Differential Motion Vector Research Articles

Modeling of the Variation Propagation for Complex-Shaped Workpieces in Multi-Stage Machining Processes

Variation prediction and quality control for complex-shaped workpieces in automotive and aerospace fields with multi-stage machining processes have drawn significant attention because of the widespread application and increasing diversity of these kinds of workpieces. To finish the final workpieces with complex shapes, multiple setups and operations are often applied in machining processes. However, sources of geometric error, such as fixture error, datum error, machine tool path error, and the dimensional quality of the product, interact complicatedly at different stages. These complex interactions pose significant challenges to final product error prediction and reduction. Manufacturing error prediction based on stream of variation is an effective way to control the machining quality. However, there are few integrated models that can describe the interactions among types of geometric error sources from different stages for different kinds of complex workpieces. This paper proposes a modified error prediction model to systematically capture the interactions of different error sources among different operations for complex-shaped workpieces in multi-stage machining processes. Using differential motion vectors, the connection of all key variations from machine, fixture, and workpiece is established. This modified model can not only handle general fixture layouts for complex workpieces, but also introduce machining-induced variations. Based on this model, the main error sources identification method and error compensation method are proposed. In order to evaluate the effectiveness of the proposed method, engine blocks are used to be machined as an example. Compared with a machining process without a compensating strategy, the average machining error of the key feature is reduced by 80.5% after compensating for the main error sources.

Characterization of Dimensional Variations in Turning Process for Multistep Rotary Shaft of High-Speed Motorized Spindle

The surface accuracy of a multistep rotary shaft is very important in manufacturing and the assembly process of the high-speed motorized spindle of CNC machine tools, which is closely related to the machined dimensional variation induced by the turning process. This paper attempts to enhance a comprehensive understanding of the impact of different locating-error sources and machine toolpaths on the machined dimensional variation for multistep rotary parts of the high-speed motorized spindle in the turning process. A modeling method and a compensation strategy of dimensional variation are introduced in this paper and based on the relationship definition between the error sources and the machined surface using the differential motion vector and stream-of-variation methods. Validation experiments were conducted to verify the proposed model. Additionally, the relationship between locating errors and dimensional variation was investigated with varied case studies, providing a theoretical methodology for the prediction and characterization of the expected dimensional variations of the surface machined with the given conditions.

A Novel Error Compensation Method for Multistage Machining Processes Based on Differential Motion Vector Sets of Multiple Contour Points

Abstract Modeling the variation propagation based on the stream of variation (SoV) methodology for multistage machining processes (MMPs) has been investigated intensively in the past two decades; however, little research is conducted on the variation reduction and the existing work fails to be applied to irregular features caused by the machining-induced variation varying with the positions of the contour points on the machined surface. This paper proposes a novel error compensation method for MMPs by modifying the tool path to reduce variation for general features. The method based on differential motion vector (DMV) sets of multiple contour points is presented to represent the deviation of the irregular feature. Then, the conventional stream of variation (SoV) model is further extended to more accurately describe variation propagation for irregular features considering the actual datum-induced variations and the varying machining-induced variations, especially the deformation errors for the low stiffness workpiece. Based on the extended SoV model and error equivalence mechanism, the datum error and fixture error are transformed to the equivalent tool path error. Then, the original tool path is modified through shifting the machine zero points of machine tools with no need for changing the original G code and workpiece setup. A real cutting experiment validates the effectiveness of the proposed error compensation method for MMPs with an average precision improvement of over 60%. The application of the extended SoV model significantly contributes to compensating more complex error sources for MMPs, such as the clamp force, the internal residual stress, etc.

Variation propagation modelling in multistage machining processes using dual quaternions

Variation propagation models play an important role in part quality prediction, variation source identification, and variation compensation in multistage manufacturing processes. These models often use homogenous transformation matrix, differential motion vector, and/or Jacobian matrix to represent and transform the part, tool and fixture coordinate systems and associated variations. However, the models end up with large matrices as the number features and functional element pairs increase. This work proposes a novel strategy for modelling of variation propagation in multistage machining processes using dual quaternions. The strategy includes representation of the fixture, part, and toolpath by dual quaternions, followed by projection locator points onto the features, which leads to a simplified model of a part-fixture assembly and machining. The proposed approach was validated against stream of variation models and experimental results reported in the literature. This paper aims to provide a new direction of research on variation propagation modelling of multistage manufacturing processes.

