Deploying time investigation of automotive active hood lift mechanism with different design parameters of hinge part

Abstract

This article investigates the change in deploying time of an active hood lift mechanism of a passenger vehicle activated by a gunpowder actuator. Especially, in this work, the deploying time is investigated by changing the principal design parameters of the hinge part of the hood mechanism. After briefly introducing the working principle of the active hood lift mechanism operated by the gunpowder actuator, the governing dynamic equations of the active hood lift mechanism are formulated for deploying motion. Subsequently, using the governing equations of motion, the response time for deploying the hood lift mechanism is investigated by changing several geometric locations such as the location of actuator. Then, a comparison is made of the total response time to completely deploy the hood lift mechanism with the existing conventional hood lift mechanism and the proposed active hood lift mechanism. In addition, the workable driving speed of the proposed active hood lift mechanism is compared with the conventional one by changing the powder volume of the actuator.

Introduction

Because of the increasing awareness of pedestrian safety and strengthening the related regulations, certain mechanisms to reduce pedestrian injuries and prevent accidents have been greatly developing in vehicle systems.^1–5 One of the advanced mechanisms to achieve this goal is to use an active hood lift mechanism (AHLM), which lifts the hood of an automobile when the vehicle collides with the pedestrian.^6–10 The main role of the AHLM is to absorb the shock that would normally be transmitted to the pedestrian, like an airbag system in automobiles for the drivers. In other words, this mechanism makes the available deformation space of the hood at internal room by raising the hood for protecting pedestrian from colliding with hard structures such as the engine. In particular, this mechanism greatly reduces an injury of the pedestrian’s head, which causes the majority of fatalities. ¹¹ It has been reported that when the AHLM is applied in a head impact test in vehicle driving speed of 40 km/h, the head impact performance criterion (HPC), which represents the injury value of the head, can be reduced by a maximum of 90%.^6,12 Furthermore, it is assessed mathematically that the pedestrian lives of maximal 80% could be saved by the AHLM. ¹³ Recently, the latch part located at the front of the hood has also been considered to be important to achieve better performance, especially for the child pedestrian that collides with front area of hood. In the operation of the AHLM, the most important factor is the response time after the first collision to obtain minimum injury. Because a sufficient operational speed has not yet been achieved, the operation cannot be completed before colliding with the pedestrian’s head. Thus, a slow response time may cause a terrible impulse, including the kinetic energy of the hood, to be directly applied to the pedestrian. If the response (or deploying) time is reduced using a high operational speed, the AHLM can be operated even if the vehicle is driven at a higher speed.

More recently, a new AHLM activated by gunpowder has been introduced. It has been demonstrated that it could be operated at a vehicle speed of 60 km/h; in contrast, the conventional AHLM normally operates at less than 40 km/h.^14,15 When the driving speed is 40 km/h, the necessary response time of the AHLM should be less than 60 ms from the worst case for protecting the child pedestrian.^14,15 It is generally known that the sensing and processing time of an electronic control unit (ECU) is 30 ms, and the necessary response time of the conventional mechanism should be less than 30 ms in vehicle speed of 40 km/h. ¹⁶ However, when the driving speed is 60 km/h, the time from the first collision of legs to collision of the head should be less than 40 ms, and thus, the necessary response time of the AHLM should be sharply decreased to less than 10 ms. It is also known that the operating method using a gunpowder actuator has the best performance for reducing the response time of the AHLM. However, in order to enhance the deploying motion performance, a parametric study of the geometrical dimensions of the AHLM should be undertaken because many design factors directly affect the response time. Because of the potential variation in the explosive of the gunpowder actuator, the collision may occur before the operation in the worst case. The safety of mechanism should be increased maximally by changing the principal design parameters to reduce the response time. In addition, as mentioned, it is very important to study the design parameters of AHLM to reduce the response time in relation to fatal pedestrian accidents because the AHLM can protect pedestrians at a broader range of vehicle speeds by reducing the response time. Today, there is a sharp increase in the number of fatal accidents when the driving speed increases.^17,18 It should be noted that lifting the hood higher in a shorter time can provide some benefits by absorbing the impact energy of the pedestrian. In other words, a pedestrian is protected more safely from the hard structure beneath the hood when the hood is lifted higher through the response time reduction. Recently, the authors studied the deploying time of the hood lift by considering latch part.²⁰ However, despite the significance of the response time to deploy the hinge or latch part, to the best of the authors’ knowledge, a study on this issue is considerably rare.

The main technical contribution of this work is to investigate geometrical dimensions of the hinge part of the AHLM and hence identify the principal design parameters which can significantly reduce the deploying (or response) time in a collision with a child pedestrian. In order to achieve this goal, a mathematical model of the AHLM is first formulated for each deploying motion. In this formulation, the dominant design factors of the hinge part that are sensitive to the performance index are defined in the governing equations of motion. In the design process, the structural constraint conditions of the mechanism, such as the limited space, are defined in detail. Because the response time of the mechanism is an important factor for the system safety, the kinematic structure of the AHLM is newly designed to decrease the response time under the imposed constraint conditions. A comparison between the proposed AHLM and the conventional one is made in terms of the deploying time and deformation. It is shown that the newly designed AHLM can provide much faster deploying time and hence smaller deformation at several vehicle speeds and gunpowder volumes.

