The Conception and Kinematic Simulation of a Cam Mechanism Continuously Variable Transmission

ZHANG Jinxi，TAN Fen，CAI Wei

Chonqing University of Technology，Chonqing 400054，China

1.Introduction

Continuously Variable Transmission(CVT)is one of the most promising research area in the field of drive at present，it can make engines and transmissions work in the best matching condition，and prolong the service life of engines effectively.Currently，mechanical stepless transmission is the most popular type of CVT，including friction type，chain type，belt type and pulsing type［1］.The study of mechanical stepless transmission in foreign countries has a long history，but started relatively late in China，so there is still a certain gap on the key technology between China and foreign countries［2］.In this paper，a new structure of mechanical stepless transmission is presented，and it can theoretically obtain a uniform output movement.By processing kinematic simulation through software ADAMS，the simulation results and the theory study are matched very well.

2.Structure

The structure of the new mechanical stepless transmission designed in this paper is shown in Fig.1，it is mainly composed of three parts—spacial conical cam mechanism，parallelogram mechanism and overrunning clutch.There are three groups of the mechanism which consists of swing link，spline shaft，parallelogram mechanism and overrunning clutch，and they are arranged evenly with an angular distance of 120 degrees around the camshaft.

Fig.1 The structure

3.Working principle

As shown in Fig.1，the uniform rotation of this transmission is input by the input shaft，transferred to the swing link through the conical cam，and passed to the parallelogram mechanism through the spline shaft.Then，the output shaft is driven to rotate by the 3 overrunning clutches and obtains an uniform motion.If the contact position of the swing link and the conical cam is changed，the input/output transmission ratio will be different.When the rotational speed of the input shaft is constant and the swing link contacts the conical cam at the large end，the rotation angle of the swing link is larger in the same long time，and the speed of swing link become faster，meanwhile the rotational speed of the output shaft become faster as well.On the contrary，when the swing link contacts the conical cam at the small end，the speed of swing link become slower，so the rotational speed of the output shaft is decreased as well.

3.1.The principle of the swing link’s uniform motion

In order to obtain a uniform rotation of the output shaft，the conical cam’s uniform rotation must be transferred to the swing link.Therefore，when we take the motion law of the swing link into account，a combined motion law of the uniform motion and sine acceleration is chosen，as shown in Fig.2.While choosing such combined motion law，the uniform rotation can not only be obtained，but also excessive impact is avoided during the operation process［3］.Fig.3 illustrates the section of the model’s conical cam，the lift angle of the swing link is 30 degrees when it is at the large end of the conical cam，the lift angle is 10 degrees when it is at the small end.The length of the conical cam is 300mm，and the base circle radius of the large end is equal to that of the small end.

Fig.2 The motion law of the swing link

Fig.3 The section of the conical cam

3.2.Stepless speed change principle

Stepless speed change can be achieved by the continuous axial changes of the contact position of swing links and the conical cam.When the input speed is constant，the output speed will be changed with the relative axial position of swing links and the conical cam.There are two methods to realize stepless speed change in this study:one is to make the cam move along the input shaft while keep the position of swing links unchanged;the other is to make the 3 swing links move the same distance along the spline shaft while keep the position of the cam unchanged.If choose the second method，the design of the spline shaft must meet a prerequisite，i.e.，the length of the spline is greater than the length of the conical cam plus the thickness of the swing link.

4.Kinematic simulation

Import the model built in solidworks2007 into ADAMS to process kinematic simulation.From Fig.1，it is known that the movement is input by the input shaft，and then drives the conical cam to do uniform rotation.The cam profile is designed according to the cam follower’s combined motion law of the uniform motion and sine acceleration.When swing links are at the large end of the conical cam，angular velocities of the 3 swing links are shown in the following figures(counting from left to right，the third swing link is named as swing link 1，and the remaining two swing links are named successively as swing link 2 and swing link 3 with the clockwise direction).From the simulation results，the maximum angular velocity of swing links is in the range of 168.5～169.5(°)/s.The movements of swing links are transferred to overrunning clutches through spline shafts and parallelogram mechanisms，so the input motions of overrunning clutches are equal to the angular velocities of swing links as the speeds of the two cranks are equal in a parallelogram mechanism.

