As critical components of aircraft skins and rocket fuel storage tank shells,large thin-walled workpieces are susceptible to vibration and deformation during machining due to their weak local stiffness.To address thes...As critical components of aircraft skins and rocket fuel storage tank shells,large thin-walled workpieces are susceptible to vibration and deformation during machining due to their weak local stiffness.To address these challenges,we propose a novel tunable electromagnetic semi-active dynamic vibration absorber(ESADVA),which integrates with a magnetic suction follower to form a followed ESADVA(follow-ESADVA)for mirror milling.This system combines a tunable magnet oscillator with a follower,enabling real-time vibration absorption and condition feedback throughout the milling process.Additionally,the device supports self-sensing and frequency adjustment by providing feedback to a linear actuator,which alters the distance between magnets.This resolves the traditional issue of being unable to directly monitor vibration at the machining point due to space constraints and tool interference.The frequency shift characteristics and vibration absorption performance are comprehensively investigated.Theoretical and experimental results demonstrate that the prototyped follow-ESADVA achieves frequency synchronization with the milling tool,resulting in a vibration suppression rate of approximately 47.57%.Moreover,the roughness of the machined surface decreases by18.95%,significantly enhancing the surface quality.The results of this work pave the way for higher-quality machined surfaces and a more stable mirror milling process.展开更多
To improve the milling surface quality of the Al-Li alloy thin-wall workpieces and reduce the cutting energy consumption.Experimental research on the milling processing of AA2195 Al-Li alloy thin-wall workpieces based...To improve the milling surface quality of the Al-Li alloy thin-wall workpieces and reduce the cutting energy consumption.Experimental research on the milling processing of AA2195 Al-Li alloy thin-wall workpieces based on Response Surface Methodology was carried out.The single factor and interaction of milling parameters on surface roughness and specific cutting energy were analyzed,and the multi-objective optimization model was constructed.The Multiobjective Particle Swarm Optimization algorithm introducing the Chaos Local Search algorithm and the adaptive inertial weight was applied to determine the optimal combination of milling parameters.It was observed that surface roughness was mainly influenced by feed per tooth,and specific cutting energy was negatively correlated with feed per tooth,radial cutting depth and axial cutting depth,while cutting speed has a non-significant influence on specific cutting energy.The optimal combination of milling parameters with different priorities was obtained.The experimental results showed that the maximum relative error of measured and predicted values was 8.05%,and the model had high reliability,which ensured the low surface roughness and cutting energy consumption.It was of great guiding significance for the success of Al-Li alloy thin-wall milling with a high precision and energy efficiency.展开更多
The shell composed of large-scale parts is the essential component of mechanical structures in the aerospace,shipping,and railway industries.These workpieces are characterized by thin walls and weak rigidity,thus requ...The shell composed of large-scale parts is the essential component of mechanical structures in the aerospace,shipping,and railway industries.These workpieces are characterized by thin walls and weak rigidity,thus requiring an effective technology for high-performance machining.Accordingly,an embedded locally resonant metamaterial with double resonators is proposed and combined with the magnetic follow-up support technology to attenuate the vibration of thin-walled parts for the first time.The band structures and parametric adjustment laws are systematically investigated and validated by analytical calculation and finite element method,which proves the proposed model is broadband,lightweight,and flexible in low frequencies.Its characteristics,as well as the relatively simple structure,are unique advantages for thin-walled structure milling.Finally,mirror milling experiments have been performed to assess the slave module with the proposed substructure.From the results,the root mean square amplitude of the thin-walled workpiece with the combined device decreases by nearly 9%,which means that the performance has been improved by the combined device.Furthermore,this work provides an integrated and efficient solution for vibration suppression in thin-walled parts milling,which extends locally resonant metamaterials to practical engineering fields and helps to improve the status quo of mirror milling from the perspective of metamaterials.展开更多
