Spatial Kinematic Analysis of a Tracked Forest Fire Engine with Fish-Bellied Swing Arm Torsion Bar Suspension

Abstract

To decrease track derailment of tracked fire trucks in forested areas, a fish-bellied swing arm torsion bar suspension system is proposed in this research. Derived from a tracked forest fire engine, this study converts the shaft tube swing arm of the original vehicle to a fish-bellied swing arm, improving the semi-rigid shaft tube suspension to a torsion bar suspension. Static and kinematic simulation analysis of the improved virtual sample vehicle is carried out, and the stress and dynamic characteristics before and after the improvement are analyzed. The simulation force cloud diagram of the improved swing arm and the motion simulation curve of the supporting wheel is obtained. The results show that the design of the fish-bellied swing arm can effectively reduce the bending moment caused by force acting on the swing arm, and that the design of the torsion bar spring suspension can reduce vertical displacement of the supporting wheel by 58.53%, and reduces horizontal displacement by 46.58% under the same impact force. According to the design of the virtual sample to build a prototype vehicle, a comparative test is carried out to determine an optimized virtual sample vehicle. The results show that the trend of the test curve is essentially consistent with that of the simulation curve.

1. Introduction

Due to the sudden nature of forest fires, taking effective control of the situation is challenging. Once a forest fire occurs, it is bound to cause significant harm to the ecological environment. The prevention and control of forest fires are significant environmental issues [1,2,3]. The burning temperature of forest fires is high, the spread speed is fast, and different types of forest fires have a diverse range of fire radiation [4,5]. Therefore, traditional firefighting methods and equipment have little effect on fighting forest fires. Tracked fire engines are mostly refitted from tracked armored vehicles, and their performance is better than wheeled fire engines, regardless of their ability to climb, cross trenches, or traverse soft ground [6,7]. The tracked vehicle relies on its high passability and mobility, and its use has steadily increased in forest areas. Furthermore, the State Forestry and Grass Administration announced the modernization of forest equipment in the 13th Five-Year Plan and the 14th Five-Year Plan for forestry and grassland.

Track derailment is a significant problem faced by tracked vehicles in operation, and the reasons for track derailment are mainly divided into three points: first, the crawler plate breaks and falls off due to the aging of or damage to parts; second, the unreasonable design of track tensioning mechanisms leads to insufficient tension, resulting in track derailment [8,9]; third, when the tracked vehicle is subjected to a significant impact load in the extreme environment, the track derailment is caused by large plastic deformation due to the insufficient strength of the swing arm suspension structure [10]. In order to avoid the occurrence of track derailment, scholars from various countries have carried out different research studies. Yang et al. [11] proposed a calculation method to estimate the thrust of track shoes on soft ground for a splayed grouser; the horizontal soil thrust of the track plate was calculated, which then provided a theoretical foundation for the design of a high strength track plate. Wang et al. [12] put forward a method of controlling track tension by a constant hydraulic drive guide wheel, which improves track stability and reduces the risk of track derailment; Zuo et al. [13] designed a torsion bar suspension structure, meeting the requirement of dynamic and cushioning performance in all-terrain articulated tracked transport vehicles, and improved the stability of the vehicle and reduced the probability of track derailment. When a forest fire breaks out, the burning temperatures near the fire site are high, as well as the fire radiation intensity, so tracked vehicles with rubber wheels cannot come into close contact with the fire site. Additionally, the fire situation rapidly changes. If the forest-tracked fire engine falls off its track while fighting a fire, this can cause fatal results. Therefore, forest-tracked fire engines urgently need a rigid chassis structure and a suspension system that is more resistant to falling off the track [14].

This study is based on an LF1352JP forest fire truck, produced in the northern forest region of the Daxing’an Mountains in China. The truck’s overall firefighting impact is good. However, when the tracked vehicle is climbing over a gully, track derailment sometimes occurs. The on-site observations found that when track derailment occurs, the swing arm of the supporting wheel is damaged and seriously deformed; as shown in Figures S1 and S2. It can be inferred that the inefficient structure of the vehicle body swing arm suspension is the main reason for the track derailment of the LF1352JP tracked forest fire engine [10].

