Abstract : The PCM process is a new RM process that combines the RP technology with the casting process based on the principle of discrete deposition. Analyzes and discusses the main factors affecting the precision and surface quality of PCM molded parts. It proposes to improve the precision of the molded parts by optimizing the CAD model of the casting mold, selecting the raw materials and injection methods correctly, and determining the control parameters and appropriate matching relationships for each process. And the goal of improving surface quality. Overview RP technology has developed to today, and its development focus has shifted from rapid prototyping (RP) to rapid manufacturing (RM-Rapid Manufacturing) and rapid manufacturing of metal parts. Various new materials and new processes in the RP field are emerging. RP technology not only applies to the design process, but also extends to the manufacturing field. In the manufacturing industry, the main factors limiting the time to market are the design and manufacturing time of molds and models. RP is an aid to rapid design. More manufacturers want to directly make molds or products from CAD data, so RM Technology is particularly interesting. The rapid casting (QC-Quick Casting) produced by the combination of RP technology and casting process is one of the main research fields of RM. In recent years, the direct-cast mold manufacturing technology developed using the rapid-formed discrete/stacking principle eliminates the need for traditional process models, and accurately controls the molding materials according to the geometric information of the mold CAD model (including process information such as the gating system). The accumulation process and the direct production of molds are major changes in the traditional casting process. The PCM (Patternless Casting Modeling) process successfully developed by Tsinghua University introduces the RP theory into the resin sand molding process, and adopts contour scanning and spray curing technology to realize the rapid manufacture of modelless casting molds. The PCM process is an integrated manufacturing process that includes CAD/CAM, numerical control, materials, ejection, process parameter settings, and post-processing. It can be summarized as the following three processes: (1) Pre-treatment process: First, the mold is planned and designed, that is, the process parameters are determined, the optimal machining direction is selected, the pouring system is designed, and the CAD model of the product/part is converted into a CAD model of the mold. Then from the CAD data of the mold, the hierarchical cross-section outline data is obtained, and then the control information is generated with the layer information. (2) Molding process: The original sand storage and sand-sanding mechanism evenly spreads the original sand on the surface of the sand box and is compacted by the rollers. The spraying device sprays the resin and the curing agent on each layer and paves the compacted sand. The binder and the catalyst reacted with each other. The local sand where the binder and the catalyst worked together was solidified. The other local sand was still granular sand. After curing a layer and then bonding the next layer, a three-dimensional solid cast can be obtained after all layers are bonded. (3) Post-treatment process: Clearing the uncured dry sand in the middle of the mold can produce a mold with a certain wall thickness, and apply or impregnate the coating on the inner surface of the sand mold. During the research of the PCM process, it has been found that the accuracy and surface quality of PCM forming parts have become increasingly prominent and are closely related to the three processes of the PCM process. Each step of each process may cause errors of one kind or another. These errors will be serious. Damages the precision and surface quality of the PCM molding and hinders its further application. In order to explore and solve this problem, this paper analyzes and discusses the main factors that affect the accuracy and surface quality of PCM molded parts. 1 Analysis and discussion For a given equipment hardware and software structure rapid prototyping system, the movement precision of the mechanical system has been basically determined, and the error caused by the approximate expression of the CAD model in the STL format file is not discussed here. The key point is to optimize the CAD model of the mold and select the right one. Raw materials and injection methods, reasonable determination of the control parameters of the various processes and a suitable matching relationship, greatly improve the precision of the molded parts and improve the surface quality. 1.1 CAD model In the PCM process, the layering process is driven by the control information generated by the CAD model of the casting mold. The CAD model of the casting mold is the basis for the manufacturing process of the moldless mold. The orientation and placement of the parts are normal to the forming process of the mold. The influence of the forming, the forming accuracy, the surface quality, and the processing time have a great influence. In order to improve the forming accuracy and the surface quality of the parts and reduce the processing time, PCM process planning and mold design must be carried out. That is to determine the process parameters, select the optimal machining direction, design the casting system, etc., and convert the CAD model of the product/part into a mold. CAD model. Optimization of the forming process direction of the forming part is one of the important research topics of the process design of the rapid prototyping technology based on the discrete/stacking forming principle. It is also one of the most important factors affecting accuracy and surface quality in the PCM process. Because the existing discrete/stack forming process produces a “step surface†feature, it is difficult to produce high-precision molded parts required in industry, which is also the future of RP technology. A key issue to be solved. The machining accuracy is mainly reflected in the area of ​​the stepped area on the surface of the part, the machining accuracy in the surface, and the dimensional accuracy in the machining direction. In addition to the area of ​​the step area, the accuracy of the in-plane machining and the