To reduce the vibration and deformation of large thin-walled workpieces during the milling process,mirror milling is widely used due to its point-to-point support and strong applicability.The influence of the support ...To reduce the vibration and deformation of large thin-walled workpieces during the milling process,mirror milling is widely used due to its point-to-point support and strong applicability.The influence of the support head on the workpiece’s dynamic characteristics is crucial in determining whether the mirror milling process is reliable and effective.Therefore,this study establishes a time-varying dynamic model for mirror milling of thin-walled workpieces with various boundary conditions to accurately analyze and predict the dynamic characteristics and response of the workpiece.First,a new analytical method for material removal with extensive applicability and high precision is proposed.In this method,the Ritz mode shape is used to approximate the workpiece’s mode shape as it changes during material removal.Next,the Hertz contact theory is adopted to establish a tool-workpiece-support head coupling model,which considers the jump-off phenomenon between them.Subsequently,the dynamic model is solved using the Newmark-β numerical integration method to obtain the workpiece’s time-domain acceleration and displacement responses under the forced vibration.Finally,the measured frequency response function(FRF)and vibration signals of workpieces verify the correctness of the proposed mirror milling model for thin-walled workpieces considering material removal.In addition,this paper analyzes the dynamic characteristics and forced vibration law of workpieces in mirror milling,which lays the foundation for high precision mirror milling.展开更多
Milling of the thin-walled workpiece in the aerospace industry is a critical process due to the high flexibility of the workpiece. In this paper, a flexible fixture based on the magnetorheological (MR) fluids is desig...Milling of the thin-walled workpiece in the aerospace industry is a critical process due to the high flexibility of the workpiece. In this paper, a flexible fixture based on the magnetorheological (MR) fluids is designed to investigate the regenerative chatter suppression during the machining. Based on the analysis of typical structural components in the aerospace industry, a general complex thin-walled workpiece with fixture and damping constraint can be equivalent as a rectangular cantilever beam. On the basis of the equivalent models, natural frequency and mode shape function of the thin-walled workpiece is obtained according to the Euler-Bernoulli beam assumptions. Then, the displacement response function of the bending vibration of the beam is represented by the product of all the mode shape function and the generalized coordinate. Furthermore, a dynamic equation of the workpiece-fixture system considering the external damping factor is proposed using the Lagrangian method in terms of all the mode shape function and the generalized coordinate, and the response of system under the dynamic cutting force is calculated to evaluate the stability of the milling process under damping control. Finally, the feasibility and effectiveness of the proposed approach are validated by the impact hammer experiments and several machining tests. (C) 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics.展开更多
Machined surface roughness will affect parts?service performance.Thus,predicting it in the machining is important to avoid rejects.Surface roughness will be affected by system position dependent vibration even under c...Machined surface roughness will affect parts?service performance.Thus,predicting it in the machining is important to avoid rejects.Surface roughness will be affected by system position dependent vibration even under constant parameter with certain toolpath processing in the finishing.Aiming at surface roughness prediction in the machining process,this paper proposes a position-varying surface roughness prediction method based on compensated acceleration by using regression analysis.To reduce the stochastic error of measuring the machined surface profile height,the surface area is repeatedly measured three times,and Pauta criterion is adopted to eliminate abnormal points.The actual vibration state at any processing position is obtained through the single-point monitoring acceleration compensation model.Seven acceleration features are extracted,and valley,which has the highest/^-square proving the effectiveness of the filtering features,is selected as the input of the prediction model by mutual information coefficients.Finally,by comparing the measured and predicted surface roughness curves,they have the same trends,with the average error of 16.28%and the minimum error of 0.16%.Moreover,the prediction curve matches and agrees well with the actual surface state,which verifies the accuracy and reliability of the model.展开更多
In this paper,the variation characteristic of the drilling force,and the influences of cutting speed,feed rate,and workpiece thickness on the drilling force,were eval・uated when drilling a silicon carbide particle rei...In this paper,the variation characteristic of the drilling force,and the influences of cutting speed,feed rate,and workpiece thickness on the drilling force,were eval・uated when drilling a silicon carbide particle reinforced aluminum matrix(SiCp/Al)composite thin-walled workpiece with a high volume fraction.Under the condition that the workpiece thickness was less than the drill tip height,three characteristic stages of drilling force variation were proposed.The results indicate that there is a sign币cant difference between the variations in the drilling force when drilling a thin-walled workpiece compared to thick-walled workpiece.When the chisel edge drills out