Structure design and verification of spaceborne ka-band channel synthesis multiplexer components

A method for the structural design of a Ka channel synthesis multiplexer is proposed in accordance with the footprint area, weight, natural frequency, and mechanical environment adaptability requirements of the space-borne equipment. This design utilizes key U-type folded design methods, in which two Ka channel synthesis multiplexers are cross-folded onto an integrated structural frame to reduce the equipment layout area to 33.6% of the original plane layout. Mechanical analysis and ground tests are utilized to verify the correctness and rationality of the Ka channel synthesis multiplexer structure design. This structural design concept for the Ka channel synthesis multiplexer provides a reference for the structural design of similar spaceborne equipment.


Introduction
This communication satellite is the first Ku/Ka-band global broadband commercial satellite developed in China [1] .Due to the confined space of the satellite platform, there are high requirements for the layout of equipment space and mechanical indicators such as weight.The Ka channel synthesis multiplexer is a passive electronic equipment on board that consists of multiple channel filters, hybrid bridges with circulators, isolators, and waveguide interconnections [2][3] .This equipment plays a crucial role in the satellite transponder subsystem by synthesizing the output signals of converters with different conversion frequencies into one or two channels to be sent to the switching/backup network of the gateway station.
The conventional structural design scheme for the Ka channel synthesis multiplexer assembly is a double-layer tiled layout [4] , which has the advantage of low design difficulty and easy assembly.However, this scheme has drawbacks, including a large installation footprint area due to the tiling of each component and high manufacturing and processing costs due to the use of aluminum honeycomb panels.To meet the layout requirements and optimize the structural design, innovative ideas need to be developed.
Currently, research on the structural design of electronic equipment often focuses on studying lightweight, vibration, and overall layout optimization of key components, with fewer studies on the complete equipment structure [5][6] .This paper analyzes the conventional structural design scheme of the Ka channel synthesis multiplexer assembly of the satellite and proposes an innovative U-shaped crossfolding design scheme.This scheme solves the design challenges of compact size, lightweight, and high stiffness of the equipment.The feasibility and reasonableness of the U-shaped cross-folding design scheme for the Ka channel synthesis multiplexer assembly are verified through physical assembly, mechanical simulation analysis, and random vibration environment testing.

Design challenges
The structural design of the Ka-channel synthesized multiplexer assembly faces challenges in significantly reducing the equipment layout size while conforming to assembly requirements, simultaneously achieving lightweight design and high rigidity.Considering the overall requirements of the satellite's payload development, the design difficulties of the Ka-channel synthesized multiplexer assembly are as follows:  The installation footprint area must be no larger than 350 mm×200 mm, and the equipment weight should be ≤ 6.5 kg. The equipment should have good assembly processability, ensuring high processing efficiency of structural parts and low processing costs. The natural frequency of the equipment should be ≥ 140 Hz, which can be evaluated through satellite random vibration testing.To address these design challenges, this paper adopts the U-shaped cross-folding scheme.