Fig.4 The angular velocity of swing link 1

Fig.5 The angular velocity of swing link 2

Fig.6 The angular velocity of swing link 3

Once putting these parameters into the formula，the maximum angular velocity of swing links can be calculated.When swing links are at the large end of the conical cam，the value is 168.75(°)/s.Furthermore，the simulation result is in the range of 168.5～169.5(°)/s，so the simulation results and the theoretical value are matched very well.

The rotation motions of 3 swing links are turned into unidirectional movements through their overrunning clutch respectively，and the negative value of the angular velocity are filtered out.In this case，the maximum output speed of three overrunning clutches is the rotation speed of the output shaft.This process could be realized through a simulation function:

MAX(AKISPL(time，0，SPLINE_1，0)*PI/180，MAX(AKISPL(time，0，SPLINE_2，0)*PI/180，AKISPL(time，0，SPLINE_3，0)*PI/180)

In the above expression，SPLINE_1，SPLINE_2 and SPLINE_3 represent the speed spline curves of swing link 1，swing link 2 and swing link 3，respectively.The function of AKISPL is to get interpolations of all spline curves according to the interpolation mode of Akima.The first two parameters are the independent variables，the first independent variable is time and the second one is set as zero，the third parameter is the name of the spline curve which is needed，and the fourth parameter is the order of the spline curve and it is set as zero.The function MAX is used to compare two numbers，and output the greater one.There are three numbers to compare，so a nested form is needed.Fig.7 shows the output shaft’s rotational speed，the maximum speed is 169.24(°)/s，the minimum speed is 168.71(°)/s and the average speed is 168.76(°)/s.

Fig.7 The rotational speed of the output shaft

Similarly，when swing links are at the conical cam’s small end，the output shaft’s maximum speed is 56.47(°)/s，the minimum speed is 56.23(°)/s and the average speed is 56.25(°)/s as illustrated in Fig.8.

Fig.8 The rotational speed of the output shaft

5.Performance analysis

There are many indexes to evaluate the performance of mechanical stepless transmission，the most important two indexes are the motion stationary and variable speed performance.The two indexes of the new-type mechanical stepless transmission designed in this paper will be discussed，respectively，in the following paragraphs.

5.1.Motion stationarity

The conical cam is the core component of CVT，and its profile is designed according to the cam follower’s combined motion law of the uniform motion and sine acceleration.Therefore，the output shaft could obtain a uniform rotation in theory.In fact，it is impossible to get an absolute uniform motion because the speed of these components is also affected by other factors such as the mass of components，inertia force and inertia moment.

The motion stationarity of machines refers to the degree of mechanical speed fluctuation，and it is usually described by speed fluctuation coefficient δ［4］:

In the above formula，ωmaxrepresents the maximum angular velocity of the output shaft，ωminrepresents the minimum angular velocity of the output shaft，ωmrepresents the average angular velocity of the output shaft.

Plug the simulation results of Fig.5 into the formula，the speed fluctuation coefficient δ could be obtained.When swing links contact the conical cam at the large end，δ=0.31%.Similarly，the speed fluctuation coefficient δ=0.43%when the swing links are at the conical cam’s small end.At the same speed，the speed fluctuation coefficient δ of traditional pulse-type stepless transmission is in the range of 25% ～30%［5］.Therefore，the CVT presented in this paper has an obvious advantage on the motion stationarity.

5.2.Variable speed performance

The transmission ratio and the variation speed ratio could be different through the design of structure size for the conical cam.For example，we can either change the taper of the came or change the length of the came with a constant taper.

6.Conclusions

The mechanism characteristics of the new-type continuously variable transmission could be described as follows:

1)The proposed mechanism is more innovative than that of traditional CVT due to the simple structure，which is composed of spacial conical cam mechanism，parallelogram mechanism and overrunning clutch.

2)Since the profile of the conical cam could be obtained according to the combination of uniform motion law and sine acceleration for cam follower，the mechanism can not only get the uniform motion，but also avoid the acceleration catastrophe during the operation process.

Although a very ideal effect has been obtained by simulation and the result is very close to the theoretical value，there are still some deficiencies.For example，the mechanism might not bear large load due to the structure of overrunning clutches.If the performance of new-type CVT could be further better on this basis，it might provide a new breakthrough for the study of mechanical stepless transmissions.

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