Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam...Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam profiles will be successfully processed or not in thedesign stage, design of the cam can be done by balancing the economization and reliability. Inaddition, an fuzzy deduction method based on Bayers formula is advanced to estimate processingreasonable of the designed precision cam profile, and it take few samples.展开更多
Digitization precision analysis is an important tool to ensure the design precision of machine tool currently. The correlative research about precision modeling and analysis mainly focuses on the geometry precision an...Digitization precision analysis is an important tool to ensure the design precision of machine tool currently. The correlative research about precision modeling and analysis mainly focuses on the geometry precision and motion precision of machine tool, and the forming motion precision of workpiece surface. For the machine tool with complex forming motion, there is not accurate corresponding relationship between the existing criterion on precision design and the machining precision of workpiece. Therefore, a design scheme on machine tool precision based on error prediction is proposed, which is divided into two-stage digitization precision analysis crucially. The first stage aims at the technology system to complete the precision distribution and inspection from the workpiece to various component parts of technology system and achieve the total output precision of machine tool under the specified machining precision; the second stage aims at the machine tool system to complete the precision distribution and inspection from the output precision of machine tool to the machine tool components. This article serves YK3610 gear hobber as the example to describe the error model of two systems and basic application method, and the practical cutting precision of this machine tool achieves to 5-4-4 grade. The proposed method can provide reliable guidance to the precision design of machine tool with complex forming motion.展开更多
Conventional reliability-based design optimization (RBDO) requires to use the most probable point (MPP) method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as th...Conventional reliability-based design optimization (RBDO) requires to use the most probable point (MPP) method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as the minimum error point (MEP) method or the MEP based method, for reliability-based design optimization, whose idea is to minimize the error produced by approximating performance functions. The MEP based method uses the first order Taylor's expansion at MEP instead of MPP. Examples demonstrate that the MEP based design optimization can ensure product reliability at the required level, which is very imperative for many important engineering systems. The MEP based reliability design optimization method is feasible and is considered as an alternative for solving reliability design optimization problems. The MEP based method is more robust than the commonly used MPP based method for some irregular performance functions.展开更多
By studying the e ects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using ...By studying the e ects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using this assumption,there is a significant error induced in high-precision computer numerical control(CNC) machine tools as compared with reality. One of the most important reasons for this error is failing to consider the error averaging e ect of motion pair elements. Therefore, this work examines a high-precision horizontal machining center as its research object, and analyzes the error averaging mechanism of a rolling guide pair under a deformation of the rolling elements. The carriage bearing forces caused by guideway straightness errors are obtained by constructing a geometric error model of a single carriage. The relationship between guideway straightness errors and carriage bearing forces is described by a transfer function in the spatial frequency domain, and its characteristics are analyzed. It quantifies the so-called error averaging e ect of the rolling guide system and, on this basis, a static model for four carriages is established to reflect the error averaging e ect of the rolling guide pair on the position and orientation errors of the motion pair. In addition, it is found that the wavelengths and phase di erences of guideway errors a ect this error averaging mechanism, but the amplitude and preload have little influence thereon. The experiment result shows that the kinematic straightness errors in the x-and y-directions were approximately 1/3 to 1/2 of the guideway straightness errors in the corresponding directions. The results can be used to guide the precision design and assembly of machine tools.展开更多