Working principle of AHLM

The photographs of the real operation of a passenger vehicle equipped with an AHLM are shown in Figure 1. The vehicle’s hood is raised immediately based on the sensor signal when it collides with an adult legform, as shown in Figure 1(b). The system raises both the front and rear of the hood to reduce the pedestrian impact using the AHLM installed at the latch and hinges of the hood. Two hinge parts of the AHLM deployed by the gunpowder actuator consist of several elements, as shown in Figure 2(a). It consists of several components named as bracket release, plate, and pole. Point A indicates a rotational joint that links bracket release and plate, named joint A. Point B indicates a rotational joint that links plate and car body, named joint B. It is noted that joint B is fixed to car body. Point C indicates a rotational joint that links bracket release and pole, named joint C. Point D indicates a rotational joint that links pole and hood, named joint D. It is seen that the vehicle hood can be raised by actuating the rotational motion of the components. When the pedestrian’s leg collides with the bumper of the automobile, the actuator is exploded based on the sensor signal. The actuator deploys upward when exploding, and bracket release is rotated in counterclockwise with causing the rotation of plate in counterclockwise through the rotational joint B. At the same time, pole contacts bracket release and rotates clockwise with causing the rotation of plate through the rotational joint C. And rotations of plate and pole cause the hood to lift through joint D. Figure 2(b) shows the final state of the hinge mechanism when the operation is completed. Therefore, the raised hood absorbs the impact energy of the pedestrian’s head before it makes contact with the engine.

Figure 1.

Operation photographs of vehicle equipped with AHLM (a) before and (b) after actuation.

Figure 2.

Schematic configuration of hinge part of AHLM (a) before and (b) after actuation.

In order to make it easier to understand the working principle, the operation sequence of the performance evaluation test of a conventional AHLM is shown in Figure 3. The white triangle indicates lifted height of the hood while the black triangle indicates the original state. In this test, the system lifts the hood by 50 mm when the operation is completed, which takes about 10 ms after the actuator starts the operation. The actuator is operated by a micro-gas generator (MGG) that quickly generates a large quantity of gas from the gunpowder. This system uses an MGG that produces a pressure of 65 MPa in a 10-cm³ volume when time passes 10 ms after the gunpowder is exploded.

Figure 3.

Sequence of photographs of performance evaluation test.

Dynamic equations

The analytically derived governing equations of motion for the deployment of the AHLM are used to determine the operating speed and response time. The material properties used in this work are presented in Table 1. I₁, I₂, and I₃ are the inertia moment of bracket release, the components that are rotated with plate, and pole, respectively. $\mu$ is the coefficient of friction. $m_{\mathrm{h}}$ is the mass of the hood that is lifted at the total system. m₁ is the mass of bracket release. m₃ is the mass of pole. The actuator force that is transmitted to bracket release is set as F₁ in this work. The friction force between actuator and bracket release is set as F_f1. The force transmitted to plate by bracket release through joint A in rotational direction of plate is set as F_2n. The force transmitted to pole by bracket release is set as F₃. The friction force between bracket release and pole is set as F_f3. The force transmitted to plate by pole through joint C in rotational direction of plate is set as F_4n. The force transmitted to hood by pole through joint D in rotational direction of pole is set as F_5n. And a rotational angle of bracket release is set by ${\theta }_1$ , a rotational angle of plate is set by ${\theta }_2$ , and a rotational angle of pole is set by ${\theta }_3$ , respectively. The value of F₁ depends on the deployed distance of the actuator and an internal volume change due to this deployed distance. As previously mentioned, the actuator force comes from an internal pressure change by the MGG. Figure 4(a) shows the pressure change in 65-MPa MGG in a 10-cm³ volume, and Figure 4(b) shows the internal pressure change in the actuator, in which the initial internal volume of the actuator (660 mm³) is applied. On the other hand, Figure 5 shows the actuator force with no volume change, which is represented by multiplying a cross-sectional area of the actuator (38.5 mm²) by its internal pressure change with a fixed initial volume. Consequently, the real actuator force F₁ can be solved using the actuator force with no volume change and the volume change in the actuator over time. The volume change in the actuator is presented by multiplying its cross-sectional area and the deployed distance by the time that is represented by R₁, R₂, ${\theta }_1$ , ${\theta }_2$ , and k as shown in Figure 6. Here, R₁ and R₂ indicate locations of actuator and bracket release, and those are defined in the next step as “parameter distances.” The thick dotted line is the deployed distance of actuator, and the value of distance is set by x. And k is an angle between deploying direction of actuator and horizontal direction. Thus, the real transmitted force, changed internal volume of the actuator, and the deployed distance of actuator are, respectively, defined as follows, respectively

$$F_{\mathrm{Real}}=\frac{F_{\mathrm{Actuator}}{V}_{\mathrm{ai}}}{V_{\mathrm{aj}}}$$

(1)

$$V_{\mathrm{aj}}=V_{\mathrm{ai}}+\mathrm{Ax}$$

(2)

$$x=\left(\frac{{\mathrm{R}}_2\sin ({\theta }_2(t))+({\mathrm{R}}_1+{\mathrm{R}}_2(1-\cos ({\theta }_2(t))))\tan ({\theta }_1(t)+{\theta }_2(t))}{\cos (k)(\tan (k)-\tan ({\theta }_1(t)+{\theta }_2(t)))}\right)$$

(3)

Table 1.

Material properties of AHLM.

I 1	I 2	I 3	µ	m h	m 1	m 3
1.6 × 10−4 kg m2	3.9 × 10−3 kg m2	3.7 × 10−4 kg m2	0.3	16.5 kg	0.1 kg	0.12 kg

Figure 4.

Pressure change by MGGs with different volumes: (a) pressure change in 35-MPa MGG with 10-cm³ volume and (b) internal pressure change in actuator with initial volume of 600 mm³.

Figure 5.

Actuator force without volume change.

Figure 6.

Schematic diagram of deployed distance of actuator.

In the above, F_Real is the real transmitted force, V_ai is the initial internal volume of actuator, V_aj is the changed internal volume of actuator, A is the cross-sectional area of the actuator (38.5 mm²), R₁ is 17 mm, and R₂ is 41 mm. k is 75°.

