Quantitative Investigation into Friction-Induced Vibration During Mold-Opening Transience in Ultra-High-Tonnage Two-Platen Injection Molding Machines with Massive Inertia and Constraint-Guided Sliding

Abstract

As extreme-scale manufacturing evolves, the dynamic response of heavy moving components under ultra-high loads becomes a critical design challenge. This study focuses on friction-induced vibration of a more than 30-ton movable mass during the mold-opening stage in a two-platen machine with a clamping force >17,000 kN. A mathematical model and a validated rigid/flexible multibody dynamics model with PID co-simulation were developed to analyze transient vibration using maximum acceleration amplitude and stability time as core metrics. The results show vibration stems from imbalance between anti-opening resistance and hydraulic driving force, amplified by vacuum collapse, static-to-dynamic friction transition at slide feet/rail interface and PID overshoot, featuring high amplitude density (>0.75 g), transience (<50 ms) and high impact (>60,000 N). The maximum vibration acceleration amplitude remains 79.22% even after there is no mold vacuum suction, indicating that a static friction force other than the vacuum suction is the dominant factor resulting in a severe friction-induced vibration. These mechanistic insights establish an applicable framework for the dynamic optimization of the heavy components in extreme-large-scale manufacturing equipment.

1. Introduction

The injection molding machine serves as the primary apparatus for fabricating plastic products, capable of the rapid prototyping and mass production of components featuring complex geometries and high dimensional accuracy. As the crucial component of the two-platen plastic injection machine, movable platen is the key movable component in production, directly relating to the energy consumption in production, product precision, production efficiency, and so on. As manufacturing equipment evolves towards extreme-large scales and the component fabricating towards integrated forming [1], the dynamic behavior of the movable component under ultra-high mold-opening forces and ultra-great inertia has become critically focal in the design of the injection molding machine.

During the mold-opening process, two factors emerge as the dominant sources responsible for the vibration observed in the dynamic response: the static frictional force and in-mold vacuum negative force. The vacuum negative suction caused by the shrinkage of the product in the cooling process makes the two molds close tightly, resulting in an immense mold-opening force generated by the hydraulic cylinder. When the two molds open, the vacuum negative suction suddenly vanishes while the hydraulic driving force remains at a high level, leading to instability of the system. At the same time, friction at the interface between the copper slide feet and the guide rails is subjected to variation due to non-uniform loading on the four slide feet. All these render the movable platen highly susceptible to friction-induced vibration. There is an assumption widely accepted in the industry that the mechanisms of the friction-induced vibration stem from the dynamic imbalance at the frictional interface, and suction collapse is the most important factor to worsen this phenomenon. However, there is no evidence to verify and quantify this hypothesis for the design of the dynamic behavior of the movable platen. Furthermore, the resulting collision between the movable platen and the tie bars could potentially degrade the tie bar precision, severely compromising product consistency and the service life of the machine. Consequently, understanding the mechanism of the friction-induced vibration systematically and thoroughly during the mold-opening phase in the plastic injection machine justifies the need for engineers to predict, mitigate, or even eliminate friction-induced vibration early in the design stage. Specifically, this study also represents an urgent and significant challenge for the poor dynamic behavior elimination in the design of extreme-large-scale equipment.

Given the structural advantages, superior performance, and stability, two-platen injection molding machines have been a dominant configuration in the modern plastic injection machine manufacturing industry [2]. Numerous publications have primarily focused on the dynamic analysis and optimization of the clamping mechanism [3,4,5,6], structural strength assessment [7], performance evaluation [8,9,10], and dynamic performance of the control strategies [11,12]. Although numerous developments have been made in the field related to the plastic injection machine, there is currently still a lack of mechanistic investigation regarding friction-induced vibration at the mold-opening phase [2], especially for large-sized two-platen injection molding machines, whose clamping load is over 10,000 kN.