The LF1352JP tracked fire engine adopts a shaft tube swing arm and semi-rigid suspension structure. The shaft tube swing arm structure is a general swing arm structure of tracked vehicles, which is simple in form but not strong in terms of bending and torsion resistance. There has been little research on semi-rigid suspension structures, and scholars from various countries mostly use torsion bar suspension structures in the design of tracked vehicles, and those studies are more in-depth. Yamakawa et al. [15] improved the off-road performance of tracked vehicles using a spatial motion analysis model of independent torsion bar suspension tracked vehicles; the motion of the tracked vehicles, including wheels, was numerically simulated. It was found that the new model had an excellent ability to predict the movement of tracked vehicles with torsion bar suspension. Tomasz et al. [16] examined how to avoid possible damage to the suspension system during an anti-tank mine explosion. An improved hyperbolic torsion spring model was proposed, which allowed a significant increase in body weight, enhanced the safety level, and improved the stability of the vehicle.

Simulation analysis has been gradually applied to the field of mechanical structure design. With continuous research, it has been found that a single static or dynamic simulation analysis can not sufficiently express the motion and mechanical characteristics of system components, so most scholars have used the static-dynamic joint simulation method for simulation analysis. Xue et al. [17] verified the accuracy of a newly developed multibody model by static-dynamic coupling simulation analysis. Li et al. [18], through static-dynamic joint simulation of the 5-degree-of-freedom manipulator, verified its load-bearing performance in practical work. Zhang [19] put forward a novel two degree of freedom (DOF) parallel manipulator with three legs, which was verified by the joint simulation of statics and dynamics, and the analytic results were verified by its simulation mechanism to be consistent with the calculated ones.

To better adapt to the forest environment, deal with forest fires, and improve the track derailment of tracked fire engines in forest areas, and based on the research of robot kinematics and tracked vehicle suspension, this paper designed a new type of fish-bellied swing arm torsion bar suspension structure. Through an combination of disciplines, the fish-bellied structure, commonly used in bridge construction, was applied to the tracked wheel shaft swing arm design, and the torsion bar suspension theory was applied to tracked fire engines in forest areas, which filled the deficiency in the literature regarding climbing and overcoming obstacles in the walking mechanisms of forest tracked fire engines. Using the method of static-dynamic joint simulation, the proposed fish-bellied swing arm torsion bar suspension was simulated and analyzed, and the rationality of its structural design was verified. At the same time, the simulation results were evaluated by outdoor vehicle tests. It provided a theoretical reference for the kinematic characteristics of tracked vehicles in forest areas and technical support for developing high-passing tracked equipment.

2. Structural Design of a Tracked Fire Engine with Fish-Bellied Swing Arm Torsion Bar Suspension

To reduce the track derailment of tracked vehicles at work and enhance maneuverability when firefighting, tracked fire engines utilize a new type of fish-bellied swing arm torsion bar chassis structure and a modular, movable upper structure. The tracked vehicle has a length of 4661 mm, a width of 2317 mm, a height of 2500 mm, and a rail gauge of 1641 mm, and is composed of a mechanical system, power system, control system, and fire protection system, as shown in Figure 1.

The mechanical system is composed of five sets of wheel axle swing arms and torsion bar suspension; the power system is composed of a 99.3 KW diesel engine, gearbox, and rear axle box; the control system is composed of the cab; the fire fighting system is composed of portable high-pressure water cannon sprinkler devices designed with a 10-foot container as a model. The new type of tracked fire engine also adds a hydraulic barrier remover and winch, as well as other devices which can better deal with forest fires and shorten the time for the tracked vehicle to arrive at the fire scene.

3. Structural Analysis of Fish-Bellied Swing Arm Torsion Bar Suspension

The biggest problem the tracked forest fire truck faces when working in the forest area is that the tracked vehicle is paralyzed due to track derailment. A stable suspension structure is very important for the work of tracked vehicles. In this research, the former shaft tube swing arm structure is changed to a fish-bellied swing arm structure, and the shaft tube sleeve suspension structure is changed to a torsion bar spring suspension structure. The mechanical analysis of the swing arm before and after the improvement is carried out, and the kinematics analysis of the new suspension structure is conducted based on the D-H coordinate change of the robot kinematics; the change position is then determined.

3.1. Stress Analysis of Fish-Bellied Swing Arm

A fish-bellied structure has the advantages of low cost, better bending resistance, torsion resistance, and has a shape like a fish belly, so it is commonly used in bridge construction [20]. Zhuang et al. [21], through simulation analysis and the establishment of a numerical model, derived a simplified formula for stiffness of a prestressed fish web steel bracing system. Yu et al. [22] theoretically determined the working mechanism and force analysis of IPS in a prestressed fish-bellied beam system, and combined it with engineering examples and finite element analysis to confirm the rationality of the theoretical analysis results. This demonstrated that the prestressed fish-bellied beam can effectively control the displacement and deformation caused by foundation pits. As can be seen from the above examples, fish-bellied structures have been widely studied and applied in the field of bridge building, but research on the application of fish-bellied structures in other areas is comparatively scarce. In this research, the shaft tube swing arm structure is replaced by the fish-bellied swing arm structure, with the aim of decreasing the force and deformation of the wheel shaft swing arm.