Chain drive system is widely used in the conditions of high-speed, overload, variable speed and load, Many studies are focused on the meshing theory and wear characteristics of chain drive system, but system design, a...Chain drive system is widely used in the conditions of high-speed, overload, variable speed and load, Many studies are focused on the meshing theory and wear characteristics of chain drive system, but system design, analysis, and noise characteristics of the chain drive system are weak. System design and noise characteristic are studied for a new type Gemini chain of dual-clutch automatic transmission. Based on the meshing theory of silent chain, the design parameters of the Gemini chain system are calculated and the mathematical models and dynamic analysis models of the Gemini chain system are established. Dynamic characteristics of the Gemini chain system is simulated and the contact force of plate and pin, plate and sprockets, the chain tension forces, the transmission error and the stress of plates and pins are analyzed. According to the simulation results of the Gemini chain system, the noise experiment about system is carried out. The noise values are tested at different speed and load and spectral characteristics are analyzed. The results of simulation and experimental show that the contact forces of plate and pin, plate and sprockets are smaller than the allowable stress values, the chain tension force is less than ultimate tension and transmission error is limited in 1.2%. The noise values can meet the requirements of industrial design, and it is proved that the design and analysis method of the Gemini chain system is scientific and feasible. The design and test system is built from analysis to test of Gemini chain system. This research presented will provide a corresponding theoretical guidance for the design and dynamic characteristics and noise characteristics of chain drive system.展开更多
According to the Fick's second law of diffusion, six analytical solutions of chloride profile in concrete were studied and discussed with regard to different boundary and initial conditions. In those analytical solut...According to the Fick's second law of diffusion, six analytical solutions of chloride profile in concrete were studied and discussed with regard to different boundary and initial conditions. In those analytical solutions, the most prevailing error-function solution which is based on semi-infinite assumption is the simple one, but may under-estimate the chloride content in concrete and over-rate the life time prediction of concrete structures. The experimental results show that compared with other solutions, the chloride content in concrete predicted by error-function model is the minimum, and the calculation difference produced by different analytical models should not be ignored. The influence of models on chloride content prediction is more than other environment and material coefficients in some time. In order to get a more realistic prediction model, modification to error-function model is suggested based on analysis and calculation examples concerning the boundary and edge effect.展开更多
The accuracy distribution of measuring instrument for 3-Ineter leadscrew by laser is studied according toerror theory. In this paper, the tables of overall accuracy distribution used as foundation of design and manufa...The accuracy distribution of measuring instrument for 3-Ineter leadscrew by laser is studied according toerror theory. In this paper, the tables of overall accuracy distribution used as foundation of design and manufactureare drafted.展开更多
Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying th...Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying the accuracy of the solution. Firstly, the minimum parameter interval of the node vector corresponding to the data point under test in the original data point sequence is determined, and the parameter interval is subdivided according to the corresponding step size, and the corresponding parameter value is obtained. Secondly, the distance from the measured point to the NURBS curve is calculated, and the nearest distance is found out. The node interval is subdivided again on one side of the nearest distance. Finally, the distance between the data point to be measured and each subdivision point is calculated again, and the minimum distance is taken as the interpolation error between the point and the NURBS curve. The simulation results of actual tool position data show that this method can more accurately obtain the error of spatial NURBS interpolation curve.展开更多
For the simultaneous wireless information and power transfer(SWIPT), the full-duplex MIMO system can achieve simultaneous transmission of information and energy more efficiently than the half-duplex. Based on the mean...For the simultaneous wireless information and power transfer(SWIPT), the full-duplex MIMO system can achieve simultaneous transmission of information and energy more efficiently than the half-duplex. Based on the mean-square-error(MSE) criterion, the optimization problem of joint transceiver design with transmitting power constraint and energy harvesting constraint is formulated. Next, by semidefinite relaxation(SDR) and randomization method, the SDRbased scheme is proposed. In order to reduce the complexity, the closed-form scheme is presented with some simplified measures. Robust beamforming is then studied considering the practical condition. The simulation results such as MSE versus signal-noise-ratio(SNR), MSE versus the iteration number, well prove the performance of the proposed schemes for the system model.展开更多
