Saleh Mobasseri
email: saleh.mobasseri@gmail.com

Mohammad Mobasseri

A Comparative Study Between ABS and Disc Braking System Using Finite Element Method

Keywords: Anti-lock braking system (ABS), Car Stability, Finite Element Simulation, Stopping Distance, Tire-Slip

This paper, refers to the history of the rise of brake system and describe its importance in passenger's lives. An Anti-lock braking system (ABS), is the safety of vehicle systems to achieve maximum braking and decelerating in terms of increasing the stability and balance of the car and reduces the braking distance is designed. The performance of disc brake system and the ABS controller are also compared with each other by the kinetic analysis of the braking system and evaluate the impact of each parameters are checked on the vehicle stopping distance. In this study, we use Finite Element software Abaqus 6.14 and we found some interesting result, such as the effect of temperature on the performance and braking system efficiency. The Anti-lock braking system (ABS) is one of the most important feature that affect on vehicle safety and for this research much efforts have been made to improve this system. One of the aims of this paper is to compare system performance between disc brake system and ABS with the help of modeling in different conditions (rainy, snowy, etc).

Introduction

Due to the advancement of technology and increase the number of automobiles, some people prefer to travel by private cars. This approach leads to increase the volume of vehicles traffic in urban and inter the city routes and increase fuel consumption [START_REF] Mobasseri | Impact of driving style on fuel consumption[END_REF][START_REF] Mobasseri | Traffic noise and it's measurement methods[END_REF].

Reducing of stopping distances and increasing the car stability, are the most important factors in the reducing number of accidents. These two factors are depended to coefficient friction between automobile tires and the ground. Due to the advancement of technology and sensors [START_REF] Mobasseri | Intelligent Circuit Application for Monitoring the Employees Attendance[END_REF] in the 80's, use of these technologies in automobiles are began. The biggest disadvantage of conventional brakes is that the driver can't precisely control the amount of brake torque applied to the wheels. If there is no precise information on road conditions, sudden and excessive pressing the brake pedal will lock the wheels. To counter the risks of collisions and reduce accidents, control the automobile and driving in different weather conditions, reduced stopping distances, increase stability and steering, avoid locking the brakes, development of new system like ABS, VDC, EBD, ESP is necessary, so that up to 40% of accidents can be avoided. Since 80's, the Anti-lock braking system (ABS) in automobiles, increased by using a safety airbag [START_REF] Petkov | Nanoporous hosts for the encapsulation of conductive nanostructured materials[END_REF]. The ABS, try to keep the maximum longitudinal and lateral tire friction coefficient. Thereby, achieving the minimum distance to stop the vehicle, increasing car's stability. The parameters that influence of the brake process:

The force applied by the driver's foot on the brake pedal, ambient air pressure and air pressure in the tire [START_REF] Mobasseri | Intelligent Circuit Application for Detecting the amount of Air in Automobile Tires[END_REF], tire quality, friction between the tire and the ground, car speed at the beginning of the braking process, orifices discharge coefficient, the external force acting on the vehicle body, how to distribute the weight of the car on wheels, type of pads, road conditions and tire, brake torque exerted on the tire.

Types of braking system:

2.1) Disc Brake System: Research, design and manufacture of disc brake system in England began in 1890 and was registered in 1902 in Birmingham by "Frederick William Lanchester" and the modified model was designed in 1949.

The way of disc brakes operation: Power of driver's foot enters the booster and then, is reinforced the power of driver's foot by the pressure difference created on both sides of the diaphragm; In fact, the force of the brake pedal and booster, brake circuit, creates hydraulic pressure and the pressure generated by the 3 hydraulic line is transferred to the wheel's cylinder and turns into the braking force and in accordance with the wheel's piston area, a force is exerted to the wheel.

In the time of booster activation, the diaphragm in front of the air and the vacuum motor is attached [START_REF] Limpert | Brake design and safety[END_REF].

The duty of booster is to increase the power of the driver's foot of 4 to 6 times. The first mode: When the brake of torque is greater than the frictional torque: (Torque brake ˃ Torque frictional)

In this situation, due to the lack of braking force, stopping distance of the car will be increase.

The second mode: Torque of brake, is greater than friction torque.

(Torque brake˂ Torque frictional)

In this situation, the wheels are locked and the car will be in a state of imbalance. Disc brake components are Brake lent, Caliper, Rotor.

Simulation:

As the simulation results of disc brake system indicate, due to the high friction, the temperature is increased and ultimately, the efficiency of braking system will be reduced.

4. The disadvantages of disc brake system:

1) Low-speed performance when pressing the brake pedal.

2) High brake stopping distance.

3) Slip vehicle on slippery distances.

4) Imbalance in the car.

5) Sensitive to dust and moisture.

6) Reduced brake system efficiency because of the rising temperatures.

5) Anti-lock braking system (ABS):

This system is an electronic device when the brake with hydraulic pressure control and associated with disc or drum pads, hold, hang up and rapid. The result of continued rapid and repeat this process is destroying the locking in brakes system. The importance of this kind of brakes will appear more, on wet and slippery surfaces or braking at high speeds. The first time was raised in 1905 in Germany. For the first time was mechanically used in the aircraft in 1930 and at the same time, many changes occurred in the aviation industry through the development of this system [START_REF] Hattwig | Synthesis of ABS hydraulic systems[END_REF][START_REF] Maier | The new and compact ABS5 unit for passenger cars[END_REF]. In 1969, the first ABS for cars were installed only on the rear wheels, was produced at Ford Motor Company and the modern ABS with electronic control unit was designed and built in 1976 by the "Daimler-Benz" and "Bosch company" [START_REF] Orthwein | Clutches and brakes: design and selection[END_REF].

All over the world, researcher in designing field, have done many kind of researches on the ABS system and achieved different results. The most important of them are:

Gerdes et al. have been studying and modeling the brake system [START_REF] Gerdes | Brake system modeling for simulation and control[END_REF]. Most of their studies have been modeling the car's vacuum booster. The main feature of this model is the static model of control boost valve with a dynamic of the air inlet. WU et al. have don modeling the brake system in more detail than previous studies [START_REF] Wu | Simulated and experimental study of hydraulic anti-lock braking system using slidingmode PWM control[END_REF]. The important parts of their paper, are designing PWM sliding mode controller and evaluation of controller which was designed in experimental test. Khan et al. have done modeling and simulation the boosters. The method used for modeling and simulation of the booster has Bond Graph [START_REF] Khan | Modeling, experimentation and simulation of a brake apply system[END_REF]. So, in their paper, the governing equations of the system are not available, and modeling of hydraulic of the ABS system has not performed. Hu et al. have done modeling and simulation the features of main cylinder of the brake system in static model [START_REF]Modeling and Simulation of the Characteristics of Hydraulic Brake Master cylinder[END_REF]. Their study is based on the main cylinder brake system.