The main factor affecting the arm deformation of the supporting wheel is usually the impact load on the supporting wheel when the tracked vehicle climbs over a gully. When the original swing arm supporting wheel is subjected to vertical impact load F_N, the force analysis of the centroid of the original supporting wheel swing arm is carried out, as shown in Figure 2a.

$$F_c=F_N·cos\alpha$$

(1)

$$F_z=F_c·sin\alpha$$

(2)

$$F_y=F_c·cos\alpha$$

(3)

$$M_1=\sqrt{F_z{}^2+{\left(G_2-F_y\right)}^2}·0.5·L$$

(4)

$$M_1=\sqrt{{\left(F_N·cos\alpha ·sin\alpha \right)}^2+{\left(G_2-F_N·cos\alpha ·cos\alpha \right)}^2}·0.5·L$$

(5)

where $F_N$ is the upward impact load of the vertical supporting wheel, N; $F_t$ is the component of $F_N$ along the spring direction, N; $F_c$ is the component of $F_N$ along the center of mass of the pendulum arm, N; $F_y$ is the component of $F_c$ perpendicular to the center of mass, N; $M_1$ is the bending moment of the original swing arm under vertical impact load $F_N$, N/m.

When the improved swing arm supporting wheel is subjected to vertical impact load, the force analysis of the centroid of the supporting wheel swing arm is carried out, as shown in Figure 2b.

$$F_{c1}=F_N·cos\gamma$$

(6)

$$F_z=F_{c1}·sin\gamma$$

(7)

$$F_y=F_{c1}·cos\gamma$$

(8)

$$M_2=\sqrt{F_z{}^2+{\left(G_2-F_y\right)}^2}·0.5·L$$

(9)

$$M_2=\sqrt{{\left(F_N·cos\gamma ·sin\gamma \right)}^2+{\left(G_2-F_N·cos\gamma ·cos\gamma \right)}^2}·0.5·L$$

(10)

where $F_N$ is the upward impact load of the vertical supporting wheel, N; $F_t$ is the component of $F_N$ along the spring direction, N; $F_{c1}$ is the component of $F_N$ along the center of mass of the pendulum arm, N; $F_y$ is the component of $F_{c1}$ perpendicular to the center of mass, N; $M_2$ is the bending moment of the improved swing arm under vertical impact load $F_N$, N/m.

By observing Formulas (5) and (10), it can be determined that the impact load of the supporting wheel both before and after the swing arm improvement is constant. The more significant the bending moment is, the greater the normal stress of the section is; the more pronounced the bending deformation is, the more likely the member is to be destroyed. Therefore, the structure of the fish-bellied swing arm is more stable and less prone to bending damage.

3.2. Kinematic Analysis of Fish-Bellied Swing Arm Torsion Bar

Having reviewed the reasons for track derailment outlined in the introduction, except for damage to the parts, there are two main reasons for track derailment; the action force of the track tensioning mechanism is not sufficient and the track is not taut enough, which causes the supporting wheel to slip out of the track plate when crossing obstacles; and the structure of the track chassis and the swing arm structure of the supporting wheel is inefficient, and the supporting wheel is subjected to a considerable impact load when the track vehicle is climbing over a gully, resulting in the deformation of the supporting wheel shaft and track derailment [23]. Over the past few decades, there has been significant research on track tensioning systems. Lv et al. [24] put forward a method to calculate the perimeter of the track. Mȩżyk et al. [25] selected system parameters by using the numerical model based on the multi-body dynamics method, and used the numerical analysis results to determine the parameter setting of the track tensioning control system. The primary purpose of the current research was to improve the track derailment caused by the unreasonable structure of the tracked chassis. Based on the torsion bar suspension of the military-tracked armored vehicle, the swing arm structure of the axle sleeve was changed into a fish-bellied swing arm structure, which is rigidly linked to one end of the torsion bar through a short keyway.

