Bezgin–Kolukırık equations (K^’_B3 and K^'_B3,H) are the last group of seven analytical equations based on the Bezgin Method. The method is based on the law of conservation of energy, rules of kinematics and a new concept, impact reduction factor, that describes the development of dynamic impact forces because of track and wheel roughness. K^'_B3 and K^’_B3,H estimate dynamic impact force factors because of wheel flats. K^'_B3,H includes the effect of Hertzian contact deformation on dynamic impact force factors. The proposed equations require up to six parameters to yield estimates. These parameters are: wheel diameter, wheel flat length, train speed, static wheel force transferred to the rail based on the tributary mass of the wheel, equivalent system stiffness of railway track and rolling stock, and length of Hertzian contact interface between wheel and rail. These equations empower users with the ability to estimate the highest values of the dynamic impact force factors because of wheel flats by manual calculations that yield realistic estimates comparable with estimates from advanced numerical methods and measurements obtained from instrumented test tracks. This paper presents the proposed Bezgin–Kolukırık equations followed by their application on hypothetical track and rolling stock conditions presenting a wide range of values for track and rolling stock stiffness, static wheel force, wheel diameters, train speed and wheel flat lengths. Estimates from the proposed equations are compared with the estimates of advanced numerical methods and experimental measurements from two previous papers.

Bezgin-Kolukırık方程（K ^“ _B3和K ^” _B3，H）是基于所述Bezgin方法7个的分析方程的最后一组。该方法基于能量守恒定律，运动学规则和一个新概念，即减震系数，该系数描述了由于履带和车轮的粗糙度而产生的动态冲击力的发展。ķ ^“ _B3和K ^” _B3，H因为车轮单位的估计动态冲击力的因素。ķ ^“ _B3，H包括赫兹接触变形对动态冲击力因子的影响。提出的方程式最多需要六个参数才能得出估算值。这些参数是：车轮直径，车轮平整长度，列车速度，基于车轮支流质量传递到轨道的静态车轮力，铁路轨道和机车车辆的等效系统刚度以及车轮与铁路之间的赫兹接触界面的长度。这些方程使用户能够通过手动计算来估算轮辋的动态冲击力因数的最大值，从而得出可以与高级数值方法的估算值和从仪器测试轨迹获得的测量值相媲美的实际估算值。本文介绍了拟议的Bezgin–Kolukırık方程，然后将其应用在假设的轨道和机车车辆条件下，为轨道和机车车辆的刚度，静态车轮力，车轮直径，列车速度和车轮平坦长度提供了广泛的值。拟议方程的估计值与高级数值方法的估计值和前两篇论文的实验测量值进行了比较。