In addition, extensive research on friction-induced vibrations in mechanical systems has also been conducted due to their potential harm to the industrial equipment. Friction-induced vibration is a complex and scientifically diverse phenomenon, which could be influenced by many parameters, such as the pushing force, load, sliding velocity, component geometries, material properties, etc. [13]. The Stribeck effect, stick/slip motion, mode-coupling instability and sprag/slip instability [14,15] are the four well-known mechanisms for the occurrence of friction-induced vibration in mechanical systems [16,17,18,19,20,21,22]. It has been noted [23,24,25] that friction-induced vibration could exert a harmful and negative influence on the components and machines, such as undesirable vibration and noise, high energy consumption, and component failure [26,27]. Contact load plays an important role in friction-induced vibration generation, relating to weak contact and strong contact, which could affect the dynamic stability of the system [28,29,30]. Studies on the stability behavior of friction-induced vibration in joints have shown that instability could arise when a joint with nonlinear dynamic behavior is integrated into the system [31,32]. And research on a brake system consisting of two-layer pads and a rigid disc has shown that the friction-induced vibration is dependent on the variations of brake pressure and the parameters of pads [33]. Despite the numerous studies on friction-induced vibration, the emergence and mechanisms of friction-induced vibrations in the plastic injection machine are still not well understood quantitatively.

As mentioned above, the friction-induced vibration of the movable platen during the mold-opening phase is transient and is limited by the constraint. The immense hydraulic driving force against the suddenly vanished vacuum negative suction and the imbalance of the inertia within the movable platen and the movable mold are both subjected to the vibration. At the same time, the tie bars which guide the movement of the platen could limit the vibration of the movable platen. Therefore, the friction-induced vibration is a transient and constrained behavior in plastic injection machines. This paper presented a feasible and verified methodology to investigate the friction-induced vibration of the plastic injection machine, synergizing a multibody rigid/flexible-body coupled dynamic model as well as a control strategy in the mold-opening phase. Furthermore, the influence of the parameters—e.g., mass center of the movable components, total mass of the movable components, frictional coefficient, and vacuum negative suction—on the amplitude and stability time of friction-induced vibration was studied. The primary novelty of this work lies in two aspects: (i) a more in-depth explanation of the underlying mechanism was quantitatively proposed to amend the current hypothesis on friction-induced vibration of the movable platen in a two-platen plastic injection molding machine; (ii) a static friction force other than the vacuum suction is the dominant factor resulting in a severe friction-induced vibration. This work aims to deliver actionable, physics-informed guidelines for the design of manufacturing systems under ultra-high loads, massive inertia and heavy constraints. It is thereby positioned to contribute substantively to the field of advanced manufacturing technology, aligning with global efforts to modernize precision machinery design and optimize industrial production practices.

The rest of this paper is organized as follows. In Section 2, a dynamic model, its verification and the control strategy are introduced in detail. Then, the dynamic behavior in the time domain, including the hydraulic driving force, the friction-induced vibration of the movable platen, and the contact features, is fully investigated in Section 3. A sensitivity analysis, and discussion and limitations are also given in Section 3. Finally, a summary of the major contributions and findings is given in Section 4.

2. Modeling and Verification

2.1. Modeling and Simplification

The primary components of the two-platen injection molding machine include the stationary platen, movable platen, clamping cylinders, mold shifting cylinders, tie bars, locking brake devices, and the ejection mechanism. Figure 1 illustrates the structure of the classic clamping mechanism in the two-platen injection molding machine. As the frictional vibration of the movable platen was focused on in this study, components irrelevant to or not involved in the mold-opening action, such as the locking mechanism, were simplified or removed, as shown in Figure 1b. Figure 1c illustrates the topological relationships between kinematic pairs of the clamping mechanism in the two-platen machine. Sliding pairs were applied between the high-pressure cylinder and tie bar, the driving hydraulic cylinder and piston rod, and the machine feet and the bed, the tie bar and the movable platen, as well as the stationary platen.

The moving actions in the manufacturing process are shown in Figure 2. The complete injection molding cycle comprises four distinct actions, namely, closing, clamping, unlocking, and retracting, as shown in Figure 2a–d, respectively. In the unlocking action shown in Figure 2c, mold shifting cylinders pull the movable platen separated from the stationary platen and move backward, overcoming the suction generated by the vacuum in the mold as well as the static friction between the slide feet of the movable platen and the guide rails. In the retracting stage shown in Figure 2d, the mold shifting cylinders provide the driving force to move the movable platen back.