The physics design of a 3 MeV, 30 mA, 352.2 MHz Radio Frequency Quadrupole (RFQ) is done for the future Indian Spallation Neutron Source (ISNS) project at RRCAT, India. The beam dynamics design of RFQ and the error an...The physics design of a 3 MeV, 30 mA, 352.2 MHz Radio Frequency Quadrupole (RFQ) is done for the future Indian Spallation Neutron Source (ISNS) project at RRCAT, India. The beam dynamics design of RFQ and the error analysis of the input beam parameters are done by using standard beam dynamics code PARMTEQM. The electromagnetic stu-dies for the two-dimensional and three-dimensional cavity design are performed using computer codes SUPERFISH and CST Microwave Studio. The physics design of RFQ consisting of the beam dynamics design near the beam axis and the electromagnetic design for the RFQ resonator is described here.展开更多
Ultra-precision machine tool is the most important physical tool to machining the workpiece with the frequency domain error requirement, in the design process of which the dynamic accuracy design(DAD) is indispensable...Ultra-precision machine tool is the most important physical tool to machining the workpiece with the frequency domain error requirement, in the design process of which the dynamic accuracy design(DAD) is indispensable and the related research is rarely available. In light of above reasons, a DAD method of ultra-precision machine tool is proposed in this paper, which is based on the frequency domain error allocation.The basic procedure and enabling knowledge of the DAD method is introduced. The application case of DAD method in the ultra-precision flycutting machine tool for KDP crystal machining is described to show the procedure detailedly. In this case, the KDP workpiece surface has the requirements in four different spatial frequency bands, and the emphasis for this study is put on the middle-frequency band with the PSD specifications. The results of the application case basically show the feasibility of the proposed DAD method. The DAD method of ultra-precision machine tool can effectively minimize the technical risk and improve the machining reliability of the designed machine tool. This paper will play an important role in the design and manufacture of new ultra-precision machine tool.展开更多
The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Slope Rotatable Designs Using Pairwise Balanced Designs. ...The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Slope Rotatable Designs Using Pairwise Balanced Designs. Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi.The paper is a copy of Dr. Rabindra Nath Das’s former article, entitled “Slope rotatability with correlated errors (Vol. 54, pp. 57-70, 2003)” and “Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in OJSVol.2 No.3, 319-327, 2012, has been removed from this site.展开更多
风洞天平的校准精度直接决定了风洞试验的气动载荷测量精度,为了提升天平校准的质量和效率,以BCS-100天平校准系统为研究对象,基于现代试验设计方法(modern design of experiments,MDOE)开展了风洞天平校准研究。针对单因子变量法(one f...风洞天平的校准精度直接决定了风洞试验的气动载荷测量精度,为了提升天平校准的质量和效率,以BCS-100天平校准系统为研究对象,基于现代试验设计方法(modern design of experiments,MDOE)开展了风洞天平校准研究。针对单因子变量法(one factor at a time,OFAT)天平校准中存在系统误差与响应量耦合的问题,采用MDOE的随机、重复和分块策略控制校准的系统误差,并选定响应面理论的中心复合设计方法生成校准矩阵。校准矩阵共计86个样本点,包括64个分级因子点、12个轴向因子点和10个中心因子点,其中所有样本点的加载顺序做随机化处理,并作为一个样本块在短时间内集中完成加载,中心因子点则用于满足重复原则。最后开展了OFAT和MDOE的对比校准,拟合载荷的残差正态概率分布显示MDOE校准中横侧向分量的样本点独立性更强,样本点残差最高可降低84%;检验载荷显示MDOE和OFAT两种方法中天平所有分量的综合加载重复性持平,MDOE校准中横侧向分量的综合加载误差最高可降低54%。研究表明MDOE能够有效降低校准的系统误差,提升横侧向小量的预测能力。展开更多
In this paper, a joint precoding and decoding design scheme is proposed for two-way Multiple-Input Multiple-Output (MIMO) multiple-relay system. The precoding and decoding matrices are jointly optimized based on Minim...In this paper, a joint precoding and decoding design scheme is proposed for two-way Multiple-Input Multiple-Output (MIMO) multiple-relay system. The precoding and decoding matrices are jointly optimized based on Minimum Mean-Square-Error (MMSE) criteria under transmit power constraints. The optimization problem is solved by using a convergent iterative algorithm which in-cludes four sub-problems. It is shown that due to the difficulty of the block diagonal nature of the relay precoding matrix, sub-problem two cannot be solved with existing methods. It is then solved by converting sub-problem two into a convex optimization problem and a simplified method is proposed to reduce the computational complexity. Simulation results show that the proposed scheme can achieve lower Bit Error Rate (BER) and larger sum rate than other schemes. Furthermore, the BER and the sum rate performance can be improved by increasing the number of antennas for the same number of relays or increasing the number of relays for the same number of antennas.展开更多
基金This project is supported by Significant Project Foundation of National 863 Program, China.