At first, they extract components of the static model of the main cylinder and their effort was to utilize the friction force between the piston and the cylinder in calculations. Harifi et al. just provided a dynamic 6 model of the vehicle body and tires [START_REF] Harifi | Designing a sliding mode controller for slip control of antilock brake systems[END_REF]. In their paper, the modeling of all components of the ABS were ignored. Kuang et al. modeled the dynamic of hydraulic brake systems about a vehicle for active controller systems of the car [START_REF] Kuang | Hydraulic brake system modeling and control for active control of vehicle dynamics[END_REF]. The name of method which used in their paper, is Bond Graph method. Soliman et al. have been created an integrated controller between the active suspension system and the ABS system using Fuzzy-Logic control theories to improve braking performance [START_REF] Soliman | Active suspension and anti-lock braking systems for passenger cars[END_REF]. The simulation result of their research obtained show that the active and ABS with integrated controlled reduces the braking time and distance in the range from 3% to 5% compared with the same without integrated controller.

Kaldas et al. have been developed a control system that combines suspension and brake system [START_REF] Kaldas | Improvement of heavy vehicles ride and braking performance via combined suspension and braking systems control[END_REF]. The simulation result of their work, demonstrates that using Fuzzy-Logic control with controlled suspension systems and the ABS provides a significant improvement in truck ride comfort and braking performance under different driving conditions. Soliman and Kaldas, they have been studied the influence of vehicle initial speed and tire-road friction coefficient is investigated [START_REF] Soliman | An investigation of anti-lock braking system for automobiles[END_REF]. The result showed that, using Fuzzy-Logic Control in ABS, improved the braking performance than the conventional ABS. Kaldas and Soliman, showed the effect of investigating the influence of the preview control of the active suspension on the vehicle ride and braking performance [START_REF] Kaldas | Influence of active suspension preview control on vehicle ride and braking performance[END_REF]. The results are generated in the time domain to simulate the vehicle response during braking, while wheels are subjected to vertical road input. Emil Precup et al.

in their research, suggest a synergy of Fuzzy-Logic and nature-inspired optimization in terms of the natureinspired optimal tuning of the input membership functions of a class of Takagi-Sugeno-Kang (TSK) fuzzy models dedicated to ABS [START_REF] Precup | Nature-inspired optimal tuning of input membership functions of Takagi-Sugeno-Kang fuzzy models for anti-lock braking systems[END_REF]. The objective of Qiang Wang et al. is to minimize total impact energy by determining the desired braking force [START_REF] Wang | Longitudinal collision mitigation via coordinated braking of multiple vehicles using model predictive control[END_REF].

5.1) Introduction ABS:

In this system, the amount of braking force on each wheel can be different.

Therefore, the wheel which has less speed than the other wheel, proportionally, the pressure of brake fluid is reduced. The pressure, reduction is across-sectional and continues until wheel's spin to be equal. The ABS start to control the brake system up to 6 km/h and if for any reason getting problem, the ABS switched off and the brake operate as normal [START_REF] Wu | Simulated and experimental study of hydraulic anti-lock braking system using slidingmode PWM control[END_REF]22]. The ABS include electronic controls, a solenoid (for releasing and re-applied brake pressure) and the sensor of speed to the wheel [START_REF] Ellis | Vehicle handling dynamics[END_REF]. Modes of the ABS performance:

The vehicle's mainframe with sensors in each wheel, checks the wheel's speed during braking. If the rotational speed of the wheel's different than other wheels, the main frame changes the pressure inside the cylinder with a required command to the electronic brake valve that makes change in amount of braking 7 force applied to the wheels and vehicles wheel is getting out of the critical situation. So the possibility of locking the wheel is decrease. The above process, are continuously done with high speed so that the process is repeated in per minute between 15 to 20 times. In ABS, we must know when the wheels are slipping or locked. Speed sensors which have been installed on each wheel, give us this information. By recognizing slip or locking of the wheels, controller commands the modulator to reduce the braking torque to prevent the wheels from locking.

Slip is [START_REF] Wu | Simulated and experimental study of hydraulic anti-lock braking system using slidingmode PWM control[END_REF]:

V R V W     = The
2-The ABS with 3 channels and 3 speed sensor: This case, more applications are in the trucks and vans with 4 Anti-lock wheels and on the front wheels, a sensor and the valve is designed; But for the rear wheel, there is only one sensor and the valve which is located on the rear axle. In fact, for each front wheel, is a separate controller so more braking force be applied to the front wheels. One of the disadvantages of this case (three-channel system with three sensor), is the rear-wheel ABS, locked and therefore, using this system may lock the rear wheels while braking that reduces the effectiveness of the brake and the car balance.

3-The ABS with a channel and sensor: This system exists in vans and trucks which their rear axle is Anti-lock. The control valve for each wheel and speed sensor is located on the rear axle. In this way, it is possible lock the wheels during the braking.

The main part of the Anti-Lock System: In ABS, there are 4 main sections:

1-Sensor of speed: The ABS must know when the car wheel, being locked up. Speed sensors, provide the necessary information for his system.

2-Valves:

In the brake pipe, 1 valve is existing.

Modeling:

6.1) Modeling and description of some of the components of braking system is as follow:

6.1.1) Modeling of pedal: Brake pedal, is the first component of the brake system, which is reinforced the force of driver's foot, is supported by the following formula: The maximum force is applied to the brake pedal, for women is about 445 Newton and for men is 823

Newton [START_REF] Wit | Dynamic tire friction models for vehicle traction control[END_REF].

6.1.2) Booster: As we explained in the disc brake section, the duty of booster is Quadruple Sextuple the force of the driver's foot [START_REF] Limpert | Brake design and safety[END_REF].

When the booster ia activated, the following relation are dominate: 6.1.3) Hydraulic section: Most important point of Anti-lock braking system is controlling the amount of the pressure of brake hydraulic fluid behind the piston caliper or wheel cylinders.

The section of ABS hydraulic system, begins from the main cylinder and continues to the wheel cylinder.

Vehicle dynamics modeling: The following shape shows a free diagram of the car which is braking.