The three-dimensional coupling rigid/flexible-body model was developed for dynamic investigation. Parameters and kinematic pairs were configured, as shown in Figure 3. A contact constraint was established between the tie bars and the movable platen, with a friction coefficient of 0.20. Similarly, a contact constraint was applied between the movable platen and the guide rails, setting the static friction coefficient to 0.15 and the dynamic friction coefficient to 0.075. The constraint between the stationary plate and the bed was simplified to be the fixed constraint. There is damping in hydraulic force due to the hydraulic features, so a damper and a high-stiffness spring were added to represent the damping features of the hydraulic pressure force.

Based on the specifications of the LN-series machine—including mold thickness, maximum mold weight, and tie bar spacing—both the limited dimensions and maximum mass of the molds were determined. The mass and geometric dimensions of the components are shown in

Table 1. Mass of the components. Unit: ton.

Parameter	Value	Parameter	Value
Movable mold	10.0	Stationary mold	6.0
Movable platen and accessories	20.0	Stationary platen and accessories	16.0

and

Table 2. Geometric dimensions of the components. Unit: mm.

Parameter	Value	Parameter	Value
Diameter of tie bar	280	Movable mold	L1650; H1480; W960
Diameter of tie bar hole	280.20	Stationary mold	L1650; H1480; W640
Distance between tie bars (Horizontal × Vertical)	1930 × 1760	Note: L—Length; H—Height; W—Width.

, respectively. There is a dimensional clearance of 0.5 mm between the tie bar and the tie bar hole on the platen. The mass of the movable components, including movable platen and the movable mold, is 30 tons.

Table 3. The mechanical and frictional properties of the plastic injection machine.

Parameter	Value	Parameter	Value
Maximum in-mold negative suction	35 kN	Attainable maximum hydraulic driving force	350 kN
Maximum clamping force	15,000 kN

shows the maximum clamping force, maximum hydraulic driving pressure, and the vacuum negative suction.

2.2. Mathematical Model

2.2.1. Equations for Geometrical Relationship

In an ideal state, there is no contact between the tie bars and the movable platen, as the tie bars serve solely as guides. When the movable platen vibrates, contact between the movable platen and the tie bar could occur. The tilting or tendency to tilt of the movable platen is inevitable due to the immense mold-opening force between the two molds and the uneven frictional forces on the four feet between the copper-block feet and the guide rails. The relationship between the movable platen and tie bar in a simplified vertical cross-section is shown in Figure 4. When tilting, two contact scenarios may occur: (i) the movable platen contacts a single tie bar, and (ii) the movable platen contacts two tie bars simultaneously. In the first scenario, it is unclear which one of the two tie bars could first contact the movable platen. A simplified mathematical model was applied to describe the geometric relationship between the tie bar and movable platen based on Figure 4, which can be written as

$$y_a-y_{a\prime }=oa\mathit{sin}({\theta }_{oa})-oa\prime \mathit{sin}({\theta }_{ob}-\theta )$$

(1)

$$y_{b\prime }-y_b=ob\prime \mathit{sin}({\theta }_{ob}+\theta )-ob\mathit{sin}({\theta }_{ob})$$

(2)

where $\theta$ is the tilt angle of the movable platen, ${\theta }_{oa}$ is the angle between $o\alpha$ and the horizontal plane, and ${\theta }_{ob}$ is the angle between $ob$ and the horizontal plane. $y_a$ and $y_b$ denote the initial positions of points $a$ and $b$ along the y-direction (vertical direction) before motion, respectively, and $y_{a\prime }$ and $y_b$ denote their corresponding positions after motion. $oa$ and $oa\prime$ are the distance from point $a$ to point $o$ before and after motion, respectively. $ob$ and $ob\prime$ are the distance from point $b$ to point $o$ before and after motion, respectively. $a$ and $b$ denote the coordinate upper and lower tie bar, respectively. Point $a$ is defined as the intersection between the upper edge of the through-hole and the left-side lateral face of the movable platen; point $b$ is the corresponding intersection between the lower edge and the right-side lateral face.