Figure 7 shows a free body diagram for solving the equilibrium equation of the force. Figure 7(a) presents a free body diagram showing the forces of bracket release and Figure 7(b) presents a free body diagram showing the friction force of bracket release. F_1x and F_1y are the force transmitted to bracket release by the actuator in horizontal and vertical directions, respectively. F_2x and F_2y are the force transmitted to plate by bracket release through joint A in the horizontal and vertical directions, respectively. F_3x and F_3y are the force transmitted to pole by bracket release in the horizontal and vertical directions, respectively. F_f1x and F_f1y are the friction force between the actuator and bracket release in the horizontal and vertical directions, respectively. F_f3x and F_f3y are the friction force between bracket release and pole in the horizontal and vertical directions, respectively. R_m1 is the distance from the rotation center of bracket release to the center of mass of bracket release, and the value of this distance is 20 mm. ${\theta }_{\mathrm{m}1}$ is the angle between the line from the rotation center of bracket release to the center of mass and horizontal line. Based on these free body diagrams, the equilibrium equation of force of bracket release is derived, as follows

$$\begin{array}{c}-{\mathrm{R}}_{\mathrm{m}1}{({\stackrel{·}{\theta }}_1(t))}^2{m}_1\hfill \\ =(-F_{1\mathrm{x}}(t)+F_{2\mathrm{x}}(t)-F_{3\mathrm{x}}(t)+F_{\mathrm{f}1\mathrm{x}}(t)+F_{\mathrm{f}3\mathrm{x}}(t))\cos ({\theta }_{\mathrm{m}1}(t))\hfill \\ +(F_{1\mathrm{y}}(t)-F_{2\mathrm{y}}(t)-F_{3\mathrm{y}}(t)+F_{\mathrm{f}1\mathrm{y}}(t)-F_{\mathrm{f}3\mathrm{y}}(t))\sin ({\theta }_{\mathrm{m}1}(t))\hfill \end{array}$$

(4)

$$\begin{array}{c}{\mathrm{R}}_{\mathrm{m}1}{\stackrel{··}{\theta }}_1(t)m_1\hfill \\ =(-F_{1\mathrm{x}}(t)+F_{2\mathrm{x}}(t)-F_{3\mathrm{x}}(t)+F_{\mathrm{f}1\mathrm{x}}(t)+F_{\mathrm{f}3\mathrm{x}}(t))\sin ({\theta }_{\mathrm{m}1}(t))\hfill \\ +(F_{1\mathrm{y}}(t)-F_{2\mathrm{y}}(t)-F_{3\mathrm{y}}(t)+F_{\mathrm{f}1\mathrm{y}}(t)-F_{\mathrm{f}3\mathrm{y}}(t))\cos ({\theta }_{\mathrm{m}1}(t))\hfill \end{array}$$

(5)

$${\theta }_{\mathrm{m}1}(t)=2\circ +{\theta }_1(t)+{\theta }_2(t)$$

(6)

Figure 7.

Free body diagram for solving the equilibrium equation of the force: (a) free body diagram showing the forces of bracket release, (b) free body diagram showing the friction force of bracket release, (c) free body diagram showing the forces of pole, and (d) free body diagram showing the friction force of pole.

Figure 7(c) presents a free body diagram showing the forces of pole and Figure 7(d) presents a free body diagram showing the friction force of pole. Similarly, equilibrium equation for pole is derived, as follows

$$\begin{array}{c}{\mathrm{R}}_{\mathrm{m}3}{({\stackrel{·}{\theta }}_3(t))}^2{m}_3\hfill \\ =-(F_{3\mathrm{x}}(t)-F_{4\mathrm{x}}(t)-F_{5\mathrm{x}}(t)-F_{\mathrm{f}3\mathrm{x}}(t))\cos ({\theta }_{\mathrm{m}3}(t))\hfill \\ +(F_{3\mathrm{x}}(t)-F_{4\mathrm{x}}(t)-F_{5\mathrm{x}}(t)+F_{\mathrm{f}3\mathrm{x}}(t))\sin ({\theta }_{\mathrm{m}3}(t))\hfill \end{array}$$

(7)

$$\begin{array}{c}{\mathrm{R}}_{\mathrm{m}3}{\stackrel{··}{\theta }}_3(t)m_3\hfill \\ =(F_{3\mathrm{x}}(t)-F_{4\mathrm{x}}(t)-F_{5\mathrm{x}}(t)-F_{\mathrm{f}3\mathrm{x}}(t))\cos ({\theta }_{\mathrm{m}3}(t))\hfill \\ +(F_{3\mathrm{x}}(t)-F_{4\mathrm{x}}(t)-F_{5\mathrm{x}}(t)+F_{\mathrm{f}3\mathrm{x}}(t))\sin ({\theta }_{\mathrm{m}3}(t))\hfill \end{array}$$

(8)

$${\theta }_{\mathrm{m}3}(t)=40\circ -{\theta }_2(t)+{\theta }_3(t)$$

(9)