dimensional accuracy of the machining direction have little to do with the machining direction. Therefore, when determining the optimum machining direction, only the size of the step area can be considered. Therefore, the machining direction will be optimized with the processing accuracy and processing time as the main goals. In order to achieve the above objectives, the following factors must be comprehensively considered when establishing the objective function: · Maximize the number of vertical faces; The process direction optimization algorithm of PCM process adopts the multi-objective function method which takes the processing accuracy as the main factor while considering the processing time. At the same time, a more practical and simple objective function is proposed in combination with the PCM process: Q=min(Qi) (i=1,2,...,m) (2-1) Qi is the target value of the i-th machining direction, and is calculated as the relative error value in the machining direction. Suppose there are m machining directions available. Where: Wij - the error weight vector assigned to the j-th patch in the ith machining direction, that is, the projection of the unit normal vector of the patch in the machining direction i; The weight coefficient reflects the degree of influence of the surface type on the forming accuracy. For the PCM process, the vertical plane and the normal upward plane can obtain the highest forming accuracy, while the inclined plane and the curved surface are relatively poor. The lower level is the free surface formed by the penetration of the resin curing agent, and the forming accuracy and surface quality are the most. difference. The effect on the machining accuracy will vary depending on the size of the angle β ij between the surface normal and the machining direction. The type of surface is the main factor that affects the projected area of ​​the "step zone." Fully horizontal and vertical planes are rare in parts, and most of the faces may be beveled, columnar or freeform. These surfaces are generally represented by a series of small surface patches, so the above algorithm can also be extended to these small surfaces. Let the free surface in the parameter space be represented by a series of surface patches. Let the surface type of each small patch be calculated according to formula (2-3). The accuracy of the weight coefficient can be controlled by the number of surface patches. The more the number of surface patches, the more accurate the determination of the weight coefficient and the more accurate the calculation of the target value. Calculate the Q values ​​for a number of alternative machining directions and analyze them using a one-dimensional optimization method. The direction with the smallest Q is the machining direction with the highest accuracy. For the parts with complex structure and shape, if the integrated forming method is adopted, even if the above optimization algorithm is adopted, it is difficult to avoid the inclined plane, the curved surface and the lower horizontal plane, and the decomposition casting molds can be manufactured according to the optimized directions respectively, and finally the casting patterns are combined. The method can obtain higher forming accuracy and surface quality. Experiments show that this is also an effective method to improve the overall precision and surface quality of the mold. 1.2 Physical Characteristics of Raw Materials The particle size of the raw sand, the viscosity of the resin and the curing agent are also important factors affecting the PCM molded parts. The difference in the specific surface area of ​​the sand caused by the coarseness of the original sand size will directly affect the size of the permeation unit and thus the scan line width; the viscosity of the resin hardener also differs from that of the original sand surface, affecting the penetration and scanning lines. width. It was found that when the viscosity is too high, the liquid of the resin and the curing agent is sprayed on the surface of the original sand to become non-wetting and become intermittent beads, and the thickness of the scanning line causes inconsistency or even the formation of nodules and vacancies. In addition, the particle size distribution, grain shape, and clay content of the raw sand will also affect the precision and surface quality of the formed part due to the influence of infiltration. 1.3 Spray form After processing with a layered slice using a three-dimensional model with small triangles, the resulting slice file has a zero-width outline. However, in the process of processing, the scanning line formed by the sprayed liquid on the forming surface has a certain width. Although in theory, the actual machining contours can be formed in the process control software through the compensation of the theoretical contour lines to eliminate such errors. However, the scanning line width varies with the scanning speed, injection pressure, viscosity of resin and curing agent, and ambient temperature during processing. In addition, since the solenoid valve is used for the on-off control of the spray head, there is a problem of the speed response, so that either nodules or vacancies will accumulate on the formed part. All of these can cause errors in the formed parts. The difference in the injection method will also have a greater impact on the accuracy of the forming part. With the sequential injection of the resin and the curing agent, the previously ejected liquid will freely diffuse in the original sand, and the diffusion of the post-injected liquid will be hindered by the rapid solidification and be within the first ejection liquid diffusion area, thereby forming a solidification line width. It is wider, and the outer surface has an adhesive layer containing only one component, which not only affects the accuracy and surface quality, but also brings inconvenience to subsequent processing. The resin and curing agent are sprayed at the same time, and the two liquid streams quickly reach the surface of the original sand after mixing. The permeation diffusion and the curing reaction proceed at the same time. The rapid solidification of the two components restricts the diffusion, thereby reducing the scanning line width, improving the accuracy and surface quality. . 