He, Gao, Bai and Wu (2013) established a virtual-work inverse-dynamics model with gravity counterbalance for a 2500 t parallel-topology servo press and validated it on the prototype with an average actuator-torque error below 15%, while explicitly deferring the omissions that define this problem: joint friction and servomotor/gear-train dynamics are absent from the model; the counterbalance-ratio study excludes stamping loads; joint clearances and manufacturing defects are not modeled; and the pneumatic counterbalance assembly rests on an approximate isothermal Boyle-law model with no scientific design methodology. The group's own continuation addressed type synthesis rather than model refinement, and later work resolves the functional analogs of the deferred items only for crank-type and eight-bar linkage presses. The production-fidelity dynamic model and counterbalance design methodology for the large-capacity parallel servo press therefore remain open.

Background

A mechanical servo press is a metal-forming machine in which the reciprocating ram (slide) is driven by servomotors through a linkage transmission, so that, unlike in a conventional crank press with a fixed stroke curve, the ram trajectory is fully programmable; the resulting process flexibility, quality and energy advantages are reviewed by Osakada, Mori, Altan and Groche (2011). Achieving very large stamping capacities with a single servo drive is difficult, and the traditional solution is redundant actuation — several motors driving the same ram. Redundant actuation, however, creates over-constraint (the actuators mutually constrain an already closed kinematic chain, so actuation errors produce internal forces) and interference among actuators, raising control difficulty and cost. To avoid this, He, Gao and Zhang (2013) and He, Gao, Bai and Wu (2013) introduced press mechanisms with parallel topology, in which the ram is moved by closed kinematic chains (parallel mechanisms) rather than by a single serial linkage; the concept culminated in a full-scale prototype rated at 2500 t, reaching 25 MN of stamping force 13 mm above bottom dead center.

He, Gao, Bai and Wu (2013) built their design methodology around inverse dynamics: given a prescribed ram motion (a quintic-polynomial trajectory with a 1200 mm stroke at 8 strokes per minute), the required actuator torques are computed from the d'Alembert virtual-work principle, an energy-based formulation that equates actuator work to the inertial, gravitational and external forces of all links mapped through the mechanism Jacobians (the velocity-mapping matrices of the mechanism). Because the ram and links are very heavy, the steady gravity load dominates the actuator torque, so the machine uses counterbalance cylinders — pneumatic cylinders that push upward on the ram to offset its weight. These were modeled by an isothermal Boyle-law relation (the ideal-gas law at constant temperature), giving cylinder pressure as a function of piston stroke, and a numerical study showed that the peak actuator torque is minimized when the ratio of the total counterbalance force to the ram weight is in the vicinity of 1.0. Torque measurements on the prototype agreed with the computation with an average error below 15% for the studied cycle.

The authors state the model's omissions explicitly, and these omissions define the open agenda. Joint and mechanism friction and the dynamic response of the servomotors and gear trains were omitted, and were identified as the main source of the roughly 15% torque error. The counterbalance-ratio study was computed without stamping loads, so actuator sizing under real production conditions was left open. Joint clearances — the small unavoidable gaps between pins and bores at revolute joints, which produce contact impacts, noise and amplified dynamic response in a machine of this scale — were not modeled. The counterbalance assembly was designed from an approximate isothermal model rather than a scientific sizing, pressure-control and stability analysis for high-speed, large-capacity presses. Finally, the practical realization of the virtual prismatic joint D (the modeled vertical guide degree of freedom at platform point D) and related load-splitting details remained prototype engineering tasks.

The adjacent literature has since advanced each ingredient for other machine topologies. Joint-clearance dynamics of press transmissions is well developed for slider-crank presses (presses driven by the classic crank-and-connecting-rod linkage; Zheng and Zhou 2014; Chen, Sun and Chen 2016; Chen, Sun and Yang 2017); electromechanical coupling between the servo motor, gear train and mechanism has been modeled for crank-type servo presses (Wang et al. 2025); actuator-side two-inertia dynamics (modeling the motor and the driven mechanism as two inertias coupled by a compliant transmission) has been incorporated into parallel-manipulator dynamics in general (Wang, Wang and Wu 2019); general gravity-compensation design theory for mechanisms exists (Arakelian and Zhang 2019); and Li et al. (2026) recently built and experimentally calibrated a press dynamics model including gravity, joint friction, balance force and stamping process load — but for an eight-bar linkage press, not a parallel one. For the parallel-topology large-capacity servo press itself, the group's own continuation (He, Gao, Meng and Guo 2015) addressed type synthesis (the systematic enumeration of candidate kinematic architectures) of 4-DOF (four-degree-of-freedom) parallel press mechanisms rather than dynamic-model refinement.