) ( 2 ) ( 2 cos ) ( 2 ) ( 2 sin ) ( 2 ) ( 2 cos ) ( 2 ) ( 2 sin r f a a r f f r f x r f r r f a a r f r r f x r f f L L H D L L WL L L H Ma L L WH W L L H D L L WL L L H Ma L L WH W                      

International Conference on researches in Science and Engineering

28 July 2016, Istanbul University, Turkey 12 6.2) Tire modeling:

Generally, tire's models can be divided into 2 categories, static model and dynamic models. Static friction models are used in terms of linear and angular velocities. Dynamic models represent the actual behavior of the tire at the time changing the speed [START_REF] Wit | Dynamic tire friction models for vehicle traction control[END_REF]. The quality of the tire and asphalt paving plays an important role in maintaining the car's balance. An appropriate road for a car is the broadband to control the car in the road. Control of the vehicle on the road depends on the wheel sticking to the ground and the other vehicle characteristics such as a height of the center of the wheel, axle length and mass distribution in the automotive and etc. In simulation and analysis of vehicle, dynamics adhesions is one of the most important parameters that must be considered in the design of the suspension.

The low graphs show the change in the coefficient of friction on the surface of the slide [START_REF] Solyom | Synthesis of a model-based tire slip controller[END_REF]:

7) The analysis of car stop in making brake is divided into 2 categories: 7.1) Kinematic analysis: kinematic situation of the car which can be analyzed at any time by 4 parameters as follows: speed, acceleration, distance and time. We assume the car is moving at a constant speed V1.

When the driver sees an obstacle in the path until the brake pedal is pressed, takes as much as "t", which is called as "driver reaction time". This time is usually between 0.75 to 1.5 seconds [START_REF] Shigley | Mechanical Engineering Design, First Metric Edit[END_REF]. After applying a force on the brake pedal, the linings are about 0.1 to 0.2 seconds connected to the disc with a time lag.

After passing "t", decelerating the car begins to increase until it reaches the maximum amount and then remains constant till its full stop. In the range of "t", acceleration is changed and at any moment can be calculated.

7.2) Kinetic analysis:

The total rolling resistance and static friction, reduce car's speed when using the brake. When the brakes are locked, the tires slip on the road surface and thus can't effectively reduce car speed. The maximum braking force occurs when there is about 11% of slip between the wheels and the road. This issue is used to increase the efficiency of ABS [START_REF] Wit | Dynamic tire friction models for vehicle traction control[END_REF]. To kinetic analysis of the brake system and optimization of its perform, the most important parameters are: Vehicle speed, stopping distance, the force on the wheel, the force applied to the brake pedal, the diameter of main cylinder and the cylinder of the wheels, the force on the wheel, the coefficient of friction between the surface in contact like the surface of lining with disc, the car's holder force.

7.

3) The advantages of ABS: Reduce stopping distance, increase vehicle stability and steering, reduce the amount of tire's vibration, reduce the torsion of tire, and prevent the diversion of car on slippery roads during heavy braking.

7.4) The disadvantages of ABS:

This system along with its advantages, has more disadvantages of the brake system, include: a) Rapid and continuous replication of connecting and disconnecting of the brake way by ABS, causing the loss of the blocking or locking the brakes. b) In ABS, serve noise is heard during the braking on extremely slippery surfaces. c) This system on soft surface (such as snow or sand) doesn't have a good performance. One of the cause of increasing the stopping distance in these situations is that, when the driver of vehicles with conventional braking system (disc brake), presses the brake pedal, because of locking wheels, some of snow or sand are collected in the wheels. The same applies helps to increase braking power. d) On the surface which is the combination of asphalt and snow, the tire will swerve to asphalt. 14 e) Given that this ABS in composed by more components than the brake disc, its repair and maintenance cost are higher.

Conclusion

According to the modeling that carried out in this paper and researcher's studies in the field of the accidents which lead to life and financial casualties, it was determined that serve or uncontrolled vehicles are around the vertical axis is the main cause of these accidents. In the perspective of vehicle dynamic, such intensive rotational motion is caused by the instability of the lateral dynamic of the car. The other important parameters that effect on the process of stopping the vehicle, can refer to the following: The of driver's feet, the geometry of the pedal. The amount of engine's vacuum, coefficient of orifices discharge, opening and closing properties of electronic valves, the effective radius of the tire, radius of brake discs, type and quality the tire, the amount of the tire's tread, road type, the amount of vertical load on the wheels, specification of hydraulic oil of brake, the amount of existence air in the hydraulic oil of the brake. The hydraulics of ABS, with a time lag of about 0.5 seconds from pressing the pedal to start reducing the vehicle's speed that the above factors are effective in changing this time duration. During pressing the brake pedal, pressure of hydraulic oil reaches about 60 times. Based on the presented entries in the paper and the importance of stopping the car in different situations by keeping the balance, the performance of ABS can be summarized as follows:

Figure 1 :

 1 Figure 1: Master Cylinder and Vacuum Booster

4 Figure 2 Figure 3 Figure 4 Figure 5 International

 42345 Figure 2

  amount of slip between tire and car V = Vehicle speed ω = Tire rotation speed R = The radius of the wheel In this case, the wheels of the car are locked. The below figure shows an example of friction sliding friction coefficient curves for the road conditions [24].

Figure 6 : 5 . 2 )

 652 Figure 6: Coefficient of friction on the slip curve [24]

Figure 7 :

 7 Figure 7: The pedal and the forces on the pedal

Fbooster

  pressure difference between the 2 sides of the diaphragm Frs= Return spring force booster Therefore, the amount of Fd can be calculated as follows: Fd = (Pa-Pν )Ad Pν = Pressure on the diaphragm Pa= Pressure behind the diaphragm Ad= The effective area Apply the force Booster has 3 modes are: Hold Force Release the force So the amount of Fd is different in each of these modes. Three considered cases can be written as following equation:

Figure 8 :

 8 Figure 8: States of the Booster [9]

Figure 9 :

 9 Figure 9: Free diagram of the braking vehicle [26]

Figure 10 :Figure 11 :

 1011 Figure 10: Longitudinal tire slip for different road surfaces [29]

Table 1 : Summary of the deceleration values [31]:

 1

	Road surface	Braking [m/s 2 ]	Acceleration [m/s 2 ]
	Ice		
	Snow		

Table 2 : Summary of braking decoration on the icy surface [30]:

 2

	Tire type	ABS	Surface	Ambient	Braking
			temperature [˚C]	temperature [˚C]	deceleration
					
	Winter	Yes	-5.4	05.9	2.65-1.47
		No			2.06-1.47
	Summer	Yes	-5.2	-3.1	1.96-1.28
		No			1.57-1.47


Saleh Mobasseri

Hassan Soltani

Traffic Noise and it`s Measurement Methods

Keywords: Noise pollution, Traffic noise, People`s health, Traffic area, Urban noise map

Background: Nowadays, the noise pollution has placed a lower priority on other pollutions, because it`s hygienic dangers are not speedily visible. Growth of pollution, increasing in the number of motorize vehicles, industry expending, On the whole, extensive life with developing technology and also human`s society by making harsh sounds cause industrial pollution which has harmful effects. The noise pollution in Iran endangers people`s hearing and health (specially the aged and children), furthermore, it has detrimental traumatic effects, particularly in industrial metropolises like: Arak, Tehran, Shiraz, Esfahan. Objective: This paper uses descriptive method to scrutinize traffic noise and level of it. Results Researches show that setting proper and functional barriers could decrease the noise about 10 to 15 decibel. Conclusion: Noise caused by traffic is never constant; it changes by changing the traffic affective elements, therefore, to securitizing, studying or legislating about its controlling, using a method which is able to calculate this changeable noise is important.