1.4 Process parameters In the experimental research of PCM process, a lot of experiments are needed to determine the best process parameters suitable for modeling. Among them, the layer thickness, offset distance (filled grid spacing) is determined based on the best bonding form of the unit body. Therefore, the two main process parameters that affect the size and shape of the cell are the scanning speed and nozzle flow. When modeling, the nozzle flow rate is determined according to the solidification content of the unit body, the working pressure of the adhesive and the catalyst is adjusted to an appropriate state, and the respective required flow rate is obtained under the corresponding working pressure. However, the adjustable flow range is limited by the spray head and the fluid delivery system. The more easily controlled parameter is the scanning speed. Combined with experimental observations and analysis of experimental results, the following conclusions can be drawn: (1) The strength of the mold increases with the decrease of the layer thickness and the offset distance (grid spacing), and the former has a more significant effect; (3) When the scanning speed is constant, the surface quality of the mold is optimal under certain intermediate conditions. At this time, the ratio of the layer thickness to the cured thickness of the unit body formed by the free penetration at the scanning speed is h:r≈2:3, and the ratio of the offset distance (or grid spacing) to the solidification line width d:b≈2: 3, as shown in Figure 2. The measurement data shows that in this condition, the strength of the mold also fully meets the requirements. Therefore, the above parameters are the optimal modeling parameters at this scanning speed. (4) The above proportional relationship does not change with the scanning speed. In the actual modeling process, the specific optimal modeling parameters must be determined through experiments. Specific steps are as follows: (1) Determine the scanning speed according to the load capacity and stability of the XY scanning system; 1.5 Modeling Process Parameters Matching In addition to the precision of the RP process, which depends on the movement accuracy of the mechanical system and the form and size of the basic forming unit, the degree of matching between the molding process parameters also has an important influence on the forming accuracy. In the PCM process, the most important process parameters include: scanning speed, jet flow rate, grit size, and layer thickness. The match between them will directly affect the size and shape of the agglomerating unit body, which will affect the forming accuracy. Therefore, the following analysis and study of the matching relationship between the above parameters. ◠Matching of scanning speed and ejection flow The mold produced by the PCM process not only has to be castable from a functional point of view, but also has to achieve a certain shape accuracy, including shape accuracy, dimensional accuracy, and surface accuracy. This process is a face-to-body accumulation process, so whether the size and shape of the agglomerate units are uniform is an important factor in determining the geometric accuracy of the mold. In the scanning process, the scanning direction changes, but the scanning speed does not change. In order to ensure that the size of the agglomerating unit is uniform and uniform, the solidification content of the liquid must be kept constant; under the condition that the flow rate of the nozzle is constant, the experimental results show that the cell size and adhesive content change with the scanning speed as shown in Fig. 3 and Fig. 4 As shown. It can be seen from FIG. 4 that when the injection flow rate is determined, the solidification content decreases as the scanning speed increases. Therefore, in order to ensure the constant content of the curing, it is necessary to increase (decrease) the ejection flow when the scanning speed increases (decreases). In the PCM process, the spray head determines whether the liquid is ejected in an open or closed manner and does not generate a driving force for the liquid itself. The driving force of the liquid jet comes from the compressed gas in the cylinder, which is obtained by depressurizing the high pressure gas. According to the Bernoulli equation available flow: In the formula: From formula (2-4), it can be seen that the injection flow rate Q is proportional to the square root of the working pressure, and changing the working pressure can cause the injection flow rate to change accordingly. Therefore, to ensure the matching of the scanning speed and the ejection flow rate, first, it must be ensured that the scanning speed matches the working pressure of the liquid; secondly, the unit body has the best curing content; when the curing content is too large, the gas generation amount is too large, and when the size is too small, the unit size is The shape is unstable. Therefore, there is also an optimal ratio (corresponding to the optimum curing content) between the scanning speed and the working pressure, which must be determined experimentally; in addition, the flow coefficients of the binder and the catalyst in the flow formula are different, both of which are in the unit body. The curing content is also not equal and the ratio needs to be determined separately. A large number of experiments have shown that when the scanning speed is determined to be 350 mm/s, the optimal ratio of the two is about 900 mm/(s·Mpa) and 1750 mm/(s·Mpa), respectively. At this time, the corresponding optimal curing content of the two is 9.4% and 4.7%, respectively, and the ratio of content meets the 2:1 requirement of the PCM process. In addition, under the premise of matching the scanning speed and the ejection flow rate, both of them have a limited range of variation. The former is mainly controlled by the motor drive capacity and the inertia of the mechanical system, and there is a maximum scanning speed; the latter is mainly determined by the resolution of the decompression device, the nozzle size of the nozzle and the injection pressure threshold, and there is a minimum ejection flow. In order to reduce the amount of gas generated during the casting process of the mold, the matching relationship between the scanning speed and the ejection flow is determined to match the minimum ejection flow rate with the maximum scanning