updated on July, 2017

## Introduction

The aim of the project is to analyze a synchroniser mechanism for manual gearbox. In literature there are many type of synchronizer:

- Pin-type (also known as Clark type)
- Baluking-type
- Lever-type
- etc.

In Fig.1 is reported the explosed view of a baulking type synchronizer assembly ; for the further steps the parts are called starting from the left:

- Shaft
- Gear
- Synchronizer Clutch
- Synchronizer Ring
- Synchronizer Hub
- Synchronizer Cone Push or (“strut detent”)
- Synchronizer Ring (for the specular part of mechanism)
- Sliding Sleeve

(In the following link it is possible to see how to mount the assembly https://youtu.be/CNz1COQIo38)

The working principle can be described by 8 fundamental steps :

- First free fly: The sleeve moves axially from the neutral position without significant mechanical resistance and make the detent face come in contact with the synchro ring face. In this phase the axial velocity is high and the axial force low.
- Start of angular velocity synchronization: The detent force creates a frictional torque that makes the ring rotate within the available space in the recesses of the synchro hub;
*the oil in between cone surfaces is removed and the spline chamfers of the synchronization ring and sleeve get the maximum contact area and a high coefficient of friction*. - Angular velocity synchronization: This phase is over when the gear, synchro ring and sleeve have the same angular velocity. Otherwise, the equilibrium of axial and tangential forces applied on the spline chamfers prevents from continuation of the gear changing process.
- Turning the synchro ring:
*The synchro ring that was previously heated by the dissipated friction energy, loses the heat and becomes stuck on the cone due to the diameter reduction*. The displacement of the sleeve turn the synchro ring and the clutch gear while the chamfers remain in contact. - Second free fly: The sleeve moves forward axially until approaching the spline chamfers of the clutch gear.
*Start of the second bump: As there is an oil that has to be broken between the chamfer surfaces, an increase of the axial force is required in order to maintain the axial velocity of the sleeve. As the oil is being discharged this axial force suffers a higher increment. This stops when the tangential force component on the chamfers is high enough to turn the synchro ring which was stuck in the cone*.- Turning the gear: The axial force required to turn the gear depends on the relative position of the sleeve splines and gear splines (obtained at the end of the synchronization, phase 3)
- Final free fly: The gear wheel is engaged.

(Italic font is used for the topic that have not been considered in this work )

The real system deals with oil and the friction surface have a certain profile with grooves that give the possibility for the oil to flow away from the friction area. In first analysis for simplify the model the influence of the grooves and the oil interaction have not been considered. The main forces calculated in this model are the Friction Torque, Blocking Torque and Fork Force.

Fork Force is located to the sliding sleeve and gives the acceleration of this body. In the strut detent this force is related to the spring force with:

Where µ_{sl} = µ_{d}_{ }= 0,16 ; φ=60°

The dynamic friction coefficient suggested from ADAMS help is µ_{d}_{ }= 0,16; for further study is appropriate to change into µ_{d}_{ }= 0,11 ÷ 0,14 according to [2],[4] .

Blocking torque or Index Torque (the torque that is generated when the teeth of the sleeve interacts to the synchro ring teeth)

Where µ_{s} = µ_{d}_{ }= 0,16 ; angle of the teeth chamfer : β = 45°; R_{sl }=31 mm

Friction Torque (the torque that is able to slow down or speed up the synch clutch to neglect the relative angular velocity)

Where µ_{c} = µ_{d}_{ }= 0,16; cone angle: α = 7,5° according to [2],[4] ; Rc= 21,375 mm

To clarify more the layout of the mechanism the diagram is shown in figure below:

The arrows represent the joints between one component to the other.

Starting from the beginning:

- Revolute Joint between the Ground and the Shaft
- Fix Joint between the Shaft and the Synchronizer Hub
- Translational Joint between the Sliding Sleeve and the Synchronizer Hub
- Cylindrical Joint between the Synchronizer Ring and the Synchronizer Clutch
- Fix Joint between the Synchronizer Clutch and the Gear
- Revolute Joint between the Gear and the Shaft

There are also a sub-system (i.e. Strut detent) made from Synchonizer Cone Push, the spring and the sphere

Sub-system joints:

- Translational Joint between Synchonizer Cone Push and the Synchronizer Hub
- Translational Joint between Synchonizer Cone Push and the Sphere
- The spring connect c.o.m. of the Synchonizer Cone Push the the c.o.m. of the Sphere

The Grubler count is :

6 d.o.f * n – (R*m + T*o + C*p + F*q)

6 * 8 – (5*2 + 5*3 + 4*1 + 6*2) = 48 – (10 + 15 + 4 + 12) = 48 – 41 = 7 d.o.f.