INTRODUCTION

Noise and hullabaloo are inseparable parts of the modern and semi modern life. Growth of population, increasing in number of motor vehicles, roads traffic, ear-rending noise of airplanes and also city and intercity trains, etc., are some examples for the noise pollution which threaten organisms` health and quiet, particularly human beings [START_REF] Pamanikabud | Geographical information system for traffic noise analysis and forecasting with the appearance of barriers[END_REF]. Todays, including the noise pollution among environmental pollutions and studying about it`s negative effects on human life make experts to scrutinize some elements of producing noise pollution like: automobiles and traffic noise, then recognize and define it`s reducer. Most of the environmental experts believe that in recent years, noise from the viewpoint of environmental pollution is in the same rank of other pollutions.

During the last decade, producers and designer mostly competed in manufacturing automobiles which use less fuel while they have most obedience but these years [START_REF] Mobasseri | Impact of driving style on fuel consumption[END_REF], designers try to decrease emitted noise in the cars. As a means of similar expression, the noise pollution is: any diffuse and emitted noise in special time and place.

Noises as the same as air pollution increases by growth of population, particularly today mechanical and industrial lifestyles intensify rate of the noise pollution; Some of the noise polluters in our modern industrial life are: using private vehicles (cars, motorcycles), public vehicles (airplanes, trains) and also other sources like power plants and producer factories. These problems caused that noise measurement becomes a prelude to the defining priority and identifying effected place, also it helps judge about noise result and it`s controlling ways.

By having information and basic data about who exposed to noise could predict condition of pollution and scrutinize it`s effects.

The noise pollution:

Harmful effects of the noise pollution can be classified in 2 groups:

a) Direct effects:

Losing the power of hearing is the most prevalent effect of noise on humans, even harmless noise when is heard for long time would be harmful for humans and reduce sensitivity of the ears toward any noise. Hearing a noise more than 100 decibels for 10 minutes need to rest about 20 minutes in a silent place in order to indemnify it`s effect.

Working in crowded noisy place would extirpate hearing cells and bring returnable deafness in its wake which idiomatically is called job deafness. Earthquake and firelight noise Quick breaking in faults of the crust causes earthquake. How much being nearer to the epicenter, louder noise would be heard.

Fire flight is a violent and rapid electrical discharge which releases so much electrical energy; this noise is product of tearing in air layers.

2-Fixed sources of noise:

It includes: Gas power plants Gas power plans make too much noise because they have some equipment like: gas turbine, compressor, combustion chamber, strong fans, etc. and it is annoying for persons who are near to such these power plants

3-Unfixed sources of noise:

All vehicles and traffic noise The use of public vehicles (city trains) or private vehicles (cars, motorcycles) makes the noise pollution. The noise caused by cars is as a result of honking, aerodynamic, tires, side mirror, and the noise which is made by trains is because of road intersections, electrical motor, turning on rails or stopping. The internal sources of noise: electric furniture, internal-combustion engine. Every electric furniture makes noise because of its electric engine. In the internal-combustion engine, compound of fuel and oxidizer react in close chamber, this process makes noise. Generally, the traffic noise is classified in 3 groups:

a) Air traffic:

This noise is caused by airplanes. There are lots of parameters that make noise in airplane but 2 mains are: Airplane engine (motor and other related parts supply energy and power of airplane moving) and passing of airflow on fuselage and wings (aerodynamic noise) (this noise is increased by gaining speed and decreasing altitude because the air molecules are more compressed in this condition)

b) Rail vehicles:

The main reasons for noise in the subway are: Road intersects (embranchments switches), turning on rail, electric motors, electric equipment, signals, locomotives, stopping and also aerodynamic noise [START_REF] Mehrzad | Pollution noise of subway train[END_REF].

c) Motor vehicles and urban traffic vehicles (traffic noise):

Driving vehicles (cars and motorcycles) and also car moving or honking make noise.

The noise makers in cars: 1-Engine:

The most important and the main source in producing car noise is engine; the noise which is made in engine divide in 2 groups:

1-a) Combustion noise: High pressure in cylinder cause to tremble, therefore it emits noise [START_REF] Anderton | Basic origins of automotive engine noise, engine noise & vibration control[END_REF][START_REF] Lalor | Mechanical Noise. Engine Noise& Vibration Control (Course Noise)[END_REF][START_REF] Russell | Combustion Noise and its Control. Engine Noise & Vibration Control[END_REF]. 1-b) Mechanical noise: This kind of noise has 2 factors, the primary and the secondary factor.

The primary factor includes: Engaging gearwheels, shaft spinning, and exerting force on cylinders in the top dead center (TDC) and the bottom dead center (BDC). The secondary factor includes: The exhaust (it spends out smog which is product of chemical reactions in cylinder), water pump and gearwheels [START_REF] Lalor | Mechanical Noise. Engine Noise& Vibration Control (Course Noise)[END_REF][START_REF] Dixon | Simulation Techniques. Engine Noise & Vibration Control[END_REF].

It is worthy of mention that noise emission in the primary factor is more than the secondary.

Transmission system:

The system has 2 functions: It transfers power of engine to drive wheels and changes in amount of torque. Each motor vehicle according to its diesel or gasoline structure of engine needs transmission system to transferring power of engine to its drive wheels. When revolution is lower than redline, by shifting gear, driver can impose the best condition to continue driving or stopping. As it shown below, this system is connected to engine by the clutch, in fact the speed of input shaft is the same as engine speed, and the output shaft is joined to drive shaft which finally caused to engine energy transfer to the drive wheel. The green shaft is connected to the engine by the clutch, this shaft and its joined green gearwheel considered as one part.