文摘Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam profiles will be successfully processed or not in thedesign stage, design of the cam can be done by balancing the economization and reliability. Inaddition, an fuzzy deduction method based on Bayers formula is advanced to estimate processingreasonable of the designed precision cam profile, and it take few samples.
基金supported by National Natural Science Foundation of China (Grant No. 51075419)Chongqing Municipal Natural Science Foundation of China (Grant No. CSTC,2009BB3234)
文摘Digitization precision analysis is an important tool to ensure the design precision of machine tool currently. The correlative research about precision modeling and analysis mainly focuses on the geometry precision and motion precision of machine tool, and the forming motion precision of workpiece surface. For the machine tool with complex forming motion, there is not accurate corresponding relationship between the existing criterion on precision design and the machining precision of workpiece. Therefore, a design scheme on machine tool precision based on error prediction is proposed, which is divided into two-stage digitization precision analysis crucially. The first stage aims at the technology system to complete the precision distribution and inspection from the workpiece to various component parts of technology system and achieve the total output precision of machine tool under the specified machining precision; the second stage aims at the machine tool system to complete the precision distribution and inspection from the output precision of machine tool to the machine tool components. This article serves YK3610 gear hobber as the example to describe the error model of two systems and basic application method, and the practical cutting precision of this machine tool achieves to 5-4-4 grade. The proposed method can provide reliable guidance to the precision design of machine tool with complex forming motion.
基金This project is supported by National Natural Science Foundation of China(No.50575072)Outstanding Youth Fund of Hunan Education Department, China (No.04B007).
文摘Conventional reliability-based design optimization (RBDO) requires to use the most probable point (MPP) method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as the minimum error point (MEP) method or the MEP based method, for reliability-based design optimization, whose idea is to minimize the error produced by approximating performance functions. The MEP based method uses the first order Taylor's expansion at MEP instead of MPP. Examples demonstrate that the MEP based design optimization can ensure product reliability at the required level, which is very imperative for many important engineering systems. The MEP based reliability design optimization method is feasible and is considered as an alternative for solving reliability design optimization problems. The MEP based method is more robust than the commonly used MPP based method for some irregular performance functions.
基金Supported by National Science and Technology Major Project of China(Grant No.2015ZX04005001)Tianjin Provincial Nature Science Foundation of China(Grant No.16JCZDJC38400)
文摘By studying the e ects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using this assumption,there is a significant error induced in high-precision computer numerical control(CNC) machine tools as compared with reality. One of the most important reasons for this error is failing to consider the error averaging e ect of motion pair elements. Therefore, this work examines a high-precision horizontal machining center as its research object, and analyzes the error averaging mechanism of a rolling guide pair under a deformation of the rolling elements. The carriage bearing forces caused by guideway straightness errors are obtained by constructing a geometric error model of a single carriage. The relationship between guideway straightness errors and carriage bearing forces is described by a transfer function in the spatial frequency domain, and its characteristics are analyzed. It quantifies the so-called error averaging e ect of the rolling guide system and, on this basis, a static model for four carriages is established to reflect the error averaging e ect of the rolling guide pair on the position and orientation errors of the motion pair. In addition, it is found that the wavelengths and phase di erences of guideway errors a ect this error averaging mechanism, but the amplitude and preload have little influence thereon. The experiment result shows that the kinematic straightness errors in the x-and y-directions were approximately 1/3 to 1/2 of the guideway straightness errors in the corresponding directions. The results can be used to guide the precision design and assembly of machine tools.