F_4x and F_4y are the force transmitted to plate by pole through joint C in horizontal and vertical directions, respectively. F_5x and F_5y are the force transmitted to hood by pole through joint D in the horizontal and vertical directions, respectively. R_m3 is the distance from the rotation center of pole to the center of mass of pole, and the value of this distance is 52.5 mm. ${\theta }_{\mathrm{m}3}$ is the angle between the line from the rotation center of pole to the center of mass of pole and horizontal line. Because F₁ and F₃ are exerted in only the vertical direction on the contact surface, F_1x, F_1y, F_3x, and F_3y can be presented mathematically by F₁ and F₃ through the location of the contact surface. Also, F_f1x, F_f1y, F_f3x, and F_f3y can be presented mathematically by F₁ and F₃. Figure 8 shows relations of those forces, and those are mathematically given as follows

$$F_{1\mathrm{x}}(t)=F_1(t)\cos (75\circ )$$

(10)

$$F_{1\mathrm{y}}(t)=F_1(t)\sin (75\circ )$$

(11)

$$F_{3\mathrm{x}}(t)=F_3(t)\cos ({\theta }_{\mathrm{i}1}(t))$$

(12)

$$F_{3\mathrm{y}}(t)=F_3(t)\sin ({\theta }_{\mathrm{i}1}(t))$$

(13)

$$F_{\mathrm{f}1\mathrm{x}}(t)=\mu F_1(t)\sin (75\circ )$$

(14)

$$F_{\mathrm{f}1\mathrm{y}}(t)=\mu F_1(t)\cos (75\circ )$$

(15)

$$F_{\mathrm{f}3\mathrm{x}}(t)=\mu F_3(t)\sin ({\theta }_{\mathrm{i}1}(t))$$

(16)

$$F_{\mathrm{f}3\mathrm{x}}(t)=\mu F_3(t)\cos ({\theta }_{\mathrm{i}1}(t))$$

(17)

$${\theta }_{\mathrm{i}1}(t)=75\circ +{\theta }_1(t)+{\theta }_2(t)+\beta (t)$$

(18)

Here, $\beta$ is the rotated angle of the vertical line on the contact surface between bracket release and pole over the shift of the contact point. Also, because the components are linked, an acceleration of joint D is related to an angular acceleration of ${\theta }_2$ and ${\theta }_3$ . That is, F_5x and F_5y can be presented mathematically by ${\theta }_2$ and ${\theta }_3$ .

Figure 8.

Relation of contact forces and forces in vertical and horizontal directions: (a) relation of F₁ and F_1x, F_1y; (b) relation of F₃ and F_3x, F_3y; (c) relation of F_f1 and F_f1x, F_f1y; and (d) relation of F₃ and F_f3x, F_f3y.

Figure 9 shows the relations of those parameters, and those are mathematically given as follows

$$\frac{F_{5\mathrm{x}}(t)}{m_{\mathrm{x}}}={\mathrm{R}}_{51}{\stackrel{··}{\theta }}_3(t)\sin ({\theta }_{\mathrm{i}2}(t))-{\mathrm{R}}_{5\mathrm{d}}{\stackrel{··}{\theta }}_2(t)\sin ({\theta }_{5\mathrm{d}}(t))$$

(19)

$$\frac{F_{5\mathrm{y}}(t)}{m_{\mathrm{y}}}={\mathrm{R}}_{51}{\stackrel{··}{\theta }}_3(t)\cos ({\theta }_{\mathrm{i}2}(t))+{\mathrm{R}}_{5\mathrm{d}}{\stackrel{··}{\theta }}_2(t)\cos ({\theta }_{5\mathrm{d}}(t))$$

(20)

$${\theta }_{\mathrm{i}2}(t)=40\circ -{\theta }_2(t)+{\theta }_3(t)$$

(21)

Figure 9.

Relation of forces transmitted to hood and angular accelerations of elements: (a) relation of F_5x, F_5y and angular acceleration of pole and (b) relation of F_5x, F_5y and angular acceleration of plate.

In the above, m_x is the mass of hood that is applied to one hinge mechanism in the horizontal direction. Because a vehicle’s hood is shifted in the horizontal direction by two hinge mechanisms installed on both sides of hood, m_x is half of the mass of hood. m_y is the mass of hood that is applied to the one hinge mechanism in the vertical direction. The hood is shifted in the vertical direction by one latch mechanism and two hinge mechanisms. Because of the distance from the center of mass of hood to each place installed, mass of hood applied to one of hinge mechanism in the vertical direction is about a quarter of the mass of hood. R₅₁ is the distance from joint C to joint D, and the value of R₅₁ is 105 mm. R_5d is the distance from joint B to joint D, and ${\theta }_{5\mathrm{d}}$ is the angle between the line from joint C to joint D and horizontal line. It should be noted that the horizontal and vertical distances from joint B to joint D can be solved through right-angled triangles that have R₅₁ and R₅₂ with hypotenuse as shown in Figure 10, and then R_5d and ${\theta }_{5\mathrm{d}}$ can be solved as follows

$${\mathrm{R}}_{5\mathrm{d}}(t)={({({\mathrm{R}}_{52}\cos ({\theta }_{\mathrm{i}3}(t))-{\mathrm{R}}_{51}\cos ({\theta }_{\mathrm{i}2}(t))}^2+{({\mathrm{R}}_{52}\sin ({\theta }_{\mathrm{i}3}(t))+{\mathrm{R}}_{51}\sin ({\theta }_{\mathrm{i}2}(t))}^2)}^{1/2}$$

(22)

$${\theta }_{5\mathrm{d}}(t)=\arctan \left(\frac{{\mathrm{R}}_{52}\sin ({\theta }_{\mathrm{i}3}(t))+{\mathrm{R}}_{51}\sin ({\theta }_{\mathrm{i}2}(t))}{{\mathrm{R}}_{52}\cos ({\theta }_{\mathrm{i}3}(t))-{\mathrm{R}}_{51}\cos ({\theta }_{\mathrm{i}2}(t))}\right)$$

(23)

$${\theta }_{\mathrm{i}3}(t)=5\circ +{\theta }_2(t)$$

(24)

Figure 10.

Right-angled triangles that have an R₅₁ and R₅₂ with hypotenuse.