Setting $y_a-y_{a\prime }=h$ and $y_{b\prime }-y_b=h$ where h is the clearance between the tie bar and the movable platen, and considering that $o\alpha =o\alpha \prime$ and $ob=ob\prime$ due to the rigidity of the movable platen, Equations (1) and (2) yield to

$$sin({\theta }_{o\alpha })-sin({\theta }_{o\alpha }-\theta )={\displaystyle \frac{h}{o\alpha }}$$

(3)

$$sin({\theta }_{ob}+\theta )-sin({\theta }_{ob})={\displaystyle \frac{h}{ob}}$$

(4)

Substituting the parameters oa = 2091 mm, ob = 1150 mm, θ_oa = 1.397 rad, θ_ob = 0.26 rad, and h = 0.1 mm into Equations (3) and (4) yields θ = 0.0107 rad and θ = 0.0131 rad, respectively. Consequently, point b contacts first, indicating that the movable platen collides with the lower tie bar first. The contact between the movable platen and the tie bars under different tilt angles is shown in

Table 4. Contact phase between the movable platen and the tie bars.

Contact Status	No Contact	Movable Platen Contacts One Tie Bar	Movable Platen Contacts Two Tie Bars
Tilt angle	0 < θ < 0.0107	0.0107 ≤ θ < 0.0131	0.0131 ≤ θ

.

2.2.2. Equations for Static Force

As mentioned above, the hydraulic driving force F_d must satisfy the following conditions to achieve mold opening in the injection molding machine:

$$F_d\ge F_m+f_s$$

(5)

where F_m is the vacuum negative suction, and f_s is the static frictional force. f_s can be calculated based on the Coulomb friction law:

$$f_s={\mu }_s{F}_N$$

(6)

where μ_s is the static frictional coefficient, and F_N is the sum load of movable platen and mold.

When the system reaches a steady state, the hydraulic driving force is equal to the dynamic frictional force, which satisfies the following conditions:

$$F_d=f_d$$

(7)

where $f_d$ is the dynamic frictional force. Dynamic frictional force can also be calculated based on the Coulomb friction law:

$$f_d={\mu }_d{F}_N$$

(8)

where μ_d is the dynamic frictional coefficient. When F_m = 35 kN, μ_s = 0.15, and μ_d = 0.075, the hydraulic driving force F_d that makes the molds separate is equal to 79,275 N, and F_d in a steady state is equal to 22,275 N.

2.3. Control Strategy

As mentioned above, following the injection and cooling phases, a vacuum forms within the two molds, generating in-mold vacuum negative pressure (suction) in the mold opening stage. To achieve mold opening, the hydraulic driving force must be higher than the mold-opening force, which consists of both the vacuum negative suction and static friction force between the guide rails and the feet. The control strategy is described in Figure 5 as follows. The dynamic control logic of the mold opening process in an injection molding machine is divided into two critical phases: “Before Mold Opening” and “After Mold Opening”.

In the “Before Mold Opening” phase, the primary objective of the control system is to overcome the initial resistance. The hydraulic driving force continuously increases until the mold opening criterion is satisfied; specifically, the driving force must exceed the sum of the in-mold pressure and the static friction force. Once this threshold is surpassed, the mold parting surface separates, causing the in-mold pressure to drop instantaneously to zero, and the process subsequently transitions to the “After Mold Opening” phase. In this phase, a PID algorithm is implemented to establish a closed-loop velocity control system. The control theory in the time domain is quantitatively governed by the following formula:

$$u(t)=K_{p}e(t) + K_i{\int }_0^{t}e(\tau )d\tau + K_d{\displaystyle \frac{de(t)}{dt}}$$

(9)

where u(t) is the calculated hydraulic driving force output; e(t) is the velocity error between the actual and preset velocities; and K_p, K_i, and K_d represent the proportional, integral, and derivative gains, respectively. It is crucial to emphasize that the entire co-simulation and parameter determination process was performed using the full nonlinear multibody dynamic model. Given the severe nonlinearities inherent in mold-opening transience, specifically the discontinuous static-to-dynamic friction transition and the instantaneous drop in the in-mold negative pressure, linearizing the system around an operating point would obscure the highly transient friction-induced vibration. Consequently, standard linear tuning methods were unsuitable. Instead, the PID parameters were determined through an iterative trial-and-error tuning process directly within the full nonlinear model. This approach ensures that the controller can accurately regulate the actual severe mechanical impacts. By comparing the actual velocity against the preset velocity, the system dynamically adjusts the hydraulic driving force to maintain the macroscopic motion.