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Assembly modeling is a very important activity for computerized analysis of product assembly, and it has been a subject of intense research over the past years. However, most of the assembly models focus on the assembly connective relationships between parts rather than assembly spatial relationships. Variation analysis is becoming a critical issue when specifying and verifying the geometric and dimensional requirements of assembly. In order to support dimensional variation analysis, a mathematical assembly model representation considering assembly spatial relationships is proposed in this paper. Four types of coordinate systems are defined. The nominal and variational spatial relationships among assembly elements are represented as homogeneous transformation matrix among different coordinate systems. The variations of assembly elements, mating interface and locating interface are represented as variation transformation matrix among corresponding coordinate systems. The variation of the final assembly is modeled as stack up of the differential motion vectors of coordinate systems of all the parts with respect to global coordinate system, and it can be calculated by homogeneous transformation and variation transformation. The different situations for two types of assemblies are distinguished in this novel assembly model representation.

A modification of DMVs based state space model of variation propagation for multistage machining processes

PurposeComplicated workpiece, such as an engine block, has special rough locating datum features (i.e. six independent datum features) due to its complex structure. This locating datum error cannot be handled by current variation propagation model based on differential motion vectors. To extend variation prediction fields, this paper aims to solve the unaddressed variation sources to modify current model for multistage machining processes.Design/methodology/approachTo overcome the limitation of current variation propagation model based on differential motion vectors caused by the unaddressed variation sources, this paper will extend the current model by handling the unaddressed datum-induced variation and its corresponding fixture variation.FindingsThe measurement results of the rear face with respect to the rough datum W and the pan face with respect to the hole Q by coordinate measuring machine (CMM) are −0.006 mm and 0.031 mm. The variation results for rear face and pan face predicted by the modified model are −0.009 mm and 0.025 mm, respectively. The discrepancy of model prediction and measurement is very small.Originality/valueThis paper modifies the variation propagation model based on differential motion vectors by solving the unaddressed variation sources, which can extend the variation prediction fields for some complicated workpiece and is useful in the future work for many fields, such as process monitoring, fault diagnosis, quality-assured setup planning and process-oriented tolerancing.

A new error compensation model for machining process based on differential motion vectors

The product variation in a machining process is mainly affected by datum error, fixture error, and machine tool path error. In spite of the success of equivalent fixture error approach to compensating datum error and machine tool path error, the machining-induced errors have not been explicitly modeled and compensated by the current compensation model based on equivalent fixture error. This will limit its application in compensation accuracy. This paper formulates a new error compensation model for machining process using equivalent fixture error concept based on differential motion vectors. With this model, datum error and machining-induced errors can be transformed to equivalent fixture locator errors and then compensated. A real cutting experiment and an error compensation simulation for machining process will be conducted in the case study to demonstrate the model validity.

A comprehensive study of linear variation propagation modeling methods for multistage machining processes

Stream of variation (SoV) model is an effective tool, which can describe the dimensional variation and propagation for multistage machining processes. Compared with traditional single-stage error models considering errors from a single machining stage only, SoV model can depict the complicated interactions between different errors at different stages. This paper reviews three major linearized SoV modeling methods for multistage machining processes based on the literature published over the last two decades. These three linearized SoV modeling methods are based on differential motion vectors, equivalent fixture error, and kinematic analysis, respectively. Each method has its corresponding advantages and disadvantages. The model using differential motion vector (DMV) concept from robotics incorporates fixture-, datum-, and machining-induced variations in the multistage variation propagation for orthogonal 3-2-1 fixturing layout while the primary datum deviation is currently overlooked. The kinematic analysis method can address general fixture layouts rather than being limited to orthogonal 3-2-1 fixture layouts. The variation propagation model using the equivalent fixture error concept can directly model the process physics regarding how fixture, datum, and machine tool errors generate the same pattern on the features of the workpiece. The results of these three models with respect to an example are also given to make a comparison. Finally, a perspective overview of the future research about SoV methods is presented.

Rigid-compliant hybrid variation modeling of sheet metal assembly with 3D generic free surface

Rigid and compliant variation models have been developed in parallel for different assembly processes all the time. However, sheet metal parts will generate not only rigid variation caused by rigid-body motion, but also compliant variation caused by deformation during the assembly process. In order to better evaluate the dimensional quality of sheet metal assembly, a rigid-compliant hybrid variation modeling methodology of sheet metal assembly is proposed in this paper. Parts, fixtures and features are considered as assembly elements in a sheet metal assembly process, and four types of coordinate systems are defined to locate them. The nominal and variational spatial relationships among assembly elements are then represented by relationships among different coordinate systems, which can be described by homogeneous transformation matrix. Based on two-dimensional stream-of-variation, the variation generation mechanism in every assembly step and the variation propagation mechanism between assembly steps are researched, and the mathematical relationship between the overall assembly variation and various variation sources is built accordingly. In this methodology, rigid variation is analyzed based on differential motion vector and homogeneous transformation matrix; compliant variation is analyzed based on method of influence coefficients; and their impact on each other is also considered. The proposed model has general applicability for sheet metal assembly with 3D generic-free surface. A case study on rigid-compliant hybrid variation modeling of a wing panel assembly is presented to demonstrate the modeling and analysis capability of the proposed methodology.

