Dynamical model for dog clutch shiftability

Ayham Aljawabrah; Laszlo Lovas

doi:10.1556/1848.2023.00745

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International Review of Applied Sciences and Engineering

Volume/Issue:: Volume 15: Issue 2

Dynamical model for dog clutch shiftability

Authors:

Ayham Aljawabrah

Ayham Aljawabrah Department of Railway Vehicles and Vehicle-System Analysis, Faculty of Transportation Engineering and Vehicle Engineering, Budapest University of Technology and Economics, Muegyetem rkp. 3., 1111 Budapest, Hungary

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aaljawabrah@edu.bme.hu https://orcid.org/0000-0002-7537-6358

and

Laszlo Lovas

Laszlo Lovas Department of Railway Vehicles and Vehicle-System Analysis, Faculty of Transportation Engineering and Vehicle Engineering, Budapest University of Technology and Economics, Muegyetem rkp. 3., 1111 Budapest, Hungary

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Pages:: 260–275

Online Publication Date:: 24 Jan 2024

Publication Date:: 10 Jun 2024

Article Category:: Research Article

DOI:: https://doi.org/10.1556/1848.2023.00745

Keywords:: dog clutch; shiftability map; engagement probability; shiftability condition; sensitivity analysis

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Abstract

The dog clutch offers advantages in mass and efficiency, but faces challenges in mismatch speed synchronization, which affects its shiftability. Face impact between dog teeth also reduces its lifespan. Our previous work introduced the kinematical shiftability condition that ensures impact-free gearshift but had limitations due to analysis assumptions. This study eliminates those assumptions, but uses a similar approach. Based on our previous work for dog clutch engagement dynamics, we develop the dynamical shiftability condition. Validation with full dog clutch dynamics showed an agreement. Employing another previous work that introduced shiftability map and parametric study method, we study system parameters impact on shiftability but based on the dynamical shiftability condition.

Abstract

1 Introduction

Global concerns over nonrenewable fuel shortages and environmental issues are driving a shift to renewable energy [1, 2] and cleaner systems [3]. Motor vehicles are now a focal point for efficiency improvements and adopting clean energy concepts. Enhancing powertrains, primarily the engine and transmission, is crucial for making vehicles environmentally cleaner. The powertrain, including the engine and transmission, is a critical subsystem in vehicles. Improving engine efficiency and exploring alternative fuels are avenues for enhancing environmental sustainability [4–6]. Another crucial element that can contribute to enhancing a vehicle's efficiency is the vehicle transmission. For the transmission, modifying gear tooth geometry in power transmission gears [7, 8] and the performance of the gearshift elements can further improve vehicle efficiency.

The gearshift element enables shifting between gear ratios and synchronizes speed differences (mismatch speed) between the transmission's input and output sides. The synchronizer is used in manual transmissions and automated manual transmission (AMT), while the multi-disk wet clutch (MDWC) is used in conventional automatic transmission (AT). Synchronizer and MDWC face challenges meeting new clean, efficient system requirements because both rely on a friction-based mechanism for speed synchronization, which causes energy waste. Also, AMTs are widely used in heavy-duty and commercial vehicles due to their high transmission torque, efficiency, and low manufacturing and maintenance costs [9, 10]. However, the friction-based mechanism in synchronizers limits their lifespan, posing challenges for heavy-duty use, where a long lifespan is required. The challenges come from limitations of materials strength and manufacturing technology [11, 12].

The dog teeth clutch is replacing the synchronizer and MDWC due to its quicker shifting time, simpler structure, larger power capacity, and lower cost [13, 14]. Heavy-duty vehicles with AMT use the dog clutch as a gearshift element [15]. Some conventional ATs employ the dog clutch as an interlocking element [16, 17], or gearshift element [18]. Electric vehicles (EVs) use clutchless AMTs with the dog clutch as a gearshift element [19–22]. The dog clutch is similar to the synchronizer but without the friction mechanism, which offers its advantages. However, the removal of the speed synchronization mechanism causes a speed synchronization problem, which affects dog clutch engagement capability (or shiftability). This requires further investigation into the dog system.

These investigations originated from Laird's research [23] on shifting characteristics of radial and face dog clutches installed into a test vehicle. Laird observed that the radial clutch has a longer shifting time and bounces 5–6 times for successful engagement, while the face clutch engages successfully on the first attempt. The bounce number correlates linearly with engagement time. The bounce number depends on the engagement probability, which depends on the shifting speed and backlash. Shifting probability is minimal for backlashes below 15° and increases with higher backlash.

Echtler et al. [24], explored the energy-saving potential of TorqueLINE, an alternative shifting element, for MDWC in ATs. TorqueLINE, consists of a conical friction element, a dog clutch, and a consecutive form-fit for high-torque transmission. They showed an 85% saving potential at mismatch speeds below 2000 RPM and decreases to 50% at 5000 RPM. In a later study, Mileti et al. [25], examined the engagement capability of five dog clutch design variants, varying in backlash, teeth number, and tooth flank angle. Utilizing SIMPACK for multibody simulation and applying different axial and mismatch speeds, they identified that a dog clutch with a high angular gap, low teeth number, and low flank angle has the largest successful engagement area, while the opposite configuration has the smallest one.

Eriksson et al. [26], conducted a parametric multibody dynamic study on the dog clutch in a truck transfer case. Their research examined how dog clutch geometry, mass, material stiffness, engagement mismatch speed, and actuator force influenced performance. Three tooth designs with variations in chamfer distance, angles, tooth angle, and tooth number were used. With ten combinations derived from clutch mass, material stiffness, engagement mismatch speed, and actuator force, multibody simulations in MSC ADAMS were performed for each design. The combination with a mass of 8 kg, mismatch speed of 539 RPM, material stiffness of 81,441 N/m, and actuator force of 198 N demonstrated the best performance. It has the lowest engagement time and bounce count among all three designs.

Andersson and Goetz [27] employed dynamic finite element analysis (FEA) using Abaqus to study the impact of chamfer angle, distance, tooth angle, and axial force on the dog clutch's performance. They created 11 alternative designs. The primary goal was to determine the maximum possible mismatch speed for each tooth geometry. The results showed that the coupling is easier as the chamfer angle is smaller, and a longer chamfer distance positively affects the maximum mismatch speed.

Experimental, multibody dynamic simulation, and dynamic FEA methods provide means to explore parameter influences, but they have limitations. Primarily, these approaches are time-consuming and limit the capability to study a vast parameter space. Additionally, the face impact between dog clutch teeth, causing back-and-forth bouncing, substantially diminishes the clutch's lifespan. To the author's knowledge, prior research lacks an analysis ensuring a face impact-free gearshift process of the dog clutch, particularly at high mismatch speeds.

To overcome the drawbacks of the aforementioned study methods, in previous work [28], we followed a different approach to study dog teeth clutch shiftability. Our approach involved a kinematic analysis of the dog clutch engagement process. This kinematic analysis assumes constant axial and mismatch speeds throughout the gearshift process. From this analysis, we derived a kinematical shiftability condition, which ensures a face impact-free gearshift process without the need for complex multibody dynamic or dynamic FEA simulations. Additionally, we visually presented the successful gearshift area through the developed shiftability map. In another study [29], we created a method to calculate shifting probability and developed a parametric study method to explore the sensitivity of the shiftability map and engagement probability to system parameters. Our analysis indicated that the number of teeth and tangential backlash positively affect engagement probability, while initial mismatch speed and overlap distance have a negative impact.

In [28], we studied dog clutch shiftability kinematically, assuming constant axial and mismatch speeds. This kinematical shiftability condition is applicable in transmissions with negligible system dynamics. However, in scenarios where gearbox losses impact mismatch speed or the gearshift actuator cannot maintain constant axial speed, its applicability is limited.

In our work [30], we developed a dynamic model for the dog clutch engagement process. This model described all the engagement stages dynamically, considering the time trajectories of the axial and mismatch speeds. So, based on [30], this work aims to develop a so-called dynamical shiftability condition to overcome the limitation of the kinematical shiftability condition. Here, the mismatch and axial speeds are considered not constant. Moreover, we utilize the dynamical shiftability condition and the parametric study method developed in [29] to investigate the system sensitivity for some selected parameters and their effect on dog clutch shiftability.

2 Dynamical shiftability model

In ref. [30] we have introduced a full dynamic model for the dog clutch engagement process. However, we briefly mention the dog clutch geometry and its engagement stages. A dog clutch (Fig. 1a) is a coupling used to transmit power. It consists of two parts having complementary geometry. These complementary shapes are referred to as dog teeth. The main dog clutch system parameters are listed in Table 1.

Fig. 1.

Dog clutch geometry, a) 3D model and a 2D schematic in b) angular representation and c) linear representation (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

Table 1.

