Multiphysics to Investigate the Thermal and Mechanical Responses in Hard Disk Drive Components Due to the Reflow Soldering Process

Abstract

In hard disk drive (HDD) manufacturing, a reflow soldering process (RSP) implements heat generated by the welding tip to melt a solder ball for bonding the following essential HDD components: a flexible printed circuit (FPC) and a printed circuit cable (PCC). Since the mentioned components are tiny and comprise many thin material layers, an experiment to study thermal and mechanical responses is complex and not worth it. Therefore, a static state multiphysics consisting of thermal analysis (TA) and structural analysis (SA) was employed to investigate both responses. First, the experiment was established to mimic the RSP, measuring the temperature generated by the actual welding tip. Then, the measured temperature was defined as the boundary conditions with the pressing force (F) for the TA and SA based on the actual operating conditions. As expected, the TA results revealed the temperature distribution in the HDD components, which was consistent with the theory and results from previous work and confirmed this work’s credibility. Significantly, the SA reported severe total deformation (δ) in FPC’s top and bottom ends. The maximum δ was 0.72–0.88 mm for the F of 0–1 N. The stronger the F, the greater the δ. This research highlights that multiphysics can investigate both responses in HDD components as slight as 0.1–100 microns thick, which can be used to develop a high-efficacy RSP.

1. Introduction

Thailand was ranked 2nd in the world in terms of hard disk drive (HDD) manufacturing. Most of the Thai production is for export. In 2017–2021, Thailand had an average HDD export value of 6384 million USD per year (1 USD for 35 Baht), 1.39% of the Thailand export value [1,2]. Therefore, Thailand always focuses on developing technology for the hard disk drive manufacturing process to remain a world leader in HDD manufacturing.

The reflow soldering process (RSP) is used to assemble surface-mounted electronic components to printed circuit boards (PCBs). It involves the application of solder paste to the pads on the PCB, placing components onto the solder paste, heating the assembly to melt the solder, and forming a solid joint between the components and the PCB [3,4,5]. The RSP’s benefits include being easily integrated into the automated assembly line, increasing production speed, and reducing cost. It provides precise temperature control for consisting soldering results, reducing the likelihood of defects. It is suitable for mass production, enhancing productivity. In HDD manufacturing, the RSP connects a flexible printed circuit (FCP) to a printed circuit cable (PCC) using a solder ball to assemble a head stack assembly (HSA) [6,7]. Figure 1 shows the RSP: Figure 1a—a location in the HSA and Figure 1b—an enlarged picture focusing on the FPC and PCC. Each point on the FCP surface is called a connecting point, which connects the FPC and PCC. For this HSA, as an example, the connecting point is about 0.15 mm², with six points in a row. The points’ area and number depend on the HSA design, defined by HDD manufacturers. Since there are many connecting points with tiny sizes, and the FCP comprises many thin layers, HDD manufacturing in Thailand needs advanced technology to support and develop the RSP. One of the ways to increase efficacy and develop the RSP is to understand the thermal and mechanical responses that occur in the HDD components.

Multiphysics, one of the computer simulation methods, was employed to investigate the WT’s thermal and mechanical responses to research advanced RSP technology [7]. The simulation results were previously applied to design the WT with a higher efficacy in HDD manufacturing. However, a limitation of this work [7] is that neither investigated the thermal and mechanical responses in the FPC, a solder ball, and PCC; therefore, some defects may occur in products. Additionally, designing both components for the next-generation HDD still required a trial-and-error experiment, which was not cost-effective in terms of time and budget. This limitation is a problem that needs to be solved.

A conclusion from the literature review in [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] confirms that multiphysics suits this problem, since the RSP relates to the current, temperature, and material structure. For example, the current can be applied to WT to create a high temperature. Then, a high-temperature heat is transferred from the WT to the HDD components, FPC, solder ball, and PCC, causing structural deformation. Multiphysics consists of transient electric analysis (TEA) and structural analysis (SA) to investigate the thermal and mechanical responses, respectively.