When impacted by the road surface, the swing arm itself will deflect and drive the torsion bar spring to produce torsion force. When the suspension was subjected to different impact loads, the change in torsion bar torsion force was analyzed. The intuitive swing diagram of the torsion bar suspension was established, as shown in Figure 3a,b. The relationship between the torsion angle, torsion bar material property, and torsion force can be obtained according to Formula (11). Formula (11) provides a theoretical basis for simulating and analyzing the stiffness characteristics of the torsion bar suspension in Section 4.

$$\mathsf{\phi }=\frac{M\times D}{G\times J}\times \frac{180}{\pi }$$

(11)

where $\mathsf{\phi }$ is the torsion angle of the torsion bar under the torsion force $M$, °; $M$ is the torsion force, N; D is the length of torsion bar, m; G is the shear modulus, Pa; J is the anti-torsional stiffness of torsion bar, N/m², of which:

$$G=\frac{E}{2\times \left(1+v\right)}$$

(12)

$$J=\frac{\pi \times D^4}{32}$$

(13)

where E is Young’s modulus, Pa; $v$ is Poisson’s ratio; D is the diameter of torsion bar, m.

The torsion bar material used in the test was 60Si₂Mn, combined with Formulas (12) and (13) to obtain the material properties of the torsion bar; as shown in

Table 1. Torsion bar material properties.

Name	Material	Diameter (m)	Lengh (m)	Young’s Modulus (Pa)	Poisson’s Ratio	Shear Modulus (Pa)	Anti- Torsional Stiffness (N/m2)
Elastic torsion bar	60Si2Mn	0.072	1.515	2.06 × 1011	0.29	7.98 × 1010	42,000

.

When the supporting wheel point C encounters the impact load, the torsion bar OA twists, the swing arm AB rotates around point A, the supporting wheel point C moves to the C’, and the swing arm AB moves to the AB’. The position relationship of the swing arm suspension is shown in Figure 3c.

The initial coordinates of points B and C are $\left(X_1{Y}_1{Z}_1\right)$,$\left(X_2{Y}_2{Z}_2\right)$, and the angle α between the initial position of the swing arm AB and the horizontal direction is 38°. According to the length of the torsion bar OA, swing arm AB, and supporting wheel shaft BC, the coordinates of points B and C can be obtained as follows:

$$\{\begin{array}{c}{X}_1=L_{AB}cos38°\\ Y_1=-L_{AB}sin38°\\ Z_1=L_{OA}\\ X_2=L_{AB}cos38°\\ Y_2=-L_{AB}sin38°\\ Z_2=L_{OA}+L_{BC}\end{array}$$

(14)

The swing arm ABC rotates $\beta$° around point A to get the new position AB’C’; the coordinates of point B’ and C’ $\left(X_1^{\prime }{Y}_1^{\prime }{Z}_1^{\prime }\right)$,$\left(X_2^{\prime }{Y}_2^{\prime }{Z}_2^{\prime }\right)$ are:

$$\{\begin{array}{c}{X}_1^{\prime }=L_{A{B}^{\prime }}cos\left(38°-\beta \right)\\ Y_1^{\prime }=-L_{A{B}^{\prime }}\left(sin38°-\beta \right)\\ Z_1^{\prime }=L_{OA}\\ X_2^{\prime }=L_{A{B}^{\prime }}cos\left(38°-\beta \right)\\ Y_2^{\prime }=-L_{A{B}^{\prime }}\left(sin38°-\beta \right)\\ Z_2^{\prime }=L_{OA}+L_{BC}\end{array}$$

(15)

To establish the kinematic model, according to the D-H coordinate transformation rule, a series of coordinate systems are found at each fish-bellied torsion bar suspension joint. The rotational motion relationship between the joints is described by the homogeneous transformation between the coordinate systems [26,27]. Because the suspension structure is symmetrical, only the coordinate system on one side is needed, as shown in Figure 4.

According to the D-H coordinate transformation rule, $a_{i-1}$ represents the length of the connecting rod i − 1, which refers to the vertical distance between the axis of the i − 1 joint and the axis of the i joint; ${\alpha }_{i-1}$ represents the torsion angle of the connecting rod i − 1, if there is an angle between the two straight lines in the space, even if they do not intersect, then the torsion angle ${\alpha }_{i-1}$ is the angle between the joint i − 1 and the joint i axis. $d_i$ denotes the offset of the connecting rod i relative to the connecting rod i − 1. There is a typical vertical line between the joint i and the front and rear joint axes, and the distance between the two standard vertical lines is the offset of the connecting rod i close to the connecting rod i − 1; ${\theta }_i$ is the joint angle, indicating the rotation angle of the connecting rod i relative to the connecting rod i − 1 around the i axis [28]. According to the above definition and the motion model of the fish-bellied swing arm torsion bar suspension, the D-H parameters corresponding to each adjacent coordinate system can be obtained, as shown in

Table 2. D-H coordinate parameters of unilateral torsion bar suspension.