2.4. System Nonlinearity

The dynamical system features two explicit sources of discontinuous transitions. First, the in-mold vacuum suction plummets from its peak value (35 kN) to zero at the exact instant of mold separation, representing a classic discontinuous excitation. Second, as the velocity surpasses the 10 mm/s threshold, the friction between the sliding shoes and the guide rails abruptly shifts from static to kinetic, causing the frictional force to halve instantaneously.

These discrete transitions and state switches introduce temporal discontinuities into the system’s differential equations, fundamentally precluding any linear approximation around a single operating point. Consequently, no form of linearization was applied to the system. All PID parameter tuning and dynamic simulations were executed directly on the comprehensive piecewise model, ensuring the authentic capture of the transient characteristics inherent to friction-induced vibrations.

The control architecture incorporates a conditional logic module to differentiate between the pre-opening and post-opening phases. Consequently, distinct control strategies are deployed for these two stages. From a macroscopic perspective, the overall control system exhibits the characteristics of a piecewise control structure, introducing pronounced nonlinearity. Furthermore, the actuation force must dynamically counterbalance abrupt friction transitions and variations in mechanical loading conditions. As a result, the real-time dynamic response of the controller under these transient states is highly nonlinear.

2.5. Verification

The experiment was carried out with the two-platen plastic machine, as shown in Figure 6. The acceleration sensor was located on the top-center of the movable platen, as shown in Figure 6b,c. A data acquisition computer connected the sensor with a high-shielded cable. During the experiment, the clamping force was 15,000 kN, the hydraulic driving force for the mold-opening phase was set to 250 kN, and the original velocity was approximately 50 mm/s.

Figure 7 presents the velocity, horizontal acceleration and mold-opening force of the movable platen in the mold-opening phase when there is in-mold vacuum negative pressure. It can be observed that the data show a good agreement between the experiment and the simulation. This confirms that the multibody dynamic model could better represent the dynamic behavior of the physical two-platen injection molding machine.

The acceleration data exhibit three distinct stages: the static-state stage, instable stage, and steady-state stage, which are colored blue, green and yellow, respectively. During the static-state stage, the hydraulic pressure gradually increases but does not reach the threshold value that could break away the mold. In the instable stage, severe vibration occurs. In this stage, the hydraulic pressure increases higher than the mold-opening force, and the vacuum negative pressure instantaneously decreases to zero, causing an increase in hydraulic pressure accompanied by horizontal fluctuations. However, the hydraulic pressure decreases fast due to the adjustment of the PID control, tending to become equal to the frictional force between the feet blocks and the rails. In the third stage, the hydraulic driving force is equal to the frictional force, and the friction-induced resistance gradually diminishes, leading to a constant velocity of the movable platen.

Figure 8 presents the velocity, horizontal acceleration and mold-opening force of the movable platen in the mold-opening phase when there is no in-mold vacuum negative pressure. Good agreement of both hydraulic driving force and acceleration between the simulation and the experiment is also illustrated, which also confirms that the multibody dynamic model is effective, and equivalent to the physical plastic injection machine. It is worth noting that the vibration of the movable platen and the hydraulic driving force without in-mold vacuum negative pressure are somewhat lower than those with in-mold vacuum negative suction.

3. Results and Discussion

3.1. Vibration of the Movable Platen

Peak acceleration determines the inertial impact on the platen and accessories, while stability time reflects system damping and control effectiveness. Figure 9 illustrates the acceleration response of the movable platen in the mold-opening phase. In the initial phase (0–0.28 s), the platen was in a stationary state. Between the time interval from 0.28 s to 0.34 s, significant fluctuations occurred. The peak acceleration appears at t = 0.29 s, immediately following mold opening, which corresponds precisely with the mold-opening critical point observed in the hydraulic force. This phenomenon originates from the sudden transition of both the combined static friction and in-mold vacuum force into dynamic friction. The drastic change in acceleration confirms the nonlinear dynamic behavior inherent in the mold-opening process.

Following the mold-opening phase, the fluctuation amplitude decays significantly and stabilizes after t = 0.34 s. This stability process lasts approximately 0.06 s, which is consistent with the vibration stability time of the hydraulic force, further validating the model.