- ϑx: longitudinal axis angle of Shaft
- ϑx: longitudinal axis angle of Gear
- ϑx: longitudinal axis angle of Synchronizer Ring
- Xcm: c.o.m. x of Synchronizer Ring
- Xcm: c.o.m. x coordinate of Sliding Sleeve
- Xcm: c.o.m. x coordinate of SynchConePush
- Zcm: c.o.m. z coordinate of Sphere

## Objectives

The dynamic simulations are cumputed by the multibody code ADAMS. The plan is to run 3 types of dynamic simulations. The first one where the velocity of the shaft is the same of the gear. In the second one the angular velocity of the gear is greater than the angular velocity of the hub and in the third one the angular velocity of the hub is greater than the angular velocity of the gear.

The system work with inertia property, e.g when velocity of the gear is greater than the velocity of the Shaft/Hub the inputs of the simulation are the angular velocity of the shaft and the angular velocity of the gear imposed such as initial condition. With this choice the angular velocity of the bodies is free according to the dynamics and only the interaction with the other bodies can modify the relative velocity. The geometry of the model considers only the main parts of the mechanism therefore the inertia of the shaft have a large value to regard the reduction inertia of the vehicles and all of the rotating bodies reported to the shaft. Similar thinking for the gear; the inertia of the gear is the sum of the geometrical mass inertia plus a term that consider the reduced inertia of all the spur gears. (This term is estimated as I_rid = 1700 kg*mm^2.)

After 0.01 s when the transitory is over, is applied a force to the sliding sleeve: F = 1550* time + 15 and the sliding sleeve can move and interact with the synchro ring, and the phase proced from 2 to 8.

With this set of simulations the mechanism could be fully charaterized, inspecting the friction torque between the synchronizer ring and the synchronizer clutch, the blocking torque through the teeth of the sliding sleeve and the synchronizer cone in the pre-synchronization phase. Also can be ispected the force of the sliding sleeve to obtain the engagement of the synch-clutch.

## The modelling problem

The main problem with this model is the choice of the contact forces parameters. In general there are 6 contact forces solid to solid type. ADAMS can deal with solid to solid contact with impact method or restitutional method.

For the impact model (i.e. used in this model) there are 4 constants :

- Stiffness
- Kelvin-Voigt exponent
- Damping
- Penetration Depth

The defalut adams value are computed considering a body :

- K = 1.0 10^5 N/mm
- e = 2.2
- C_max= 10 N * s / mm
- Penetration Depth = 0.1

Default parameters doesn’t fit to the model, and gives failure when profile of the sliding sleeve tooth first engage the external surface of the synchro ring diameter.

In the first 2 phases there is some discrepancy dealing with the wrong parameter. In particular when the sleeve detect the synchro ring there is an impact force that dosen’t allow the relative movement to the considered bodies.

According to the Adams Help Solver it can be used the Reduction Mass ( M=M1*M2/(M1+M2) ) and it can be calculated the relative stiffness and damping with it.

Sliding sleeve / synchronizer cone

- M1 = 0.3 kg
- M2 = 0.1 kg
- M = 0,075 kg
- K=6000 N/mm
- C = 40 N * s /mm

Sliding sleeve / synchronizer clutch

- M1 = 0.3 kg
- M2 = 0.1 kg
- M = 0,075 kg
- K=6000 N/mm
- C = 40 N * s /mm

synchronizer clutch / synchronizer cone

- M1 = 0.1 kg
- M2 = 0.1 kg
- M = 0,05 kg
- K=10000 N/mm
- C = 50 N * s /mm

Sliding sleeve / Ball

- M1 = 0.3 kg
- M2 = 0.01 kg
- M = 0,0097 kg
- K=1000 N/mm
- C = 10 N * s /mm

Synchronizer hub / synchronizer cone

- M1 = 0.3 kg
- M2 = 0.1 kg
- M = 0,075 kg
- K=6000 N/mm
- C = 40 N * s /mm

Synchronizer Cone Push / synchronizer cone

- M1 = 0.01 kg
- M2 = 0.1 kg
- M = 0,009 kg
- K=1000 N/mm
- C = 10 N * s /mm

For the penetration depth there are also some difficulties, after many tries the best solution is to give the value 0.1 for all the bodies excluding the synch ring and synch cone with 0.01 p-d and for the first detection between sleeve and synchro ring with 0.3 p-d. Increasing the penetration depth the clearance of the model increase, based on this consideration it can be accepted for a first inspection.

## Simulations and analysis of results

For the computation is used GSTIFF-I3 method with the contact default generator with 600 nodes. I3 gives a good result in term of computational time but gives some spikes due to the unconstrained velocity. The first set of simulation where the velocity of the shaft is equal to the velocity of the gear it’s used to have a first look of the effective work of the model.The solution can be plotted with three diagrams: the first friction torque vs time, blocking torque vs time and friction torque vs Xc.o.m. of the sliding sleeve.