3D layout design
The channel-synthesized multiplexer assembly consists of various components such as 6-channel filters, waveguide isolators, circulators, hybrid bridges, and waveguide converters (referring to Figure 1).If a tiled layout is used, the length dimension would exceed the design requirement of ≤ 350 mm, and therefore, an optimization of the layout is necessary to reduce the X-direction size.After analyzing the tiled layout, the design layout optimization involves using a curved waveguide to bend the multiplexer by 180° at the mixing bridge, resulting in a U-shaped layout (referring to Figure 2).This U-folding scheme significantly reduces the X-direction size of the device.The hybrid bridge is mounted perpendicularly to the channel filters, creating a 60 mm space between the front and rear layers of each 3-channel filter in the Y direction.
To further improve space utilization and reduce equipment layout space, the two multiplexers are cross-combined at the U-shaped opening created by folding.The folded and cross-combined components are skillfully assembled onto the one-piece frame in the middle, as shown in Figure 3.With this scheme, the footprint area is (290 mm×158 mm), which is smaller than the requirement of (350 mm×200 mm), and the weight of the equipment is 3.9 kg, which is less than the requirement of 6.5 kg, meeting the design requirements for equipment layout space and weight.
The multiplexer can be divided into two layers based on the mounting position of the channel filters，as shown in Figure 4.The outer channel filters are fixed on the bracket by using filter mounting lugs, while the inner channel filters are tapped at the waveguide flanges and secured on the bracket with screws.The mixing bridges on both sides are also fixed on the bracket by using mounting lugs.
During assembly, it is important to ensure that the inner and outer channel filters do not interfere with each other.This is achieved by adjusting the length of the straight waveguide section, allowing the inner and outer channel filters to be installed staggered.A debugging window is also reserved for the electrical performance tuning of the filters.Regarding the assembly process, one exemplary assembly sequence is introduced here, focusing on the fasteners between the curved waveguide and the waveguide isolator.Before assembly, the entire assembly is divided into three parts: filter assembly, curved waveguide assembly, and hybrid bridge assembly.To ensure space for screw mounting and facilitate assembly and disassembly, the parts are initially pulled out to one side, exposing the curved waveguide mounting part for fastener installation.Once the bent waveguide is secured, the single-channel multiplexer assembly is pushed back into its original position as a whole and fixed to the frame.
Assembly tolerances primarily accumulate in the X and Y directions.The X-direction assembly errors mainly arise from the hybrid bridge waveguide port spacing error, bracket mounting surface spacing error, and curved waveguide flange spacing error.To compensate for these processing and assembly errors, a theoretical 0.2 mm gap is reserved between the hybrid bridge and the curved waveguide, and adjustment shims are designed.
The Y-direction tolerance mainly originates from the straight waveguide length error, annualized dimension error, and waveguide isolator dimension error.To accommodate these tolerances, a 0.2 mm gap is reserved between the straight waveguide and the isolator, and adjustment shims are designed.The filter mounting lugs and bracket mounting holes are designed as long round holes.

Finite element model
 Unit selection: The main body structure is constructed by using a tetrahedral unit mesh, consisting of a total of 31, 578 model units. Material properties: The material employed is aluminum alloy 2A12, characterized by a density (ρ) of 2.8 g/cm 3 , an elastic modulus (E) of 71 GPa, a Poisson's ratio (ν) of 0.3, and a yield strength (σ s ) of 245 MPa. Constraint conditions: For the internal screw connections within the device, spot weld simulation is utilized, applying constraints to the 6 degrees of freedom of the mounting holes.

Simulation analysis and validation
The Ka-channel synthetic multiplexer assembly is installed in the north and south panels and bulkhead area of the communication module.To ensure that the equipment meets the environmental requirements, random vibration tests are conducted according to the test specifications provided by the satellite.These test conditions are listed in Table 1.The quasi-qualification testing ensures that equipment can withstand the required vibration loads during launch and operation.

Modal analysis.
Modal analysis is primarily used to determine the natural frequency and corresponding vibration mode of a structure.The results obtained from modal analysis are an essential indicator for verifying structural safety and reasonableness, and they serve as the basis for subsequent random vibration analysis [7] .The cumulative effective modal quality factor for modal analysis is typically 90% [8] .In the frequency range of 10 Hz~2, 000 Hz, the principal modes in each direction are intercepted.
The principal modes and vibration shapes of each order are shown in Figure 5.This information provides insight into the vibration characteristics of the multiplexer assembly and enables the design team to make informed decisions regarding necessary modifications to improve structural integrity and ensure optimal performance during launch and operation.The results of modal analysis effective mass are shown in Table 2.The results indicate that the first-order intrinsic frequency of the device is 217 Hz, which is greater than the minimum requirement of 140 Hz.This shows that the stiffness of the device meets the design specifications, and the structural design is strong enough to withstand the expected vibration loads during launch and operation.

