Badges are commonly used as a gamification tool in Question-and-Answer communities to encourage knowledge sharing. However, the impact of badge design on motivation has been insufficiently explored. This study addresses this gap by optimizing badge design to maximize its motivational effect. Using reinforcement theory, an incentive model is developed and validated with panel data from user log records in a Q&A community. The results show that both the total value and the number of badges significantly enhance user knowledge contributions. Additionally, a U-shaped relationship is found between the time interval of badge issuance and user behavior, which is further amplified when badge attributes are aligned with user actions. These findings provide valuable theoretical insights and practical guidelines for improving badge design to effectively motivate users in Q&A communities.