This is the only case where the value doesn’t count so much because the initiale angular velocities are the same and there aren’t any force interaction except the friction part, so the spikes are caused by the I3 solver. In particular when the relative angular velocity is 0 the sleeve can move throughout the synchro ring and there are a large acceleration and result a big step of velocity. This phenomenon is true only qualitatively not quantitatively.

The simulation which gives the truth or the fault of the model is e.g. when the velocity of the gear is greater than the velocity of the hub (Video of the simulation below) .

It can be notice that t=0,0586 correspond with the time when relative angular velocity of the gear and the hub is 0; Δt = 0,0486 s. To estimate the average torque for the comparison with theoretical data it can be used the average theorem integrals as shown in the following figures.

For the friction torque (TX):

Blocking torque (TI):

Sliding sleeve force (Fs_s):

Fork Force (FX):

When the angular velocity of the Hub is greater than the velocity of the shaft, in this case Δt = 0,05 s :

For the friction torque (TX):

Blocking torque (TI):

Fork Force (FX):

The simulation data are condensed into the table below:

SIMULATION RESULTS |
|||

Vel_Gear_gr_Vel_Hub |
Vel_Hub_gr_Vel_Gear | ||

∫TX*dt [N*mm*s] |
Δt [s] | ∫TX*dt [N*mm*s] |
Δt [s] |

90 |
0,0486 | 107 |
0,05 |

Tx_avg [N*mm] |
1851,852 | Tx_avg [N*mm] |
2140,000 |

Relative error [%] |
11,765 | Relative error [%] |
4,902 |

∫TI*dt [N*mm*s] |
Δt [s] | ∫TI*dt [N*mm*s] |
Δt [s] |

62 |
0,0486 | 87 |
0,05 |

TI_avg [N*mm] |
1275,720 | TI_avg [N*mm] |
1740,000 |

Relative error [%] |
36,148 | Relative error [%] |
28,780 |

∫Fs_s*dt [N*mm*s] |
Δt [s] | ∫Fs_s*dt [N*mm*s] |
Δt [s] |

3,2343 |
0,0486 | 3,38 |
0,05 |

Fs_s_avg [N] |
66,549 | Fs_s_avg [N] |
67,600 |

Relative error [%] |
25,227 | Relative error [%] |
21,858 |

∫FX*dt [N*mm*s] |
Δt [s] | ∫FX*dt [N*mm*s] |
Δt [s] |

2,8665 |
0,0486 | 3,42 |
0,05 |

FX_avg [N] | 58,981 | FX_avg [N] |
68,400 |

THEORETICAL DATA

Case: Angular Velocity of the Gear greater than Angular Velocity of the Hub

- TX = 2099 N*mm
- TI = 1998 N*mm
- FX = 89,002 N

Case: Angular Velocity of the Hub greater than Angular Velocity of the Gear

- TX = 2040 N*mm
- TI = 2443 N*mm
- FX = 86,510 N

## Conclusion

The model can predict the real case of the synchronizer mechanism, with limitations due to the parameters of the contact forces. This limitation can be referred to the geometry because throughout literature the process of synchronization is well known but there aren’t many mechanical model for free consultation. This is a big limit, but the good results reveal that the main parameters are chosen correctly.

In second instance it doesn’t considered the influence of the oil flow and the grooves geometry. These two aspects certainly affect the model.

Another side to improve is the computational method using SI2 algorithm; which give smoother solution in terms of velocity constraints. Another aspect is the stress and strain behavior of the synch cone, synch clutch and sliding sleeve, that can be developed in future analysis.

The difference between the computed solution from the theoretical model is up to 10% but the phase of the synchronizer mechanism is well distinguishing without stop and re-run the simulation. This aspect gains to say that the model is correct although of a 10% error of friction torque (i.e. the main parameter for comparison).

## References

[1] Ana Pastor Bedmar, “Synchronization processes and synchronizer mechanisms in manual transmissions”, Master’s Thesis in the International Master Programme in Applied Mechanics, 2013

[2] Ottmar Back , “Basics of Synchronizers”, Hoerbiger, January 2013

[3] Umesh Wazir, “Manual Gearbox Synchronizers – An Overview,” Mechanical Engineering ADE University Of Petroleum & Energy Studies , Bidholi, Dehradun, 248 007 , Uttarakhand – India, September 2013

[4] Daniel Häggström, “On synchronization of heavy truck transmissions” Licentiate thesis, Department of Machine Design, KTH Royal Institute of Technology, SE-100 44 Stockholm,2016

[5] Prof. M. Massaro, “Contacts Lectures” Modelling and Simulations of Mechanical Systems A/A 2016/17 Università degli Studi di Padova, 2017