Here, R₅₂ is the distance from joint B to joint C, and the value of R₅₂ is 128 mm. The distances of the elements are denoted to calculate the moment of components for formulating the dynamic equation using the variables r₁₁, r₁₂, r₂₁, r₂₂, r₃₁, r₃₂, r_f1, r_f2, and r_f3. r₁₁ is the distance used to calculate the moment transmitted to bracket release by the actuator force. r₁₂ is the distance used to calculate the moment transmitted to bracket release by the reacted force of pole. r₂₁ is the distance used to calculate the moment transmitted to plate by bracket release through joint A and that is the distance from joint A to joint B. r₂₂ is the distance used to calculate the moment transmitted to plate by pole through joint C and that is the distance from joint B to joint C. r₃₁ is the distance used to calculate the moment transmitted to pole by the force of bracket release. r₃₂ is the distance used to calculate the moment transmitted to pole by the reacted force of hood through joint D and that is the distance from joint C to joint D. r_f1 is the distance used to calculate the moment transmitted to bracket release by the friction force between bracket release and actuator. r_f2 is the distance used to calculate the moment transmitted to bracket release by the friction force between bracket release and pole. r_f3 is the distance used to calculate the moment transmitted to pole by the friction force between bracket release and pole. Here, r₂₁, r₂₂, and r₃₂ are fixed values and each value has 40, 128, and 105 mm. And the values of distances to calculate the moment of components, which change over time, are given as follows

$$r_{11}(t)=l_{11}\sin ({\theta }_{\mathrm{i}4}(t))$$

(25)

$$r_{12}(t)=l_{12}\sin ({\theta }_{\mathrm{i}5}(t))$$

(26)

$$r_{31}(t)=l_{31}\sin ({\theta }_{\mathrm{i}6}(t))$$

(27)

$$r_{\mathrm{f}1}(t)=l_{11}\cos ({\theta }_{\mathrm{i}4}(t))-s_{\mathrm{a}}$$

(28)

$$r_{\mathrm{f}2}(t)=l_{12}\cos ({\theta }_{\mathrm{i}5}(t))-s_{\mathrm{b}}$$

(29)

$$r_{\mathrm{f}3}(t)=l_{31}\cos ({\theta }_{\mathrm{i}6}(t))$$

(30)

$${\theta }_{\mathrm{i}4}(t)=10\circ +{\theta }_1(t)+{\theta }_2(t)$$

(31)

$${\theta }_{\mathrm{i}5}(t)=40\circ +\beta (t)$$

(32)

$${\theta }_{\mathrm{i}6}(t)=65\circ +{\theta }_1(t)+\beta (t)$$

(33)

Here, s_a is the radius of arc that indicates a contact surface between actuator and bracket release, and the value of s_a is 50 mm. And s_b is a radius of arc that indicates a contact surface between bracket release and pole, and the value of s_b is 25 mm. As shown in Figure 11(a), the point of contact between actuator and bracket release is shifted as following the arc that is presented by thick dotted line when the actuator is deployed. So the distance of r₁₁ can be presented through the sine value of the l₁₁ to express the change over time. And the rotational angle of the vertical line on the contact surface of actuator and bracket release is sum of rotational angles of bracket release and plate. r_11i is the distance of r₁₁ when the moment is transmitted at the first time. l₁₁ is the line from joint A to point E that is the center of an arc, and the value of l₁₁ is 65 mm. And r₁₂ can be presented through Figure 11(b). Because the point of contact between bracket release and pole is shifted as following the arc that is presented by the thick dotted line in Figure 11(b), the distance of r₁₂ can be presented through the sine value of the l₁₂. r_12i is the distance of r₁₂ when moment is transmitted at the first time. l₁₂ is the line from joint A to point F that is the center of an arc and the value of l₁₂ is 71 mm. Here, the rotational angle of the vertical line on the contact surface of bracket release and pole over the shift of the contact point is set at $\beta$ , and that is mathematically presented in equation (34) to express the relation with rotational angle of bracket release

$$\beta (t)=\frac{{\beta }_{\mathrm{fr}}}{{\theta }_{\mathrm{fr}1}}{\theta }_1(t)$$

(34)

${\beta }_{\mathrm{fr}}$ is the rotated angle of the vertical line on the contact surface of bracket release and pole until bracket release and pole are completely rotated. And ${\theta }_{\mathrm{fr}1}$ is the value of ${\theta }_1$ when bracket release and pole are rotated completely. That is, the increase in $\beta$ is proportionate to the increase in ${\theta }_1$ , and $\beta$ is increased to ${\beta }_{\mathrm{fr}}$ while ${\theta }_1$ is increased to ${\theta }_{\mathrm{fr}1}$ . Here, the value of ${\beta }_{\mathrm{fr}}$ is 27°, and ${\theta }_{\mathrm{fr}1}$ is 11°. Also, r₃₁ can be presented through the sine value of l₃₁ as shown in Figure 11(c) and (d). r_31i is the distance of r₃₁ when moment is transmitted at the first time. l₃₁ is the distance from the rotation center of pole to the contact point between bracket release and pole, and the value of l₃₁ is 30 mm. Because the reasons of increasing the rotational angle of the vertical line on the contact surface from the initial state are the rotation of bracket release and the shifting of the contact point as following the arc, that is presented by sum of rotational angle of bracket release and $\beta$ . In the same way, r_f1 can be presented through the cosine value of l₁₁. r_f2 can be presented through the cosine value of l₁₂. r_f3 can be presented through the cosine value of l₃₁.

Figure 11.

Distances to calculate moment of components which change over time: (a) r₁₁, (b) r₁₂, (c) r₃₁ when moment is transmitted at the first time and (d) r₃₁.