Three-dimensional variation propagation modeling for multistage turning process of rotary workpieces

In spite of the success of state space modeling approach to describe variation propagation for multistage milling processes (MMPs), the current models cannot be directly applied into variation propagation analysis for multistage turning processes (MTPs) due to the differences of the locating datum schemes. MTPs are widely adopted in manufacturing industry for fabricating rotary workpieces. In this paper, a generic framework for three-dimensional variation propagation modeling for MTPs of rotary workpieces based on differential motion vectors (DMVs) is developed. The explicit three-dimensional datum error and fixture error expressions are derived. By a series of homogeneous transformations of different error sources, a three-dimensional variation propagation model for MTPs is built, in which the datum error, fixture error and so on are described and transmitted in six degrees of freedom. The effectiveness of the proposed model is validated by an example of MTPs of valve shell.

Research on the Variation Propagation Model for Complex Mechanical Product Processing

The high precision requirements of complex mechanical product (CMP) results in that its processing often contains multiple stages. When part was processed and transmitted in multiple stages, dimensional variation of part will be accumulated, coupling and transformed as well. Since the high precision requirements of the CMP, there are more process parameters impacted the machining errors than general multistage process, and more diverse process parameters should be considered in CMP's processing. To describe machining variation propagation process accurately and effectively, the variation propagation model for CMP processing was proposed. Firstly, the parts and fixtures in CMP processing are described by differential motion vector based on the robot's kinematics principle, and the change of theirs space pose are obtained by homogeneous transformation. Then, the fixture-induced variation, datum-induced variation, machining-induced variation and cutting-tool wear induced variation are analyzed and derived. The machining-induced variation is the dimension deviation produced by cutting force impacting on part's machining surfaces, and the cutting-tool wear induced variation is mainly caused by tool's normal wear. Lastly, the coupling relationship of datum-induced variation, fixture-induced variation, machining-induced variation and cutting-tool wear induced variation of each process stage is described, and the state space model of variation propagation is developed. The relationship of dimensional variation from all work stages and all kinds of variations is explored. By a real case study, feasibility and effectiveness of the model is validated. The model has great potential to be applied in the fault diagnosis, root cause identification of variation, sensor placement optimization, variation simulation, machining parameter and fixture design and optimization in quality control and improvement of complex product.

Assembly Model Representation for Variation Analysis

Assembly modeling is a very important activity for computerized analysis of product assembly, and it has been a subject of intense research over the past years. However, most of the assembly models focus on the assembly connective relationships between parts rather than assembly spatial relationships. Variation analysis is becoming a critical issue when specifying and verifying the geometric and dimensional requirements of assembly. In order to support dimensional variation analysis, a mathematical assembly model representation considering assembly spatial relationships is proposed in this paper. Four types of coordinate systems are defined. The nominal and variational spatial relationships among assembly elements are represented as homogeneous transformation matrix among different coordinate systems. The variations of assembly elements, mating interface and locating interface are represented as variation transformation matrix among corresponding coordinate systems. The variation of the final assembly is modeled as stack up of the differential motion vectors of coordinate systems of all the parts with respect to global coordinate system, and it can be calculated by homogeneous transformation and variation transformation. The different situations for two types of assemblies are distinguished in this novel assembly model representation.

Unified variation modeling of sheet metal assembly considering rigid and compliant variations

Variation modeling of sheet metal assemblies is quite critical when specifying and verifying the geometric and dimensional requirements of parts. However, sheet metal parts’ compliant behavior makes the variation modeling approach more complex when coupling both rigid variation in the in-plane direction and compliant variation in the out-of-plane direction. In order to completely model the overall three-dimensional variation of sheet metal assembly, a unified variation modeling approach considering both rigid and compliant variations is proposed in this article. Four types of coordinate systems are defined. In the in-plane direction, homogeneous transformation matrix is used to describe the position and orientation relationships between assembly elements, and differential motion vector is used to represent rigid variation. In the out-of-plane direction, a vector composed of the deviations of selected key characteristic points is used to represent compliant variation, and the method of influence coefficients is adopted to analyze compliant variation. The overall three-dimensional variation of sheet metal assembly is the superposition of both in-plane rigid variation and out-of-plane compliant variation. Three types of variation sources that are fixture locators’ deviations, datum features’ deviations and joint features’ deviations are considered here. A case study is presented to illustrate the proposed approach.

