INFINITELY VARIABLE TRANSMISSION USING FOUR BAR MECHANISM

Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) INFINITELY VARIABLE TRANSMISSION USING FOUR BAR MECHANISM Dr.N. ARUNKUMAR1 1 Professor, Department of Mechanical Engineering, St. Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai,Tamil Nadu-600119, India. [email protected] R. SANTHOSH2 2 Graduate, Department of Mechanical Engineering, St. Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu-600119, India. [email protected] S. SUNIL SUBRAMANIAM3 3 Graduate, Department of Mechanical Engineering, St. Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu-600119, India. [email protected] ABSTRACT Most of the continuously variable transmission systems in automobiles now-a-days are non-positive drives. This means that they cannot be used in heavy vehicles that require very high torque to be transmitted. This new type of infinitely variable transmission is aimed at transmitting high torques by making it a positive drive, thus making continuously variable transmission systems to be suitable for heavy vehicles. Infinitely variable transmission system and continuously variable transmission system are both the same except that there is an extra zero gear ratio in infinitely variable transmission system. This newly developed transmission system is basically a four bar mechanism with variable crank radius which makes it possible to have continuously variable mechanical advantage. The output lever which oscillates in the four bar mechanism is connected to a ratchet mechanism which turns the output shaft intermittently, two four bar mechanisms with a phase difference of 180 degrees is used to avoid the intermittent rotation of the output shaft. A flywheel is used in the output shaft to reduce the fluctuations in both speed and torque. Keywords- Continuously variable transmission (CVT), Infinitely Variable Transmission (IVT), four bar mechanism, angular velocity ratio theorem, mechanical advantage, Positive drive. 1. Introduction The continuously variable transmissions used now- a-days in two wheelers (scooters) consists of a belt drive with variable diameter pulley. This works very well for two wheelers, since it requires only less torque to be transmitted. But it cannot be used for heavy duty vehicles, since the belt will start to slip at higher torques. It is not used in cars for the same reason. For this reason, an infinitely variable transmission has been developed which does not have non-positive drives. The drive is also smooth because there is no need for changing gears manually. The manufacturing cost is also reduced with this design. The cost is reduced since the components used are relatively simple to manufacture. It can be easily automated. This type of transmission does not need much maintenance because of the reduced number of components compared to the other types of automobile transmission. Many types of continuously variable transmissions have been developed, but most of the commercially available continuously variable transmission systems are non-positive drives. Most of them are continuously variable type which means that they cannot be brought to neutral or zero gear ratio. But this type of infinitely variable transmission with easier control on gear ratios could be very useful for automobiles. The output shaft from the transmission is driven by a ratchet because of which the torque cannot be transmitted in the reverse direction i.e. from the vehicle’s wheel to the engine; this is a very big advantage as it is very comfortable to the passengers in the vehicle (the dragging feeling is not felt when the driver releases the throttle pedal). Another advantage of this type of transmission system is that there is no need of clutch, because the power can be transmitted from the engine crank shaft to the vehicle’s wheels and the reverse is not possible. So the engine will still be running even if the vehicle stops suddenly, there is no need of a clutch. ISSN : 0975-5462 Vol. 6 No.4 Apr 2014 170 Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) 2. Components A four mechanism consists of four links, three moving links with one fixed link. The components involved in this design are shown in fig. 2.1. The components in this transmission system are: 1. Four bar mechanism – two numbers (with phase difference of π radians) (i) Crank – variable radius (lead screw mechanism) (ii) Lever – connected to output shaft with ratchet mechanism (iii) Connecting rod (iv) Fixed frame – body of the mechanism 2. 3. Pulley in input shaft – connected to engine with a belt. Output shaft Fig. 2.1 CAD model of the transmission system. 