Joint i	ai−1	αi−1	di	θi
11	0	0°	L1	θ11 (38°)
12	b1	0°	0	θ12 (0°)
13	0	0°	c1	θ13 (360°)
2	m1	0°	0	θ2 (38°)
21	0	0°	L2	θ21 (0°)
22	b2	0°	0	θ22 (0°)
23	0	0°	c2	θ23 (360°)
3	m2	0°	0	θ3 (0°)
31	0	0°	L3	θ31 (38°)
32	b3	0°	0	θ32 (0°)
33	0	0°	c3	θ33 (360°)
4	m3	0°	0	θ4 (0°)
41	0	0°	L4	θ41 (38°)
42	b4	0°	0	θ42 (0°)
43	0	0°	c4	θ43 (360°)
5	m4	0°	0	θ5 (0°)
51	0	0°	L5	θ51 (38°)
52	b5	0°	0	θ52 (0°)
53	0	0°	c5	θ53 (360°)

.

According to the above definition and the D-H parameter, the position transformation matrix of the coordinate system i relative to the coordinate system i − 1 is established. According to the change matrix of Formula (16), the coordinate change matrix of each joint of the left first supporting wheel of the fish-bellied swing arm torsion bar suspension is as follows:

$${}^{i-1}T_i=\left[\begin{array}{cccc}C{\theta }_i& \hfill -C{\alpha }_{i}S{\theta }_i& S{\alpha }_{i}S{\theta }_i& a_{i}C{\theta }_i\\ S{\theta }_i& \hfill C{\alpha }_{i}C{\theta }_i& -S{\alpha }_{i}C{\theta }_i& a_{i}S{\theta }_i\\ 0& \hfill S{\alpha }_i& C{\alpha }_i& d_i\\ 0& \hfill 0& 0& 1\end{array}\right]$$

(16)

where $C{\theta }_i=Cos{\theta }_i$; $S{\theta }_i=Sin{\theta }_i$; $C{\alpha }_i=Cos{\alpha }_i$; $S{\alpha }_i=Sin{\alpha }_i$.

$${}^{0}T_{11}=\left[\begin{array}{c}C{\theta }_{11} -S{\theta }_{11} 0 0\\ S{\theta }_{11} C{\theta }_{11} 0 0\\ 0 0 1 L_1\\ 0 0 0 1 \end{array}\right]$$

(17)

$${}^{11}T_{12}={\left[\begin{array}{c} 1 0 0 b_1\\ 0 1 0 0\\ 0 0 1 0\\ 0 0 0 1 \end{array}\right]}^{ }$$

(18)

$${}^{12}T_{13}={\left[\begin{array}{c}1 0 0 0\\ 0 1 0 0\\ 0 0 1 c_1\\ 0 0 0 1 \end{array}\right]}^{ }$$

(19)

The total transformation matrix of the left swing arm and the left supporting wheel can be obtained by multiplying the coordinate transformation matrix of ⁰$T_{11},$¹¹$T_{12},$¹²$T_{13}$.

$${}^{0}T_{12}=\left[\begin{array}{c}C{\theta }_{11}-S{\theta }_{11} 0 C{\theta }_{11}{b}_1\\ S{\theta }_{11} C{\theta }_{11} 0 S{\theta }_{11}{b}_1\\ 0 0 1 L_1\\ 0 0 0 1 \end{array}\right]$$

(20)

$${}^{0}T_{13}={\left[\begin{array}{c}C{\theta }_{11}-S{\theta }_{11} 0 C{\theta }_{11}{b}_1\\ S{\theta }_{11} C{\theta }_{11} 0 S{\theta }_{11}{b}_1\\ 0 0 1 C_1{L}_1\\ 0 0 0 1 \end{array}\right]}^{ }$$

(21)

Based on the coordinate transformation relationship, ⁰$T_{12}$ can be simplified as:

$$\left[\begin{array}{c}C{\theta }_{11}-S{\theta }_{11} 0 C{\theta }_{11}{b}_1\\ S{\theta }_{11} C{\theta }_{11} 0 S{\theta }_{11}{b}_1\\ 0 0 1 L_1\\ 0 0 0 1 \end{array}\right]=\left[\begin{array}{c}\begin{array}{cc}{n}_x& n_y\\ o_x& o_y\end{array} \\ \begin{array}{cc}{a}_x& a_y\\ 0& 0\end{array} \end{array}\begin{array}{c}\begin{array}{cc}{n}_z& p_x\\ o_z& p_y\end{array}\\ \begin{array}{cc}{a}_z& p_z\\ 0& 1\end{array}\end{array}\right]$$