Assembly Accuracy Prediction and Adjustment Process Modeling of Precision Machine Tool Based on State Space Model

In precision machine assembly process,the product quality is not only depended on the tolerance design,but also on the assurance of the assembly process planning.Therefore,there is a strong need to develop a mathematical analysis method to predict and control the variation in assembly process,and to find out the assembly process effect to final accuracy.By the expression of the variation state in different assembly process in form of differential motion vector(DMV) method,a generic mathematical model that directly links variation of key characteristics(KCs) and the assembly process variation sources is built.The state space model describing variation propagation of KCs in machine tool assembly,measurement and adjustment is proposed.Based on this model,the effect of current assembly and adjustment process to final accuracy can be predicted to decide the current adjustment method to the final assembly accuracy assurance.The method’s validity is verified by a simulation of the assembly of a precision horizontal machining center.

State Space Modeling of Variation Propagation in Multistation Machining Processes Considering Machining-Induced Variations

In spite of the success of the stream of variation (SoV) approach to modeling variation propagation in multistation machining processes (MMPs), the absence of machining-induced variations could be an important factor that limits its application in accurate variation prediction. Such machining-induced variations are caused by geometric-thermal effects, cutting-tool wear, etc. In this paper, a generic framework for machining-induced variation representation based on differential motion vectors is presented. Based on this representation framework, machining-induced variations can be explicitly incorporated in the SoV model. An experimentation is designed and implemented to estimate the model coefficients related to spindle thermal-induced variations and cutting-tool wear-induced variations. The proposed model is compared with the conventional SoV model resulting in an average improvement on quality prediction of 67%. This result verifies the advantage of the proposed extended SoV model. The application of the new model can significantly extend the capability of SoV-model-based methodologies in solving more complex quality improvement problems for MMPs, such as process diagnosis and process tolerance allocation, etc.

State Space Modeling for 3-D Variation Propagation in Rigid-Body Multistage Assembly Processes

Dimensional variation propagation modeling is a critical enabling technique for product quality variation reduction in a multistage assembly process (MAP). However, the complex inter-stage correlations make the modeling extremely difficult. This paper aims to improve the existing techniques by developing a generic state space approach to modeling 3-D variation propagation induced by various types of variation sources in general MAPs. A concept of differential motion vector (DMV) is adopted to represent deviations with respect to four types of coordinate systems and to formulate the variation propagation as a series of homogeneous transformation among different coordinate systems. Based on this representation and formulation strategy, a novel generic mechanism is proposed to model the effect of variations induced by part fabrication processes and a MAP. A case study on 3-D variation propagation in a panel fitting process is presented to demonstrate the modeling and analysis capability of the proposed methodology.

Motion information scalability for MC-EZBC

Interframe wavelet video coding algorithm has received much attention lately because of its high coding efficiency and flexible temporal and spatial scalability. It combines the motion-compensated temporal filtering technique together with the wavelet embedded zeroblock coding technique. Blending these two techniques in a nice manner enables it achieving three types of scalability: SNR, temporal and spatial, in one single bit-stream. However, the performance of the interframe wavelet video coding at low bit-rates is less satisfactory because the bit-rate of the non-scalable motion information is too high. In this paper, we extend the framework of Motion Compensated Embedded Zero Block Coding (MC-EZBC) proposed by RPI (Improved MC-EZBC with Quarter-pixel Motion Vectors, ISO/IEC/JTC1 SC29/WG11 doc. No. m8366, Fairfax, May 2002). Our major contribution is splitting the motion information in MC-EZBC into a few layers. At very low bit-rates only the “coarse” motion vectors are transmitted. Therefore, we are able to produce compressed bit streams at a lower bit-rate and the associated picture quality is significantly better than that of the original scheme. The overhead due to motion information partitioning is negligible at higher rates. Hence, the rate-distortion performance at high rates is about the same as that of the original scheme. In addition, a Hilbert curve scan order is proposed to increase the efficiency up to 5% in encoding the differential motion vectors.

State space modeling of dimensional variation propagation in multistage machining process using differential motion vectors

In this paper, a state space model is developed to describe the dimensional variation propagation of multistage machining processes. A complicated machining system usually contains multiple stages. When the workpiece passes through multiple stages, machining errors at each stage will be accumulated and transformed onto the workpiece. Differential motion vector, a concept from the robotics field, is used in this model as the state vector to represent the geometric deviation of the workpiece. The deviation accumulation and transformation are quantitatively described by the state transition in the state space model. A systematic procedure that builds the model is presented and an experimental validation is also conducted. The validation result is satisfactory. This model has great potential to be applied to fault diagnosis and process design evaluation for complicated machining processes.

Comment on "Consistent Integration and Propagation of Disparate Sensor Observations" by H.F. Durrant-Whyte

A small change in a homogeneous transform may be repre sented by either the change in the description vector of the transform or by a differential translation and rotation transfor mation. The differential motion vector describing the differential translation and rotation transformation is in general not equal to the change in the description vector. The calculations in Durrant-Whyte (1987a) are based on the assumption that they are equal and have to be modified accordingly.