3. Working The four bar mechanism should strictly follow Grashof’s theorem which states that “for a planar four-bar linkage, the sum of the shortest and longest link lengths cannot be greater than the sum of the remaining two links length if there is to be continuous relative rotation between two members” [1]. This transmission works on the principle that the angular speed of the lever varies directly with the radius of the crank shaft. The magnitude of this angular velocity ratio could be found using the angular velocity ratio theorem which states that “the angular-velocity ratio of any two bodies in planar motion with respect to a third body is inversely proportional to the segments into which the common instant center cuts the line of centers” [1].The crank is connected to the engine and the lever is connected to the output shaft. Since we can obtain only oscillating motion in the lever, a ratchet mechanism is used, which converts oscillating motion to rotating motion of the output shaft. This output shaft will rotate only half a revolution for every rotation of the crank shaft, so another crank is used with a phase difference of π radians. So, continuous rotation is obtained in the output shaft. When the crank radius is small, the speed ratio is large and viz versa. The radius of the crank is varied with lead screw mechanism. The lead screw mechanism is placed radially in the crank.The connecting rod is attached to the nut of the lead screw mechanism through a rotary joint. Thus, the radius of the crank is now varied just by rotating the lead screw which moves the nut inwards or outwards depending on the direction of rotation of the lead screw. So when the lead screw is rotated, the nut moves, which increases or decreases the radius of the crank depending on the direction of rotation of the lead screw. The lead screw is rotated with a small electric motor (not shown in the fig. 2.1) which itself is placed in the crank and rotates with it. This electric motor is coupled directly to the lead screw. Therefore this electric motor has direct control of the lead screw rotation which leads to the control of crank radius. The crank radius is therefore controlled electronically based on the output torque requirements. The wires seen in the crank in fig. 3.1 are the electrical connections to the motor. The two motors are connected in parallel configuration. The wires connecting the two electric motors pass through the hollow input shaft. ISSN : 0975-5462 Vol. 6 No.4 Apr 2014 171 Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) Fig. 3.1 Actual picture of the working model. The working model shown in fig. 3.1 is driven manually for testing purposes. The actual transmission system will have the input shaft connected to the engine crank shaft. When the crank rotates, the lever oscillates causing the ratchet mechanism to turn the output shaft intermittently.This intermittent motion is avoided by using two four bar mechanisms which have a phase difference of π radians. Therefore when one of the levers is in its idle stroke the other lever is in its driving stroke. This leads to the continuous smooth motion of the output shaft. In the working model a ratchet spanner has been used as a lever which serves as a ratchet mechanism as well. The working model shown in fig. 3.1 has a variable crank length of 0 to 200 mm, connecting rod of length 400 mm, lever of length 200 mm, and a fixed link length of 400 mm. 4. RESULTS AND DISCUSSION The evaluation of the performance of this transmission system is carried out based on the output torque vs. crank or input shaft angle diagram. This diagram is used particularly because of the four bar linkage used in this system. The four bar linkages are characterised by an important parameter called the transmission angle [1]. Since the transmission angle varies continuously when the transmission system is operating, the output torque transmitted by the system also fluctuates. The transmission angle is one of the indices of merit of the linkage. John Joseph Uicker et al. [1] suggests that a mechanism should have transmission angle of about 90° for maximum efficiency and superior mechanical advantage [1]. The theoretical analysis on the torque vs. crank angle relation will be derived in the following discussions for this transmission system. 4.1 Theoretical output torque vs. crank angle relation The transmission angle of the four bar linkage is entirely dependent on the geometry of the four bar linkage, so it can be found accurately with some trigonometric calculations. First the mathematical relation between the output lever angles to the input crank angle is derived. Based on this relation the transmission angle is derived. The force due to the torque on the input shaft is resolved, based on the angles between the various members of the four bar linkage, the output force and the output torque on the lever is evaluated. A mathematical relation is obtained for the output torque with the crank angle as the input parameter. This is plotted in a graph to evaluate the results. The steps discussed above are detailed using the following mathematical equations. ISSN : 0975-5462 Vol. 6 No.4 Apr 2014 172 Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) Fig. 4.1 fouur bar mechanism The distancce between thee points A and B is given by, AB CB B cos θ OC OA c θ cos C CB sin θ OA sin θ Eq. (1) Using the above equationn the value of θ' is found byy trial and errorr in Microsoft Visual Basic 2010 2 express for f mputer program m substitutes different d valuess of θ’ in the aabove equation till the equatioon every value of θ. The com ks are known. satisfied, since the lengthhs of all the link Using the value of θ' ob btained above, the length of the diagonal OB O is found byy using the