For example, the transient TEA based on finite element analysis was employed to develop the RSP for HDD manufacturing [6,7], to develop thermoelectric devices for energy conversion and management [8,9,10,11], to study Joule’s heating and pulse direct current in metal lines for development in a complementary metal–oxide semiconductor (CMOS) circuit [12]. However, validating the simulation results is a major limitation of the transient TEA and a disadvantage. Some settings require temperature-dependent values obtained from complicated experiments that can adjust electric parameters in a transient state to obtain accurate and practical simulation results, wasting time and budget [6,7,13,14]. To avoid this limitation, another of the computer simulation methods, a thermal analysis in a static state, is suitable [15,16,17,18]. For example, it was employed to solve thermal problems in electronics and PCB cooling [15], reduce temperature variations in thermal management in battery packs [15], increase automobile piston efficiency [16], design an induction motor for a hydraulic pumping system [17], design and optimize a novel heatsink for electronic devices [18], and analyze ball grid arrays of a solder joint for the RSP [19]. The advantage of steady-state thermal analysis is that the experiment or theoretical calculation assigned for validating the simulation results is more straightforward than the transient TEA, since the simulation results of thermal analysis are independent of time and electricity, while those of the transient TEA are not.

Structural analysis, for example, uses computer simulation-based finite element analysis to determine the effects of loads on physical structures and their components [20,21]. This analysis ensures that structures can withstand the anticipated loads without failing.

Accordingly, this collaborative research between the authors and an HDD manufacturer aims to employ multiphysics, consisting of thermal analysis and structural analysis, to investigate thermal and mechanical responses in the RSP. First, the experiment was established to measure the temperature generated by the WT. Then, the measured results were defined as boundary conditions for thermal and structural analysis settings. Next, thermal analysis was used to investigate the thermal response between the HDD components: FPC, solder ball, and PCC. The thermal analysis results were compared with the theoretical results to validate the credibility. After that, the structural analysis was used to investigate the mechanical response of HDD components. Lastly, all the simulation results were analyzed to examine both responses to changes in some parameters.

The benefit of this research is that we used multiphysics without a complicated experimental setup. Measuring tools are commonly available in the marketplace with low prices, saving time and costs for HDD manufacturing. Importantly, multiphysics can investigate both responses in HDD components as slight as 0.1–100 microns thick, which no research has ever achieved before. The findings can be practically implemented, since the simulation setting is based on the actual operating conditions of the RSP from an HDD factory, which the authors have collaborated on for research.

2. Theoretical Background

This section explains the theoretical background involved in the RSP. It consists of the materials and RSP principle, the governing equations for 1D heat transfer, and multiphysics.

2.1. Materials and RSP Principle

Figure 2 shows materials in the RSP, simplified from Figure 1, as an example, by ignoring some irrelevant materials for ease of explanation. When the RSP operates, the WT, carrying the electric current, is pressed down with force onto the connecting point of the FPC. The heat and force will transferred from the WT to the head tip, generating a high temperature and pressure at the head tip. Then, the high temperature and pressure will be transferred from the head tip to the material layers of FPC and the solder ball lead, respectively. Lastly, the solder ball will heat up and melt, causing the FPC and PCC to bond together. Significantly, the FPC containing thin layers of stainless steel, polyimide, glue, and copper layers can deform due to heat and force. Improper heat and force may cause defects, leading to substandard products that must be prevented [6,7]. It is difficult to investigate thermal and mechanical responses using the experiment, since the FPC, solder ball, and PCC are small and thin; about 225 μm thick in micron size, for example. Therefore, thermal analysis and structural analysis were employed as multiphysics.

2.2. One-Dimensional Heat Transfer Equations

This section explains 1D heat transfer and governing equations, simple equations applied to validate the thermal analysis results.

By considering a steady state and a 1D heat transfer without a heat-generating source in materials, negligible radiation, and constant thermal conductivity, Fourier’s law of conduction obeys [22].

$$\dot{q}=-k{\displaystyle \frac{dT}{dx}}$$

(1)

where $\dot{q}$ is the heat flux (W/m²), k is the material’s conductivity (W/m·°C), and ${\displaystyle \frac{dT}{dx}}$ is the temperature gradient in x direction (°C/m).