Clutch:

As you know the clutch is a part in car which lets driver disconnect or connect the engine to the transmission system. When driver depresses the clutch pedal, cuts the link between engine and the transmission system and by taking off foot, the link is made between them and input shaft spins as fast as engine.

The red shaft and it`s joined gear wheel (lay shaft) are one part, which is affected by the green shaft and spins with it. The yellow shaft joined to the lay shaft so it is affected by wheel spin.

The blue gearwheels are installed to the lay shaft and spin on the yellow shaft. The time when driving on a slope although the car is off and the blue shafts are motionless, the yellow shaft and wheels are spinning. The utilization of the collar is making link between the yellow shaft and one of the two blue gearwheels. By sliding to left or right, the dog teeth can entangle in teeth of one of the two blue shafts.

Fig. 3: Junctions and parts in a system

It is comprehensible, whatever junctions and parts in a system (like cars) are more, it`s noise is also more.

3-Tires:

Noise emission in the tires is caused by vibration in tire wall, it is happening in 500 Hz frequency. Noise which is caused by passing air through tire treads happened in 1000 Hz frequency. In addition, pumping air while tires are spinning makes noise [START_REF] Mobasseri | Intelligent Circuit Application for Detecting the amount of Air in Automobile Tires[END_REF], in the first step, air is detained and compressed between asphalt and tire treads, next, the air spews out with highly pressure. The most important reason of making noise in tires is the tire wall vibration, it is because tire tread blocks smash into road, so noise is produced in the tire tread blocks, indeed the tired treads vibration is the main source.

Noise which is caused by distribution of aerodynamic pressure around car`s body:

This noise is made because of shear motion (caused by viscosity) around car and also chaotic air current in the discontinuous surfaces (like the areas around side mirrors and the first column), it is increased by speeding and wind fluctuation, so aerodynamic noise could be the main reason of making noise in high speed and high frequency [START_REF] George | Automobile aerodynamic noise[END_REF][START_REF] Shojaefard | Numerical study of airflow around vehicle a-pillar region and windnoise generation prediction[END_REF].

From aerodynamic and aerostatic points of view, the side mirrors in car are known as adverse effects producing. The side mirrors change air current pattern and the result is chaotic air flow in the first column of the car, so the side mirrors makes aerodynamic drag force and acoustic noise.

Brake:

How the brake makes noise is as the follow? When driver depresses the brake pedal, this pressure causes the piston of main brake pump goes forward, then piston compresses the brake oil which exists in brake cylinder. As the time pushing, the oil, firmly presses toward the wheel cylinder (by steel hoses connector that are resistant to lateral pressure), consequently internal pistons of wheel cylinder relocated, these pistons transfer the pressure to the brake shoe, then, the brake shoe joins to brake drum, it is obvious that, this process creates friction between the brake drum and shoe. Any kind of jam in parts of the brake wheel cylinder caused problems like noise. Another reason of brake noise is breaking suddenly, in this condition, the friction between tires and earth creates noise. Whichever mentioned above depended on the kind of motor vehicle, car load, quality of parts, speed and acceleration, the road quality (asphalt) in streets and freeways [START_REF] Wilson | Noise control: measurement, analysis, and control of sound and vib ration[END_REF].

Fig. 4: the method of the brake makes noise

Traffic noise:

Recent researches show that major portion of the environmental noise is the noise caused by transportation [START_REF] Fhwa | Highway traffic noise analysis and abatement: Policy and guidance[END_REF].

Daily increasing in highway traffic noise around cities makes problems for our life. Growing the number of motor vehicles and their high speed bring problems around highways [START_REF] Al-Mutairi | Measurements and model calibration of urban traffic noise pollution[END_REF]. Approximately, 120 million of people in the Europe union are exposing to the road traffic noise about 55 decibels and more than 50 thousand of people are vulnerable to about 45 decibel traffic noise. In the reports published by the management of federal highways of America (FHWA), range of noise in Pico state is more than normal range [START_REF] Alesheikh | Application of GIS in urban traffic noise pollution[END_REF].

Standard definer and active international organizations in field of noise pollution: 1-World health organization (WHO):

This organization is one of the specialized institutions in the United Nations organization which practices in worldwide hygienic problems.

2-International labor organization (ILO):

This organization tries in the course of improvement in worker's condition.

3-International civil aviation organization (ICAO):

This organization has a special investigating committee of aircraft noise (CAN).

4-International standard organization (ISO):

This organization is an international nongovernmental organization, Based on these all over the world in lots of small and big cities noise map is prepared and an extensive research has done to reduce noise [START_REF] López | Noise map of the Madrid region[END_REF]. For example, London noise map (London is spacious city from the point of area in Europe) or some parts in the Madrid city (the third gig city from the point of area)

Noise measurement was a prelude to the defining priorty and identify affected place, also it helps to judge about noise results and it`s controlling. Indeed, these researches are very important to determine exact location of hospitals, Infirmary and similar centers (which should be far from noise but in city center). Many international valid standards are defined in term of noise which debate ways of measuring traffic noise and permitted range of noise balance [START_REF] Iso | Acoustics-Measurement of noise emitted by accelerating road vehicles-Engineering method[END_REF][START_REF] Iso | Acoustics Measurmant of noise emitted by stationary road vehicles-Survey method[END_REF].

8. The noise level depends on factors that are divided in 3 groups from one standpoint:

1-Traffic volume:

(Traffic noise of 2000 cars in an hour is twice as much as 200 cars.

2-Traffic speed:

(Traffic noise by the speed of 65 mph, is twice as much as traffic noise by the speed of 55 mph)

3-Kinds of motor vehicles exist in traffic:

(Noise caused by a truck by the speed of 65 mph is as much as the noise of 28 cars by the speed of 55 mph)

Theoretical calculation of traffic noise:

Traffic noise in the proximity of freeways is predictable according to emitted noise by motor vehicles based on their speed, volume, kind of the motor vehicle, distance of the observer from the freeway and noise blocker between them.

In 1978, Rigan has offered a way to calculating noise of engines in the cars, trucks and buses.