基金Supported by National Natural Science Foundation of China(Grant No.51305154)Jilin Provincial Science and Technology Development Program:Automobile Coordinated Action,China(Grant No.20116004)
文摘Chain drive system is widely used in the conditions of high-speed, overload, variable speed and load, Many studies are focused on the meshing theory and wear characteristics of chain drive system, but system design, analysis, and noise characteristics of the chain drive system are weak. System design and noise characteristic are studied for a new type Gemini chain of dual-clutch automatic transmission. Based on the meshing theory of silent chain, the design parameters of the Gemini chain system are calculated and the mathematical models and dynamic analysis models of the Gemini chain system are established. Dynamic characteristics of the Gemini chain system is simulated and the contact force of plate and pin, plate and sprockets, the chain tension forces, the transmission error and the stress of plates and pins are analyzed. According to the simulation results of the Gemini chain system, the noise experiment about system is carried out. The noise values are tested at different speed and load and spectral characteristics are analyzed. The results of simulation and experimental show that the contact forces of plate and pin, plate and sprockets are smaller than the allowable stress values, the chain tension force is less than ultimate tension and transmission error is limited in 1.2%. The noise values can meet the requirements of industrial design, and it is proved that the design and analysis method of the Gemini chain system is scientific and feasible. The design and test system is built from analysis to test of Gemini chain system. This research presented will provide a corresponding theoretical guidance for the design and dynamic characteristics and noise characteristics of chain drive system.
基金Funded by the National Key Technology R&D Program(No.2011BAG07B04)
文摘According to the Fick's second law of diffusion, six analytical solutions of chloride profile in concrete were studied and discussed with regard to different boundary and initial conditions. In those analytical solutions, the most prevailing error-function solution which is based on semi-infinite assumption is the simple one, but may under-estimate the chloride content in concrete and over-rate the life time prediction of concrete structures. The experimental results show that compared with other solutions, the chloride content in concrete predicted by error-function model is the minimum, and the calculation difference produced by different analytical models should not be ignored. The influence of models on chloride content prediction is more than other environment and material coefficients in some time. In order to get a more realistic prediction model, modification to error-function model is suggested based on analysis and calculation examples concerning the boundary and edge effect.
文摘The accuracy distribution of measuring instrument for 3-Ineter leadscrew by laser is studied according toerror theory. In this paper, the tables of overall accuracy distribution used as foundation of design and manufactureare drafted.
文摘Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying the accuracy of the solution. Firstly, the minimum parameter interval of the node vector corresponding to the data point under test in the original data point sequence is determined, and the parameter interval is subdivided according to the corresponding step size, and the corresponding parameter value is obtained. Secondly, the distance from the measured point to the NURBS curve is calculated, and the nearest distance is found out. The node interval is subdivided again on one side of the nearest distance. Finally, the distance between the data point to be measured and each subdivision point is calculated again, and the minimum distance is taken as the interpolation error between the point and the NURBS curve. The simulation results of actual tool position data show that this method can more accurately obtain the error of spatial NURBS interpolation curve.
基金supported by the National Great Science Specif ic Project (Grants No. 2014ZX03002002-004)National Natural Science Foundation of China (Grants No. NSFC-61471067)
文摘For the simultaneous wireless information and power transfer(SWIPT), the full-duplex MIMO system can achieve simultaneous transmission of information and energy more efficiently than the half-duplex. Based on the mean-square-error(MSE) criterion, the optimization problem of joint transceiver design with transmitting power constraint and energy harvesting constraint is formulated. Next, by semidefinite relaxation(SDR) and randomization method, the SDRbased scheme is proposed. In order to reduce the complexity, the closed-form scheme is presented with some simplified measures. Robust beamforming is then studied considering the practical condition. The simulation results such as MSE versus signal-noise-ratio(SNR), MSE versus the iteration number, well prove the performance of the proposed schemes for the system model.
文摘The physics design of a 3 MeV, 30 mA, 352.2 MHz Radio Frequency Quadrupole (RFQ) is done for the future Indian Spallation Neutron Source (ISNS) project at RRCAT, India. The beam dynamics design of RFQ and the error analysis of the input beam parameters are done by using standard beam dynamics code PARMTEQM. The electromagnetic stu-dies for the two-dimensional and three-dimensional cavity design are performed using computer codes SUPERFISH and CST Microwave Studio. The physics design of RFQ consisting of the beam dynamics design near the beam axis and the electromagnetic design for the RFQ resonator is described here.