the lower surface of the workpiece,there is an abrupt decrease in the thrust forces of the thin-walled and thick-walled workpieces.In addition,there is an abrupt decrease in the torque of the thick-walled workpiece,whereas that of the thinwalled workpiece increases.According to the thickness of the thin-walled workpiece,the instant of the abrupt decrease in the thrust force may lead or lag behind the theoretical instant at which the chisel edge reaches the lower surface of the workpiece without deformation.When drilling a thin-walled hole,the cutting speed has a slight influence on the thrust force,and there is a slight increase in the torque in accordance with an increase in the cutting speed.The thrust force and torque increase in accordance with an increase in the feed rate.When drilling a thinwalled workpiece with a thickness of 1 mm,the critical thickness of workpiece cracking decreases in accordance with an increase in the cutting speed,and increases in accordance with an increase in the feed rate.When drilling a thin-walled workpiece with a thickness of 0.5 mm,the concave deformation of the workpiece and the critical thickness of the workpiece cracking increase in accordance with an increase in the feed rate.However,the increment in the critical thickness of the workpiece cracking is less than that in the concave deformation of the workpiece.展开更多
The milling stability of thin-walled components is an important issue in the aviation manufacturing industry, which greatly limits the removal rate of a workpiece. However, for a thin-walled workpiece, the dynamic cha...The milling stability of thin-walled components is an important issue in the aviation manufacturing industry, which greatly limits the removal rate of a workpiece. However, for a thin-walled workpiece, the dynamic characteristics vary at different positions. In addition, the removed part also has influence on determining the modal parameters of the workpiece. Thus,the milling stability is also time-variant. In this work, in order to investigate the time variation of a workpiece's dynamic characteristics, a new computational model is firstly derived by dividing the workpiece into a removed part and a remaining part with the Ritz method. Then, an updated frequency response function is obtained by Lagrange's equation and the corresponding modal parameters are extracted. Finally, multi-mode stability lobes are plotted by the different quadrature method and its accuracy is verified by experiments. The proposed method improves the computational efficiency to predict the time-varying characteristics of a thin-walled workpiece.展开更多
Inspection techniques for aero-engine blades are a hot topic in industry. Since these blades have a sculptured surface and a small datum, measurement results may deviate from an actual position. There are few proper a...Inspection techniques for aero-engine blades are a hot topic in industry. Since these blades have a sculptured surface and a small datum, measurement results may deviate from an actual position. There are few proper approaches compensating for non-uniform distribution errors that are within specified tolerance ranges. This study aimed to develop a meshing structure measuring approach for the distortion of blades via non-contact optical 3D scanning. A rough measurement and a registration procedure are initially adopted to rectify the coordinate system of a blade, which avoids the initial coordinate system errors caused by the small datum. A measurement path with meshing structure is then unfolded on the blade surface. For non-uniform distribution errors, the meshing structure measurement is more visual and clear than the traditional constant height curves method. All measuring points take only 7 min to complete, and the distribution of error is directly and accurately presented by the meshing structure. This study provides a basis for future research on distortion control and error compensation.展开更多
Metal droplet deposition is a kind of additive manufacturing(3D Printing)technique that fabricates near-net part through droplets deposition with lower cost and higher efficiency.This paper proposed a solution to prob...Metal droplet deposition is a kind of additive manufacturing(3D Printing)technique that fabricates near-net part through droplets deposition with lower cost and higher efficiency.This paper proposed a solution to problems of electric power fittings that large inventories,high procurement costs,low manufacturing efficiency and transportation cost.Using additive Manufacturing technique-metal droplet deposition,electric power fittings fabricated on power construction site.This paper describes the manufacturing process of typical thin-walled samples(the structure optimized based on additive manufacturing principle)and ball head rings of electric power fittings.Aiming at the integral AM forming for ball and ball socket electric power fitting workpiece,a novel easy removal forming support material(ceramics and gypsum mixed with UV cured resin)have been developed.Here this support material was used to fabricate nested integral workpieces.Dimensional accuracy and microstructure of the test pieces were analyzed.The error of the height and width of the forming workpiece is within 5%.No obvious overlap trace(such as overlap line and cracks)observed,and the internal microstructure is equiaxial crystal.The average density of the component is 99.51%,which measured by drainage method and 13.39%higher than the cast raw material.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12172248,12021002,12302022,and 12132010)the Tianjin Research Program of Application Foundation and Advanced Technology of China(No.22JCQNJC00780)IoT Standards and Application Key Laboratory of the Ministry of Industry and Information Technology of China(No.202306)。
