为了更深入地了解内燃机工况与敲缸振动的关系，通过建立数学模型和仿真计算验证了内燃机气缸敲击振动峰峰值与发动机转速的非线性关系及与发动机负载的线性关系。内燃机扭矩平衡方程包含了发动机转速、负载和动力扭矩等信息，通过动力扭矩与活塞所受侧推力之间的几何关系将活塞径向加速度引入扭矩平衡方程，以活塞径向加速度在燃烧膨胀冲程上止点处的冲击信号峰峰值来表征敲缸振动的剧烈程度，整理后的数学模型显示加速度振动与内燃机转速为非线性关系、与负载为线性关系，经AVL-EXCITE仿真计算验证了数学模型的正确性。研究结果可以帮助在线监测系统和故障诊断人员根据敲缸振动对转速和负载的敏感性判断是否发生敲缸，为敲缸故障预警提供参考依据。Abstract：The nonlinearity of piston-slap vibration peak-to-peak values as a function of engine speed as well as their linearity as a function of load have been verified using mathematical modeling and simulations. Engine speed, load and power torque were included in the balanced equation for internal combustion engine torque, in which piston radial acceleration refers to the geometrical relationship between power torque and piston side thrust. The severity of vibrations was formulated using the peak-to-peak values of the impulse signal of the radial acceleration around the fire phase. An integrated mathematical model confirmed both the nonlinearity between speed and vibration, and the linearity between load and vibration, and these results were verified using simulations with AVL-EXCITE. Given the dependence of piston-slap vibration on engine speed and load, an on-line monitoring system and on-site staff are able to diagnose piston-slap faults more accurately, allowing a piston-slap alarm to be implemented.