(22)

Then, according to Formula (22), we can obtain the corresponding coordinates of point 12, which is the bottom of the left swing arm:

$$\{\begin{array}{c}{p}_x=C{\theta }_{11}{b}_1\\ p_y=S{\theta }_{11}{b}_1\\ p_z=L_1\end{array}$$

(23)

Similarly, the coordinates of the left supporting wheel point 13 are:

$$\{\begin{array}{c}{p}_x=C{\theta }_{11}{b}_1\\ p_y=S{\theta }_{11}{b}_1\\ p_z=C_1{L}_1\end{array}$$

(24)

4. Simulation Analysis of Fish-Bellied Swing Arm Torsion Bar Suspension

4.1. Static Simulation Analysis of Swing Arm Suspension

During the process of pushing, the forest-tracked fire engine is primarily subjected to the impact force in the vertical direction and the lateral extrusion force in the vertical direction. According to the force, the statics simulation model of the swing arm, using Workbench software (Workbench 18.0; PIT, USA), is established. Figure 5 shows the simulation results when the supporting wheel swing arm (the swing arm structure of each set of supporting wheels in the tracked vehicle is the same, so there is no particular emphasis on which supporting wheel corresponds to the simulation here) is subjected to an impact force of 100,000 N in both the vertical direction and the vertical tracked vehicle forward direction.

After the observation and comparison of Figure 5a,b, it can be found that the local stress of the shaft tube swing arm exceeds the yield strength of its material (material Q235; yield strength is 370 MPa), resulting in irrecoverable deformation of the shaft tube swing arm. While the fish-bellied swing arm is subjected to the same impact force, the surface stress distribution of the swing arm does not exceed its yield strength; therefore, the design of the fish-bellied swing arm can improve the bending and torsion resistance of the swing arm.

In order to explore the mechanical characteristics of fish-bellied torsion bar suspension, simulate the force of the supporting wheel swing arm (the swing arm structure of different supporting wheels in each swing arm suspension structure is the same, so there is no particular emphasis on which supporting wheel swing arm corresponds to the simulation here) under three different swing arm suspension structures (shaft tube swing arm semi-rigid suspension, fish-bellied swing arm semi-rigid suspension, and fish-bellied swing arm torsion bar suspension) under different impact loads in a vertical direction and vertical vehicle forward direction. Record the changes in the centroid position (vertical and horizontal) of the supporting wheel swing arm under different simulation results. The rotation angle of the centroid of the swing arm is estimated with the combination outlined in Formula (11), and the analysis and calculation results are illustrated in Figure 6.

From (a) and (b) in Figure 6, it can be seen that: (1) with the increase of load, the swing amplitude and centroid rotation angle of the shaft tube swing arm and the fish-bellied swing arm continue to increase. (2) Compared with the shaft tube swing arm, the fish-bellied swing arm with the changed structure has no significant improvement in the centroid rotation angle, but decreases by 6.76%. (3) Because the fish-bellied arm’s centroid is lower than that of the shaft tube arm, the swing range of the fish-bellied arm is smaller when the centroid rotates at the same angle. Under different forces, compared with the shaft tube swing arm, the displacement of the fish-bellied arm in the horizontal direction decreases by 15.76%, and the displacement in the vertical direction decreases by 23.96%.

By observing (b) and (c) in Figure 6, it can be determined that: (1) when the load of the torsion bar suspension is increasing, the rotation angle of the centroid and the swing amplitude of the swing arm continue to increase, but the rise is not significant. (2) After the semi-rigid suspension structure is changed to the torsion bar suspension structure, when the swing arm is subjected to impact and extrusion pressure, the rotation angle and the displacement in the horizontal and vertical direction of the swing arm centroid considerably decrease. (3) Compared with the fish-bellied swing arm, after connecting the torsion bar spring, the average centroid rotation angle of the suspension swing arm decreases by 52.34%, the average horizontal displacement decreased by 53.85%, and the average vertical displacement decreases by 45.44%.

As can be seen from Figure 6, the stability of the fish-bellied torsion bar suspension is significantly improved compared with the original shaft tube semi-rigid suspension, in which 50,000 N impact load and 50,000 N lateral extrusion force are taken as examples. Compared with the original suspension structure, the rotation angle of the swing arm centroid under the new suspension structure reduces by 55.54%, the horizontal displacement of the swing arm centroid reduces by 45.57%, and the displacement in the vertical direction reduces by 60.86%.