Motors vehicles are divided in 3 groups, from the viewpoint of weight and number of axles: 1-Automobile (A): Any motor vehicle with 2 axles and 4 wheels and also small trucks lighter than 450 kg 2-Middle trucks (MT): Any motor vehicle with 2 axles and 6 wheels and also motor vehicles which weight 450 to 12000 kg 3-Heavy trucks (HT): Any motor vehicle with 3 axles or more, like 3axle buses, etc. Calculation, the type of vehicle to the desired speed is done. For certain vehicle types and speeds specified, we take the help of the following equation:

 (1) dt I dt I            2 2 0 0 r D (2)
In the above formula (r) is the distance between the observer and the motor vehicles

         S V L L eqH (4)

Noise traffic securitizing method:

There are some factors which measurement and policy of noise traffic depend to them: Time of measurement: for example, measurement is gotten in peak hour's traffic or in other hours. The day in week: holidays, working days, near the end of week, the early days of week. The months and seasons: hot and cold weather directly effects on traffic noise Every above factor could change measuring result. In a street, measurement should be taken in different places like: Residential zones, commercial zones, amusement parks, educational center, infirmities, offices, etc.

Paying attention to these 2 objects is important: 1-The regulations of this field are different in each county and they depended on the highway kind, street and it`s function.

Noise caused by traffic is never constant; it changes by changing the traffic affective elements, therefore, to securitizing, studying or legislating about its controlling, using a method which is able to calculate this changeable noise is important.

Inference:

There are multiple ways suggested for abating noise pollution caused by motor vehicles traffic, some of them are mentioned below [START_REF] Wilson | Noise control: measurement, analysis, and control of sound and vib ration[END_REF]:

Inter space:

In this way, a space could be left between the highways and the residential zone around them, indeed residential zone should be built far from highways.

The use of sound semi-insulating walls:

These walls are known as (Acoustic obstacle); they could be placed between highways and houses. Appropriate and functional barriers would reduce 10 to 15 decibel of traffic noise. These barriers might be a hill (highly enough), barrier wall or short walls (made of wood, stone, gypsum, concrete or other materials)

The use of appropriate vegetation:

If this kind of insulator has appropriate length, width, thickness and density, it could abate 10 decibel of traffic noise; in addition, this insulator economically and durability is cost-effective.

to insulating buildings:

This way effectively reduces noise.

to stop driving of old motor vehicles:

Stopping the cars which old made has positive effect on noise abating 6. Prevent traffic of some motor vehicles: the cars which install loud honk so produce and emit stridulating.

Identifying and obviating noise makers: a) Engine:

It is the main and the most important source of making noise in motor vehicles, this noise is caused by combustion in engine, noise of injector, mechanical noise, cooling fan noise.

b) Which materials the parts body of motor vehicle is made from:

There are some methods to abate this kind of noise: Changing in materials which used in parts body of vehicle, using of steel or plastic foils with high density, putting steel fixer to reduce and damp the vibration in valve hubcap.

c) Gearwheel noise:

If a pair of gearwheels be completely fixed and regulated, suitable oiling and improving in gearwheel`s surface is useful to abate noise.

Fig. 1 :

 1 Fig. 1: Energy transfer to the drive wheel

Fig. 2 :

 2 Fig. 2: The two-gear system It is clear in the picture that:The green shaft is connected to the engine by the clutch, this shaft and its joined green gearwheel considered as one part.

r 2 D 2

 22 distance from the road If the equations number 2 and 3 placed in equation number 1 get to this formula:

Table 1 :

 1 Permitted limit table of the noise pollution"

	zone	Daytime average level (7 Am-10 Pm)	Night time average level (10 Pm-7 Am)
	Residential zone	55	45
	Residential-commercial zone	60	50
	Commercial zone	65	55
	Residential-industrial zone	70	60
	Industrial zone	75	65
	b) Indirect effects:
	These are some examples of indirect effects:
	Neural sensitivity, extreme provocation, muscles cramp, dizziness, physical and mental tiredness,
	perturbation in sleep, eyesight deteriorating, racing heartbeat
	2.1. Sources of noise:
	1 -Natural sources of noise:


independent researcher Vincent Van Dongen
email: vincent.vandongen@gmail.com

Lifted Aperiodic Hat and Turtle Other bricks, and grids, in the wall

The monotile known as the hat can cover the entire plane and only non-periodically. It is made of 8 kites glued together. This paper presents a version of the hat lifted in 3D. The corresponding polyhedron has some nice properties. In particular, it can be used to erect textured walls. Several versions can be defined but we concentrate on one that provides continuity on the surface of the wall. It is made by gluing together a lifted version of the double-kite. We define this module by integer coordinates on an irrational grid. We also present some layout for creating this module with a sheet of paper. And we show how to lift a variant of the hat called the turtle. Finally, we propose an alternate lift for the double-kite, and therefore also for the hat and the turtle, made only of square grids.

Introduction

A lot of literature exists on aperiodic tiling. See for example (1). In simple words, a tiling is said to be periodic when it is formed of the same tiles being placed the same way in a repeated manner along both dimensions. A tile set is said to be aperiodic when it can pave the entire plane and only non-periodically, The Ein-Stein problem is to find one tile that can cover the plane but only in a non-periodic manner. In other words, such a tile is not able to pave the plane in a periodic manner. See more details in (2). In particular, a recently discovered tile is presented as an answer to that problem, a tile known as the hat. It can be constructed by gluing 8 kites together. A variant of the hat, known as the turtle, is also made of kites; this one is made of 10 kites. Figure 1 shows (a) the kite, (b) three double-kites glued together to form an hexagon, (c) the hat and (d) the turtle. In this paper, we show how to lift the hat and the turtle in 3D. We first explain how to lift a cube. Then we explain how to lift a double-kite. And finally we explain how to lift the hat and the turtle.

Lifting a regular hexagon

Tile lifting is an operation that consists of going from a 2D space into a higher dimension. Our starting point is the regular hexagon shown in Figure 2. The vertices of the cube have integer coordinates in the (dx, dy, dz) grid space.

A regular hexagon can be seen as a projected cube. The coordinates of this cube are all integer values in the basis (dx, 0, 0), (0, dy, 0) and (0, 0, dz), where dx= sqrt(1/6), dy= sqrt(1/2) and dz= sqrt(1/3). These coordinate values are given in Figure 2.

In this document, we will be interested in tiles that are lifted into 3D polyhedrons with mirror sides. We now explain how to lift a regular hexagon this way. There are different possibilities.

Figure 3 shows one such example. Figure 3 also provides the integer coordinates of the lifted hexagon using the irrational (dx, dy, dz) grid. The result of the lift is a polyhedron of 12 faces shown in Figure 4. For a better understanding of this lifted regular hexagon, Figure 5 presents it in spaceframe mode. Lifting a double-kite

The method explained above for lifting a regular hexagon is now applied to lift a double-kite.