In the case of $\dot{q}$ generated by the WT transferring to materials 1, 2, …, and 6, thicknesses are d₁, d₂, …, d₅, and d₆, and conductivities are k₁, k₂, …, k₅, and k₆, respectively. The 1D heat transfer and boundary conditions to mimic Figure 2 are defined in Figure 3. From Equation (1), it can be proved that $\dot{q}$ is a constant, and is expressed by [22].

$$\dot{q}={\dot{q}}_{12}={\dot{q}}_{23}={\dot{q}}_{34}={\dot{q}}_{45}={\dot{q}}_{56}={\dot{q}}_{67}$$

(2)

where ${\dot{q}}_{12}$, ${\dot{q}}_{23}$, ${\dot{q}}_{34}$, ${\dot{q}}_{45}$, ${\dot{q}}_{56}$, and ${\dot{q}}_{67}$ are the heat flux transferring from materials 1 to 2, 2 to 3, 3 to 4, and so on.

Equation (2) can written in an alternative form as:

$$\begin{array}{l}\dot{q}=k_1{\displaystyle \frac{\left(T_{01}-T_{12}\right)}{d_1}}=k_2{\displaystyle \frac{\left(T_{12}-T_{23}\right)}{d_2}}=k_3{\displaystyle \frac{\left(T_{23}-T_{34}\right)}{d_3}}\\ =k_4{\displaystyle \frac{\left(T_{34}-T_{45}\right)}{d_4}}=k_5{\displaystyle \frac{\left(T_{45}-T_{56}\right)}{d_5}}=k_6{\displaystyle \frac{\left(T_{56}-T_{67}\right)}{d_6}}\end{array}$$

(3)

where T₀₁ is the temperature generated by the WT and is also the temperature at the interface between material 0 (at the WT) and material 1 (stainless steel), T₁₂ is the temperature at the interface between materials 1 and 2, T₂₃ is at the interface between materials 2 and 3, T₃₄ is between materials 3 and 4, and so on.

Based on the boundary conditions in Figure 3 and Equation (3), the temperature gradient in the x direction (°C/m) is presented in Figure 3. It can be proved that [22]:

$$T_{67}=T_{01}+\left({\displaystyle \frac{d_1}{k_1}}+{\displaystyle \frac{d_2}{k_2}}+{\displaystyle \frac{d_3}{k_3}}+{\displaystyle \frac{d_4}{k_4}}+{\displaystyle \frac{d_5}{k_5}}+{\displaystyle \frac{d_6}{k_6}}\right)\dot{q}$$

(4)

The heat flux ($\dot{q}$) in Equations (2) and (4) will be used to validate the thermal analysis results of the RSP and confirm the credibility of multiphysics and research methodology, as discussed in Section 4.2.

2.3. Principle of Multiphysics

Multiphysics is a computer simulation that investigates materials’ thermal and mechanical responses due to thermal and force loads.

In a static state, thermal analysis in ANSYS software, based on the finite element method, is given by [7,23].

$$\left[K(T)\right]\left\{T\right\}=\left\{Q(T)\right\}$$

(5)

where T is the temperature, [K(T)] is the thermal conduction matrix, and {Q(T)} is the convection vector. The two latter are dependent on temperature.

Also, structural analysis based on the finite element method is expressed by [7,20].

$$\left[K\right]\left\{u\right\}=\left\{F\right\}$$

(6)

where [K] is the stiffness matrix, {u} is the nodal displacement vector, and {F} is the external load vector.

Solving Equation (5) reveals the temperature and heat flux for validation as a thermal response, which can be defined as boundary conditions for structural analysis. Solving Equation (6) yields total deformation (δ) as a mechanical response of HDD components focusing in this research.

3. Methodology

Figure 4 shows the methodology flowchart consisting of designing and inventing the WT, measurement of T, theoretical calculation, and thermal analysis. Significantly, yellow boxes present multiphysics, a key to success in this work. ANSYS software version 2021 was employed for multiphysics in this research.

3.1. Designing and Inventing the WT

Since the actual WTs used in the actual HDD manufacturing [6,7] have a complex shape, this work designed a novel WT with a simple shape for easy analysis to avoid a conflict of interest. Figure 5 shows the WT: Figure 5a—the designed model with rough dimensions and Figure 5b—the actual model. In Figure 5a, a small picture focuses on the head tip, consisting of twelve connecting points highlighted as red, with a dimension of 6.0 × 2.2 mm². The designed solid model for thermal analysis in Figure 5a was invented and implemented for the measurement T presented in Figure 5b. Notably, this design of WT is a simple model that is not employed in actual HDD manufacturing and is used explicitly for this research.