coosine law for thhe triangle OB BC. OB OC O BC OC BC cos θ Eq. (2) Using the length l of diagoonal OB, the coosine law is appplied to the triaangle OAB to find the value of Φ. Φ cos F I O O Eq. (3) O The force acting a on the crank is given by, b Eq. (4) O The force due d to the torq que applied on the t input shaftt is perpendicullar to the crankk, this force should be resolveed to get the component c of force f that is actting on the connnecting rod. F F γ 6 F F cos Φ Eq. (5) The sum of o angles insid de a quadrilateeral is 360 deggrees, so the trransmission anngle γ can be found using thhe following equation, e θ Φ θ Eq. (6) The outputt force acting on o the lever is given g by, cos γ Eq. (7) The outputt torque is giveen by, Output torrque F leenth of lever BC Eq. (8) The mechaanical advantagge is given by, Mechanicaal advantage ISSN : 0975-5462 Eq. (9) Vol. 6 No.4 Apr 2014 173 Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) The mechanical advantage changes for different values of crank angle, so the entire calculation is done for every crank angle from 0 to 6.28 radians in Microsoft Visual Basic 2010 express and they are plotted. The various plots of mechanical advantage (gear ratio) vs. crank angle for different crank radius are shown below, Crank radius = 20 mm Crank radius = 50 mm 12 Mechanical advantage→ 4.5 Mechanical advantage → 4 10 3.5 8 3 2.5 6 2 4 1.5 1 2 0.5 0 0 0 2 4 6 8 0 2 4 6 Crank angle (radians) → Crank angle (radians) → 8 Fig. 4.2. Mechanical advantage vs crank angle for crank radius 20mm and 50mm Crank radius = 150 mm Mechanical advantage → Mechanical advantage → Crank radius = 100 mm 2.5 2 1.5 1 0.5 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0 2 4 6 8 Crank angle (radians) → 0 2 4 6 8 Crank angle (radians) → Fig. 4.3. Mechanical advantage vs crank angle for crank radius 100mm and 150mm From the above plots it is observed that the mechanical advantage is higher for smaller crank radius and decreases as the crank radius is increased. And the momentary lag of one four bar mechanism is compensated by the other which is operating with 180° phase difference. Thus a continuous rotation is obtained at the output shaft. To have a constant torque output a flywheel is used, from which the output is transmitted to the wheels. Thus the fluctuations in the mechanical advantage vs. crank angle diagrams shown in fig 4.2 and fig 4.3 are reduced using a flywheel; therefore the output shaft will have a constant mechanical advantage for all crank angles as shown in fig 4.4. ISSN : 0975-5462 Vol. 6 No.4 Apr 2014 174 Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) Mechanical advantage → Crank radius = 20 mm 10 9 8 7 6 5 4 3 2 1 0 0 2 4 6 Crank angle (radians) → Fig. 4.4 Mechanical advantage vs. crank angle with flywheel for crank radius 20 mm. crank angle vs. lever angle(θ'), crank radius = 50 mm 2.5 Lever angle(radians) → Lever angle (radians) → crank angle vs. lever angle(θ'), crank radius = 100 mm 2.5 2 1.5 2 1.5 1 1 0.5 0.5 0 0 2 4 Crank angle (radians) → 0 0 6 2 4 6 Crank angle (radians)→ crank angle vs. lever angle(θ'), crank radius = 150 mm Lever angle(radians) → 3 2.5 2 1.5 1 0.5 0 0 2 4 6 Crank angle (radians) → Fig 4.5 Crank angle vs. lever angle (θ') for different values of crank radius ISSN : 0975-5462 Vol. 6 No.4 Apr 2014 175 Dr.N. Arunkumar et al. / International Journal of Engineering Science and Technology (IJEST) The plot shown in fig 4.5 is based on the calculations in section 4.1 and the values have been generated by using a simple computer model programmed in visual basic 2010 express, the calculations have been programmed in the computer model. It is obvious from the plots in fig 4.5 that the lever stroke angle (difference between the maximum and minimum lever angles) is directly proportional to the crank radius and thus the speed ratio is directly proportional to the crank radius. 5. CONCLUSION AND SCOPES IN FUTURE Infinitely variable transmission system can be an effective replacement for the conventional continuously variable mechanism .This can be used in heavy vehicles, SUVs etc., and the maintenance of this mechanism is easier compared to the conventional continuously variable transmission (CVT). The construction is also very simple compared to continuously variable transmission (CVT).There are several other types of infinitely variable transmission, but most of them are non- positive type, but thistype of transmission is positive type so it can be used for higher torque transmission. It is also suitable for buses and military vehicles, so it reduces the effort made by the driver. It also reduces driver’s effort in shifting gears which increases his concentration on the road. This type of transmission can also provide rapid acceleration and deceleration of the vehicle. This type of transmission also has lesser moving parts which considerably reduces the frequency of maintenance. One of the main advantage is that, clutch is not required in this type of transmission.It is the most fuel efficient transmission since it can be in neutral (engine turns but power not transmitted like bicycle) when the vehicle is moving in inertia force. 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