文摘As critical components of aircraft skins and rocket fuel storage tank shells,large thin-walled workpieces are susceptible to vibration and deformation during machining due to their weak local stiffness.To address these challenges,we propose a novel tunable electromagnetic semi-active dynamic vibration absorber(ESADVA),which integrates with a magnetic suction follower to form a followed ESADVA(follow-ESADVA)for mirror milling.This system combines a tunable magnet oscillator with a follower,enabling real-time vibration absorption and condition feedback throughout the milling process.Additionally,the device supports self-sensing and frequency adjustment by providing feedback to a linear actuator,which alters the distance between magnets.This resolves the traditional issue of being unable to directly monitor vibration at the machining point due to space constraints and tool interference.The frequency shift characteristics and vibration absorption performance are comprehensively investigated.Theoretical and experimental results demonstrate that the prototyped follow-ESADVA achieves frequency synchronization with the milling tool,resulting in a vibration suppression rate of approximately 47.57%.Moreover,the roughness of the machined surface decreases by18.95%,significantly enhancing the surface quality.The results of this work pave the way for higher-quality machined surfaces and a more stable mirror milling process.
基金This research is supported by the National Natural Science Foundation of China(Grant Nos.51475087 and 51304105)the Natural Science Foundation of Liaoning Province(Grant No.20180550167)+1 种基金the Key Projects of Liaoning Province(Grant Nos.LJ2019ZL005 and LJ2017ZL001)the Oversea Training Project of High Level Innovation Team of Liaoning Province(Grant No.2018LNGXGJWPY-ZD001).
文摘To improve the milling surface quality of the Al-Li alloy thin-wall workpieces and reduce the cutting energy consumption.Experimental research on the milling processing of AA2195 Al-Li alloy thin-wall workpieces based on Response Surface Methodology was carried out.The single factor and interaction of milling parameters on surface roughness and specific cutting energy were analyzed,and the multi-objective optimization model was constructed.The Multiobjective Particle Swarm Optimization algorithm introducing the Chaos Local Search algorithm and the adaptive inertial weight was applied to determine the optimal combination of milling parameters.It was observed that surface roughness was mainly influenced by feed per tooth,and specific cutting energy was negatively correlated with feed per tooth,radial cutting depth and axial cutting depth,while cutting speed has a non-significant influence on specific cutting energy.The optimal combination of milling parameters with different priorities was obtained.The experimental results showed that the maximum relative error of measured and predicted values was 8.05%,and the model had high reliability,which ensured the low surface roughness and cutting energy consumption.It was of great guiding significance for the success of Al-Li alloy thin-wall milling with a high precision and energy efficiency.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172248,12021002,12302022,12132010)Tianjin Research Program of Application Foundation and Advanced Technology(Grant No.22JCQNJC00780)the IoT Standards and Application Key Laboratory of the Ministry of Industry and Information Technology(Grant No.202306).
文摘The shell composed of large-scale parts is the essential component of mechanical structures in the aerospace,shipping,and railway industries.These workpieces are characterized by thin walls and weak rigidity,thus requiring an effective technology for high-performance machining.Accordingly,an embedded locally resonant metamaterial with double resonators is proposed and combined with the magnetic follow-up support technology to attenuate the vibration of thin-walled parts for the first time.The band structures and parametric adjustment laws are systematically investigated and validated by analytical calculation and finite element method,which proves the proposed model is broadband,lightweight,and flexible in low frequencies.Its characteristics,as well as the relatively simple structure,are unique advantages for thin-walled structure milling.Finally,mirror milling experiments have been performed to assess the slave module with the proposed substructure.From the results,the root mean square amplitude of the thin-walled workpiece with the combined device decreases by nearly 9%,which means that the performance has been improved by the combined device.Furthermore,this work provides an integrated and efficient solution for vibration suppression in thin-walled parts milling,which extends locally resonant metamaterials to practical engineering fields and helps to improve the status quo of mirror milling from the perspective of metamaterials.