Dog clutch shiftability parameters

Parameter	Unit	Parameter	Unit
$ξ$	[rad/s] ( $[°]$ )	$x_{0}$	[mm]
$Δ ω$	[rad/s] ([min⁻¹])	$x_{f e d}$	[mm]
$F_{a c t}$	[N]	$Φ_{b}$	$[°]$
z	[–]	m	[kg]

The axial dog clutch has an angular pitch ϕ and an angular backlash given by Eq. (1) and Eq. (2), respectively. Here,

ϕ_{t}

is the tooth thickness angle.

ϕ = \frac{2 π}{z}

(1)

Φ_{b} = ϕ - 2 ϕ_{t}

(2)

For easier understanding, the dog teeth geometries shown in Fig. 1c are unrolled and visualized as if they undergo linear motion (Fig. 1b). At the start of the shifting process, Fig. 1b shows that there is an axial gap, denoted x₀, and an initial relative angular position, denoted ξ₀, between the red-marked teeth, between the sliding sleeve (s) and the meshing gear (g). Figure 2a shows further parameters. The sliding sleeve has the capability to move axially, while it concurrently undergoes relative angular rotation in relation to the target gear. The relative angular rotation is referred to as the mismatch speed

Δ ω

. The angular relative position

ξ (t)

, and mismatch speed

Δ ω (t)

between the sliding sleeve and the meshing gear are given by Eq. (3), and Eq. (4), respectively. Eq. (4), assuming that the output side, or the sleeve side, exhibits very high inertia and thus maintains a constant speed

{\dot{θ}}_{s}

(or

ω_{s}

) which makes it independent of time.

ξ (t) = θ_{g} (t) - θ_{s} (t)

(3)

Δ ω (t) = \frac{d ξ (t)}{d t} = ω_{g} (t) - ω_{s}

(4)

Fig. 2.

Schematics of dog clutch engagement stages (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

The engagement of the complementary geometries is eased with an angular backlash $Φ_{b}$ .

Throughout the engagement process, it is possible for a tooth on the gear to pass many teeth on the sliding sleeve. To represent this, a dotted green line is utilized in Fig. 2b–d to indicate the inclusion of many teeth in this region. The value of ξ can be much larger than

ϕ

. This requires that ξ shall be transferred to the first cycle (or between

[0, ϕ]

) according to Eq. (5). Here,

ξ^{'}

denotes the relative position within the first cycle and is measured between the red-marked teeth on the meshing gear (g) and the brown-marked teeth on the sliding sleeve (s), as illustrated in Fig. 2c:

ξ^{'} = \mod (ξ, ϕ)

(5)

The engagement process can be broken down into four primary stages: 1) free fly axial motion, 2) axial (face) impact stage, 3) tangential (side) impact stage, and 4) full engagement stage.

At the start of the shifting, time t₀ (Fig. 2a), the constant actuator force F_act drives the sliding sleeve axially until the axial gap is eliminated at t₁. During this time, the dog clutch components undergo relative rotation, and the relative angular position changes from $ξ_{0} to ξ_{1}$ , as seen in Fig. 2b.

As stage 2 begins, the teeth of the sliding sleeve and the gear meet at the face impact position x₀ (or x_s,0). At this position, the sleeve motion is subject to three possibilities, as illustrated in Fig. 3 for $x_{s}$ trajectories. In the first case, the sliding sleeve continues to move without impacting the gear. In the second case, it impacts the gear, stops for a certain period, and then moves again. In the third case, the gear blocks the sleeve and cannot advance further toward the final position, so there is no possible gearshift. In [30], we investigated these cases and graphically illustrated them. However, this work focuses on the first case, face impact-free gearshift. So, this case is only illustrated in Fig. 2, and in Fig. 3 for $Δ ω$ curve.

Fig. 3.

Dynamics of dog clutch engagement (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

It is assumed that if a tooth on the sliding sleeve can overlap a certain distance with a tooth on the gear sleeve without face impact, the sliding sleeve will not rebound, which ensures successful engagement. This overlapping distance is referred to as x_fed. The face impact can possibly happen until the overlap distance is fully covered at time t₂ (Fig. 2c). During this phase, a relative rotation between the dog clutch and the target gear occurs, and the relative angular position changes from $ξ_{1}$ to $ξ_{2}$ .

In stage 3, the sliding sleeve continues its axial movement until it completely covers the full tooth height, reaching a position denoted as x₀+h_t (or x_0,f) in the axial direction (Fig. 2d). Throughout this stage, the $Δ ω$ curve in Fig. 3 exhibits a fluctuating pattern around zero until it eventually dampens to zero. This variation in mismatch speed results from multiple side (or tangential) impacts occurring between the sides of the teeth on the sliding sleeve and those on the gear sleeve. These side impacts facilitate the synchronization of speed between the components, ultimately eliminating mismatched speeds. Also, the $Δ ω$ curve in Fig. 3 shows a decrease in the first stage because of the transmission losses at the input side.

Stage 4 marks the completion of the gear shift process. It is characterized by the synchronization of mismatch speed and the sliding sleeve while the sliding sleeve reaches its ultimate axial position $x_{0} + h_{t}$ .

In our study, we focus on the face impact-free gearshift process. The condition to achieve this is based on two sub-conditions. Firstly, at the end of stage 1, the sleeve's tooth shall be within the tangential gap region for the gear, or mathematically speaking:

0 \leq \mod (ξ_{1}, \frac{2 π}{z}) \leq Φ_{b}

(6)

For a successful shifting, we assume that a sleeve's tooth shall cover an overlap distance without impacting a gear's tooth. Beyond this position, there is no possible face impact, and the sleeve will not bounce back. While reaching the overlap, a relative rotation

(ξ_{2} - ξ_{1})

between the sleeve and the target gear occurs. This adds extra restrictions on Eq. (6). Figure 4a shows the solid-lined gear tooth has zero overlap at the end of the free fly stage but at the end of the overlap coverage, it has

ξ_{2} - ξ_{1}

relative position as Fig. 4b. However, the dashed-lined gear tooth has

Φ_{b} - (ξ_{2} - ξ_{1})

relative position, and it is

Φ_{b}

at the end of the overlap coverage, as Fig. 4b shows, where the tangential gap ends. Because of this relative rotation, the possible region that the relative position at the end of stage 1,

ξ_{1}

, can be within is shrunk, according to the following equation:

0 \leq \mod (ξ_{1}, \frac{2 π}{z}) \leq Φ_{b} - (ξ_{2} - ξ_{1})

(7)

Fig. 4.

Possible region for ${ξ_{1}}^{'}$ in case of positive mismatch speed $Δ ω_{1}$ , a) end of free fly phase b) end of overlap distance coverage phase (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

If ${ξ_{1}}^{'}$ is larger than $Φ_{b}$ , a face impact will occur directly at the end of stage 1. Also, if ${ξ_{1}}^{'}$ is larger than $Φ_{b} - (ξ_{2} - ξ_{1})$ , a face impact will occur during the overlap distance coverage, and the sliding sleeve will bounce back.

The notion of mismatch speed states that one part rotates quicker than the other. In our case, if the gear is the quickest, then we consider the mismatch speed has a positive sign. This is shown in Fig. 4, when the red-blue part (the gear) is moving upwards regarding to the standing green part (sleeve). Generally, there are cases when the green part (sleeve) is the one moving quicker. In this case, we consider that the mismatch speed has a negative sign.

Figure 4 and Eq. (7) show the analysis for the case of positive mismatch speed. However, in the case of negative mismatch speed, the direction of rotation is opposite. Figure 5a shows the dashed-lined gear tooth has

Φ_{b}

initial relative position but it is

Φ_{b} - (ξ_{2} - ξ_{1})

at the end of the overlap coverage, as Fig. 5b shows. However, the solid-lined gear tooth has

ξ_{2} - ξ_{1}

relative position at the end of the free fly stage but at the end of the overlap coverage, it has zero relative position, as Fig. 5b shows, where the tangential gap ends. So, the possible region that the relative position at the end of stage 1,

ξ_{1}

, can be within is shrunk according to:

(ξ_{1} - ξ_{2}) \leq \mod (ξ_{1}, \frac{2 π}{z}) \leq Φ_{b}

(8)

Fig. 5.

Possible region for ${ξ_{1}}^{'}$ in case of negative mismatch speed $Δ ω_{1}$ a) end of free fly phase b) end of overlap distance coverage phase (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

If ${ξ_{1}}^{'}$ is larger than $Φ_{b}$ , a face impact will occur directly at the end of stage 1. Also, if ${ξ_{1}}^{'}$ is less than $ξ_{1} - ξ_{2}$ , a face impact will occur during the overlap distance coverage, and the sliding sleeve will bounce back.

Equations (7) and (8) have 0 or 1 values: 1 for face impact-free gearshift and 0 for gearshift with impact, or unsuccessful gearshift. As our study focuses on face impact-free gearshift, the later tow cases are referred to as unsuccessful gearshift, while the first case is just a successful gearshift.