3.2. Measurement

Figure 6 shows the measurement setup in a laboratory: Figure 6a—an actual image and Figure 6b—a schematic image. This measurement setup was modified from the work in [6,7] to measure the temperature (T) at the head tip. The tools included the WT, thermal imaging camera, and computer with analysis software. The thermal imaging camera is an Optris-modeled Xi 410 LT. Optris’s specifications include, for example, 384 × 240-pixel detector resolution, a measured range of −20 to +900 °C, and an accuracy of ±2%, compatible with the analysis software. In the measurement process, first, an AC voltage of 0.6 V, a factory’s operating condition, was applied from a Uniflow, an AC generator for the RSP, to the WT, creating a high T at the head tip based on Joule’s heating effect [6,7]. Then, the Optris measured T at the head tip and recorded it in pixels. Next, the measured T results were transferred to a computer for processing with analysis software. Last, after completing the analysis, the computer formed a high-resolution thermal image, reporting T in all pixels and exporting a thermal image. The measurement setting in Figure 6 helped accurately measure the T in a tiny size, specifically established for this work, since a standard thermal camera, a handheld camera, cannot measure T accurately. The measured results of T will be discussed in Section 4.1, detailing the validation. In addition, the T results will be defined as boundary conditions for thermal analysis in Section 3.4.2.

3.3. Theoretical Calculation

As explained in Section 2.2, which outlines the 1D heat transfer equations, since the d, k, and T are known parameters collected from CAD models and boundary conditions in thermal analysis, solving Equations (2) and (4) yields the heat flux and T for comparison with the simulation results to validate the simulation results and ensure the credibility of the research methodology. The comparison results will be reported in Section 4.2, detailing the validation.

3.4. Multiphysics

This section explains the methodology used for multiphysics, covering the CAD model, a mesh model with mesh-independent analysis, the boundary conditions, and the material properties’ settings.

3.4.1. Models

To mimic the RSP, first, CAD models of related components, the WT, FPC, PCC, and solder ball, were created, as shown in Figure 7a. The solder balls are not shown here, since they are too small compared to other components. Then, the connecting points at an interface between the head tip and the FPC were stamped as imprints. The imprints help us define the boundary conditions here. Figure 7b shows HDD components with imprints marked as red at the top surface of the FPC. The FPC and PCC are new design components for the next HDD generation but are not yet available for manufacturing.

Figure 8 reveals the HDD components without the WT in detail, extending from Figure 2, Figure 3 and Figure 7, and the rough dimensions: Figure 8a—a disassembled model and Figure 8b—an enlarged picture, with a side view of an assembled model. Each color stands for each material type. The copper layer is a circuit embedded inside the glue layer, in Figure 8b. In Figure 8b, the value of 41 µm includes the stainless steel, polyimide, copper, and glue layers. The 90 µm and 100 µm values are for the solder ball and PCC layers, respectively. This figure also confirms that the RSP components are tiny and have complex shapes; therefore, setting up an experiment to investigate thermal and mechanical responses is difficult. Multiphysics was first employed to investigate both responses in this research, instead of using a trial-and-error method like the factory previously used. In this work, we focus on the thermal and mechanical responses of HDD components consisting of material layers shown in Figure 8, ignoring the WT.

Figure 9 shows the mesh model created from the CAD model in Figure 8. Since the model has symmetry, the mesh model was created in a half-model. After completing the mesh-independent analysis [24,25], the suitable mesh model is a hexahedral model, including 1,287,283 elements and 6,056,937 nodes with an element size of around 2–10 µm, depending on material thicknesses. The small elements are for the thinner thickness, and the larger ones are for the thicker thickness.

3.4.2. Boundary Conditions and Material Property Settings

Figure 10 depicts the boundary conditions defined in the model: Figure 10a—top view and Figure 10b—bottom view. The thermal analysis includes a convection of 10⁻¹² W/mm², which defined all the surface areas marked as yellow, a temperature of 350 °C at the back, marked as orange, and a temperature of T₀₁ at the connecting points, marked as red. Particularly, T₀₁ is the temperature collected from the measurement mentioned in Section 3.2, which is the same temperature as in Figure 3, and 350 °C is the controlled temperature for manufacturing.

The structural analysis includes force due to a pressing force from the WT, marked red, and a fixed support, marked orange. In addition, T₀₁ and F are parameters that vary when investigating the thermal and mechanical responses, which are detailed in Section 4.3.