基金supported by the National Natural Science Foundation of China (Grant No.52175025)。
文摘To reduce the vibration and deformation of large thin-walled workpieces during the milling process,mirror milling is widely used due to its point-to-point support and strong applicability.The influence of the support head on the workpiece’s dynamic characteristics is crucial in determining whether the mirror milling process is reliable and effective.Therefore,this study establishes a time-varying dynamic model for mirror milling of thin-walled workpieces with various boundary conditions to accurately analyze and predict the dynamic characteristics and response of the workpiece.First,a new analytical method for material removal with extensive applicability and high precision is proposed.In this method,the Ritz mode shape is used to approximate the workpiece’s mode shape as it changes during material removal.Next,the Hertz contact theory is adopted to establish a tool-workpiece-support head coupling model,which considers the jump-off phenomenon between them.Subsequently,the dynamic model is solved using the Newmark-β numerical integration method to obtain the workpiece’s time-domain acceleration and displacement responses under the forced vibration.Finally,the measured frequency response function(FRF)and vibration signals of workpieces verify the correctness of the proposed mirror milling model for thin-walled workpieces considering material removal.In addition,this paper analyzes the dynamic characteristics and forced vibration law of workpieces in mirror milling,which lays the foundation for high precision mirror milling.
基金supported by the National Basic Research Program of China (Grant No. 2013CB035802)the 111 Project of China (Grant No. B13044)
文摘Milling of the thin-walled workpiece in the aerospace industry is a critical process due to the high flexibility of the workpiece. In this paper, a flexible fixture based on the magnetorheological (MR) fluids is designed to investigate the regenerative chatter suppression during the machining. Based on the analysis of typical structural components in the aerospace industry, a general complex thin-walled workpiece with fixture and damping constraint can be equivalent as a rectangular cantilever beam. On the basis of the equivalent models, natural frequency and mode shape function of the thin-walled workpiece is obtained according to the Euler-Bernoulli beam assumptions. Then, the displacement response function of the bending vibration of the beam is represented by the product of all the mode shape function and the generalized coordinate. Furthermore, a dynamic equation of the workpiece-fixture system considering the external damping factor is proposed using the Lagrangian method in terms of all the mode shape function and the generalized coordinate, and the response of system under the dynamic cutting force is calculated to evaluate the stability of the milling process under damping control. Finally, the feasibility and effectiveness of the proposed approach are validated by the impact hammer experiments and several machining tests. (C) 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.52022082 and 52005413)the 111 Project(Grant No.B13044).
文摘Machined surface roughness will affect parts?service performance.Thus,predicting it in the machining is important to avoid rejects.Surface roughness will be affected by system position dependent vibration even under constant parameter with certain toolpath processing in the finishing.Aiming at surface roughness prediction in the machining process,this paper proposes a position-varying surface roughness prediction method based on compensated acceleration by using regression analysis.To reduce the stochastic error of measuring the machined surface profile height,the surface area is repeatedly measured three times,and Pauta criterion is adopted to eliminate abnormal points.The actual vibration state at any processing position is obtained through the single-point monitoring acceleration compensation model.Seven acceleration features are extracted,and valley,which has the highest/^-square proving the effectiveness of the filtering features,is selected as the input of the prediction model by mutual information coefficients.Finally,by comparing the measured and predicted surface roughness curves,they have the same trends,with the average error of 16.28%and the minimum error of 0.16%.Moreover,the prediction curve matches and agrees well with the actual surface state,which verifies the accuracy and reliability of the model.
基金This work is supported by the National Natural Science Foundation of China(Grant No.51775356)the Distinguished Professor Funding Project of Liaoning Province,and the Key Laboratory Basic Research Project of the Department of Education of Liaoning Province(Grant No.LZ2015063).