Figure 10 shows the angular displacement of the movable platen. As the mold-opening action occurs, the tilt angle increases rapidly with distinct fluctuations. When the angle reaches 0.0107 and 0.0131 rad, the platen contacts two lower tie bars and then all four tie bars, respectively. Then, the movable platen continues to tilt, reaching a peak of approximately 0.0156 rad. This correlates directly to the suddenly vanished in-mold suction and its amplitude correlates directly with contact constraints from the tie bars, which also implies the bending deformation of the tie bars. Between 0.298 s and 0.305 s, the platen contacts four tie bars, suggesting a tendency for larger vibration amplitudes that are physically limited by the tie bars. From 0.310 s to 0.343 s, the tilt angle decays, with significantly reduced fluctuation. This indicates a continuous micro-amplitude oscillation during steady-state operation.

The dynamic response of the hydraulic driving force during the mold-opening phase is shown in Figure 11. The process consists of three distinct phases: ramp-up phase, adjustment phase, and steady-state phase. Notably, the hydraulic driving force plays a dominant role in dynamic stability of the movable platen, and is decided by the control logic of the hydraulic driving pressure.

3.2. Hydraulic Driving Force

In the first phase (0–p₁), the hydraulic driving force continuously rises, primarily to counteract the in-mold negative vacuum suction and the static friction between the feet and rails. During this phase, the movable platen remains stationary, and the hydraulic force increases almost linearly. In the adjustment phase (p₁–p₂), the hydraulic driving force exceeds the mold-opening force, leading to the separation of the two molds and movement of the movable platen. There is an inevitable overshoot over the breakaway point A, after which the system enters the third phase (p₂–1.0). The overshoot exceeds the theoretical breakaway force of 79,275 N, which is the sum of vacuum suction force and the static frictional force. In the third phase, the hydraulic force fluctuates lightly. After a transient adjustment period, the hydraulic force gradually stabilizes to the dynamic frictional force of 22,275 N, indicating that the system has reached a steady state. This stability time is 0.06 s, which is a vital dynamic metric for evaluating the dynamic smoothness in the mold-opening process.

3.3. Contact Between the Tie Bar and Movable Platen

Figure 12 presents the deformation of the tie bars in the mold-opening phase to show the collision between the movable platen and tie bars. Synchronous fluctuations appear in both upper and lower tie bars due to the tilt increase of the movable platen. The lower tie bar and upper tie bars contact the platen for approximately 0.017 s and 0.012 s, respectively. The lower tie bars deform first, implying that the lower tie bars contact the platen earlier than the upper bars. Furthermore, the upper and lower tie bars exhibit positive and negative deformation of approximately 0.082 and 0.005 mm, respectively. This implies the deformation of the upper and lower tie bars is in the opposite direction. After 0.312 s, the deformation decays to zero, implying no contact occurs anymore.

3.4. Discussion

Our study strongly revises the previous hypothesis and provides a more in-depth explanation of the underlying mechanism of the phenomenon quantitatively, namely that the friction-induced vibration from the movable platen is caused by the dynamic imbalance between the anti-mold-opening force and the driving force. The anti-mold-opening force is so complex that it consists of the vacuum suction between the two molds, and static friction between the slide feet and the guide rails.

The previous hypothesis proposed that when the vacuum suction suddenly disappears, the hydraulic driving force remains at a high level, leading to the imbalance of the system. The transition of the friction state in mold-opening transience is ignored in the mold-opening stage and is considered unimportant and will not play a dominant role. However, as shown in Figure 7 and Figure 8, the VAA_max is approximately 7700 mm/s² and 6100 mm/s² in the conditions with and without mold vacuum suction, respectively. The VAA_max still remains 79.22% even after there is no mold vacuum suction, indicating that the static coefficient of friction (SCoF) is the dominant factor resulting in a severe friction-induced vibration. This amends the generation mechanism of the friction-induced vibration in the previous hypothesis that the in-mold vacuum suction is the governing factor.

Unlike classical friction-induced creep or stick/slip phenomena such as those observed in lower velocity, heavy load, and free-sliding mechanical systems (e.g., seals [34], piezoelectric stick-slip actuator [35], and vehicle brake pad [36]), the friction-induced vibration of the movable platen is strongly constrained by the tie bars and the guide rails. It exhibits distinct features such as high energy density (VAA_max$>$0.75 g), transience $(<$50 ms), impact-driven mode excitation (hydraulic driving force > 55,000 N), and high impact force (>60,000 N). Beyond the numerical validation, our outcomes provide quantitatively verified guidelines to not only streamline accurate diagnostic workflows but also enable the design of targeted mitigation strategies to enhance operational stability and extend service lifecycles.