Table 1. Material properties for thermal analysis.

Material	ρ (×10−6 Kg/mm3)	cp (×105 mJ/kg·°C)	k (W/mm·°C)	d (µm)	ν	E (MPa)	h (W/mm2 ·°C)
Stainless steel	8.02	4.80	0.0151	15	0.32	1.93 × 105	10−12
Polyimide	1.40	23.00	0.0003	10	0.30	6190
Copper alloy	8.30	3.85	0.4010	0.1	0.34	1.1 × 105
Glue (Epoxy)	1.19	15.79	0.0003	14	3000	3000
Solder (lead)	8.90	2.10	0.4948	90	14,870	14,870
FCC (FR−4)	1.90	11.00	0.0004	100	24,600	11.03 × 105

reports the material properties defined in Figure 8 for thermal and structural analysis, using data from references [6,7] and vendors.

The simulation results of the thermal analysis in Section 3.4 were compared with the experimental results in Section 3.2 and theoretical results in Section 3.3. The multiphysics process was revised until the thermal and structural analysis results were accurate. If the multiphysics results did not agree with the experimental or theoretical results, the multiphysics process was repeated to modify CAD and mesh models or redefine boundary conditions and material properties to ensure that the multiphysics results were credible.

4. Results and Discussion

This section includes the measured temperature results at the head tip, the validation of thermal analysis results, and the investigation of thermal and mechanical responses in HDD components.

4.1. Measured Temperature Results at the Head Tip

This section validates the temperature results measured at the head tip mentioned in Section 3.2. Figure 11 reports the temperature at the head tip after processing using the analysis software. The left picture shows an overview of the temperature distribution heatmap, while the right picture shows an enlarged image of a specific area, in which the temperature in each pixel was displayed as numerical results in detail. The measured results revealed that the temperature at the connecting points was uneven. In particular, by comparing Figure 11 with Figure 2 and Figure 5a, the highest temperature was generated at the connecting points of the head tip, corresponding to the design concept. Outside the connecting points, the temperature was lower, supporting the report in [6,7], as expected. Accordingly, the measurement results are credible since the temperature distribution of measurement relied on the design concept and was supported by the previous work [6,7].

However, the temperatures in Figure 11 are unsuitable for the boundary condition settings in the thermal analysis, since the temperature greatly varies at each point. It was found that the connecting points marked in red had maximum and minimum temperatures of 521.3 °C and 319.8 °C, respectively, which was highly contrasted with the other areas, and an average temperature of 410.0 °C with a standard deviation (SD) of 16.7 °C. The temperature of 410.0 °C was used to set the boundary conditions as T₀₁ in Figure 10, for easy simulation and analysis. In addition, 410.0 °C is the same temperature generated by the welding tips reported in [6,7]. Even if the welding tip in this work and the work in [6,7] have a different design, they have the same temperature, confirming the accuracy of the measured results. Accordingly, all reports in this section indicate that the measurement set in Section 3.2 can effectively monitor the head tip’s temperature, and T₀₁ is a proper temperature to be defined in the boundary conditions for multiphysics.

4.2. Validation of Multiphysics Results

Using the T₀₁ of 410.0 °C and F of 0.5 N, the actual operating conditions, as boundary conditions, the temperature distribution calculated by thermal analysis was shown in Figure 12 in an isometric view, while Figure 13 shows the same results in a side view of a focused plane of Figure 12.

In a qualitative validation, by considering Figure 8, Figure 12 and Figure 13, the highest temperature, 410.0 °C, was found at the top of the stainless steel layer, while the lowest temperature, 350.0 °C, was found at the bottom of the PCC layer, decreasing from top to bottom, consistent with theory described in Figure 2 and Figure 3, as expected. Moreover, in Figure 13, the simulation results also report that the heat flux transfer into (${\dot{q}}_{in}$) and out (${\dot{q}}_{out}$) of the HDD components was 0.193 W/mm² and −0.193 W/mm², respectively. The negative sign confirms that the ${\dot{q}}_{out}$ has an opposite direction to the ${\dot{q}}_{in}$. The ${\dot{q}}_{in}$ and ${\dot{q}}_{out}$ were equal, so they have a thermal equilibrium, obeying the heat transfer principle, as also expected [22]. Because the melting point of the solder ball is 350–400 °C [6,7], the temperature in the solder ball layer was about 382–390 °C, which was suitable to melt it, as intended in the design concept.