Figure 12 shows a free body diagram for solving the moment using the force and friction force. Figure 12(a) presents a free body diagram showing the forces for solving the moment of bracket release and Figure 12(b) presents a free body diagram showing the friction force of bracket release. Based on these free body diagrams, the moment equation of bracket release is derived using the sum of the moments, as given in equations (35). Figure 12(c) presents a free body diagram showing the forces for solving the moment of plate. Based on these free body diagrams, the moment equation of bracket release is derived using the sum of the moments, as given in equation (36). Figure 12(d) presents a free body diagram showing the forces for solving the moment of pole and Figure 12(e) presents a free body diagram showing the friction force of pole. Based on these free body diagrams, the moment equation of bracket release is derived using the sum of the moments, as given in equation (37)

$$I_1{\stackrel{··}{\theta }}_1(t)=r_{11}{F}_1-r_{12}{F}_3+r_{\mathrm{f}1}\mu F_1-r_{\mathrm{f}2}\mu F_3$$

(35)

$$I_2{\stackrel{··}{\theta }}_2(t)=r_{21}{F}_{2\mathrm{n}}+r_{22}{F}_{4\mathrm{n}}$$

(36)

$$I_3{\stackrel{··}{\theta }}_3(t)=r_{31}{F}_3-r_{32}{F}_{5\mathrm{n}}+r_{\mathrm{f}3}\mu F_3$$

(37)

Figure 12.

Free body diagram for solving moment: (a) free body diagram showing forces of bracket release, (b) free body diagram showing friction forces of bracket release, (c) free body diagram showing forces of plate, (d) free body diagram showing forces of pole, and (e) free body diagram showing the friction force of pole.

Because the direction of F_2n and F_4n is the rotational direction of plate, F_2n and F_4n can be presented by F_2x, F_2y, F_4x, F_4y, and ${\theta }_2$ . Also, because the direction of F_5n is rotational direction of pole, F_5n can be presented by F_5x, F_5y, ${\theta }_2$ , and ${\theta }_3$ . Figure 13 shows the relations of those forces, and those are given mathematically as follows

$$F_{2\mathrm{n}}(t)=F_{2\mathrm{x}}(t)\sin ({\theta }_{\mathrm{i}7}(t))+F_{2\mathrm{y}}(t)\cos ({\theta }_{\mathrm{i}3}(t))$$

(38)

$$F_{4\mathrm{n}}(t)=-F_{4\mathrm{x}}(t)\sin ({\theta }_{\mathrm{i}7}(t))+F_{4\mathrm{y}}(t)\cos ({\theta }_{\mathrm{i}3}(t))$$

(39)

$$F_{5\mathrm{n}}(t)=F_{5\mathrm{x}}(t)\sin ({\theta }_{\mathrm{i}2}(t))+F_{5\mathrm{y}}(t)\cos ({\theta }_{\mathrm{i}2}(t))$$

(40)

Figure 13.

Relation of the force in rotational direction of elements and force in vertical and horizontal directions: (a) relation of F_2n and F_2x, F_2y; (b) relation of F_4n and F_4x, F_4y; and (c) relation of F_5n and F_5x, F_5y.

On the other hand, equation (35) is a kinematic relation between ${\theta }_1$ and ${\theta }_3$

$${\stackrel{·}{\theta }}_1(t)=\frac{r_{31}}{r_{12}}{\stackrel{·}{\theta }}_3(t)$$

(41)

Now, the unknown quantities of ${\theta }_1$ , ${\theta }_2$ , ${\theta }_3$ , F_2x, F_2y, F₃, F_4x, and F_4y can be solved using eight independent equations (equations (4), (5), (7), (8), (29), (30), (31), and (35)).

The deployment is finished when the height of joint D that is linked to the hood increases by 50 mm in the vertical direction from the initial state. That time is defined as the response time of system. Because the height of joint D can be presented by the distance from joint B to joint D in the vertical direction, the lifted height of the hood, x_h, can be presented mathematically as follows

$$\begin{array}{l}{x}_{\mathrm{h}}={\mathrm{R}}_{51}\left(\sin \left(40°-{\theta }_2(t)+{\theta }_3(t)\right)-\sin (40°)\right)\\ +{\mathrm{R}}_{52}\left(\sin \left(5°+{\theta }_2(t)\right)-\sin (5°)\right)\end{array}$$

(42)

Design parameters

Because bracket release and actuator are added to original hinge for lifting the hood, the location of actuator and bracket release is adjusted to reduce the response time. And the location of a contact point between bracket release and pole is also adjusted to improve the deploying performance. The distances that present three parameters are denoted as R₁, R2, and R3 as shown in Figure 14 and all the distances to be adjusted for the new design are named “parameter distance.” R₁ is indicated to the location of actuator, and that is the distance from a rotational center of bracket release to a contact point between actuator and bracket release in the horizontal direction. R₂ is indicated to the location of bracket release, and R₃ is the distance from the contact point of bracket release and pole to the rotational center of pole in the horizontal direction. All the distances to be adjusted to reduce the response time are directly related to several distances to set up the moment equations or other equations that is used to set up the governed equation. In this work, the independent influence on the response time is investigated by changing R₁, R₂, and R₃ from −20% to +100% as given in Table 2. According to the table, the response time is reduced by increasing all the parameters in different ratios.

Figure 14.

Distances of elements to be adjusted to reduce response time.

Table 2.

Response time due to change in parameter distance.

