The Dynamic Simulation with Rotary Inertia on Vehicle-Slope II

Abstract

According to formula we can simulate the driven force and acceleration in the slope of vehicle. The mechanical formula shall be used to obtain force and theoretical dynamics in the slope. The driven force decreases when rotation increases. When power increases the acceleration increases.  it shall reduce when its weight raises. It is found that the acceleration and force will decrease as slope becomes high from 5 to 11° to 22°, which fit the formula too. Meantime, as the radius shall provide high from 0.3m, 0.4m to 0.47m it will be low. The needed force shall increase as the slope decreases becomes big at the same power. The acceleration may indicate from 45m/s2 to 16m/s2; from 87m/s2 to 30m/s2; from 157m/s2 to 60m/s2 with tire radius 0.3m and slope 5º for 115 hp, 2.0 tons; 283 hp, 2.5 tons; 574 hp, 2.9 tons correspondingly. The force may afford 110kN, 20kN & 4kN with the rotational speed of 20r/m, 100r/m & 380r/m for power to be 208kW vehicles respectively.

Keywords: Simulation; dynamic; vehicle; Acceleration; driven force; rotary inertia; slope; power; rotational speed; weight; tire radius

Introduction

The power transmission of a vehicle is driven by power on the gradient, which is generated by the engine. Therefore, the measurement of power is the evaluation of the vehicle engine system on the gradient, has an important role. This paper studies the overall performance of the vehicle, including whether the gradient performance of the vehicle achieves the best performance, through the power and revolution of the vehicle engine. The kinematics of the vehicle takes speed and acceleration as research parameters and acceleration as the main purpose of design. Therefore, the organic combination of power and movement is the real purpose of evaluating the vehicle. Audi’s 3.0t Engine has a maximum power of 333hp, while Mercedes-Benzes’ A45 AMG has a 2.0t engine of 360hp.With the increase of horsepower, their dynamic analysis and kinematics become particularly important for example driven force, acceleration, vehicle weight, engine power & rotational speed analysis with changing slope size for using rotary inertia. The horsepower of a truck is the most important factor. It is the main condition that designers should expect in advance that they can finish the task without failure. The vehicle’s load and acceleration etc. less trouble is the embodiment of its design level ability. The acceleration of the vehicle is the main performance of the vehicle, the force and acceleration is directly reflected in its engine function. A good engine function will be achieved in a relatively short time in a slope. Therefore, this paper explores whether the data of the vehicle design are feasible based on the high power and acceleration of the vehicle on here, and discusses the status of high power and high acceleration to meet the needs of future vehicle development on a slope [1-16]. This paper shall describe the systematic computation as the parameters change for slope of vehicle in order to explore the significant role of them with rotary inertia. That shall become the main destination for us to explore further and forwards.

Calculation Courses and Formulas

As shown in Figure 1 it is a vehicle driving forwards along the slope with q. Here a is the tire acceleration, F is the force, and m is the mass. If C is the center of mass of the tire, R is the radius of the tire, and Mc is the torque of C.

If the vehicle runs at slope plane with q, there is   (1)

Figure 1 The relation of torque and Force on tire on the slope load in vehicle, here q is slope angle.

Referring to C it has  (2)

Referring to C it has too  (3)

Substitute to below equation (4)

(4)

Obtain

(5)

1. (6)

Due to   (7)

Substitute (5) into (2)

(8)

ie.

(9)

And since it has

(10)

It has  (11)

ie.

(12)

and

(13)

Prove too above equation.

Substitute (12) into above has

(14)

Discussions

As shown in Table 1 it is used with these parameters for this study. There are massˎ tire radius & powers respectively. When the slope is provided with 5~22° the acceleration and force is computed. It is needed to compare between radiusˎ power and weight for optimum parameters. Otherwise the ceased fire will happen due to weak power.

Table 1 The mechanical parameters in vehicle

As horsepower increases and the mass of the vehicle increases the acceleration increases, they provide inverse one proportionally. It is caused for the big horsepower firstly then the mass little. Therefore, when we are choosing parameters, it is necessary to choose big power one and the weight as possible so as to increase the acceleration in a very short time. It is found that the acceleration will decrease as slope becomes high from 5 to 11° to 22°, which fit the formula too. Meantime as the radius is high from 0.3m to 0.4m to 0.47m it is going to indicate low one. So it shall choose the small slope and tire radius for promoting acceleration in vehicles movement.

• 115 hp; 2.0tons
• 183 hp; 2.5tons
• 574 hp; 2.9tons

Figure 2 The relationship between acceleration and rotational speed with power 85.3kWˎ 208kW  & 423KW in vehicles.

In Figure 2(a~c) the acceleration will change with enhancing rotational speed at three power and vehicle mass to be 115 hp, 2.0 tons; 283 hp, 2.5 tons; 574 hp, 2.9 tons correspondingly. The acceleration may indicate 45m/s² and 16m/s²; 87m/s² and 30m/s²; 157m/s² and 60m/s² respectively with tire radius 0.3m and slope 5º in light of Figure 2(a~c). The acceleration may provide 0.5~4m/s² between adjacent two ones in accordance with those figures. With enhancing tire radius and slope the acceleration will incline as well. At the same time, with enhancing vehicle power as mentioned above the acceleration may enhance whilst it may decrease as the vehicle mass as above enhances.

• 3kW

85. 3kW
86. 208kW
87. 208kW

Figure 3 The force and rotational speed with power 85.3kW and 208kW in vehicles.

In Figure 3(a~d) the force and rotational speed will change for vehicle mass 2.9 tons & slope 22º and 2.03 tons & slope 5º. The force for driving vehicles may indicate 45kN, 10kN & 3kN with enhancing rotational speed 20r/m, 100r/m & 380r/m for power 85.3kW correspondingly in  of Figure 4(a). The force may provide 0.3kN for adjacent conditions only, so that the little force between them may be indicated with various mass and slope in power to be 85.3kW. In Figure 3(c) the force may afford 110kN, 20kN & 4kN with the same rotational speed mentioned above for power to be 208kW vehicles. The force may afford 0.5kN for adjacent vehicle masses and slopes in 208kW vehicles in light of Figure 3(d). The force will decrease a little when power is 208KW to compare with 85.3KW from Figure 3(a,c). It expresses that the a little more force is produced in high power. In addition, a big decreasing happens too below 50r/m due to relatively high velocity. Meantime the force will maintain a about constant after this point with a sluggish decrease. This is since the low torque caused by high rotary and slope angle increases where it results in some dragging down. These two factors interact together to offset force. This is main reason to be found why the sluggish force decreases here in this paper. The needed force will increase as the slope decrease becomes little big at the same power.

Conclusions

1. According to formula we can simulate their driven force and acceleration on the slope in vehicle. The mechanical formula is used to obtain force and theoretical dynamics on the slope. The driven force decreases when rotation increases. When power increases the acceleration increases as well. It reduces when its weight raises.
2. It is found that the decreasing value happens as slope becomes high from 5 to 11° to 22°, where it fits the formula too. Meantime, as the radius is high from 0.3m, 0.4m to 0.47m acceleration is going to indicate low. The needed force will increase as the slope declining indicates little big at the same power.
   3. The acceleration may indicate from 45m/s2 to 16m/s2; from 87m/s2 to 30m/s2; from 157m/s2 to 60m/s2 with tire radius 0.3m and slope 5º for 115 hp, 2.0 tons; 283 hp, 2.5 tons; 574 hp, 2.9 tons correspondingly. The force may afford 110kN, 20kN & 4kN with the rotational speed of 20r/m, 100r/m & 380r/m for power to be 208kW vehicles respectively.

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