In a quantitative validation, by considering Figure 3, Figure 8 and Figure 13, using the known parameters in Table 1, solving 1D heat transfer in Equation (2) with the area average of temperature for each layer, the theory found that $\dot{q}$ was 0.189 W/mm², which is nearly the same as ${\dot{q}}_{in}$ and ${\dot{q}}_{out}$ of 0.193 W/mm², calculated by the thermal analysis with a difference of 2.07%. Similarly, solving Equation (4) found that ${\dot{q}}_{out}$ was −0.179 W/mm², which is 7.25% different from ${\dot{q}}_{out}$ of −0.193 W/mm² calculated by the thermal analysis. Notably, ${\dot{q}}_{out}$ and ${\dot{q}}_{in}$ in Figure 13 are ${\dot{q}}_{67}$ and $\dot{q}$ in Figure 3, respectively. The differences may result from the theory being based on 1D calculation, but the thermal analysis is based on the 3D depiction. Moreover, the material properties from Table 1 are temperature-independent. If multiphysics employed temperature-dependent properties, the multiphysics results credibility would be enhanced. Since the difference mentioned is slight and employing 410 °C is not too high a temperature, using the temperature-independent values in Table 1 did not alter the conclusion of the research. The comparison between both heat fluxes to support the quantitative analysis, from theory and simulation, is shown in

Table 2. The comparison of heat flux between theory and thermal simulation.

Heat Flux	Theory (W/mm2)	Thermal Analysis (W/mm2)	Difference
${\dot{q}}_{out}$	−0.179	−0.193	7.25%
$\dot{q}$	0.189	0.193	2.07%

. Since the thermal analysis setting based on 3D calculation is closer to the actual RSP than the theory based on 1D calculation, we believe that the thermal analysis results reported in this article are more reliable than the theoretical results.

Using the thermal analysis results as loads, Figure 14 reveals the total deformation (δ) in HDD components as a disassembled model calculated by structural analysis for a standard operating condition, T₀₁ of 410.0 °C and F of 0.5 N. The shapes of HDD components have been overscaled by δ for ease of analysis, but the δ reported in a color scale is the true value from the structural analysis results. The simulation showed that deformation occurred more at the edge and mostly at the corners, top, and bottom ends of the HDD components, bending upward, consistent with the actual results preliminary investigated in the RSP. The highest δ was 0.80 mm in the stainless steel layer, since it was the first layer pressed by the WT. The deeper the layer, the smaller the value of δ. This confirms a qualitative validation, as expected.

As discussed in Figure 12, Figure 13 and Figure 14, and Table 2, all values reasonably confirm that the multiphysics results and research methodology are credible and suitable for investigating thermal and mechanical responses in HDD components.

4.3. Thermal and Mechanical Responses in HDD Components

All multiphysics settings remained the same, but T₀₁ and F were changed to investigate the thermal and mechanical responses in the HDD components.

4.3.1. Thermal Response

An applied heat generated by the WT causes this response. Figure 15 reveals the temperature distribution in the HDD component layers for T₀₁ of 410.0 °C and F of 0.5 N. The model in Figure 15 is a disassembled model of Figure 12 for investigating the thermal response in each layer. As expected, the temperature lowers with depth, from the top layer to the bottom layer. As expected, the highest T of 410 °C was found in the stainless steel layer, and the lowest T of 350 °C was found in the PCC layer, since both T are boundary conditions. Interestingly, the T in the solder ball layer was around 386–398 °C, sufficient to melt the solder ball, and joining FPC with PCC, as intended, since the melting point of the solder ball is 350–400 °C [6,7]. The thermal analysis helps understand the T distribution in each thin layer, especially in the copper layer with an electrical circuit, which is helpful for designing and developing the RSP.

