’s L18matrix experiment.The optimal mounted spherical grinding parameters for surface grinding were then applied to the surface ?nish of a freeform surface carrier. To improve the surface roughness, the ground surface was further burnished, using the optimal ball burnishing parameters.

Fig. 1. Schematic diagram of the spherical grinding process

Fig. 2. Schematic diagram of the ball-burnishing process

Fig. 3. Flowchart of automated surface ?nish using spherical grinding and ball burnishing processes

2 Design of the spherical grinding tool and its alignment device

To carry out the possible spherical grinding process of a freeform surface, the center of the ball grinder should coincide with the z-axis of the machining center. The mounted spherical grinding tool and its adjustment device was designed, as shown in Fig. 4. The electric grinder was mounted in a tool holder with two adjustable pivot screws. The center of the grinder ball was well aligned with the help of the conic groove of the alignment components. Having aligned the grinder ball, two adjustable pivot screws were tightened; after which, the alignment components could be removed. The deviation between the center coordinates of the ball grinder and that of the shank was about 5 μm, which was measured by a CNC coordinate measuring machine. The force induced by the vibration of the machine bed is absorbed by a helical spring. The manufactured spherical grinding tool and ball-burnishing tool were mounted, as shown in Fig. 5. The spindle was locked for both the spherical grinding process and the ball burnishing process by a spindle-locking mechanism.

3 Planning of the matrix experiment

3.1 Con?guration of Taguchi’s orthogonal array

The effects of several parameters can be determined ef?ciently by conducting matrix experiments using Taguchi’s orthogonal array [8]. To match the aforementioned spherical grinding parameters, the abrasive material of the grinder ball (with the diameter of 10 mm), the feed rate, the depth of grinding, and the revolution of the electric grinder were selected as the four experimental factors (parameters) and designated as factor A to D (see Table 1) in this research. Three levels (settings) for each factor were con?gured to cover the range of interest, and were identi?ed by the digits 1, 2, and 3. Three types of abrasive materials, namely silicon

carbide (SiC), white aluminum oxide (Al2O3, WA), and pink aluminum oxide (Al2O3, PA), were selected and studied. Three numerical values of each factor were determined based on the pre-study results. The L18 orthogonal array was selected to conduct the matrix experiment for four 3-level factors of the spherical grinding process.

Fig. 4. Schematic illustration of the spherical grinding tool and its adjustment

device

Fig. 5. a Photo of the spherical grinding tool b Photo of the ball burnishing tool

3.2 De?nition of the data analysis

Engineering design problems can be divided into smaller-the-better types, nominal-the-best types, larger-the-better types, signed-target types, among others [8]. The signal-to-noise (S/N) ratio is used as the objective function for optimizing a product or process design. The

surface roughness value of the ground surface via an adequate combination of grinding parameters should be smaller than that of the original surface. Consequently, the spherical grinding process is an example of a smaller-the-better type problem. The S/N ratio,η, is de?ned by the following equation [8]:

η=?10 log10（mean square quality characteristic)

=?10 log10

?

?

??

?

?∑

=

n

i

i

y n1

2 1

where:

y i: observations of the quality characteristic under different noise conditions

n: number of experiment

After the S/N ratio from the experimental data of each L18 orthogonal array is calculated, the main effect of each factor was determined by using an analysis of variance (ANOV A) technique and an F-ratio test [8]. The optimization strategy of the smaller-the better problem is to maximize η, as de?ned by Eq. 1.Levels that maximize η will be selected for the factors that have a signi?cant effect onη. The optimal conditions for spherical grinding can then be determined.

Table 1. The experimental factors and their levels

4 Experimental work and results

The material used in this study was PDS5 tool steel (equivalent to AISI P20) [9], which is commonly used for the molds of large plastic injection products in the ?eld of au tomobile components and domestic appliances. The hardness of this material is about HRC33 (HS46) [9]. One speci?c advantage of this material is that after machining, the mold can be directly used for further ?nishing processes without heat treatment due to its special pre-treatment. The specimens were designed and manufactured so that they could be mounted on a dynamometer to measure the reaction force. The PDS5 specimen was roughly machined and then mounted on the dynamometer to carry out the ?ne milling on a three-axis machining center made by YangIron Company (type MV-3A), equipped with a FUNUC Company NC-controller (type 0M) [10]. The pre-machined surface roughness was measured, using Hommelwerke T4000 equipment, to be about 1.6 μm. Figure 6 shows the experimental set-up of the spherical grinding process. A MP10 touch-trigger probe made by the Renishaw Company was also integrated with the machining center tool magazine to measure and determine the coordinated origin of the specimen to be ground. The NC