In Eqs (7) and (8), $ξ_{1}$ is $ξ (t_{1})$ , and $ξ_{2}$ is $ξ (t_{2})$ . The aim now is to find $t_{1}$ and $t_{2}$ as well as an expression for $ξ (t)$ , to identify $ξ_{1}$ and $ξ_{1}$ , respectively.

As seen from Fig. 3, $t_{1}$ and $t_{2}$ are connected with linear position, so let us start by focusing on the linear dynamics.

Let us assume that the actuator provides a force

F_{a c t} (t)

and the shifting mechanism has a mass m, then the linear acceleration is given according to:

a (t) = \frac{F_{a c t} (t) - F_{f}}{m}

(9)

Many models are available to model friction force, such as Coulomb friction, viscous friction combined with Coulomb friction, and Stribeck. The second model assumes the friction force is a linear function of the speed and is used in many applications for automotive transmission, such as [31], due to its simplicity. This model is employed here.

F_{f} = c_{l} \cdot v (t) + F_{c l}

(10)

Here

c_{l}

and

F_{c l}

are linear viscous friction coefficient and Coulomb friction force, respectively. In our study, we assume that the actuator force is constant. So, Eq. (9) can be written as:

\frac{d^{2} x_{s} (t)}{{d t}^{2}} = \frac{F_{a c t} - F_{c l} - c_{l} ∙ \frac{d x_{s} (t)}{d t}}{m}

(11)

In the first case, let us assume a zero linear viscous friction coefficient-no linear viscous friction-so, Eq. (11) reduces to:

\frac{d^{2} x_{s} (t)}{{d t}^{2}} = \frac{F_{a c t} - F_{c l}}{m}

(12)

This is a system with constant acceleration. With zero initial position and speed, the linear speed and position are given as:

v (t) = \frac{F_{a c t} - F_{c l}}{m} t

(13)

x_{s} (t) = \frac{1}{2} \frac{F_{a c t} - F_{c l}}{m} t^{2}

(14)

To find

t_{1}

and

t_{2}

, we know that at

t_{1}

x_{s} (t_{1})

x_{0}

, and at

t_{2}, x_{s} (t_{2})

x_{0} + x_{f e d}

and If we substitute these in Eq. (14) and solve for

t_{1}

and

t_{2}

respectively then:

t_{1, N F} = \sqrt{\frac{2 m x_{0}}{F_{a c t} - F_{c l}}}

(15)

t_{2, N F} = \sqrt{\frac{2 m (x_{0} + x_{f e d})}{F_{a c t} - F_{c l}}}

(16)

NF stands for no linear viscous friction case

(c_{l} = 0)

. The required time to cover the overlap distance is the difference between

t_{2}

and

t_{1}

{∆ t}_{N F} = \sqrt{\frac{2 m (x_{0} + x_{f e d})}{F_{a c t} - F_{c l}}} - \sqrt{\frac{2 m x_{0}}{F_{a c t} - F_{c l}}}

(17)

In the second case, let us also consider the linear viscous friction. Eq. (11) can be rearranged in the form of a typical second-order nonhomogeneous ordinary differential equation (ODE) as:

\frac{d^{2} x_{s} (t)}{{d t}^{2}} + \frac{c_{l}}{m} \times \frac{d x_{s} (t)}{d t} = \frac{F_{a c t} - F_{c l}}{m}

(18)

The general solution for this ODE includes the homogenous and nonhomogeneous parts. The homogeneous part has exponential functions while the nonhomogeneous part shall be in the same form as the nonhomogeneous term in Eq. (18), which is polynomial. The nonhomogeneous term is zero order polynomial while Eq. (18) is second-order ODE. So, a second-order polynomial will be enough. The homogenous and nonhomogeneous solutions can be given as:

{x_{s} (t)}_{h o m o g e n e o u s} = C_{1} e^{r_{1} t} + C_{2} e^{r_{2} t}

(19)

{x_{s} (t)}_{n o n h o m o g e n e o u s} = a_{2} t^{2} + a_{1} t + a_{0}

(20)

Substituting Eq. (19) in the homogeneous ODE (setting the right-hand side in Eq. (18) to zero), r₁, and r₂ can be obtained. Also, substituting Eq. (20) in the nonhomogeneous ODE (Eq. (18)) and comparing the coefficients of the polynomial terms, a₂, a₁, and a₀ can be determined. This yield:

r_{1} = 0, r_{2} = - \frac{c_{l}}{m} a_{2} = 0, a_{1} = \frac{F_{a c t} - F_{c l}}{c_{l}}, a_{0} = 0

(21)

The full solution can be given as:

x_{s} (t) = C_{1} + C_{2} e^{- \frac{c_{l}}{m} t} + \frac{F_{a c t} - F_{c l}}{c_{l}} t

(22)

C₁, and C₂ can be determined from the initial conditions of zero initial linear position and speed. This gives:

C_{2} = \frac{(F_{a c t} - F_{c l}) m}{{c_{l}}^{2}}, C_{1} = - \frac{(F_{a c t} - F_{c l}) m}{{c_{l}}^{2}}

(23)

x_{s} (t) and v_{s} (t)

can be given as:

x_{s} (t) = (e^{- \frac{c_{l}}{m} t} - 1) \frac{(F_{a c t} - F_{c l}) m}{{c_{l}}^{2}} + \frac{F_{a c t} - F_{c l}}{c_{l}} t

(24)

v_{s} (t) = - \frac{(F_{a c t} - F_{c l})}{c_{l}} e^{- \frac{c_{l}}{m} t} + \frac{F_{a c t} - F_{c l}}{c_{l}}

(25)

The aim now is to analytically express the time t as a function of

x_{s}

. However, Eq. (24) is more complicated than Eq. (14). The analytical solution has been obtained using MATLAB Symbolic Toolbox as:

t (x_{s}) = \frac{x_{s} {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) c_{l}} + \frac{m}{c_{l}} W_{0} (- e^{- \frac{x_{s} {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) m}})

(26)

Here, W₀ is the principal branch of the Lambert W function. The Lambert W function-also referred to as the product logarithm-consists of a set of functions denoted as

W (y)

, where y represents a complex number. This mathematical concept is the inverse of the function

f (W) = W e^{w}

for a complex number formulated as

z = W (y)

, implying

z e^{z} = y

. The Lambert W function is useful in solving equations that involve both exponential and logarithmic terms. A detailed description for the Lambert W function is provided in [32]. The Lambert W function has applications in many fields, such as control theory [33] and signal processing [34]. One of the most common forms of the Lambert W function is the Lambert W(y) for real numbers with the branch

W_{0}

. However, this form is defined only in the range

y \geq - e^{- 1}

[32, 35]. The aim now is to check if our system is in the possible range for y, ignoring the substituted parameters values. Let us write the term for Lambert W function in Eq. (26) as:

\begin{matrix} W_{0} (- e^{- \frac{x_{s} {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) m}}) = W_{0} (y) \\ y = - e^{- u} \\ u = \frac{x_{s} {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) m} \end{matrix}

(27)

The goal now is to show that

y \geq - e^{- 1}

. From the system behavior,

F_{a c t} > F_{c l}

. Also, all other parameters in the variable u in Eq. (27) are positive, so, it is clear that

u > 0

. Also, the nominator is larger than the denominator in the variable u, so, it is clear that u > 1. The rest of the proof is introduced below.

u > 1 0 < e^{- u} < e^{- 1}, f o r a l l u > 1 - e^{- 1} < - e^{- u} < 0, f o r a l l u > 1 - e^{- 1} < y < 0, f o r a l l u > 1

(28)

So, the condition

y \geq - e^{- 1}

is satisfied, ignoring the system parameters substituted. Also, the MATLAB Symbolic Toolbox mentioned that Eq. (26) is valid only if the condition below is satisfied.

u + W_{0} (y) > 0

(29)

Here, the variables u and y are the same as defined in Eq. (27). We already proved that

u > 1

, and y is in the allowable range. Also

W_{0} (y) \geq - 1

[32], so:

u > 1 W_{0} (y) \geq - 1 u + W_{0} (y) > 0

(30)

So, the condition in Eq. (29) is satisfied, ignoring the system parameters substituted. Since, the conditions $y \geq - e^{- 1}$ and (29) are satisfied, ignoring the system parameters substituted, Eq. (26) is valid, ignoring the substituted parameters. In other words, Eq. (26) is applicable for our system without restriction.

Equation (24) for x_s(t) and its inverse Eq. (26) for t(x_s) are plotted against each other in Fig. 6 for the constant values in Table 2 except with 500 N actuator force and c_r of 4 N.s/m. It is well known the function inverse is a mirror of the original function along the 45° line, and Fig. 6 shows that Eq. (26) is a mirror of Eq. (24) along the 45° line.