文摘In this paper,the variation characteristic of the drilling force,and the influences of cutting speed,feed rate,and workpiece thickness on the drilling force,were eval・uated when drilling a silicon carbide particle reinforced aluminum matrix(SiCp/Al)composite thin-walled workpiece with a high volume fraction.Under the condition that the workpiece thickness was less than the drill tip height,three characteristic stages of drilling force variation were proposed.The results indicate that there is a sign币cant difference between the variations in the drilling force when drilling a thin-walled workpiece compared to thick-walled workpiece.When the chisel edge drills out the lower surface of the workpiece,there is an abrupt decrease in the thrust forces of the thin-walled and thick-walled workpieces.In addition,there is an abrupt decrease in the torque of the thick-walled workpiece,whereas that of the thinwalled workpiece increases.According to the thickness of the thin-walled workpiece,the instant of the abrupt decrease in the thrust force may lead or lag behind the theoretical instant at which the chisel edge reaches the lower surface of the workpiece without deformation.When drilling a thin-walled hole,the cutting speed has a slight influence on the thrust force,and there is a slight increase in the torque in accordance with an increase in the cutting speed.The thrust force and torque increase in accordance with an increase in the feed rate.When drilling a thinwalled workpiece with a thickness of 1 mm,the critical thickness of workpiece cracking decreases in accordance with an increase in the cutting speed,and increases in accordance with an increase in the feed rate.When drilling a thin-walled workpiece with a thickness of 0.5 mm,the concave deformation of the workpiece and the critical thickness of the workpiece cracking increase in accordance with an increase in the feed rate.However,the increment in the critical thickness of the workpiece cracking is less than that in the concave deformation of the workpiece.
基金co-supported by the National Natural Science Foundation of China (No.51575319)the Young Scholars Program of Shandong University (No. 2015WLJH31)+1 种基金the Major National Science and Technology Project (No. 2014ZX04012-014)the Tai Shan Scholar Foundation (No. TS20130922)
文摘The milling stability of thin-walled components is an important issue in the aviation manufacturing industry, which greatly limits the removal rate of a workpiece. However, for a thin-walled workpiece, the dynamic characteristics vary at different positions. In addition, the removed part also has influence on determining the modal parameters of the workpiece. Thus,the milling stability is also time-variant. In this work, in order to investigate the time variation of a workpiece's dynamic characteristics, a new computational model is firstly derived by dividing the workpiece into a removed part and a remaining part with the Ritz method. Then, an updated frequency response function is obtained by Lagrange's equation and the corresponding modal parameters are extracted. Finally, multi-mode stability lobes are plotted by the different quadrature method and its accuracy is verified by experiments. The proposed method improves the computational efficiency to predict the time-varying characteristics of a thin-walled workpiece.
基金supported by a grant from the National Science and Technology Major Projects of China (No. 2013ZX04001051)
文摘Inspection techniques for aero-engine blades are a hot topic in industry. Since these blades have a sculptured surface and a small datum, measurement results may deviate from an actual position. There are few proper approaches compensating for non-uniform distribution errors that are within specified tolerance ranges. This study aimed to develop a meshing structure measuring approach for the distortion of blades via non-contact optical 3D scanning. A rough measurement and a registration procedure are initially adopted to rectify the coordinate system of a blade, which avoids the initial coordinate system errors caused by the small datum. A measurement path with meshing structure is then unfolded on the blade surface. For non-uniform distribution errors, the meshing structure measurement is more visual and clear than the traditional constant height curves method. All measuring points take only 7 min to complete, and the distribution of error is directly and accurately presented by the meshing structure. This study provides a basis for future research on distortion control and error compensation.
基金This research was funded by National Natural Science Foundation of China under grant number 51575313 and 51775420.This paper got help from Du Jun and Wang Xin of Xi’an Jiaotong University.
文摘Metal droplet deposition is a kind of additive manufacturing(3D Printing)technique that fabricates near-net part through droplets deposition with lower cost and higher efficiency.This paper proposed a solution to problems of electric power fittings that large inventories,high procurement costs,low manufacturing efficiency and transportation cost.Using additive Manufacturing technique-metal droplet deposition,electric power fittings fabricated on power construction site.This paper describes the manufacturing process of typical thin-walled samples(the structure optimized based on additive manufacturing principle)and ball head rings of electric power fittings.Aiming at the integral AM forming for ball and ball socket electric power fitting workpiece,a novel easy removal forming support material(ceramics and gypsum mixed with UV cured resin)have been developed.Here this support material was used to fabricate nested integral workpieces.Dimensional accuracy and microstructure of the test pieces were analyzed.The error of the height and width of the forming workpiece is within 5%.No obvious overlap trace(such as overlap line and cracks)observed,and the internal microstructure is equiaxial crystal.The average density of the component is 99.51%,which measured by drainage method and 13.39%higher than the cast raw material.