	R1 (ms)	R2 (ms)	R3 (ms)
−20%	9.91	9.99	10.1
−10%	9.75	9.79	9.81
0%	9.60	9.60	9.60
+10%	9.46	9.42	9.38
+20%	9.34	9.23	9.15
+30%	9.22	9.05	8.91
+40%	9.11	8.86	8.67
+50%	9.02	8.67	8.42
+60%	8.92	8.47	8.16
+70%	8.83	8.24	7.90
+80%	8.75	7.97	7.65
+90%	8.68	7.69	7.40
+100%	8.61	7.35	7.17

In the practical application of the AHLM, several geometric constraint conditions exist. Figure 15 shows a configuration of R₁, R₂, and R_brack when the operation of the mechanism is completed. R_brack is the distance of bracket release, and that is the distance from joint A to the end of the bracket release in the horizontal direction as shown in Figure 16. The geometric relation of distances can be expressed mathematically by the following equation

$${\mathrm{R}}_{\mathrm{brack}}=\frac{{\mathrm{R}}_1+{\mathrm{R}}_2-{\mathrm{R}}_2\cos ({\theta }_{\mathrm{f}2})+{\mathrm{R}}_2\cot (k)\sin ({\theta }_{\mathrm{f}2})}{\cos ({\theta }_{\mathrm{f}1}+{\theta }_{\mathrm{f}2})-\cot (k)\sin ({\theta }_{\mathrm{f}1}+{\theta }_{\mathrm{f}2})}$$

(43)

Figure 15.

Geometric relation of distance of bracket release and parameter distances.

Figure 16.

Distances of bracket release and plate.

As mentioned, k is the angle between deploying direction of actuator and horizontal direction. And ${\theta }_{\mathrm{f}1}$ and ${\theta }_{\mathrm{f}2}$ are the rotated angles of bracket release and plate when the hood is lifted by 50 mm. Because the equation shows R_brack is proportionate to R₁ and R₂, R_brack should be increased maximally in order to achieve the main purpose. And because bracket release should exist on plate because of the internal distance limitation of the car, the maximal value of R_brack can be presented by R_plate as given in equation (44). Here, R_plate is the distance of plate, and that is the distance from joint B to joint C in the horizontal direction as shown in Figure 16. And the value of R_plate is 127 mm. Because ${\theta }_{\mathrm{f}1}$ and ${\theta }_{\mathrm{f}2}$ can be regarded as the function of parameter distance, the geometric constraint condition means the relations of R₁, R₂, and R₃. Through maximal R_brack, the geometric constraint condition is redefined as follows

$${\mathrm{R}}_{\mathrm{brack}}={\mathrm{R}}_{\mathrm{plate}}-{\mathrm{R}}_2$$

(44)

$${\mathrm{R}}_{\mathrm{plate}}=\frac{{\mathrm{R}}_1+{\mathrm{R}}_2-{\mathrm{R}}_2\cos ({\theta }_{\mathrm{f}2})+{\mathrm{R}}_2\cot (k)\sin ({\theta }_{\mathrm{f}2})}{\cos ({\theta }_{\mathrm{f}1}+{\theta }_{\mathrm{f}2})-\cot (k)\sin ({\theta }_{\mathrm{f}1}+{\theta }_{\mathrm{f}2})}+{\mathrm{R}}_2$$

(45)

When R_brack has the maximal value, the distance of arc in the horizontal direction is increased to R₃ as shown in Figure 17(a). And ${\beta }_{\mathrm{fr}}$ can be expressed by R₃ and s_b as shown in Figure 17(b) and that is presented mathematically by

$${\beta }_{\mathrm{fr}}=30\circ +\arcsin \left(\frac{{\mathrm{R}}_3-s_{\mathrm{b}}\sin (30\circ )}{s_{\mathrm{b}}}\right)$$

(46)

Figure 17.

Schematic diagrams of ${\beta }_{\mathrm{fr}}$ and ${\theta }_{\mathrm{fr}1}$ : (a) relation of distance of arc in horizontal direction and R₃; (b) relation of R₃, s_b, and ${\beta }_{\mathrm{fr}}$ ; (c) relation of R_brack, R₃, and ${\theta }_{\mathrm{fr}1}$ ; and (d) angle added to ${\theta }_{\mathrm{fr}1}$ due to the shape of arc.

Figure 17(c) shows the relations of R_brack, R₃, and ${\theta }_{\mathrm{fr}1}$ when the shape of arc is ignored. And Figure 17(d) shows the influence of the shape of arc on ${\theta }_{\mathrm{fr}1}$ , and that is presented by ${\theta }_{\mathrm{add}}$ that is the changed angle due to the shape of arc. Then, equations of ${\theta }_{\mathrm{add}}$ and ${\theta }_{\mathrm{fr}1}$ can be presented mathematically as follows

$${\theta }_{\mathrm{add}}=\arctan \left(s_{\mathrm{b}}\left(\cos (30°)-\cos \left(\arcsin \left(\frac{{\mathrm{R}}_3-s_{\mathrm{b}}\sin (30°)}{s_{\mathrm{b}}}\right)\right)\right)/{\mathrm{R}}_{\mathrm{brack}}\right)$$

(47)

$${\theta }_{\mathrm{fr}1}=2\mathrm{arc}\csc \left(\frac{2{\mathrm{R}}_{\mathrm{brack}}}{{\mathrm{R}}_3}\right)+{\theta }_{\mathrm{add}}$$

(48)

It should be noted here that the value of ${\theta }_{\mathrm{f}1}$ should be smaller than ${\theta }_{\mathrm{fr}1}$ . ${\theta }_{\mathrm{f}1}$ larger than ${\theta }_{\mathrm{fr}1}$ means that the operation is finished before the hood is lifted by 50 mm.