Problem Statement

As stated in the further-work agenda of He, Gao, Bai and Wu (2013) for their 2500 t parallel servo press — and not addressed by the subsequent literature — the problem is to bring the dynamic model and the gravity-counterbalance design of the large-capacity parallel-topology servo press to production fidelity:

  1. Extend the virtual-work inverse-dynamics model so that the computed actuator torques include joint and mechanism friction and the dynamic response characteristics of the servomotors and gear trains — the omissions identified as the main source of the baseline model's roughly 15% average torque error — and validate the extended model against measured actuator torques.

  2. Incorporate the forming (stamping) loads that were absent from the numerical counterbalance-ratio study, and characterize how these loads couple with the inertial, gravitational and counterbalance effects, so that actuator sizing under real production conditions becomes possible.

  3. Include joint clearances and manufacturing defects in the model, and quantify the resulting internal reaction forces, impact loads, noise, and amplified dynamic response for a machine in the 2500 t class.

  4. Replace the approximate isothermal Boyle-law counterbalance model with a scientific evaluation and design optimization of inertial-force balance assemblies — that is, the pneumatic gravity-counterbalance cylinder assemblies that offset the ram weight — for high-speed, large-capacity presses, including the sizing of pneumatic volumes, pressure control, and stability under transient operating conditions.

These four items jointly support one objective: a validated, production-fidelity predictive model of the parallel servo press together with a rational counterbalance design method. "Production fidelity" here denotes a predictive model whose computed actuator torques are quantitatively validated against the prototype's measured torques — the average actuator-torque error against measurement being the validation criterion used in the source's own validation — under production conditions that include the forming load; the stated objective is resolved only when all four items are addressed, while each item is an independently assessable sub-problem whose resolution leaves the remaining items open. The practical realization questions raised in the source (for example the physical implementation of the virtual prismatic joint D and the splitting of joint loads) belong to prototype engineering and set the context, but are not themselves the scientific target.

References

  1. Jun He, Feng Gao, Yongjun Bai, Shengfu Wu. Dynamic modeling and experiment of a new type of parallel servo press considering gravity counterbalance. Chinese Journal of Mechanical Engineering, 26(6):1222–1233, 2013. DOI: 10.3901/cjme.2013.06.1222, https://doi.org/10.3901/cjme.2013.06.1222
  2. Jun He, Feng Gao, Yongjun Bai. A two-step calibration methodology of multi-actuated mechanical servo press with parallel topology. Measurement, 46(8):2269–2277, 2013. DOI: 10.1016/j.measurement.2013.03.031, https://doi.org/10.1016/j.measurement.2013.03.031
  3. Jun He, Feng Gao, Dan Zhang. Design and performance analysis of a novel parallel servo press with redundant actuation. International Journal of Mechanics and Materials in Design, 10(2):145–163, 2013. DOI: 10.1007/s10999-013-9237-7, https://doi.org/10.1007/s10999-013-9237-7
  4. Jun He, Feng Gao, Xiangdun Meng, Weizhong Guo. Type synthesis for 4-DOF parallel press mechanism using GF set theory. Chinese Journal of Mechanical Engineering, 28(4):851–859, 2015. DOI: 10.3901/cjme.2015.0427.065, https://doi.org/10.3901/cjme.2015.0427.065
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  6. Yu Chen, Yu Sun, Chong Chen. Dynamic analysis of a planar slider-crank mechanism with clearance for a high speed and heavy load press system. Mechanism and Machine Theory, 98:81–100, 2016. DOI: 10.1016/j.mechmachtheory.2015.12.004, https://doi.org/10.1016/j.mechmachtheory.2015.12.004
  7. Yu Chen, Yu Sun, Dong Yang. Investigations on the dynamic characteristics of a planar slider-crank mechanism for a high-speed press system that considers joint clearance. Journal of Mechanical Science and Technology, 31(1):75–85, 2017. DOI: 10.1007/s12206-016-1209-z, https://doi.org/10.1007/s12206-016-1209-z
  8. Liping Wang, Dong Wang, Jun Wu. Dynamic performance analysis of parallel manipulators based on two-inertia-system. Mechanism and Machine Theory, 137:237–253, 2019. DOI: 10.1016/j.mechmachtheory.2019.03.023, https://doi.org/10.1016/j.mechmachtheory.2019.03.023
  9. Jun Wang, Yu Wang, Kai Wu, Jun Ni, Han Zheng, Yu Sun. Electromechanical coupling dynamic modeling and dynamic response analysis of servo press. International Journal of Non-Linear Mechanics, 179:105234, 2025. DOI: 10.1016/j.ijnonlinmec.2025.105234, https://doi.org/10.1016/j.ijnonlinmec.2025.105234
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  12. Vigen Arakelian, Yang Zhang. An Improved Design of Gravity Compensators Based on the Inverted Slider-Crank Mechanism. Journal of Mechanisms and Robotics, 11(3):034501, 2019. DOI: 10.1115/1.4043049, https://doi.org/10.1115/1.4043049