4.2. Kinematic Simulation Analysis of Swing Arm Suspension

Because the tracked fire engine has a long body and rear-wheel drive, most of the body is suspended when climbing a hill or crossing a gully. After driving up a hill or ravine, the suspended body falls vertically under the action of gravity, which will exert a particular impact load on the front supporting wheel, which may lead to track derailment. Aimed toward this kind of motion trajectory, the kinematic simulation models of the original suspension structure and the improved suspension structure were established in Recurdyn (Recurdyn V9R1, FunctionBay, Korea), and the simulation process is shown in Figure 7.

Through simulation research, the motion curves of the first load-bearing wheel on the left side before and after the suspension swing arm improvement are obtained under different slopes. Taking the tan30°, tan40°, and tan44° slopes as examples, the simulation results are shown in Figure 8.

As can be seen from Figure 9, when the slope rises to tan44°, before and after the suspension swing arm improvement, the tracked fire engines all fail to climb the slope (as shown in Figure 8e,f). In addition, the trend of the centroid displacement of the supporting wheel and the suspension spring force before and after the suspension swing arm improvement is consistent.

(a)

At the beginning of the simulation, the tracked vehicle falls to the ground from a height of 280 mm and moves at a uniform speed in the horizontal direction. The position of the centroid of the supporting wheel remains unchanged, except for the falling height in the range of 0–4 s; when the tracked vehicle falls, the suspension spring is subjected to a certain squeezing pressure under the action of gravity, and when the tracked vehicle moves horizontally, the suspension spring swings up and down in a specific range. Compared with (a–d) of Figure 8, it can be seen that the extrusion pressure of the suspension spring after the improved chassis is smaller than before the improvement. The position of the centroid of the supporting wheel is the same as the up and down swing of the suspension spring when driving horizontally.

(b)

At 4–9 s, the tracked vehicle drives along the slope, the centroid position of the supporting wheel continues to rise, and the suspension spring tends to stabilize after being squeezed on the slope.

(c)

At 9–11 s, the suspended tracked body falls to the ground in a parabola under the action of gravity and driving force, the centroid position of the supporting wheel rapidly drops, and the pressure of the suspension spring quickly increases when it touches the ground. Compared with Figure 9a,b in Figure 9, it can be observed that when the tracked vehicle body hits the ground before the suspension improvement, the centroid position of the supporting wheel is lower, and the suspension spring is subjected to more significant pressure; the pressure on the improved suspension spring is decreased by 29.6%, and the centroid position is increased by 46.61 mm.

(d)

At 11–15 s, the tracked vehicle begins to cross the obstacle, and the centroid position of the supporting wheel first rises and then decreases; the suspension spring pressure drops, and after the front supporting wheel hits the ground crossing the obstacle, the suspension spring pressure rapidly increases, thus completing the simulation process of 15 s.

5. Experimental Verification of Fish-Bellied Swing Arm Torsion Bar Suspension

The principle prototype of the fish-bellied swing arm torsion bar suspension was developed and carried out during the actual vehicle test to verify the correctness of kinematics analysis and simulation of fish-bellied swing arm torsion bar suspension in this study.

5.1. Test Device

The testing of the fish-bellied swing arm torsion bar suspension included a speed test, displacement test, and pressure test. The movement track of the first supporting wheel on the left side of the tracked vehicle was recorded by the displacement sensor; the vehicle speed was measured by the speed sensor; and the pressure change of the suspension spring of the first supporting wheel on the left side of the tracked vehicle during the experiment was obtained by the pressure sensor. The test equipment is shown in Figure 9a–c.

Figure 9. Obstacle climbing test of real vehicle. (Test equipment: (a–c); real vehicle test process under tan30° slope: (d–f)).

Figure 9. Obstacle climbing test of real vehicle. (Test equipment: (a–c); real vehicle test process under tan30° slope: (d–f)).

5.2. Test Plan

By using the method of elevation measurement of road slope, slopes with different angles were selected for the vehicle climbing obstacle test. The test results were combined with the statics and kinematics virtual simulation results to compare the track derailment of the actual vehicle under the same climbing and obstacle conditions. Figure 9d–f shows the climbing process of the fish-bellied torsion bar suspension crawler fire engine on a slope of 30°. The test results are shown in Figure 10. The rest of the test process is shown in Figures S3–S7.

