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The accurate shape of roller cavity surfaces is vital part for net-shape rolling. This paper presents a new design method of roller cavity surfaces with high accuracy for rolling compressor blades based on the geometrical inheritance and evolution of the net-shape profiles. Firstly, a process model of the blade is modeled by adding process allowance and locating basis at the CAD (Comput-er Aided Design) model of th e blade to represent the roll formed blade, the process model inherits the net-shape profiles of the blade at the pressure and suction surfaces. Secondly, an algorithm is proposed to discretize a curve to a set of ranked points with the restriction of the maximum chord height, and a new section curve which represents the geometrical feature of the pressure and suction surfaces are distributed on the process model based on the algorithm. Finally, a mapping algorithm is proposed to transform the section curves to the cavity section curves around the roller axis based on the conjugate movement between rollers and blade, and the cavity surfaces are reconstructed based on the transformed section curves. The design method is implemented for the roll-er cavities of a variable cross-section compressor blade, and the accuracy of the designed cavities is checked based on the precision of the roll formed blade by the finite element method. The results reveal that the designed cavities achieved the net-shape precision at pressure and suction surfaces of the blade. The paper provides an effective method for designing rolling cavity surfaces with excellent design quality.

Rollforming is one kind of important machining method of high compressor blade, due to the characteristics of the rolling blade with large quantity, thin thickness, and high precision requirement. In a blade rolling process, a blank is rolled between a pair of rotated rollers with a shaped surface and produced plastic deformation. With the cross sectional shape being progressively decreasing, a blade is printed along the rolling direction at the outlet. In order to meet the high precision required by manufacture and good uniformity demanded by assembly, an accurate shape of rolling cavity is necessary for blade rolling.

In previous studies, many works have been done on rolling process, such as rolling parameter optimization [

The conjugate movement between rollers and component is fundamental for designing roller cavity. Cai [

In order to design the roller with acceptable accurate requirement for a complex part, it is vital for transforming the profile of the rolled part to the cavity surfaces of the rollers. In this paper, a numerical design method for blade rolling cavity surfaces is studied with geometric inheritance of the blade’s profiles. The rolling cavity design process is demonstrated for a high compressor blade with varying cross-section, and the simulative method are implemented to estimate the designed cavities. The results show that the rolling formed blade achieved net-shape at pressure and suction surface when using the designed roller. The proposed design method of roller cavity surfaces surmounts traditional method which based on trial and error, and shortens the setting period of roller with a high design precision.

This paper proposes a new method to design roller cavity surfaces for complex part based on geometrical inheritance and evolution, and the geometrical inheritance and evolution accuracy of the part is emphasized. A stator blade model of compressor is used to illustrate the design method of the rolling cavity surface. The original cross section curves of the blade and CAD model of the blade are showed in

based on the transformed section curves and the rolling dies are created based on designed cavity surfaces. The designed roller for the blade is showed in

According to the flowchart of the method to design the rolling cavities for producing compressor blades, the development of the process model, the creation of the section curves of the process model, and the creation of section curves of the cavity are discussed below in details.

The process model is an imaginary model based on the CAD model of the blade to describe the shape of the blade blank after rolling process. It inherits and develops the geometrical characteristic of the pressure and suction surface of the blade, and intermediates the original blade model to the rolling cavity model. The process model is represented by its cross section curves, which are evolved from the section curves of the original CAD model of blade. The overflow boundaries at the leading and trailing edges are added to the suture pressure and suction surface. The machining allowances are added by extrapolating the root and top section curves of the blade to ensure integrity of the blade profiles. A location block is also appended at the root section of process model for holding and positioning in manufacturing process. The process model evolves from the original blade CAD model, and it seems like that the compressor blade inlaid in the process model. The procedure of developing process model is presented as followed.