Fig. 6.

Equation (24) for x_s(t) and its inverse Eq. (26) for t(x_s) (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

Table 2.

Fixed values and the study ranges for the variables and parameters

Parameter	Unit	Fixed value	Range
Initial relative position $ξ_{0}$	$[°]$	4	0– $ϕ$
Mismatch speed ${∆ ω}_{0}$	[rad/s] ([min⁻¹])	20 (200)	2–120 (19–1146)
Actuator force $F_{a c t}$	[N]	1000	100–2000
Number of teeth Z	[–]	5	2–10
Feed distance $x_{f e d}$	[mm]	0.5	0.5–3
Backlash $\emptyset_{b}$	$[°]$	15	2–20
Axial gap $x_{0}$	[mm]	10	–
Mass M	[kg]	3	–
Inertia J_g	[kg m²]	0.2	–
Columb friction T_cl	[N.m]	0	–
Rotational viscous friction c_r	[N.m.s/rad]	0.02	–
Columb friction force F_cl	[N]	0	–
Linear viscous friction c_l	[N.s/m]	0	–

We can find

t_{1}

and

t_{2}

, from Eq. (26), with

x_{s} (t_{1})

x_{0}

, and

x_{s} (t_{2})

x_{0} + x_{f e d}

, as:

t_{1, W F} = \frac{x_{0} {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) c_{l}} + \frac{m}{c_{l}} W_{0} (- e^{- \frac{x_{0} {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) m}})

(31)

t_{2, W F} = \frac{(x_{0} + x_{f e d}) {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) c_{l}} + \frac{m}{c_{l}} W_{0} (- e^{- \frac{(x_{0} + x_{f e d}) {c_{l}}^{2} + (F_{a c t} - F_{c l}) m}{(F_{a c t} - F_{c l}) m}})

(32)

WF stands for the case with linear viscous friction. Now, for $t_{1}$ and $t_{2}$ , we have Eqs (15) and (16), respectively, for no linear viscous friction case (NF), and Eqs (31) and (32), respectively, for linear viscous friction case (WF).

Now, let us focus on the angular dynamics to find an expression for

ξ (t)

. During the gearshift, the input torque to the transmission is zero, and the only present torque is friction or loss torque (T_Loss). If the engine side has an inertia J_g, and the wheels side has infinite inertia compared to the engine side, the angular speed of the wheel side or sleeve (s) is constant but the engine side or gear (g) angular speed decreases due to the friction torque. According to this, the gear angular acceleration is given as:

α_{g} (t) = - \frac{T_{L o s s} (t)}{J_{g}}

(33)

The loss torque is expressed as a linear form of the engine (or gear) side speed as in [31]:

T_{L o s s} (t) = c_{r} \cdot ω_{g} (t) + T_{c l}

(34)

Here c_r and T_cl are rotational viscous friction coefficient and Coulomb friction torque, respectively. Eq. (4) can be solved for

ω_{g}

, and substituting this results in Eq. (34), we can express T_Loss as a function of

Δ ω (t)

, or

d ξ (t) / d t

. Substituting this function for T_Loss in Eq. (33), the differential equation for

ξ (t)

is:

\frac{d^{2} ξ (t)}{{d t}^{2}} = - \frac{c_{r} \cdot (\frac{d ξ (t)}{d t} + ω_{s}) + T_{c l}}{J_{g}}

(35)

Equation (35) can be rearranged in the form of a typical second-order nonhomogeneous ordinary differential equation (ODE) as:

\frac{d^{2} ξ (t)}{{d t}^{2}} + \frac{c_{r}}{J_{g}} \times \frac{d ξ (t)}{d t} = - \frac{ω_{s} c_{r} + T_{c l}}{J_{g}}

(36)

This ODE is similar to the ODE in Eq. (18), and the general solution includes the homogenous and nonhomogeneous parts given as:

{ξ (t)}_{h o m o g e n e o u s} = C_{3} e^{r_{3} t} + C_{4} e^{r_{4} t}

(37)

{ξ (t)}_{n o n h o m o g e n e o u s} = b_{2} t^{2} + b_{1} t + b_{0}

(38)

Similar to the procedure followed to solve Eq. (18), by substituting Eq. (37)in the homogeneous ODE (setting the right-hand side in Eq. (36) to zero), r₃, and r₄ can be obtained. Also, substituting Eq. (38) in the nonhomogeneous ODE (Eq. (36)) and comparing the coefficients of the polynomial terms, b₂, b₁, and b₀ can be determined. This yield:

r_{3} = 0, r_{4} = - \frac{c_{r}}{J_{g}} b_{2} = 0, b_{1} = - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}}, b_{0} = 0

(39)

The full solution can be given as:

ξ (t) = C_{3} + C_{4} e^{- \frac{c_{r}}{J_{g}} t} - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}} t

(40)

C₃, and C₄ can be determined from the initial conditions

ξ_{0}, and Δ ω_{0} where ξ (0) = ξ_{0} and Δ ω (0) = Δ ω_{0}

. This gives:

\begin{matrix} C_{4} = - \frac{∆ ω_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} J_{g} \\ C_{3} = ξ_{0} + \frac{∆ ω_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} J_{g} \end{matrix}

(41)

ξ (t) a n d Δ ω (t)

can be given as:

ξ (t) = ξ_{0} + J_{g} (1 - e^{- \frac{c_{r}}{J_{g}} t}) \cdot \frac{{∆ ω}_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}} t

(42)

∆ ω (t) = \frac{{∆ ω}_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{c_{r}} e^{- \frac{c_{r}}{J_{g}} t} - \frac{T_{c l} + ω_{s} c_{r}}{c_{r}}

(43)

To find

ξ_{1}

and

ξ_{2}

, we substitute the values t₁ and t₂ from Eq. (15) and Eq. (16), respectively, into Eq. (42).

ξ_{1}

and the relative rotation

ξ_{2} - ξ_{1}

during stage 2 for no linear viscous friction case (NF) are:

ξ_{1, N F} = ξ_{0} + J_{g} (1 - e^{- \frac{c_{r}}{J_{g}} \sqrt{\frac{2 m x_{0}}{F_{a c t} - F_{c l}}}}) \dot{} \cdot \frac{{∆ ω}_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}} \sqrt{\frac{2 m x_{0}}{F_{a c t} - F_{c l}}}

(44)

{(ξ_{2} - ξ_{1})}_{N F} = J_{g} (e^{- \frac{c_{r}}{J_{g}} \sqrt{\frac{2 m (x_{0} + x_{f e d})}{F_{a c t} - F_{c l}}}} - e^{- \frac{c_{r}}{J_{g}} \sqrt{\frac{2 m x_{0}}{F_{a c t} - F_{c l}}}}) \cdot \frac{{∆ ω}_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}} (\sqrt{x_{0} + x_{f e d}} - \sqrt{x_{0}}) \sqrt{\frac{2 m}{F_{a c t} - F_{c l}}}

(45)

Similarly, we can find

ξ_{1}

and

ξ_{2}

, by substituting the values t₁ and t₂ from Eq. (31) and Eq.(32), respectively, into Eq. (42).

ξ_{1}

and the relative rotation

ξ_{2} - ξ_{1}

during stage 2 for linear viscous friction case (WF) are:

ξ_{1, WF} = ξ_{0} + J_{g} (1 - e^{- \frac{c_{r}}{J_{g}} t_{1, W F}}) \cdot \frac{{∆ ω}_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}} t_{W F}

(46)

{(ξ_{2} - ξ_{1})}_{W F} = J_{g} (e^{- \frac{c_{r}}{J_{g}} t_{2, W F}} - e^{- \frac{c_{r}}{J_{g}} t_{1, W F}}) \cdot \frac{{∆ ω}_{0} c_{r} + ω_{s} c_{r} + T_{c l}}{{c_{r}}^{2}} - \frac{ω_{s} c_{r} + T_{c l}}{c_{r}} (t_{2, W F} - t_{1, W F})

(47)

Having $ξ_{1} a n d ξ_{2} - ξ_{1}$ , these can be substituted in Eq. (7) or (8), which gives the full dynamical shiftability condition. Later on, wherever no linear viscous friction case (c_l = 0) is considered, Eqs (44) and (45) are implicitly used in Eqs (7) and (8), while for viscous friction case, Eqs (46) and (47) are implicitly used in Eqs (7) and (8).

3 Parametric study method

The geometric condition outlined in Eqs (7) and (8) for shiftability encompasses numerous parameters. They can be divided into three sets of parameters: the dog geometry parameters, including $z, x_{0}, x_{f e d}, Φ_{b}, J_{g},$ and m, the system friction parameters, including c_r, T_cl, and c_l, and F_cl and the dynamic and kinematic parameters including, $F_{a c t}, ξ_{0}, Δ ω_{0}, and ω_{s}$ .