Results and discussions

A preferable structure for the AHLM to reduce the response time can be achieved by adjusting the design parameters of the hinge part. The suitable distances of R₁, R₂, and R₃ are obtained based on the imposed geometric constraints. Because ${\theta }_{\mathrm{f}1}$ and ${\theta }_{\mathrm{f}2}$ are solved by only solving the dynamic equation, suitable R₁ should be found in the process to solve the dynamic equation using the first geometric constraint condition presented by equation (45). The response time can be solved by the dynamic equation while R₁ is solved by changing R₂ and R₃. R₂ is increased by 10%, 20%, 30%, 40%, 50%, and 60%, and R₃ is increased by 5%, 10%, 15%, 20%, and 25% to investigate the influences on the response time and the change rate of R₁. The calculated results from the equations are presented in Table 3. The results show that the response time decreases maximally when R₂ is increased by 50% and R₃ is increased maximally as far as possible. When R₂ is increased by 10% and 20%, the response time cannot be solved after R₃ is increased by 20% because ${\theta }_{\mathrm{f}1}$ is larger than ${\theta }_{\mathrm{fr}1}$ at that time. That is, the operation is finished before the hood is lifted by 50 mm. When R₂ is increased by 30%, 40%, and 50%, the response time cannot be solved after R₃ is increased by 15%. And when R₂ is increased by 60%, the response time cannot be solved after R₃ is increased by 10% due to the same reason. Consequently, the response time decreases maximally when R₂ is increased by 50% and R₃ is increased by 15% and that is presented by bold values in Table 3. And R₁ is decreased by 17% as following the table. In other words, R₁ should decrease from 17 to 14.11 mm, R₂ should increase from 41 to 57.4 mm, and R₃ should increase from 30 to 34.5 mm to reduce the response time maximally. The response time for deploying the AHLM is calculated with the different actuating forces, and the results are presented in Table 4. The response time of the existing AHLM is 9.60 ms at 65-MPa MGG, which is very similar to the performance evaluation test result (about 10 ms) shown in Figure 4. It is seen from the table that the response time of the newly designed AHLM is 8.54 ms which is faster than the existing one. In addition, it is seen that when 55-MPa MGG is used, the response time is reduced from 10.14 to 9.00 ms by the new design. In addition, when 45-MPa MGG is used, the response time is reduced from 10.84 to 9.58 ms. And when 35-MPa MGG is used, the response time is reduced from 11.83 to 10.42 ms. As previously stated, the response time reduction is directly related to being able to operate at a high vehicle driving speed. Table 5 presents the workable driving speeds of vehicles when the response time of the AHLM is reduced based on this work. The workable driving speed is increased from 60.8 to 63.1 km/h when the new design is applied to the AHLM with an actuator that uses 65-MPa MGG. It is also noted from the table that the workable driving speed is increased from 59.7 to 62.1 km/h, from 58.4 to 60.9 km/h, and from 58.4 to 60.9 km/h, with actuators that use 55-MPa MGG, 45-MPa MGG and 35-MPa MGG, respectively. This increment of workable driving speed directly indicates the effectiveness of the proposed AHLM which can significantly reduce the collision injuries due to the fast deployment of the hood at higher vehicle speed.

Table 3.

Changing rate of R₁ and response time due to changes in R₂ and R₃.

		1.0 R2	1.1 R2	1.2 R2	1.3 R2	1.4 R2	1.5 R2	1.6 R2
1.00 R3	R1	+90%	+69%	+46%	+24%	+1%	−24%	−55%
	Response time (ms)	8.97	8.94	8.92	8.89	8.87	8.87	8.94
1.05 R3	R1	+90%	+69%	+47%	+24%	0%	−26%	−55%
	Response time (ms)	8.90	8.86	8.83	8.8	8.78	8.78	8.82
1.10 R4	R1	+90%	+70%	+47%	+24%	+1%	−25%	−53%
	Response time (ms)	8.83	8.78	8.75	8.72	8.69	8.68	8.7
1.15 R4	R1	+93%	+72%	+50%	+29%	+6%	−17%	–
	Response time (ms)	8.76	8.71	8.67	8.62	8.58	8.54	–
1.20 R4	R1	+100%	+80%	+60%	–	–	–	–
	Response time (ms)	8.71	8.66	8.61	–	–	–	–
1.25 R4	R1	–	–	–	–	–	–	–
	Response time (ms)	–	–	–	–	–	–	–

Table 4.

Comparison of response times of existing AHLM and newly designed AHLM with different actuator specifications.

	Existing system	Newly designed system
65-MPa MGG	9.60 ms	8.54 ms
55-MPa MGG	10.14 ms	9.00 ms
45-MPa MGG	10.84 ms	9.58 ms
35-MPa MGG	11.83 ms	10.42 ms

MGG: micro-gas generator.

Table 5.

Workable driving speeds of existing AHLM and newly designed AHLM with different actuator specifications.

	Existing system	Newly designed system
65-MPa MGG	60.8 km/h	63.1 km/h
55-MPa MGG	59.7 km/h	62.1 km/h
45-MPa MGG	58.4 km/h	60.9 km/h
35-MPa MGG	56.5 km/h	59.2 km/h

MGG: micro-gas generator.

Conclusion

In this work, an AHLM for a passenger vehicle that is deployed by the gunpowder actuator was introduced, and design parametric investigation to reduce the deploying (response) time was undertaken. In order to achieve this goal, the governing equations of motion were derived from free body diagrams as a first step. After carefully investigating the influences of the design parameters with geometric constraints on the response time, new values for the principal geometric design parameters that could provide faster response time were chosen for the AHLM. It has been demonstrated through computer simulations that the proposed AHLM with the new design parameter values can provide much better performance than the conventional one in terms of the total response time. In addition, it has been observed that the response time can be shortened by changing the volume of gunpowder. This directly indicates that the response time of the AHLM can be shortened through both the actuator capacity (gunpowder volume) and geometric values. It is finally remarked that a solid mathematical model integrated with optimization method to further reduce the deploying time with same constraints such as contact problem will be developed as a second phase of this work. Moreover, an experiment to evaluate the deploying time will be undertaken as a future work of this study.