In order to minimize machining allowance at the leading and trailing edges to suture the pressure and suction surfaces by an arc smoothly after rolling, meanwhile, to avoid misrun defect on the pressure and suction surface, the convergent overflow boundaries are added at the leading and trailing edges of every cross section curve. First, an unbroken section curve is discretized to many points confined by a chord height tolerance Δ which is the same as the blade tolerance (it is 0.02 mm in this paper). The leading and trailing edges are matched by circles respectively. The discretized points are divided into four groups which describe the leading edge curve, the pressure surface curve, the trailing edge curve and the suction surface curve respectively, see

lines and the mean camber curve of the blade, see

A wire electrode cutting process will be used to separate the blade from the rolling formed blade at root and tip sections after machining arcs, which suture the pressure and suction surfaces at the leading and trailing edges. Hence, the machining allowances are added at the root and the tip of blade, see _{t} to set up the tip machining allowance, and root section curve of blade is stretched outwards by a length of l_{r} to set up the root machining allowance, see

manufacturing process. This block is used as a locating device which is connected with the blade by a plate. Coordinate systems are needed in parameter design of blade rolling cavities. Because the thickness of the root section is bigger than the tip’s thickness, rolling direction is chosen from tip to root of blade. The center point of the maximum inscribed circle at root section is set as original coordinate for modeling coordinate system. Z axis is a vector from blade root to tip, X axis is a vector from trailing edge curve center point to leading edge curve center point, and Y axis is determined by following the right hand rule in the Cartesian coordinate system. The complete blade process model is showed in

The CAD model of blade is sketched by sequential cross section curves at different locations from the blade root, i.e., stacking height, and the manufacturing accuracy is estimated by comparing the cross section curve of rolling formed blade with the original section curve of CAD model. Designing rolling cavity surfaces is to convert the blade profiles to roller cavity around their axes. It is a coordinate transformation for spatial surfaces. Generally, a 3-dimensional profile is discretized to a set of points. These points are transformed to new points by mapping their coordinate. After that, a new surface is reconstructed based on the new set of points, see e.g. Ali et al. [

A curve can be discretized into points using different methods, such as the length restriction of segmented units, the restriction of chord height, and the restriction of angle, etc. In order to use less number of points to represent a smooth curve with required accuracy, a discretizing method is proposed by limiting the chord height of the discretized units. The threshold value is related to the requirement of the blade tolerance. The chord height is the largest distance from the bow to the line between start and end point in each unit. If the chord height is smaller than the threshold value, the curve can be simplified to the line. Otherwise, a new point is inserted on the curve at the farthest point from the line. Then, the new units are checked by limiting the chord height again until every discretized unit meets the limitation of the threshold value. In the case illustrated in the inset of

The orientational curve of blade describes rotation and translation of the pressure and suction surface along the stacking direction. The orientational curve is discretized into a ranked point set by limiting chord height as discussed in Section 3.2.1, see

The final step to design the roller cavity is to revolve the updated section curves of the process model to the section curves of the cavity surfaces. According to the coordinate systems presented in Section 3.1.2, the corresponding coordinates of the points of the cavity section curve are mapped from the new section curves. The springback compensation was implemented to achieve net-shape of the cross sections and forward slip compensation was implemented to calculate the mapping angle of the sections [

The updated section curves are discretized into ranked points used the discretizing algorithm presented in Section 3.2.1. The coordinates of the ranked point set are rotated around the roller axis and generated the corresponding ranked point set which represents the section curve of cavity. The distance between the top roller’s axis and the bottom roller’s axis is D. The coordinate mapping algorithm for the top and the bottom roller cavity surfaces are presented in Equation (1) and Equation (2), respectively,

{ x ′ = x y ′ = D 2 − ( D 2 − y ) cos ( θ k ) z ′ = ( D 2 − y ) sin ( θ k ) (1)

{ x ′ = x y ′ = − D 2 − ( y − D 2 ) cos ( − θ k ) z ′ = ( y − D 2 ) sin ( − θ k ) (2)

where ( x y z ) is the discretized point’s coordinates of the updated section curve, ( x ′ y ′ z ′ ) is the point coordinates of the section curve of the cavity surfaces, θ k is the rotational angle.