Figure 6 shows the double-kite made of rhombuses and half-rhombuses. Just like the regular hexagon, it fits on the irrational grid (dx, dy, dz) defined above. All the vertices of its lifted version can therefore fit on this grid. Like for the lifted hexagon, the vertices are split in two parts, the ones with a positive z value, and their mirror counterparts. The total number of distinct vertices is 15 as p8 and m8 are the same. The faces of the polyhedron created by lifting this way the double-kite are: -<p1, p2, p6 > and <m1 m2, m6> (i.e. its mirror counterpart) -<p2, p6, p7> and <m2, m6, m7> (i.e. its mirror counterpart) -<p2, p3, p7> and <m2, m3, m7> (i.e. its mirror counterpart) -<p6, p7, p3, p8> and <m6, m7, m3, m8> (i.e. its mirror counterpart) -<p3, p4, p8> and <m3, m4, m8> (i.e. its mirror counterpart) -<p4, p5, p6, p8> and <m4, m5, m6, m8> (i.e. its mirror counterpart) -<p1, p2, m2, m1>, <p2, p3, m3, m2>, <p3, p4, m4, m3>, <p4, p5, m5, m4> -<p1, p6, p5, m5, m6, m1> The polyhedron corresponding to this lifted double-kite can be created by folding a single piece of paper as shown in Figure 7. Please note here also the symmetry of the layout due to the way we decided to lift the double-kite. Using such a layout, one can create the polyhedron shown in Figure 8.

Lifting the aperiodic hat

By gluing together 4 lifted double-kites, we can obtain the lifted hat shown in Figure 9. Figure 10 shows the positive z values and the corresponding vertices p1 to p24. In the irrational (dx, dy, dz) grid, the vertices of the lifted hat of Figure 10 are:

The final values of the vertices in the 3D space can be easily calculated by multiplying the integer values of the vertices given above by the definition of dx, dy and dz. Take for example p1= (1, 0, 2). Since dx= sqrt(1/6), dy= sqrt(1/2) and dz= sqrt(1/3), its final coordinates become: (sqrt(1/6), 0, 2 sqrt(1/3)). The same conversion can be done for all other vertices.

The polyhedron corresponding to this lifted hat can be used as a brick. By assembling many of these bricks, one can erect a wall. The surface of this wall is continuous, and its texture creates interesting patterns. In order to demonstrate this, we mark the lifted double-kite as shown in Figure 11a. The hat created with 4 of these double-kites is shown in Figure 11b. The logic of this marking is as follows. A red circle is placed on the pyramid pointing outside, ie. of z-value equal to 2. . (We could have decided to mark the pyramid pointing inside, i.e. of z-value equal to zero, what's important is to remain consistent.) The partial pyramids are marked in blue. The patterns created with such marks are well structured, with hexagons in green, all containing 3 red dots and surrounded by blue triangles. The position of the red dots changes from one hexagon to the next and this makes the structure non-periodic.

By creating the lifted version with the proposed 3D layout and no marking, we obtain the same structure: the blue triangles and the red dots are pointing-out 3D pyramids, while the green triangles are pyramids pointing inside.

Lifting the aperiodic turtle

The aperiodic turtle is made of 5 double-kites. The lifted turtle can be obtained by gluing together 5 lifted double-kites. Using the same marking as above, we can compare the lifted turtle to the lifted hat. See Figure 12. The definition of the lifted turtle can make use of the irrational grid (dx,dy,dz) introduced above.

Figure 13 shows the turtle. On the left, the assembly of the 5 double-kites and the positive z values for the vertices. On the right, the simplified version as all z-value is the same at any given vertex, ie. its surface is continuous.

Now with square grids

We now show an alternate implementation of the lifted double-kite that is only made of square grids. The idea here is to create the module for the hat and for the turtle that is not a polyhedron but assembled square-grid surfaces instead. Note that there is a corresponding polyhedron but it is a more complicated one.

In other words, instead of creating the lifted double-kite with folded paper, we make the lifted double-kite out of grids, by bending them and assembling them, without anything else than grids. The application is a space-frame module made of grids. This module can be used as a building block to create large planar frame structures.

Figure 14 shows the lifted double-kite using the same the (dx, dy, dz) as before. On the left, the positive z values, in terms of dz, are provided at every vertex. The vertices are numbered on the right. As an example, the coordinates of p1 are in this case: (2, 0, 3). Figure 14 provides the coordinates of all vertices of positive z value. As before, there is a mirror image as well with minus z values instead. As an example, the coordinates of m1, the mirror vertex of p1, are (2, 0, -3).

Figure 14: A lifted double-kite that can be implemented with square grids.

Here the number of vertices is 20, i.e. 2x7+6, as 6 of them are of zero z coordinate. In order to create this object with grids, one can bend a single grid. Figure 15 shows the grid layout of this object.

Figure 15: Grid layout of the lifted double-kite.

Figure 16 shows the result of using the layout of Figure 15. Finally, when removing the colors of Figure 17 and keeping only the grid, we obtain the grid modules and structures of Figure 18.

Conclusion

There are many ways to lift the aperiodic hat monotile. This paper presents a polyhedron that is a lifted version of the hat made by gluing together 4 times a lifted version of a double-kite. It can be used to erect walls and its texture is continuous with patterns that never repeat. A variant of the hat, known as the turtle, was also lifted the same way.

There are many different ways of lifting the double-kite. Another way is presented that makes use of square grids. This module can be used as a building block to create large planar frame structures. By choosing the proposed lifted aperiodic hat as a module, or the proposed lifted aperiodic turtle as a module, one can create aperiodic structures.

Interesting markings of these lifted structures were presented that highlight this. Further analysis of these marks may provide more insights on their properties, but this is outside the scope of this paper. One brick at a time...

Figure 1 :

 1 Figure 1: (a) The kite, (b) a regular hexagon made of 3 double-kites, (c) the aperiodic hat monotile and (d) its variant called the turtle.

Figure 2 :

 2 Figure 2: On the top left corner, a cube projected into a regular hexagon. At the bottom left corner, the cube shown from above. All the vertices of the cube are on a grid of size (dx, dy, dz).The vertices of the cube have integer coordinates in the (dx, dy, dz) grid space.

Figure 3 :

 3 Figure 3: On the top left corner, the regular hexagon. Just below, its lifted version that is seen from the top; it is symmetrical along the z axis. For any vertex (x,y,z) with a positive z value, there is a vertex (x, y, -z). The positive z vertices are noted p1 to p7. The minus z vertices are noted m1 to m7. The layout for a paper version of the corresponding polyhedron is shown at the center. Please note the mirror symmetry of the layout.