5.3. Test Result

The climbing pressure test curve and virtual prototype simulation curve of the test vehicle on tan30° slope are shown in Figure 11, and the actual vehicle passing situation and sample vehicle simulation passing situation on different slopes are shown in

Table 3. The situation of real vehicle climbing over obstacles on different slopes (P for pass; F for failure).

	Tan24°	Tan26°	Tan28°	Tan30°	Tan32°	Tan34°	Tan36°	Tan38°	Tan40°	Tan42°	Tan44°
Test	P	P	P	P	P	P	P	P	F	F	F
Simulation	P	P	P	P	P	P	P	P	P	P	F

.

Through the comparison and verification of the fish-bellied torsion bar suspension prototype test and virtual prototype simulation, it can be seen that the changing trend of the pressure test curve of the principle prototype is consistent with that of the virtual prototype simulation curve (as shown in Figure 11). The only difference is that the peak of the test curve appears later than that of the simulation curve, and the peak of the test curve is greater than that of the simulation curve. As the simulation system can not completely restore the actual road surface, the friction resistance of the tracked vehicle is more significant, and the driving speed of the sample vehicle is slower, so the peak pressure occurs for a longer time. Furthermore, the woodland soil contains a lot of gravel and plant rhizomes, and when plastic deformation occurs, the deformation of the forest and grass ground is smaller and more compact than that of the simulated ground in Recurdyn. Therefore, when the ground is subjected to the same impact load, the ground reaction force of the suspension spring in the actual vehicle test is greater, and the peak pressure of the test curve is more considerable.

Table 3 shows no track derailment in the actual vehicle test and virtual simulation when the climbing angle is less than tan38°. Nevertheless, when the slope reaches tan40°, track derailment occurs in the first supporting wheel of the actual vehicle, and after many tests, it was found that the track derailment of the supporting wheels on the left and right sides is random. It is speculated that this may be related to the ground environment of the tracks on the left and right sides; however, the track derailment does not occur when the virtual sample car passes through the tan40° climbing obstacle. This is because, compared with the virtual simulation road surface, the actual situation is more complex, the road surface is rougher, and the impact load caused by the falling of the vehicle body is more significant. When the actual tracked vehicle is working in the forest area, impurities such as branches and stones will become involved between the supporting wheel and the track plate. When the supporting wheel is subjected to the same impact load as in the virtual simulation, the position of the centroid will be higher, resulting in a track derailment. When the slope increases to tan42° and tan44°, the tracked vehicle cannot pass through the slope, and the virtual prototype passes through the slope of tan42° in the simulation, but it can not pass through the slope of tan44°. There are two main reasons for this phenomenon. First, when the tracked vehicle is walking, the tracked plate directly touches the forest soil, the largest area of forest vegetation, and the interaction force between the vehicle and the ground is less than the vehicle driving resistance, which leads to failure in climbing. Second, the concentration of dust in the air of forest areas is high, and the power of the engine will be reduced due to the increase of the pressure drop of the air filter during operation; the tail gas emission of the tracked vehicle may increase in the process of climbing. As a result, engine power can be reduced by several percentage points [29,30,31].

6. Conclusions

In this paper, through theoretical analysis, simulation analysis, and experimental verification of a fish-bellied swing arm torsion bar suspension structure, the following conclusions were obtained:

(1)

Based on D-H coordinate change theory, the kinematics mathematical model of fish-bellied swing arm torsion bar suspension in a forest with an unstructured terrain environment was established. The kinematics equation of the arm swing torsion bar of a tracked fire engine was derived. Furthermore, the position and pose information of a tracked fire engine’s arm swing torsion bar were obtained. The theoretical basis for the kinematic characteristics analysis of the fish-bellied swing arm torsion bar suspension was provided;

(2)

The static and dynamic simulation model of fish-bellied swing arm suspension was established, and the climbing obstacle and falling impact conditions in the unstructured forest environment were simulated. The force cloud diagram and displacement simulation curve of the fish-bellied swing arm were obtained, which provided the basis for the theoretical verification of the kinematics characteristics of the fish-bellied swing arm torsion bar suspension;

(3)

The principle prototype of fish-bellied swing arm torsion bar suspension was developed and carried out in the actual vehicle test. The test results verified the accuracy of theoretical calculation and the effectiveness of simulation analysis, which provides technical support for the actual development of forest-tracked fire trucks.

The results also show that a virtual simulation with the combination of statics and kinematics can make the simulation analysis more precise, but compared with the actual vehicle test, the results of the virtual simulation are slightly different, so we cannot rely on the simulation results. The actual test analysis based on the simulation results can make the test results more accurate.