The presence of many parameters can pose challenges for conducting a parameter study. In [29], we proposed a parametric study method to study the parameters effect based on the kinematical shiftability condition. As summarized below, the same method is used here but based on the dynamical shiftability condition.

Let us consider two variables, $F_{a c t} and Δ ω_{0}$ . which can have values within the ranges $[F_{a c t, \min}; F_{a c t, \max}]$ , and $[Δ ω_{0, \min}; Δ ω_{0, \max}]$ , respectively. Additionally, a third variable, denoted as y, is selected to investigate the overall system sensitivity over a range of $[y_{\min}; y_{\max}]$ . To manage these parameters effectively, the continuous spaces of $F_{a c t}, Δ ω_{0}, and y$ are discretized with a fixed step for each variable. Subsequently, the range of each variable is converted into a vector comprising discrete points.

The parameter sensitivity analysis goes in the following manner: Initially, the shiftability condition described in Eq. (7) is evaluated for a given value of y, across each point ( $Δ ω_{0, i}, F_{a c t, j}$ ). This process generates a shiftability map shown in Fig. 7. All points on this map correspond to a particular parameter value $y_{i}$ . The points satisfying the shiftability condition are represented in blue, while those not satisfying it are represented in red. Later in this work, the red points in Fig. 7 will be omitted to have a simpler shape, as shown in Fig. 9a.

Fig. 7.

Illustration of the study procedure: shiftability map (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

This shiftability map is plotted at a fixed initial relative position $ξ_{0}$ , but it is worth knowing how this shiftability map changes with the initial relative position and the parameter of interest y. A convenient method to study this is to find the ratio of the successful region area (sum of the blue regions areas), to the whole studied area. In other words, we are calculating the successful region portion. At each point $(y_{i}, ξ_{0, j})$ , the shiftability map is obtained and from it, this portion is calculated. A surface and contour plots similar to those in Fig. 9c and d, respectively, can be obtained.

The above parametric study considers

ξ_{0}

to be known. In fact, the initial relative position

ξ_{0}

is considered to be a free variable, as it is difficult to measure in the gearshift process for many systems, and it has a random value in the interval [0, 2π/z]. So, the engagement process must be handled based on probability. The engagement probability at each point (y_j) shall be calculated according to:

P (y) = \frac{\int_{0}^{2 π / z} G (y) d ξ_{0}}{2 π / z}

(48)

Here, G is the shiftability condition given in Eq. (7) or (8). However, as the study method discretized all the parameters ranges, Eq. (48) shall be modified to be used in the discretized space. Let us assume the

ξ_{0}

interval ([0, 2π/z]), is discretized to n discrete points, the engagement probability can be calculated as:

P (y) = \frac{N u m b e r o f p o i n t s i n ξ_{0} i n t e r v a l w i t h G = 1}{n}

(49)

However, G has 0 or 1 values only, so, the number of points with G = 1 is the same as the sum of G values at all points in

ξ_{0}

interval. So, Eq. (48) can be modified for the discrete space as:

P (y) = \frac{\sum_{i = 1}^{n} G (y, ξ_{0, i})}{n}

(50)

The higher the discrate points number n is, the more accurate the probability is. We discretized this interval to 2000 points.

In what follows, various parameters and variables will be selected to study their effect one by one on the shiftability map and engagement probability.

4 Results of the parameter study

In this chapter, we examine the effect of the variables on the dog clutch shiftability in two parts. The first part examines the effect of some selected geometry parameters on the dog clutch shiftability while ignoring the linear viscous friction. The second part investigates the effect of some selected system friction parameters. For the first part, Table 2 lists the fixed values and study ranges for the parameter.

However, firstly, let us validate the developed shiftability condition with our work for dog clutch dynamics [30]. Similar dynamics are employed in our previous paper [30] to describe the dog clutch during each stage. Ten cases are chosen to compare the actual dynamics with the shiftability conditions, listed in Table 3. In Table 3, the actuator force, the mismatch speed coulomb friction force, and the linear viscous friction coefficient are changed, while other system parameters are fixed according to the fixed value in Table 2. For cases 1 and 2 in Fig. 8a, case 5 in Fig. 8b, and case 8 in Fig. 8c, the sleeve has been blocked by the gear at the end of the axial gap (x_s = 10 mm) due to the face impact. So, these gearshifts were not successful. The shiftability condition could detect the same results for the aforementioned cases, as Table 3 shows. For case 4 in Fig. 8a, cases 6 and 7 in Fig. 8b, and cases 9 and 10 in Fig. 8c, the sleeve could reach its final position at 15 mm, without impact, and the shiftability condition detected the same results as Table 3 shows. For case 3 in Fig. 8a, the sleeve impacted with the gear and is blocked by the gear for a short time, then continues to move until it reaches the final position. Even though the sleeve reached its final position, this was considered an unsuccessful gearshift due to the presence of the face impact, and the shiftability condition detected the same results.

Table 3.

Shiftability condition validation cases

case	1	2	3	4	5	6	7	8	9	10
$F_{a c t}$ [N]	100	250	300	500	200	350	500	200	350	250
${∆ ω}_{0}$ [rad/s]	100	160	120	50	140	200	240	160	100	160
c_l [N.s/m]	0	0	0	0	0	0	0	0.5	4	8
F_cl [N]	0	0	0	0	0	0	0	1	10	5
Full dynamic simulation Successful (1) Unsuccessful (0)	0	1	0	0	0	1	1	0	1	1
Shiftability condition Successful (1) Unsuccessful (0)	0	1	0	0	0	1	1	0	1	1

Fig. 8.

Shiftability condition validation: a) cases 1–4, b) cases 5–7, and c) cases 8–10 (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

After we validated our work, we show the results of the parametric study. Firstly, we examine the effect of different overlap distances $x_{f e d}$ on the shiftability map at different overlap distances $x_{f e d}$ , with zero initial angular relative position $ξ_{0}$ . Figure 9a illustrates that as $x_{f e d}$ increases, the blue regions begin to disappear, and the largest blue region shrinks.

Fig. 9.

System sensitivity for overlap distance: a) shiftability map, b) engagement probability, c) surface plot, and d) contour plot of the successful region portion e) minimum portion and its rate of change, f) relative rotation $ξ_{2}$ – $ξ_{1}$ (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

The shiftability map in Fig. 9a is plotted at a fixed $ξ_{0}$ value equal to 4°. To better understand how the overlap distance affects the shiftability map, we calculate the ratio of the successful region area (Sum of Blue areas) to the entire domain area at various $x_{f e d}$ and $ξ_{0}$ values. Later, this ratio will be called the successful region portion. The outcomes are illustrated in Fig. 9c, which illustrates the resulting surface response, and Fig. 9d, which presents the contour plot. These representations clearly indicate a decrease in the portion of the successful region as $x_{f e d}$ increases. Also, it can be observed from Fig. 9d that holding $x_{f e d}$ constant, this portion decreases with $ξ_{0}$ until it reaches a minimum value at a specific $ξ_{0}$ – let us call it $ξ_{0, \min}$ – then starts to increase. The minimum portion value decreases as $x_{f e d}$ increases, as Fig. 9e shows. Also, it shows that the curve trends for the rate of change for the portion with respect to $ξ_{0}$ at $ξ_{0, \min}$ decreases as $x_{f e d}$ increases, which damps the growth of the portion value. This illustrates the expansion of the dark blue region as $x_{f e d}$ increases.

The negative effect of the overlap distance comes from its effect on the relative rotation $ξ_{2}$ – $ξ_{1}$ , as Eq. (44) shows. Figure 9f shows that $x_{f e d}$ positively affects the relative rotation $ξ_{2}$ – $ξ_{1}$ , since a higher overlap distance requires more time ∆t to cover, as shown in Eq. (17), resulting in an increased relative rotation $ξ_{2}$ – $ξ_{1}$ . Also, increased relative rotation causes the left side of Eq. (7) to decrease, which will impose more restrictions on the shiftability condition, and decrease the chance to be satisfied. So, the overlap distance will negatively affect the successful region areas, which decreases the successful region portion.

The previous explanation assumed that the initial relative position was known. However, in cases where the initial relative position is unknown and randomly distributed within the range [0, 2π/z], we consider the engagement probability (denoted in Fig. 9b). Figure 9b presents the probability plot at different overlap distances, revealing a negative effect on the probability. As ∆t increases due to higher $x_{f e d}$ , the chances for successful gearshift decrease. This finding aligns with our previous results in [29].

Figure 10a provides the shiftability map at various backlash values. It is observed that the blue regions rapidly expand with increasing backlash values.

Fig. 10.