Focusing on the copper layer, Figure 16 reports the temperature distribution for T₀₁ of 410.0 °C and F of 0.5 N. It was found that T in this layer was in a range of 386–402 °C. The higher T was found in the electrical circuit near the layer’s edge. In contrast, the lower T was found in the connecting points around the center. In this work, the factory prefers that the T in this layer not exceed 430.0 °C. Beyond this T, the mechanical and electrical properties of copper may degrade. This implies that a T which is too high causes materials to degrade, but a T which is too low leads to an solder ball that does not melt. For other factories, the T of 430.0 °C required for the copper layer and 350–400 °C required for the solder ball layer may differ from this work, depending on their standard. Again, the thermal response results in Figure 15 and Figure 16 provide helpful information to the factory for designing high-performance HDD components, especially an electrical circuit.

4.3.2. Mechanical Response

The coupling of thermal and force loads causes this response. T₀₁ was fixed as a constant at 410.0 °C, while F was changed from 0 N to 0.25 N, 0.5N, 0.75 N, and 1.0 N to investigate the δ. Figure 17 shows the δ in disassembled model of HDD components for T₀₁ of 410.0 °C and F of 1.0 N as an example result. The simulation results indicate the δ increase with increasing F, as expected. The HDD components were bent upward at the top and bottom ends. Comparing between Figure 14 and Figure 17, the shape of δ was nearly identical. However, the maximum total deformation (δ_max) increased from 0.80 mm in Figure 14 to 0.84 mm in Figure 17, about a 5.0% increment. Significantly, δ_max still remained at the corners, top, and bottom ends of HDD components. Other δ_max for varying T₀₁ and F were reported in the heatmap result at the end of this section.

The copper layer was considered, since it has an electrical circuit. Hence, its δ may affect the HSA performance. Figure 18 reveals the δ in the copper layer for F of Figure 18a—0.5 N and Figure 18b—1.0 N. It was found that the maximum total deformations (δ_max) were 0.205 mm and 0.243 mm for the F of 0.5 N and 1.0 N, respectively. The δ_max increased an increasing in F, as expected. The high δ was found in the marked area; therefore, this may make this area likely to have defects during manufacturing. Figure 17 and Figure 18 are examples of using structural analysis to predict areas in HDD components at risk of defects. The factory can use these findings to design HDD components to reduce the risk of defects.

Figure 19 reports the heatmap results of the δ_max for varying T₀₁ and F, 20 cases simulated by multiphysics, extrapolating from Figure 17. As expected, the stronger the applied force, the greater the total deformation, and the higher the applied temperature, the larger the total deformation. All cases showed a similar trend in δ, as depicted in Figure 17. The δ_max was 0.88 mm at the stainless steel layer when applying an F of 1.0 N and a T₀₁ of 430 °C. In addition, it was 0.72 mm for applying a T₀₁ of 400 °C without force. The heatmap helps to determine the proper operating conditions for the RSP.

5. Conclusions

This article proposes multiphysics to investigate thermal and mechanical responses in tiny, thin HDD components manufactured in the RSP. The multiphysics consists of thermal analysis and structural analysis for thermal and mechanical responses, respectively. The HDD components include the WT, FPC, PCC, and solder ball. The FPC comprises thin layers of stainless steel, polyimide, glue, and copper layers, about 41 μm thick, while the solder ball and PCC layers are 90 μm and 100 μm thick, respectively. First, the measurement was established to measure the temperature at the WT based on the actual operating conditions of the factory. The measured results revealed that the highest temperature was about 410.0 °C in the connecting points of the WT, as intended for a design concept of the WT. Next, a temperature of 410.0 °C and a force of 0.5 N were employed as the operating conditions in the multiphysics boundary conditions. The multiphysics revealed the heat flux ($\dot{q}$), temperature (T), and total deformation (δ) in HDD components. Then, the heat fluxes in and out of the HDD components were compared with the 1D heat transfer principle; a theory. The comparison confirmed that multiphysics and the research methodology are credible, since both heat fluxes from multiphysics and theory are consistent. Significantly, the higher total deformation was found near the edge of the HDD components, and the inner area had lower values. The highest total deformation was in the stainless steel layer. The deeper the layer, the lower the total deformation and the equivalent stress. Lastly, multiphysics investigated both responses for varying temperatures from 400 to 430 °C and force from 0 to 1 N, applied by the WT as parameters in 20 cases. The multiphysics results reported the maximum of δ for all cases. All indicate that multiphysics is a powerful tool for investigating thermal and mechanical responses in thin, tiny HDD components, which may not be suitable or worthwhile for measurement. The findings were applied to improve the RSP and HDDs for higher efficiency.