A new point set which represents the section curve of cavity surface is created based on the mapping algorithm. The cavity section curves are reconstructed through the new point sets. The mapping process of the section curves of the top and bottom cavity surface is shown in

curves of process model which are created in Section 3.3.2. The red curves S ′ k are ranked section curves of cavity surfaces. The section curves of the processes model and cavity surface are the same at the exit section ( θ 0 = 0 ), see

The designed cavity surfaces are reconstructed based on the mapped section curves, as showed in

In order to validate the new design method, the FEM simulation were carried out to form a rolled blade, and four groups of corresponding section curves at the different stacking height are investigated.

A high-pressure compressor statorblade (

surface were transformed from the section curves based on the mapping algorithm, see Section 3.3. The distance between the top roller’s axis and the bottom roller’s axis is 136 mm which discussed in Equation (1) and Equation (2). The cavity surfaces were reconstructed based on the mapped section curves of the cavity, see

A simulation model was created for the blade rolling process. The rolling process was replicated in the numerical simulation using a non-linear Explicit FE code (ABAQUS/Explicit 6.14-1). The reduced integration, hourglass control (C3D8I) is used to mesh the blank, and the mesh size is 0.1 mm. The blank is a flat plate and the thickness reduction is 30%. The properties of the blank are showed in

The precision of profile of the produced blade is evaluated by its section curves [

GH4169_{ } | ||
---|---|---|

Density (Kg/m^{3}) | 8250 | |

Young’s modulus (MPa) | 220,000 | |

Poisson’s Ratio | 0.3 | |

Plastic parameters | Yield Stress (MPa) | Plastic Strain |

989 | 0 | |

1119 | 0.0042 | |

1190 | 0.0092 | |

1236.4 | 0.0192 | |

1282.7 | 0.0272 |

The section curves from FEM simulation are compared with the original section curves on CAD model at the same stacking height. The results demonstrate that the section curves from simulation have a good consistency with the CAD model. The largest error of every section curves is smaller than the required tolerance (0.02 mm) of the blade. The results reveal that the designed cavities meet the precision of net shape at the pressure and suction surfaces of the blade. The design method is suitable for designing the roller cavity surface for the compressor blade.

A new design method of cavity surfaces for rolling compressor blades is proposed for complex part based on geometrical inheritance and evolution, and the geometrical inheritance and evolution accuracy of the part are emphasized. The design procedure and algorithm are discussed in detail. The major works are summarized below.

• The new cavity surface design method for net shape rolling blade is proposed based on the motion relation and geometrical inheritance. A process model between the blade and the cavity surface is introduced in design process to represent the pressure and suction surface of the blade before transformation.

• An algorithm is used to discretizea curve to a set of ranked points with the restriction of the maximum chord height. The discretizing algorithm connects the discretizing precision with the design tolerance of a blade. It is an effective method to improve design accuracy under a tolerance requirement.

• A mapping algorithm is presented for designing a compressor blade rolling cavity surfaces. The coordinate transformation formula from the updated section curves to the section curves of cavity surfaces is derived based on the conjugate movement between the rollers and blank.

• A case study is implemented based on the new design method to design a pair of rollers for rolling a compressor blade. The numerical simulation was used to evaluate the precision of the designed cavities. The results indicated that the formed blade satisfied with the tolerance requirement of blade. The proposed method is suitable for designing roller cavity surfaces.

This work was supported by National Natural Science Foundation of China (No.51475374), the Fundamental Research Funds for the Central Universities (No.3102015ZY087) and China Scholarship Council.

Qichao Jin designed, conducted the research and wrote the paper. Wenhu Wang and Ruisong Jiang improved the design method and developed the program. Zongyan Cai and Datao Li discussed the research and editing the paper.

The authors declare no conflict of interest.

Jin, Q.C., Wang, W.H., Jiang, R.S., Cai, Z.Y. and Li, D.T. (2019) Geometric Accuracy Design Method of Roller Cavity Surfaces for Net-Shape Rolling Compressor Blades. Open Access Library Journal, 6: e5279. https://doi.org/10.4236/oalib.1105279