System sensitivity for backlash: a) shiftability map, b) engagement probability, c) surface plot, and d) contour plot of the successful region portion, e) minimum portion and its rate of change (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

Furthermore, Fig. 10c and d demonstrate that backlash positively affects the portion of the successful region. At a constant $ξ_{0}$ , the portion increases with increasing backlash. Additionally, at a constant backlash, the portion initially decreases until it reaches a minimum value at $ξ_{0, \min}$ . In contrast to Fig. 9d, the dark blue region shrinks as the backlash increases due to two reasons. Firstly, the minimum portion value increases as backlash increases, as Fig. 10e shows. Secondly, the curve trends -within the backlash interval corresponding to the dark blue region-for the rate of change of the portion with respect to $ξ_{0}$ at $ξ_{0, \min}$ increases as backlash increases, which stimulates the portion value growth.

Increasing the backlash will increase the left side of Eq. (7), which creates more relief on the shiftability condition, allowing it to be satisfied at more points. As a result, the blue regions of the shiftability map and the portion increase. From a system perspective, as the backlash increases, ${ξ_{1}}^{'}$ is allowed to reach higher values at the end of the free-fly phases. So, the backlash positively affects the dog clutch shiftability.

Figure 10b illustrates that the probability is highly sensitive to changes in backlash and exhibits a direct linear relationship. Higher backlash provides a greater tangential space for teeth engagement during the overlap distance covering phase, thereby increasing the available time to cover this distance. This extended duration enhances the chance of a successful gearshift.

Figure 11a illustrates the shiftability map at different teeth number values, revealing a high sensitivity of the successful region to changes in the teeth number. Additionally, Fig. 11c and d demonstrate that the portion of the successful region increases with the teeth number, z. In Fig. 11c and d, the surface and contour plots are cropped down as the teeth number increases, since $ξ_{0}$ will be restricted to narrower intervals or [0, 2π/z]. Figure 11d shows that the dark blue region shrinks as the teeth number increases, similar to Fig. 10d. With the aid of Fig. 11e, this can be explained for the same two reasons explaining this behavior for the system sensitivity for backlash.

Fig. 11.

System sensitivity for teeth number: a) shiftability map, b) engagement probability, c) surface plot, and d) contour plot of the successful region portion, e) minimum portion and its rate of change (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

In Eq. (7), a higher teeth number decreases the maximum value that the middle side can reach, which is 2π/z. This increases the chance for the condition to be satisfied, even though the left-hand side remains constant. So, the teeth number positively affects dog clutch shiftability.

Figure 11b shows that the probability increases with the teeth number and exhibits a direct linear relationship, similar to the relationship observed in Fig. 10b. A higher tooth number decreases the randomness of $ξ_{0}$ , which is restricted by the interval [0, 2π/z].

In the previous part, the focus was on the system sensitivity to its geometry parameters. For this reason, the rational friction parameters are kept constant, and the linear friction is ignored. In the following part, we investigate the effect of the system friction on the dog clutch shiftability. In the following explanation, the same fixed values in Table 2 are used, except with 10 teeth to show better the results.

Figure 12 shows the linear viscous friction coefficient c_l effect on the shiftability map (or portion of the successful region). Figure 12a shows that the system is not sensitive to the change in c_l since the contour lines are almost parallel to c_l axis. In fact, the max c_l value is 40 N.s/m while the max F_act is 2000 N, and the friction is very low compared to the maximum available actuator force. Figure 12a is extended to 400 N.m/s as Fig. 12b shows. The contour lines are not parallel to c_l axis, so, the system is sensitive to c_l change, and this dependency increases at higher c_l values since the contour lines deviate from the c_l axis. On the other hand, F_act range in Fig. 12a is reduced, with 500 N as the maximum available actuator force, as Fig. 12c shows. Compared to Fig. 12a, the counter lines are not parallel to c_l axis. However, the comparison between Figure 12b and Figure 12c shows that the system is more sensitive to c_l change in Fig. 12c. However, both Fig. 12b and c show low dependency on c_l, especially at lower values, since the contour lines are nearly parallel to the c_l axis. Figure 12c is extended to 400 N.m/s as Fig. 12d shows. Figure 12d shows that the system, in this case, is highly dependent on c_l, especially at higher values. However, in Fig. 12d, the friction values are comparable to the actuator force, which is an unrealistic case. Figure 12a and c show the most realistic cases for the friction in dog clutch systems and gearshift actuators. Both aforementioned cases show low dependency on the linear viscous friction.

Fig. 12.

System sensitivity for linear viscous friction coefficient (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

Besides the dependency, Fig. 12b–d shows that the linear viscous friction negatively affects the dog clutch shiftability; while holding $ξ_{0}$ constant and crossing these figures horizontally, the successful region portion decreases at higher c_l values. Also, the dark blue region is wider, in the vertical direction, at higher c_l values, as clearly seen in Fig. 12b–d. At a given actuator force, the linear viscous friction slows down the system. This will increase the time required to cover the axial gap, which means a higher t₁ value. As time passes, the mismatch speed decreases due to the loss torque, and with higher t₁, the mismatch speed $Δ ω_{1}$ will be lower at the end of axial gap coverage. This reduces the relative rotation $ξ_{2}$ – $ξ_{1}$ during the overlap distance coverage. So, higher c_l helps in decreasing this relative rotation during the overlap distance coverage. On the other hand, slowing down the system will increase the time to cover the overlap distance, and increasing this time increases the relative rotation $ξ_{2}$ – $ξ_{1}$ during the overlap distance coverage. So, c_l has two conflicting effects on the relative rotation $ξ_{2}$ – $ξ_{1}$ . However, Fig. 14a- generated based on Eq. (47) and constant values in Table 2 except with 10 teeth and 500 N actuator force-shows that the negative effect outfitted the positive effect; crossing Fig. 14a vertically, $ξ_{2}$ – $ξ_{1}$ increases. We already explained above that increased $ξ_{2}$ – $ξ_{1}$ negatively affects the shiftability condition, Eq. (7). So, the linear viscous friction negatively affects the dog clutch shiftability, as clearly seen in Fig. 12b–d.

Figure 13 shows the rotational viscous friction coefficient c_r effect on the shiftability map. Figure 13a shows that the system is not sensitive to the change in c_r since the contour lines are almost parallel to c_r axis. F_act range in Fig. 13a is reduced, with 500 N as the maximum available actuator force, as Fig. 13b shows. The contour lines are not parallel to c_r axis, so, the system is sensitive to c_r change. Both the actuator force and rotational viscous friction positively affect the shiftability condition. Higher F_act reduces the time to cover the overlap distance, and higher c_r reduces the mismatch speed $Δ ω_{1}$ at the end of axial gap coverage. Both of these reduce the relative rotation $ξ_{2}$ – $ξ_{1}$ , which positively affects the shiftability condition, Eq. (7). However, higher maximum available actuator force tends to cover the effect of increased rotational viscous friction coefficient c_r. For this reason, c_r change is more sensible at a lower maximum available force.

Fig. 13.

System sensitivity for rotational viscous friction coefficient (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

Moreover, the effect of both rotational and linear viscous friction on the successful region portion is combined and illustrated in Fig. 14b, at fixed $ξ_{0}$ and according to the fixed values in Table 2, except with 10 teeth. Again, this figure shows that c_r positively affects while c_l negatively affects the portion value, as concluded above. However, the portion is more sensitive to c_r as the contour lines are closer to c_l (vertical) axis. This can be explained by the relative rotation $ξ_{2}$ – $ξ_{1}$ sensitivity to both c_r and c_l, as these two parameters are included in $ξ_{2}$ – $ξ_{1}$ equation, Eq. (47), and $ξ_{2}$ – $ξ_{1}$ has a major effect on the shiftability condition, Eq. (7). Figure 14a shows that the relative rotation is more sensitive to c_r as the contour lines are closer to c_l (vertical) axis.

Fig. 14.

System sensitivity for rotational and linear viscous friction coefficients: a) relative rotation $ξ_{2}$ – $ξ_{1}$ , and b) Successful region portion (Own source)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00745

5 Conclusion

In this study, we developed a dynamic model for dog clutch shiftability. This work aims to overcome the limitation of the previous work for dog clutch shiftability based on a kinematical model. This model considers the system dynamics regarding the mismatch speed and the axial velocity, where they are considered not constant variables. The developed condition is based on our previous work for the dog clutch engagement dynamics. Based on this condition, and our previously developed method for parametric study, we analyzed the system parameters' effect on the dog clutch shiftability, including the shiftability map, the successful region portion, and the engagement probability.

The study included two main parts: one with a known initial relative angular position and the other with a random initial position. The first part has two significant points. Firstly, it can be employed for the design of the dog clutch system to meet the requirements Secondly, it can be used to design a gearshift algorithm. The second part has significance in identifying the best actuator force that guarantees the highest engagement probability, knowing the mismatch speed.