Furthermore, regarding the control strategy, there is a high degree of matching between the experimental results and the theoretical simulation. The strong agreement between the experimental observations and the simulation curves validates the effectiveness of the proposed nonlinear framework. It suggests that the interaction between the discontinuous friction transition and the active control logic is the dominant factor in describing the system’s transient response, highlighting the necessity of nonlinear modeling for ultra-large mechanical systems. As observed in the transient responses, the PID controller effectively regulates the severe friction-induced vibration. Both the experimental and simulated systems rapidly overcome the initial transient overshoot and converge to the steady-state driving force with comparable settling time. The overall trend and steady-state stability strongly validate the accuracy of the full nonlinear model and the effectiveness of the applied control theory.

A critical perspective should be emphasized from the results that the frictional vibration has a potentially great impact on the tie bars and the interface between the four feet of the movable platen and the guide rails, leading to potential damage, fatigue, and wear on the tie bars, slide feet and guide rails. The vibration, whose amplitude could exceed 7700 mm/s², will collide the movable platen with the tie bars, leading to the deformation of the latter. The maximum bending deformation reaches 75.0 μm on the two lower tie bars, the deformation position of which is very close to the locking mechanism, easily inducing the fatigue, and even the early fracture, of the tie bars. Compared to the stability time, we believe that VAA_max plays the most significant role in the precision and reliability of the equipment because VAA_max determines the extent of the potential risk that vibration poses to the other components, e.g., tie bars and guide rails, further leading to a negative influence on the production precision and quality of the two-platen plastic injection molding machine.

Although there are important discoveries revealed in this study, a few possible limitations should be borne in mind. First, only the tie bars and the sliding feet were treated as flexible bodies in the dynamic model to save computation resources. However, all components may undergo deformation in actual operating conditions. Additionally, the contacts between the components are assumed to be ideal, but various errors inevitably occur during the assembly process of the system. These two aspects impact the precision of the model results. It is maybe better to develop a more precise multibody dynamic model for a more realistic simulation.

4. Conclusions

This study investigated the friction-induced vibration of a large-scale manufacturing platform under ultra-high loads and massive inertial forces, specifically, a clamping mechanism of a two-platen plastic injection molding machine with a clamping force exceeding 17,000 kN and a movable mass of over 30 tons, by an experimentally verified multibody dynamic model. The dynamic features of the movable platen during the mold-opening phase were systematically analyzed. Additionally, the influence of five variables on the vibration was investigated. The main conclusions were as follows.

(1)

A multibody dynamics model for the clamping system of a large-scale two-platen injection molding machine was developed and well verified by a 1:1 scaled experiment, featuring co-simulation with PID controller and coupling of rigid bodies with flexible ones. This model enables both qualitative and quantitative evaluation of the friction-induced vibration phenomena of the movable platen.

(2)

The amended mechanism of the friction-induced vibration from the movable platen is that the shift from static friction to dynamic friction between the sliding feet and slide rails plays the most important role in deciding the severity of the vibration rather than the in-mold vacuum suction. VAA_max could remain above 79% even after there is no mold vacuum suction.

This study reveals the fundamental mechanism underlying friction-induced vibrations originating from the movable platen, namely, the stick/slip instability arising at the sliding interface between the platen and guide rails under transient mold-opening time. By establishing this mechanistic insight, this work provides a theoretical framework for optimizing the dynamic performance of the clamping system, thereby contributing to extending the service life of the injection molding machine. Moreover, these improvements collectively lower maintenance frequency, decrease unplanned downtime, and support long-term consistency in high-precision production.

An interesting avenue for future research would be to develop advanced control strategies—particularly those leveraging preset consistency adjustment of the geometric centroid of the sliding feet and center of the movable mass, thereby effectively suppressing vibration amplitude during mold-opening transience. The development of a fully flexible multibody dynamic model—fully considering design tolerances and assembly errors to ensure realistic representation of geometric imperfections and their dynamic consequences and rigorous validation against high-fidelity experimental data—will significantly enable more accurate simulation results.