Figure 4 :

 4 Figure 4: Polyhedron obtained by lifting a regular hexagon.

Figure 5 :

 5 Figure 5: Spaceframe version of the polyhedron obtained by lifting a regular hexagon.

Figure 6 :

 6 Figure 6: A way to lift the double-kite.

Figure 7 :

 7 Figure 7: Layout for creating the polyhedron of the lifted double-kite in paper. Note that the line in the middle is only there to show the symmetry.

Figure 8 :

 8 Figure 8: Lifted version of the double-kite. Paper version and spaceframe mode.

Figure 9 :

 9 Figure 9: (a) The lifted double-kite and (b) the lifted hat obtained by gluing together 4 lifted double-kites. At any given vertex, all z values are the same, ie. its surface is continuous.

Figure 10 :

 10 Figure 10: The lifted hat created by gluing together 4 lifted double-kites. Its vertices of positive z value are shown. On the left, for each vertex, the integer value is the number of its dz units. On the right, a label is provided for each vertex of positive z value.

Figure 11 :

 11 Figure 11: (a) Double-kite with a marking that creates interesting patterns, (b) hat using such a marking, and (c) pattern obtained by assembling several hat tiles together.

Figure 12 :

 12 Figure 12: (a) The aperiodic hat made of 4 double-kites with lifting decoration vs (b) the aperiodic turtle using 5 of the same double-kite.

Figure 13 :

 13 Figure 13: The aperiodic turtle and its integer coordinates on the (dx, dy, dz) irrational grid.

Figure 16 :

 16 Figure 16: Handmade lifted double-kite using one single grid layout.

Figure 17 :

 17 Figure 17: Grid-based implementation of (a) the hat and (b) the turtle and the corresponding non-periodic patterns created when tiling.

Figure 18 :

 18 Figure 18: (a) the lifted hat made of square grids and (b) the lifted turtle made of square grids, and tilings created using them.

-p1= (1, 0, 2) and m1= (1, 0, -2) (ie. its mirror counterpart) -p2= (0, 1, 1) and m2= (0, 1, -1) (ie. its mirror counterpart) -p3= (3, 2, 1) and m3= (3, 2, -1) (ie. its mirror counterpart) -p4= (3, 4, 1) and m4= (3, 4, -1) (ie. its mirror counterpart) -p5= (5, 4, 2) and m5= (5, 4, -2) (ie. its mirror counterpart) -p6= (6, 5, 1) and m6= (6, 5, -1) (ie. its mirror counterpart) -p7= (9, 4, 1) and m7= (9, 4, -1) (ie. its mirror counterpart) -p8= (9, 2, 1) and m8= (9, 2, -1) (ie. its mirror counterpart) -p9= (11, 2, 2) and m9= (11, 2, -2) (ie. its mirror counterpart) -p10= (12, 1, 1) and m10= (12, 1, -1) (ie. its mirror counterpart) -p11= (9, 0, 1) and m11= (9, 0, -1) (ie. its mirror counterpart) - p12= (6, 1, 1) andm12= (6, 1, -1) (ie. its mirror counterpart) -p13= (5, 0, 2) and m13= (5, 0, -2) (ie. its mirror counterpart) -p14= (3, 0, 1) and m14= (3, 0, -1) (ie. its mirror counterpart) -p15= (2, 1, 2) and m15= (2, 1, -2) (ie. its mirror counterpart) -p16= (4, 1, 0) = m16 -p17= (5, 2, 2) and m17= (5, 2, -2) (ie. its mirror counterpart) -p18= (4, 3, 0)= m18 -p19= (6, 3, 1) and m19= (6, 3, -1) (ie. its mirror counterpart) -p20= (7, 2, 2) and m20= (7, 2, -2) (ie. its mirror counterpart) -p21= (7, 4, 2) and m21= (7, 4, -2) (ie. its mirror counterpart) -p22= (8, 3, 0)= m22 -p23= (8, 1, 0)= m23 -p24= (10, 1, 2) and m24= (10, 1, -2) (ie. its mirror counterpart)

We can now list the faces of the polyhedron corresponding to this lifted hat:

-<p1, p2, p14> and <m1, m2, m14> (ie. its mirror counterpart) -<p2, p14, p15> and <m2, m14, m15> (ie. its mirror counterpart) -<p2, p3, p15> and <m2, m3, m15> (ie. its mirror counterpart) -<p3, p16, p14, p15> and <m3, m16, m14, m15> (ie. its mirror counterpart) -<p3, p12, p16> and <m3, m12, m16> (ie. its mirror counterpart) -<p12, p13, p14, p16> and <m12, m13, m14, m16> (ie. its mirror counterpart) -<p3, p4, p18> and <m3, m4, m18> (ie. its mirror counterpart) -<p3, p16, p12, p17> and <m3, m16, m12, m17> (ie. its mirror counterpart) -<p3, p18, p19, p17> and <m3, m18, m19, m17> (ie. its mirror counterpart) -<p4, p5, p19, p18> and <m4, m5, m19, m18> (ie. its mirror counterpart) -<p12, p17, p19> and <m12, m17, m19> (ie. its mirror counterpart) -<p4, p5, p19> and <m4, m5, m19> (ie. its mirror counterpart) -<p6, p19, p21> and <m6, m19, m21> (ie. its mirror counterpart) -<p12, p19, p20> and <m12, m19, m20> (ie. its mirror counterpart) -<p6, p7, p21> and <m6, m7, m21> (ie. its mirror counterpart) -<p7, p22, p19, p21> and <m7, m22, m19, m21> (ie. its mirror counterpart) -<p8, p20, p19, p22> and <m8, m20, m19, m22> (ie. its mirror counterpart) -<p8, p23, p12, p20> and <m8, m23, m12, m20> (ie. its mirror counterpart) -<p11, p12, p23> and <m11, m12, m23> (ie. its mirror counterpart) -<p8, p23, p11, p24> and <m8, m23, m11, m24> (ie. its mirror counterpart) -<p8, p9, p10> and <m8, m9, m10> (ie. its mirror counterpart) -<p8, p10, p24> and <m8, m10, m24> (ie. its mirror counterpart) -<p10, p11, p24> and <m10, m11, m24> (ie. its mirror counterpart) -<p1, p2, m2, m1> -<p2, p3, m3, m2> -<p3, p4, m4, m3> -<p4, p5, m5, m4> -<p5, p6, m6, m5> -<p6, p7, m7, m6> -<p7, p8, m8, m7> -<p8, p9, m9, m8> -<p9, p10, m10, m9> -<p10, p11, m11, m10> -<p11, p12, m12, m11> -<p12, p13, m13, m12> -<p1, p14, p13, m13, m14, m1>