The application of this parametric study method is demonstrated by applying it to different selected parameters. The overlap distance negatively affected both the successful region portion and the probability. The backlash and the teeth number positively affected both the successful region portion and the probability. The linear friction negatively affects, but the rotational friction positively affects the successful region portion.

Lastly, the employed models for the linear and rotational friction are linear. However, other models can be used, provided that an analytical solution exists for the differential equation of the linear and angular dynamics.

Later on, this model will be employed with our current test rig to design an algorithm for the gearshift in dog clutch system. At the beginning of the gearshift process, the mismatch speed and relative position can be measured, and based on these two measures, an algorithm can be designed to identify the optimal gearshift parameters. As seen, the shiftability condition contains three sets of parameters, the dog geometry parameters, the system friction parameters, and the dynamic and kinematic parameters. Once the dog clutch geometry and its system are identified, the geometry and system friction parameters can be considered fixed in the shiftability condition. The only left parameters are $ξ_{0}$ , $Δ ω_{0}$ , and $F_{a c t}$ . $ξ_{0}$ , and $Δ ω_{0}$ are considered uncontrolled while only Fact is controlled parameters. So, for known $ξ_{0}$ , and $Δ ω_{0}$ , Fact can be chosen to satisfy the shiftability condition. From the actuator force, the linear acceleration can be calculated, and from the linear acceleration, the linear velocity trajectory can be calculated, then, the linear position trajectory can be obtained from the linear velocity trajectory. This position trajectory is considered the optimal reference position trajectory for the sliding sleeve that the controller shall follow. Also, the gearshift can start at any $ξ_{0}$ , so, it can be chosen freely, but different $ξ_{0}$ requires different Fact to satisfy the shiftability condition. The algorithm will provide the optimal $ξ_{0}$ and reference position trajectory that guarantee the best performance. These are considered as the optimal gearshift parameters.

Acknowledgements

The authors acknowledge that this research has received no external funding.

References

[1]↑
O. Al-Oran, F. Lezsovits, and A. Aljawabrah, “Exergy and energy amelioration for parabolic trough collector using mono and hybrid nanofluids,” J. Therm. Anal. Calorim., vol. 140, no. 3, pp. 1579–1596, 2020.
- Search Google Scholar
- Export Citation
[2]↑
A. Qazi, F. Hussain, N. ABD. Rahim, G. Hardaker, D. Alghazzawi, K. Shaban, and K. Haruna, “Towards sustainable energy: a systematic review of renewable energy sources, technologies, and public opinions,” IEEE Access, vol. 7, pp. 63837–63851, 2019.
- Search Google Scholar
- Export Citation
[3]↑
R. A. Burgelman and A. S. Grove, “Toward electric cars and clean coal: A comparative analysis of strategies and strategy-making in the US and china,” 2010.
- Search Google Scholar
- Export Citation
[4]↑
M. A. Mallouh, B. Denman, B. Surgenor, and B. Peppley, “A study of fuel cell hybrid auto rickshaws using realistic urban drive cycles,” Jordan J. Mech. Ind. Eng., vol. 4, no. 1, pp. 225–229, 2010.
- Search Google Scholar
- Export Citation
[5]
D. Liu, S. Li, and H. Liu, “Experimental study on formaldehyde emission from environmental protection and energy-saving alcohol fuel for vehicles,” Jordan J. Mech. Ind. Eng., vol. 15, no. 1, pp. 1–6, 2021.
- Search Google Scholar
- Export Citation
[6]
G. Á. Szíki, A. Szántó, and T. Mankovits, “Dynamic modelling and simulation of a prototype race car in matlab/simulink applying different types of electric motors,” Int. Rev. Appl. Sci. Eng., vol. 12, no. 1, pp. 57–63, 2021.
- Search Google Scholar
- Export Citation
[7]↑
S. Bodzás, “Geometric design, modelling and finite element analysis of spur gear pairs having normal teeth based on the modification of the pressure angle,” Int. Rev. Appl. Sci. Eng., vol. 13, no. 3, pp. 285–297, 2022.
- Search Google Scholar
- Export Citation
[8]↑
S. Bodzás, “Computer aided designing and modelling of spur gear pairs having normal and modified straight teeth,” Int. Rev. Appl. Sci. Eng., vol. 10, no. 2, pp. 157–163, 2019.
- Search Google Scholar
- Export Citation
[9]↑
A. Myklebust and L. Eriksson, “Modeling, observability, and estimation of thermal effects and aging on transmitted torque in a heavy duty truck with a dry clutch,” IEEE/ASME Trans. mechatronics, vol. 20, no. 1, pp. 61–72, 2014.
- Search Google Scholar
- Export Citation
[10]↑
B. Gao, H. Chen, Y. Ma, and K. Sanada, “Design of nonlinear shaft torque observer for trucks with automated manual transmission,” Mechatronics, vol. 21, no. 6, pp. 1034–1042, 2011.
- Search Google Scholar
- Export Citation
[11]↑
B. Chen, J. Guo, M. Yan, F. Wang, and F. Liu, “Study on a ni-p-nano tin composite coating for significantly improving the service life of copper alloy synchronizer rings,” Appl. Surf. Sci., vol. 504, 2020, Art no. 144116.
- Search Google Scholar
- Export Citation
[12]↑
K. Barathiraja, G. Devaradjane, A. Bhattacharya, V. Sivakumar, and V. Yadav, “Automotive transmission gearbox synchronizer sintered hub design,” Eng. Fail. Anal., vol. 107, 2020, Art no. 104213.
- Search Google Scholar
- Export Citation
[13]↑
D. T. Vierk and S. J. Kowal, “Composite friction and dog clutch,” ed: US Patent 10,060,485, 2018.
- Search Google Scholar
- Export Citation
[14]↑
I. Shiotsu, H. Tani, M. Kimura, Y. Nozawa, A. Honda, M Tabuchi, H. Yoshino, and K. Kanzaki, “Development of high efficiency dog clutch with one-way mechanism for stepped automatic transmissions,” Int. J. Automot. Eng., vol. 10, no. 2, pp. 156–161, 2019.
- Search Google Scholar
- Export Citation
[15]↑
G. Bóka, J. Márialigeti, L. Lovas, and B. Trencséni, “External synchronization strategies for automated mechanical transmissions with face dog clutch and countershaft brake,” 8th Int. Multi-discip. Conf., 2009.
- Search Google Scholar
- Export Citation
[16]↑
A. Dick, J. Greiner, A. Locher, and F. Jauch, “Optimization potential for a state of the art 8-speed at,” SAE Int. J. Passenger Cars Mech. Syst., vol. 6, nos 2013-01-1272, pp. 899–907, 2013.
- Search Google Scholar
- Export Citation
[17]↑
L. Gaertner and M. Ebenhoch, “The zf automatic transmission 9hp48 transmission system, design and mechanical parts,” SAE Int. J. Passenger Cars Mech. Syst., vol. 6, nos 2013-01-1276, 2013.
- Search Google Scholar
- Export Citation
[18]↑
L. Pointner, M. Mileti, H. Pflaum, and K. Stahl, “Characterization of high-dynamic form-fit shifts in automatic transmissions,” ATZ worldwide, vol. 121, no. 10, pp. 64–69, 2019.
- Search Google Scholar
- Export Citation
[19]↑
P. D. Walker, Y. Fang, and N. Zhang, “Dynamics and control of clutchless automated manual transmissions for electric vehicles,” J. Vib. Acoust., vol. 139, no. 6, 2017, Art no. 061005.
- Search Google Scholar
- Export Citation
[20]
J.-q. Xi, L. Wang, W.-q. Fu, and W.-w. Liang, “Shifting control technology on automatic mechanical transmission of pure electric buses,” Trans. Beijing Inst. Technol., vol. 1, pp. 42–45, 2010.
- Search Google Scholar
- Export Citation
[21]
H. Liu, Y. Lei, Z. Li, J. Zhang, and Y. Li, “Gear-shift strategy for a clutchless automated manual transmission in battery electric vehicles,” SAE Int. J. Commer. Veh., vol. 5, nos 2012-01-0115, pp. 57–62, 2012.
- Search Google Scholar
- Export Citation
[22]
J. Li, P. Sheng, and K. Shao, “Optimization of clutchless amt shift control strategy for electric vehicles,” Jordan J. Mech. and Ind. Eng., vol. 14, no. 1, pp. 109–117, 2020.
- Search Google Scholar
- Export Citation
[23]↑
M. P. Laird, B. Lawton, and R. P. Gregory, “Dog clutches for rapid gear changes in automotive gearboxes,” Proc. Inst. Mech. Eng. First Int. Conf. Gearbox Noise Vib, pp. 102–112, 1990.
- Search Google Scholar
- Export Citation
[24]↑
P. Echtler, M. Mileti, and A. Damm, “Torqueline-konische kupplung mit formschluss als alternatives schaltelement für automatikgetriebe,” VDI-Fachtagung Kupplungen und Kupplungssysteme in Antrieben, Ettlingen, 2017.
- Search Google Scholar
- Export Citation
[25]↑
M. Mileti, L. Pointner, H. Pflaum, and K. Stahl, “Torqueline cone clutch: performance analysis of highly dynamic form-fit shifts in automatic transmissions,” Intt. Conf. Adv. Veh. Powertrains, 2019.
- Search Google Scholar
- Export Citation
[26]↑
F. Eriksson,J. L. Kuttikkal, and A. Mehari, “Parametric study of a dog clutch used in a transfer case for trucks,” Graduate Thesis, 2013. https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A632773&dswid=-8516.
- Search Google Scholar
- Export Citation
[27]↑
M. Andersson and K. Goetz, “Fe analysis of a dog clutch for trucks withall-wheel-drive,” Graduate Thesis, 2010. https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A634202&dswid=8486.
- Search Google Scholar
- Export Citation
[28]↑
A. Aljawabrah and L. Lovas, “Körmös tengelykapcsoló kapcsolás kinematikai modellje [kinematical model of the dog clutch shifting],” GÉP, vol. 74, no. 1, pp. 9–12, 2023.
- Search Google Scholar
- Export Citation
[29]↑
A. Aljawabrah and L. Lovas, “Sensitivity analysis of dog clutch shiftability to system parameters,” Int. Rev. Appl. Sci. Eng., 2023. [Published Online] https://doi.org/10.1556/1848.2023.00644.
- Search Google Scholar
- Export Citation
[30]↑
A. Aljawabrah and L. Lovas, “Dynamic modeling of the dog clutch engagement process using hybrid automata,” JJMIE, vol. 17, no. 1, pp. 127–138, 2023.
- Search Google Scholar
- Export Citation
[31]↑
G. Bóka, “Shifting optimization of face dog clutches in heavy duty automated mechanical transmissions,” Dissertation, 2011. https://repozitorium.omikk.bme.hu/bitstream/handle/10890/1120/tezis_eng.pdf?sequence=3&isAllowed=y.
- Search Google Scholar
- Export Citation
[32]↑
R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey, and D. E. Knuth, “On the lambert w function,” Adv. Comput. Math., vol. 5, pp. 329–359, 1996.
- Search Google Scholar
- Export Citation
[33]↑
S. Yi, P. W. Nelson, and A. G. Ulsoy, “Analysis and control of time delayed systems via the lambert w function,” IFAC Proc. Volumes, vol. 41, no. 2, pp. 13414–13419, 2008.
- Search Google Scholar
- Export Citation
[34]↑
A. Feltane, G. F. Boudreaux-Bartels, and Y. Boudria, “Using the lambert-w function to create a new class of warped time-frequency representations,” Circuits, Systems, Signal Process., vol. 37, pp. 3191–3205, 2018.
- Search Google Scholar
- Export Citation
[35]↑
D. Barry, J.-Y. Parlange, L. Li, H. Prommer, C. Cunningham, and F. Stagnitti, “Analytical approximations for real values of the lambert w-function,” Mathematics Comput. Simulation, vol. 53, nos 1-2, pp. 95–103, 2000.
- Search Google Scholar
- Export Citation