speed. ◠Matching layer thickness and grit size The experiment found that the osmotic diffusion form of the adhesive liquid and the size of the unit body also have a great relationship with the size of the sand. The smaller the grit size, the smaller the gap between them, and the greater the resistance of the three-dimensional network of capillary structures to liquid diffusion, the more regular the diffusion phenomenon, and the smaller cell size. During the molding process, it must be ensured that the layers and layers can be bonded smoothly without excessive permeation between them. Therefore, the thickness of the unit body corresponding to sand particle size should be slightly larger than the layer thickness; if the unit body section thickness is far more than one layer thickness, not only will the layer and layer interpenetrate, but also the horizontal diffusion within the current layer tends to serious. The excessive penetration of the transverse and longitudinal directions leads to an abnormally rough cast surface, and the shape accuracy and geometry of the profile cannot be guaranteed. Therefore, it is necessary to ensure the matching between the layer thickness and sand particle size. The larger the grit size, the larger the unit size, and the layer thickness must be increased accordingly; otherwise, it can be reduced. ◠Matching of stratified thickness and jet flow On the premise of the determination of the scanning speed, there is also a matching relationship between the layer thickness and the ejection flow. The larger the jet flow rate, the higher the solidification content of the unit body, the more serious the diffusion phenomenon, and the increase in the size of the unit body, so the layer thickness must be increased accordingly; otherwise, it can be reduced. In order to improve the precision of the forming part, the layer thickness value at the minimum scanning line width should be matched with the minimum jet flow experiment. In fact, the matching between process parameters is not a single correspondence, but they are related to each other, affect each other and restrict each other. In the four parameters of scanning speed, jet flow rate, sand particle size and layer thickness, any of several parameters are fixed, then there is a definite functional relationship between the remaining parameters. For example, when the scanning speed is fixed, the jet flow and sand particle size increase, and the layer thickness must increase. When the jet flow and sand particle size are fixed, the scanning speed increases, and the layer thickness must decrease. By analogy, you can get all other matching relationships. 2 Conclusion After the above discussion, it can be seen that all parts that make up the entire process process have an effect on the error of the formed part. The multi-objective function method that takes the processing accuracy as the main factor while considering the processing time is used to optimize the processing direction of the formed part; the finer grain size is selected. Sand and low-viscosity resin and curing agent; resin and curing agent sprayed at the same time; reasonably determine the scanning speed, jet flow, sand particle size, layer thickness and offset distance and other process parameters and the appropriate matching relationship; It can greatly improve the precision of the forming parts and improve the surface quality, meet the casting requirements of the PCM process casting mold, and realize the modelless rapid manufacturing of various metal parts. references
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• Maximize the normal upward water level;
· Maximize the area of ​​the processing base surface;
• Minimize the normal downward water level;
· Minimize the number of bevels;
• Minimize the total number of tiers. 
(j =1,2,...,n ; i=1,2,...,m) (2-2)
k - is a constant coefficient less than 1 and varies with the error model;
Aj - the area of ​​the jth patch;
D--layer thickness;
n - number of patches. 
(2-3)
(2) The layer thickness has a greater influence on the surface quality of the mold, and the offset distance (grid spacing) has less influence. The surface quality peaks as the layer thickness decreases, the surface quality begins to decrease as the layer thickness decreases, and the nodulation increases and the roughness increases. The reason for the analysis is that the reduction in layer thickness when the layer thickness is large weakens the “sawtooth phenomenon†of the side profile of the mold when the unit body is longitudinally bonded, thereby improving the surface quality of the mold, as shown in Fig. 1(a). As shown in (b) and (b), when the layer thickness is small, the continuous decrease in the layer thickness leads to an increase in the lateral diffusion of the binder liquid during curing of the unit body, which in turn reduces the surface quality of the casting mold, as shown in Fig. 1(c). . Similarly, if the offset distance (mesh spacing) is too small, the surface quality of the mold will be reduced due to the increased lateral diffusion. Therefore, we must choose the appropriate layer thickness and offset distance (grid spacing) under the premise of ensuring the necessary strength of the mold, so that the surface quality of the mold can be optimized. 
(a) When the layer thickness is large (b) When the layer thickness is suitable (c) When the layer thickness is too small Figure 1 The effect of layer thickness on the surface quality of the mold 
(a) Free-permeable unit body (b) h:r≈2:3 (c)d:b≈2:3
Fig. 2 Sketch of optimal modeling parameters
(2) A linear scanning experiment was conducted at this scanning speed to measure the cured thickness and solidification line width of the free-penetrating unit body. Based on the above conclusions, the layer thickness h and the offset distance d (grid spacing) were calculated under the corresponding conditions. 
Figure 3 Relationship between cell size and scan speed 
Fig. 4 Relationship between cell adhesive content and scanning speed 
(2-4)
Q--adhesive flux per unit time;
K-- flow coefficient, 
Where g is the gravitational acceleration, Ï is the adhesive density, and Ax is the nozzle cross-sectional area. This value does not change when the nozzle structure and adhesive type are fixed;
∆P-- is the pressure difference of the fluid;
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