Random vibration analysis.
According to the relevant provisions of the vibration test in the national military standard [9] , the equipment needs to be analyzed in each of the three mutually orthogonal axes.Considering typical engineering practices with small damping, and based on design experience, a damping coefficient of 0.03 is assumed.Along the X, Y, and Z directions of the equipment, the vibration conditions specified in Table 1 are applied.
The resulting random vibration acceleration and stress response cloud diagrams are shown in Figure 6.These diagrams provide a visual representation of the dynamic behavior and response of the multiplexer assembly under random vibration loads.They help in evaluating the structural integrity and identifying potential areas of concern that may need further design optimization or reinforcement to ensure that the equipment can withstand the vibration environment during launch and operation.The results of the random vibration simulation analysis reveal that the equipment experiences the highest acceleration response under Y-direction vibration excitation, with a value of 95 g.Currently, the response value at the monitoring point is 36.2g.On the other hand, the stress response of the equipment under Z-direction vibration excitation is the highest, with the maximum stress occurring in the equipment mounting holes, reaching a value of 51.9 MPa.This stress value is significantly lower than the yield limit of the aluminum alloy frame, which is 245 MPa.By calculating the safety margin using the following formulas, we find that the margin of safety (MS) is calculated to be 2.15, indicating that the strength of the equipment meets the safety margin requirements.The safety margin indicates that the equipment has sufficient structural strength and can withstand the applied vibration loads without compromising its integrity or performance.
where MS is the safety margin; σ s is the material yield strength limit; f is the safety factor, generally taken as 1.5; σ max is the maximum stress response of the structural member when subjected to an external load.

Comparison of test and simulation.
To verify the structural design and validate the results of the finite element simulation analysis, a random vibration environment test was conducted on the device.The sensor measurement points in the test were located at the same positions as the response monitoring points in the simulation analysis, as shown in Figure 7.The test results of the equipment in the Y and Z directions are provided in Table 3.These results provide valuable information on the acceleration response of the device under different vibration excitations.The measured data from the sensor during the random vibration test is compared with the data obtained from the simulation analysis.The comparison results are summarized in Table 3.Based on the comparison between the simulation analysis and test results, the following conclusions can be drawn: The relative error between the base frequency of the equipment obtained from the test and the base frequency predicted by the simulation analysis is 6.7%.This indicates a reasonably good agreement between the predicted and measured base frequencies, with a relatively small deviation.
The relative error between the root-mean-square acceleration response predicted by the simulation analysis and the measured root-mean-square acceleration response at the monitoring point is less than 20%.This verifies the correctness of the finite element model used in this paper.
These comparison results demonstrate that the simulation analysis accurately predicts the dynamic behavior and response of the device under random vibration loads.The small deviations between the simulation and test results confirm the reliability of the finite element model employed in the analysis.This validation process provides confidence in the accuracy of the simulation analysis and further validates the structural design of the device.

Conclusion
To address the challenges posed by footprint area, weight, fundamental frequency, and resistance to environmental adaptability in installing the satellite channel synthesizer, a U-shaped cross-fold design scheme was implemented.The structural design scheme underwent thorough verification through physical assembly, resistance simulation analysis, and random vibration testing.The results demonstrated that the scheme was not only reasonable and feasible but also surpassed expectations by meeting the requirements for equipment layout space and weight design.This innovative approach has garnered full recognition from experts in the field and has paved the way for new design concepts in future on-board electronic devices.Its potential applications in high-throughput satellites are vast.

Figure 5 .
Figure 5. Principal modes and vibration shapes of each order.

Figure 6 .
Figure 6.Random vibration acceleration and stress response

Figure 8
Figure8presents the results of the random vibration test response curve in the X direction.The test results indicate that the equipment exhibits a 1st order resonance peak frequency of 202.5 Hz in the X direction, which corresponds to the fundamental frequency of the equipment.The root-mean-square acceleration response measured by the sensor at the monitoring point is 36.6 g.The test results of the equipment in the Y and Z directions are provided in Table3.These results provide valuable information on the acceleration response of the device under different vibration excitations.

Figure 8 .
Figure 8.The response curve of the X-direction random vibration test.

Table 1 .
Random vibration test conditions.

Table 2 .
Modal analysis of effective mass.

Table 3 .
Comparison of simulation and test acceleration response.