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International Review of Applied Sciences and Engineering

Print ISSN:: 2062-0810

Online ISSN:: 2063-4269

Editorial Board

Mohammad Nazir AHMAD, Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia

Murat BAKIROV, Center for Materials and Lifetime Management Ltd., Moscow, Russia

Nicolae BALC, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Umberto BERARDI, Toronto Metropolitan University, Toronto, Canada

Ildikó BODNÁR, University of Debrecen, Debrecen, Hungary

Sándor BODZÁS, University of Debrecen, Debrecen, Hungary

Fatih Mehmet BOTSALI, Selçuk University, Konya, Turkey

Samuel BRUNNER, Empa Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland

István BUDAI, University of Debrecen, Debrecen, Hungary

Constantin BUNGAU, University of Oradea, Oradea, Romania

Shanshan CAI, Huazhong University of Science and Technology, Wuhan, China

Michele De CARLI, University of Padua, Padua, Italy

Robert CERNY, Czech Technical University in Prague, Prague, Czech Republic

Erdem CUCE, Recep Tayyip Erdogan University, Rize, Turkey

György CSOMÓS, University of Debrecen, Debrecen, Hungary

Tamás CSOKNYAI, Budapest University of Technology and Economics, Budapest, Hungary

Anna FORMICA, IASI National Research Council, Rome, Italy

Alexandru GACSADI, University of Oradea, Oradea, Romania

Eugen Ioan GERGELY, University of Oradea, Oradea, Romania

Janez GRUM, University of Ljubljana, Ljubljana, Slovenia

Géza HUSI, University of Debrecen, Debrecen, Hungary

Ghaleb A. HUSSEINI, American University of Sharjah, Sharjah, United Arab Emirates

Nikolay IVANOV, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

Antal JÁRAI, Eötvös Loránd University, Budapest, Hungary

Gudni JÓHANNESSON, The National Energy Authority of Iceland, Reykjavik, Iceland

László KAJTÁR, Budapest University of Technology and Economics, Budapest, Hungary

Ferenc KALMÁR, University of Debrecen, Debrecen, Hungary

Tünde KALMÁR, University of Debrecen, Debrecen, Hungary

Milos KALOUSEK, Brno University of Technology, Brno, Czech Republik

Jan KOCI, Czech Technical University in Prague, Prague, Czech Republic

Vaclav KOCI, Czech Technical University in Prague, Prague, Czech Republic

Imre KOCSIS, University of Debrecen, Debrecen, Hungary

Imre KOVÁCS, University of Debrecen, Debrecen, Hungary

Angela Daniela LA ROSA, Norwegian University of Science and Technology, Trondheim, Norway

Éva LOVRA, Univeqrsity of Debrecen, Debrecen, Hungary

Elena LUCCHI, Eurac Research, Institute for Renewable Energy, Bolzano, Italy

Tamás MANKOVITS, University of Debrecen, Debrecen, Hungary

Igor MEDVED, Slovak Technical University in Bratislava, Bratislava, Slovakia

Ligia MOGA, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Marco MOLINARI, Royal Institute of Technology, Stockholm, Sweden

Henrieta MORAVCIKOVA, Slovak Academy of Sciences, Bratislava, Slovakia

Phalguni MUKHOPHADYAYA, University of Victoria, Victoria, Canada

Balázs NAGY, Budapest University of Technology and Economics, Budapest, Hungary

Husam S. NAJM, Rutgers University, New Brunswick, USA

Jozsef NYERS, Subotica Tech College of Applied Sciences, Subotica, Serbia

Bjarne W. OLESEN, Technical University of Denmark, Lyngby, Denmark

Stefan ONIGA, North University of Baia Mare, Baia Mare, Romania

Joaquim Norberto PIRES, Universidade de Coimbra, Coimbra, Portugal

László POKORÁDI, Óbuda University, Budapest, Hungary

Roman RABENSEIFER, Slovak University of Technology in Bratislava, Bratislava, Slovak Republik

Mohammad H. A. SALAH, Hashemite University, Zarqua, Jordan

Dietrich SCHMIDT, Fraunhofer Institute for Wind Energy and Energy System Technology IWES, Kassel, Germany

Lorand SZABÓ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Csaba SZÁSZ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Ioan SZÁVA, Transylvania University of Brasov, Brasov, Romania

Péter SZEMES, University of Debrecen, Debrecen, Hungary

Edit SZŰCS, University of Debrecen, Debrecen, Hungary

Radu TARCA, University of Oradea, Oradea, Romania

Zsolt TIBA, University of Debrecen, Debrecen, Hungary

László TÓTH, University of Debrecen, Debrecen, Hungary

László TÖRÖK, University of Debrecen, Debrecen, Hungary

Anton TRNIK, Constantine the Philosopher University in Nitra, Nitra, Slovakia

Ibrahim UZMAY, Erciyes University, Kayseri, Turkey

Andrea VALLATI, Sapienza University, Rome, Italy

Tibor VESSELÉNYI, University of Oradea, Oradea, Romania

Nalinaksh S. VYAS, Indian Institute of Technology, Kanpur, India

Deborah WHITE, The University of Adelaide, Adelaide, Australia

International Review of Applied Sciences and Engineering
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2023
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International Review of Applied Sciences and Engineering
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International Review of Applied Sciences and Engineering
Language	English
Size	A4
Year of Foundation	2010
Volumes per Year	1
Issues per Year	3
Founder	Debreceni Egyetem
Founder's Address	H-4032 Debrecen, Hungary Egyetem tér 1
Publisher	Akadémiai Kiadó
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ISSN	2062-0810 (Print)
ISSN	2063-4269 (Online)