2.1 Aviation stringer parts analysis
Stringer parts of aerospace aluminum materials are widely used in the aircraft seat slide rail, wing skeleton and so on[24]. Aviation stringer parts are made of slender, thin-walled aluminium profiles through hole, edge and groove milling processes. As shown in Fig. 1, the cross section of the part is similar to H-type. Most machining characteristics are distributed on the upper and lower surfaces. The length of the parts ranges from 2m to 6m.
As shown in Fig. 2, the processing benchmark of the stringer part is located on one side of the flange to be machined. Due to the bending deformation of the aluminum blanks, it is necessary to adjust the processing benchmark in addition to the stable clamping of the stringer parts to ensure the machining accuracy before the CNC machining starts.
In the actual production, it is very difficult to adjust the machining benchmark of straightness accuracy through the manual clamping ways. The time of manual clamping is much longer than the running time of CNC program, which has become a common problem in the processing of stringer parts. Therefore, it is necessary to study an intelligent fixture with automatic clamping and processing benchmark self-adjustment function.
2.2 Mechanism of clamping and deformation correction
It is necessary to analyze the process of girder deformation correction in order to obtain the basic clamping and deformation correction law of stringer parts. Due to the thin thickness of the upper and lower flange plates of the parts, it is not convenient to clamp and apply load, so the fixture is designed to clamp the web of the parts and apply extra load to correct the deformation.
The clamping force Fre is obtained by Eq. (1).
$${F_{{\text{re}}}}={F_{{\text{cl}}}}+{F_{{\text{at}}}}$$
1
where Fcl is the pre-clamping force to ensure the clamping stability of parts, which is determined by test or simulation. Fat is the sum of all deformation correction forces in the clamping area. which is related to the deformation of the part to be corrected in the clamping area, and can be expressed as Eq. (2).
$${F_{{\text{at}}}}{\text{=}}\sum {{F_{{\text{a}},i}}} ,i=1,2......n$$
2
where Fa,i is the force required to correct the i-th deformation in the clamping area. n is the number of deformations to be corrected in the clamping area.
The main deformation of the parts after positioning and pre-clamping force clamping is bending deformation. Analyze the correction process for any deformation in the part. The influence of shear force on bending deformation is ignored, and the deformation correction process in the clamping area of the part is within the linear elastic range of the material, which conforms to Hooke's law, namely Eq. (3).
$$\sigma {\text{=}}E\varepsilon$$
3
where, σ is stress, E is elastic modulus, and ɛ is strain.
As shown in Fig. 3, the deformation of the parts is abstracted as a simply supported beam structure. The process of stringer parts deformation correction is analyzed by means of the theory of force bending and deformation of simply supported beam.
From the statics relation, the following formula can be obtained:
$$\frac{1}{{\rho (x)}}=\frac{{M(x)}}{{EI}}$$
4
where, EI is the bending stiffness of the part, 1/ρ(x) and M(x) represent the curvature at any point and the bending moment of the cross section at that point, respectively.
By substituting the curvature equation of the plane curve into Eq. (4), the flexural approximate differential Eq. (5) of part bending deformation correction is obtained as follows:
$$EI\omega ^{\prime\prime}{\text{=}}M(x)$$
5
Based on the mechanical model of bending deformation of parts, the bending moment equation at the deformation center is expressed as:
$$M(x){\text{=}}\frac{F}{2}x$$
6
After substituting Eq. (6) into Eq. (5), integrate and determine the bending deformation boundary conditions of the parts, and obtain:
$$EI\omega =\frac{{F{x^3}}}{{12}} - \frac{{F{l^2}}}{{16}}x$$
7
When x = l/2, the relationship between the deformation correction force Fa and the amount of corrected deformation in the clamping area ωst can be obtained as follows:
$${F_{\text{a}}}=\frac{{ - 48EI}}{{{l^3}}}{\omega _{{\text{st}}}}$$
8
The relationship between the flange deformation correction amount ωfl and the deformation correction amount in the clamping area ωst is determined by the approximate Eq. (9).
$${\omega _{{\text{st}}}}{\text{=}}\gamma {\omega _{{\text{fl}}}}$$
9
where, γ is the transfer coefficient of the flange deformation correction amount and the deformation correction amount of the clamping area, which is related to the properties of the part, the clamping area, and other factors.