基金Supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ16E050012)National Natural Science Foundation of China(Grant Nos.51705462 and 51275115)International Science and Technology Cooperation Program of China(Grant No.2015DFA70630)
文摘Ultra-precision machine tool is the most important physical tool to machining the workpiece with the frequency domain error requirement, in the design process of which the dynamic accuracy design(DAD) is indispensable and the related research is rarely available. In light of above reasons, a DAD method of ultra-precision machine tool is proposed in this paper, which is based on the frequency domain error allocation.The basic procedure and enabling knowledge of the DAD method is introduced. The application case of DAD method in the ultra-precision flycutting machine tool for KDP crystal machining is described to show the procedure detailedly. In this case, the KDP workpiece surface has the requirements in four different spatial frequency bands, and the emphasis for this study is put on the middle-frequency band with the PSD specifications. The results of the application case basically show the feasibility of the proposed DAD method. The DAD method of ultra-precision machine tool can effectively minimize the technical risk and improve the machining reliability of the designed machine tool. This paper will play an important role in the design and manufacture of new ultra-precision machine tool.
文摘The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Slope Rotatable Designs Using Pairwise Balanced Designs. Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi.The paper is a copy of Dr. Rabindra Nath Das’s former article, entitled “Slope rotatability with correlated errors (Vol. 54, pp. 57-70, 2003)” and “Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in OJSVol.2 No.3, 319-327, 2012, has been removed from this site.
文摘风洞天平的校准精度直接决定了风洞试验的气动载荷测量精度,为了提升天平校准的质量和效率,以BCS-100天平校准系统为研究对象,基于现代试验设计方法(modern design of experiments,MDOE)开展了风洞天平校准研究。针对单因子变量法(one factor at a time,OFAT)天平校准中存在系统误差与响应量耦合的问题,采用MDOE的随机、重复和分块策略控制校准的系统误差,并选定响应面理论的中心复合设计方法生成校准矩阵。校准矩阵共计86个样本点,包括64个分级因子点、12个轴向因子点和10个中心因子点,其中所有样本点的加载顺序做随机化处理,并作为一个样本块在短时间内集中完成加载,中心因子点则用于满足重复原则。最后开展了OFAT和MDOE的对比校准,拟合载荷的残差正态概率分布显示MDOE校准中横侧向分量的样本点独立性更强,样本点残差最高可降低84%;检验载荷显示MDOE和OFAT两种方法中天平所有分量的综合加载重复性持平,MDOE校准中横侧向分量的综合加载误差最高可降低54%。研究表明MDOE能够有效降低校准的系统误差,提升横侧向小量的预测能力。
基金Supported by the National Science and Technology Specific Project (2011ZX03005-004-003)the National Natural Science Foundation of China (No. 61071090, 61171093)+2 种基金973 Project of Jiangsu Province (BK2011027)the Project 11KJA510001 and PAPDthe Jiangsu Postgraduate Research Project (CXZZ11_0384)
文摘In this paper, a joint precoding and decoding design scheme is proposed for two-way Multiple-Input Multiple-Output (MIMO) multiple-relay system. The precoding and decoding matrices are jointly optimized based on Minimum Mean-Square-Error (MMSE) criteria under transmit power constraints. The optimization problem is solved by using a convergent iterative algorithm which in-cludes four sub-problems. It is shown that due to the difficulty of the block diagonal nature of the relay precoding matrix, sub-problem two cannot be solved with existing methods. It is then solved by converting sub-problem two into a convex optimization problem and a simplified method is proposed to reduce the computational complexity. Simulation results show that the proposed scheme can achieve lower Bit Error Rate (BER) and larger sum rate than other schemes. Furthermore, the BER and the sum rate performance can be improved by increasing the number of antennas for the same number of relays or increasing the number of relays for the same number of antennas.