Eq. (10) can be obtained from simultaneous Eqs. (2), (8) and (9), which expresses the relationship between deformation correction force and part correction deformation.
$${F_{{\text{at}}}}= - 48EI\gamma \sum {\frac{{{\omega _{{\text{fl}},i}}}}{{{l_i}^{3}}}} ,i=1,2......n$$
10
where, the bending stiffness EI and the transfer coefficient γ of the parts are not constant, and can be determined by simulation or experiment.
The flange deformation correction amount and span of deformation are determined by the straightness curve obtained from the measurement, as shown in Fig. 4.
The clamping force Fre can finally be expressed as:
$${F_{{\text{re}}}}={F_{{\text{cl}}}} - 48EI\gamma \sum {\frac{{{\omega _{{\text{fl,}}i}}}}{{{l_i}^{3}}}} ,i=1,2......n$$
11
2.3 Clamping simulation optimization analysis
According to mechanism of clamping and deformation correction, it is known that the transfer coefficient γ and the bending stiffness of the web clamping area EI have an influence on the clamping effect. These two factors are not only related to the properties of the parts, but also affected by the fixture structure. Therefore, this section mainly on the width and position of clamping area simulation optimization, guide fixture design.
Firstly, the simulation model is established. The shape and size of the part model are shown in Fig. 5 (a), with a wall thickness of 2mm. The material of the parts is aluminum alloy, and there is a deformation. The assembly model is shown in Fig. 5 (b). One side of the part web is positioned, and the other side is clamped by the clamping module.
The width of clamping area is simulated and analyzed. Firstly, the preliminary parameter optimization is carried out. Too small width of clamping area will lead to excessive local force of parts, resulting in warping and shear failure. Too large width of clamping area will disperse the clamping force and reduce the effect of deformation correction. Therefore, a moderate clamping width range of 20 mm to 40 mm is chosen. The clamping module is clamped at a 2 mm distance from the inner surface of the flange to be machined, and a clamping force of 5000 N is applied for simulation analysis.
The simulation results of different widths of clamping area are shown in Fig. 6. It can be seen that as the width of the clamping area increases, ωfl that reflects the effect of deformation correction, increases first and then decreases slowly after the width of the clamping area reaches 25 mm. The main reason is that EI increases with the increase of the width of clamping area, so ωst tends to decrease. In addition, when the width of clamping area is too small, the warping of the web offsets part of the deformation correction effect, leading to the increase of γ first and then keep the same. Therefore, a smaller width of clamping area should be selected under the condition that the web of the parts does not warp.
The position of clamping area is simulated and analyzed. The position of clamping area is represented by the distance between the clamping area and the inner surface of the flange to be machined. Six positions close to the inner surface of the flange to be machined are chosen. The width of the clamping area is 25mm, and a clamping force of 5000N is applied for simulation analysis.
The simulation results of different positions of clamping area are shown in Fig. 7. It can be seen that the farther the clamping area is from the flange to be machined, the worse the correction effect of flange deformation is. The main reason is that with the increase of the distance between the clamping area and the flange to be machined, although ωst will increase slowly, γ shows a decreasing trend and the effect is more obvious. Therefore, in order to ensure the effect of deformation correction, the clamping area should be as close as possible to the flange to be machined.
2.4 The overall design of intelligent fixture
According to the structural characteristics of stringer parts and the adjustment requirements of processing benchmark, a modular intelligent fixture integrating measurement, clamping and calibration functions is proposed. As shown in Fig. 8, the fixture mainly includes the base, clamping unit, measuring unit, and protective cover. The number of clamping units can be configured according to the maximum length of the processed parts. The measuring unit adopts displacement sensor, which can be magnetized on the spindle box to measure the straightness of the parts.
The clamping unit includes a lateral clamping mechanism, a positioning mechanism and an auxiliary clamping mechanism. As shown in Fig. 9, the stringer parts are placed on the positioning mechanism, and the under-positioning clamping is carried out by relying on two positioning surfaces A and B. The lateral clamping mechanism is driven by a piston rod cylinder, which can push the parts web onto the positioning surface A of the positioning mechanism. The auxiliary clamping mechanism composed of a swing clamp cylinder can press the parts on the positioning surface B.
The stringer parts will be pressed onto the positioning surface B by the swing clamp cylinder after they are inserted into the fixture. Then the lateral clamping mechanism works to push the parts web onto the positioning surface A with a reasonable clamping force. The swing clamp cylinder raise up and reset to the state without processing interference. In order to ensure that the parts meet the requirements of straightness, the measuring unit and intelligent adjusting control method are proposed. Based on the measuring values, the straightness accuracy is adjusted by controlling the actuating pressure of the piston rod cylinder.